This dissertation is dedicated to my mother, Song Guizhi,
and father, Liu Qinghe,
to my wife, Yi Yue,
and my daughter, Liu Chang
Acknowledgments
First of all, I would like to express my sincere gratitude and appreciation to my
promoter, Prof. F. De Smedt, for providing me the opportunity to fulfil this PhD, and
for his patience, encouragement and financial support throughout my PhD research in
the Frije Universiteit Brussel. I really thank him for guiding me to conduct my PhD
research in an area that is challenging and enjoyable in the field of water resources
engineering: Development and application of a GIS-based hydrological model for
flood prediction and watershed management. It was a fruitful and enriching
experience for me in my life. Thank you very much.
I would like to thank Mr. O. Batelaan, lecture of IUPWARE (Interuniversity Program
in Water Resources Engineering), for his constructive suggestions and fruitful
discussions on my study. Special thanks are given to Prof. J.W. Delleur, (Purdue
University, Indiana, USA), for whom I served as a teaching assistant for the course
Advanced Hydraulics, IUPWARE, for 4 academic years, and I really gained a lot
from this experience. My thanks also go to former and current fellow colleagues: Z.
Wang, T. Van Dale, L. Feyen, A. Deng, J. Cools, J. Corluy, A. Aish, A. Bahremand, I.
Houcyne, L.Q. Hung, M. Charles, Y. Meyus, J. Rwetabula, J. Severyns, B. Verbeiren,
S. Tuccu, and the technical staff members of the department: H. De Coninck, E. Van
Den Stoeme, E. Verbeken and A. Cosemans, for their help during my PhD, and for
making my stay at VUB enjoyable.
During the study of my PhD, I had the opportunities to participate in several Belgian
and European projects, e.g. the project of modelling floods in three Belgian
watersheds, Barebeek, Ijse and Veuren-Ambacht; the FRHYMP (Flood Risk and
HYdrological MAPping towards sustainable flood risk management in the Rhine and
Meuse river basins) project; and the Tisza River project. These projects also form the
case studies of this PhD research. I thank Dr. L. Pfister of the Centre de Recherche
Public – Gabriel Lippmann, Grand-Duchy of Luxembourg for his kind cooperation
and for providing all the required data of the Alzette River basin. Thanks are also
given to Mrs. J. Poorova, L. Velcicka and M. Dobiasova of the Slovak
Acknowledgments
Hydrometeorological Institute, Slovakia, for providing all necessary data of the
Hornad River Basin and the fruitful discussions in Bratislava and Brussels.
I am really grateful to my jury members: Prof. J. Wastiels (Vrije Universiteit Brussel),
Prof. J. Vereecken (Vrije Universiteit Brussel), Prof. W. Bauwns (Frije Universiteit
Brussel), Prof. L. Hoffmann (Centre de Recherche Public-Gabriel Lippmann, GrandDuchy Luxembourg), Prof. Jacques W. Delleur (School of Engineering, Purdue
University, USA), and Prof. J. Bogaert (Université Libre de Bruxelles),for their
willingness to review and evaluate this thesis. Their critical comments and
suggestions make this PhD thesis a reality.
I am grateful to my parents who are living in China. I owe much of my success in this
endeavour to their loving efforts and never-ending support. This thesis would not
have been possible without the complete support of my wife, Yue Yi. Her support,
patience and understanding during the research and writing process, along with the
love of my beautiful daughter, Chang Liu, made this task more worthwhile and
fulfilling. I am deeply indebted for not having spent much time with them throughout
my study at Katholieke Universiteit Leuven and Vrije University Brussel in the
Belgium. Their love reminded me of what is truly important and helped me maintain
perspective on life while completing this research. I love you all!
ii
Abstract
A GIS-based distributed hydrological model, WetSpa Extension, that operates on
catchment scale is developed for flood prediction and watershed management. It is a
continuous simulation model that may operate at a different time scale, e.g. hourly or
daily, and at a different spatial resolution, which well represent the river basin
characteristics. The required inputs to the model include digital maps of elevation, soil
type and land use, and time series of precipitation, temperature, potential
evapotranspiration and flow discharge, where temperature data is optionally used for
modelling snowmelt, and discharge data is required for model calibration. The model
enables one to simulate the complex hydrological regimes of a river basin within a
GIS framework, estimate runoff for each grid cell and route the flow along its flow
path to the basin outlet or any converging points in the stream network, and
eventually to simulate the spatial distribution of hydrological variables in a river basin,
such as surface runoff, interflow, soil moisture and groundwater recharge, etc.
The hydrological processes considered in the model include precipitation, interception,
snow accumulation and melting, depression storage, infiltration, evapotranspiration,
percolation, surface runoff, interflow and groundwater flow. Surface runoff in each
cell is computed by a modified rational method, which is controlled by the rainfall
intensity and soil moisture content. Potential runoff coefficient is obtained from
literature and a lookup table is created linking potential runoff coefficient with
different categories of slope, soil type, land use and the proportions of bare soil and
impervious areas in a grid cell. The excess rainfall is routed along the flow paths by
using the diffusive wave approximation. The interflow and percolation are controlled
by soil characteristics and modelled by Darcy’s law and kinematic approximation.
The groundwater flow is modelled by a linear reservoir method on small GIS derived
subcatchment scale, while a non-linear reservoir method is optional in the model.
Actual evapotranspiration is composed of evaporation from interception and
depression storage, and transpiration from root zone and groundwater storage.
Snowmelt is estimated using a simple degree-day model. Algorithms derived as much
as possible from physical processes, together with more conceptual or empirical
algorithms have been selected. The structure of the model with regard to interception,
Abstract
depression, root-zone and groundwater storage compartments is variable, allowing
much flexibility to simulated different systems.
The application of the WetSpa model is demonstrated in three case studies, i.e.
Barebeek (Belgium), Steinsel (Luxembourg) and Margecany (Slovakia), which are
described in this dissertation. The Barebeek catchment is a typical suburban
watershed with drainage area of 67.8 km2 situated northeast of Brussels, Belgium.
The resulting calculated hydrographs with WetSpa model compare favourably with
measurements at the gauging sites. The usefulness and utility of the model are
subsequently demonstrated by forecasting peak discharges resulting from an observed
102 years precipitation series. The resulting hourly discharges were analyzed
statistically to determine the characteristics of extreme flood events and compared
with the results computed from design storms. Comparison of the two methods shows
that the model is capable to predict both normal and extreme floods. The Steinsel
catchment is a highly urbanized watershed with a drainage area of 407 km2 located in
the upstream part of the Alzette River basin, Grand Duchy of Luxembourg. Results of
WetSpa model simulation show that the model’s level of representativeness to be
quite satisfactory. Next, the runoff contribution from different land use areas and the
impacts of land use change and natural river restoration for the headwater areas on the
flood behaviours are assessed using WetSpa model on an hourly time scale and 50×50
m resolution results. The Margecany catchment is a typical mountainous watershed
with a drainage area of 1133 km2 situated in the upstream part of the Hornad River
basin, Slovakia. Simulation results of WetSpa model show that the flow hydrographs
of both snow melting floods and storm floods are well reproduced on a daily time
scale and 100×100 m resolution. Moreover, it is demonstrated that the spatial
distribution of input data has a large influence on the modelling results, particularly
for a mountainous catchment.
The WetSpa model makes full use of the remote sensed data and calculations are for
the most part performed by standard GIS tools, such that the model is especially
useful for flood prediction on complex terrain and analyzing the effects of topography,
soil type, and land use or soil cover on the flood. Additionally, the model can be
easily coupled with other water quality and soil erosion models, and used for
simulating spatial hydrological behaviour of a river basin.
iv
Table of contents
Acknowledgments.......................................................................................................... i
Abstract........................................................................................................................ iii
Table of contents........................................................................................................... v
List of figures............................................................................................................. xiii
List of tables ............................................................................................................. xvii
List of publications..................................................................................................... xix
Chapter I:
General introduction........................................................................... 1
1.
Background and significance............................................................................ 1
2.
Objectives of the research…............................................................................. 3
3.
Outline of the dissertation…............................................................................. 4
References…..................................................................................................... 7
Chapter II:
GIS-based hydrological modelling and watershed analysis............ 9
Abstract ............................................................................................................ 9
1.
Introduction ...................................................................................................... 9
2.
Effects of watershed characteristics on runoff…............................................ 11
2.1.
Effects of topography...................................................................................... 11
2.2.
Effects of soil type........................................................................................... 13
2.3.
Effects of land use........................................................................................... 14
3.
GIS applications in watershed modelling........................................................ 16
3.1.
Watershed description..................................................................................... 16
3.2.
Hydrological parameter determination............................................................ 17
3.3.
Integration with hydrological models.............................................................. 18
4.
Modelling of watershed hydrology................................................................. 20
4.1.
Popular GIS-based hydrological models......................................................... 21
4.2.
Assessment of future scenarios....................................................................... 23
5.
WetSpa model overview................................................................................. 24
5.1.
Model history.................................................................................................. 24
5.2.
WetSpa Extension........................................................................................... 25
6.
Summary......................................................................................................... 28
Table of contents
References ...................................................................................................... 29
Chapter III: Development of a diffusive transport approach for flow routing
in GIS-based watershed modelling.............................................................. 35
Abstract .......................................................................................................... 35
1.
Introduction .................................................................................................... 35
2.
Methodology................................................................................................... 38
3.
Model application ........................................................................................... 43
4.
Sensitivity analysis…...................................................................................... 50
4.1.
Effect of hydraulic radius................................................................................ 50
4.2.
Effect of channel roughness............................................................................ 51
4.3.
Effect of minimum slope................................................................................. 52
4.4.
Effect of area threshold in delineating channel networks............................... 53
4.5.
Other effects.................................................................................................... 55
5.
Conclusions..................................................................................................... 56
References ...................................................................................................... 58
Chapter IV: Flood modelling for complex terrain using GIS and remote sensed
information..................................................................................................... 61
Abstract .......................................................................................................... 61
1.
Introduction .................................................................................................... 61
2.
The modelling approach.................................................................................. 63
2.1.
Runoff production………............................................................................... 64
2.2.
Water balance.................................................................................................. 68
2.3.
Flow routing………………............................................................................ 70
3.
GIS implementation ....................................................................................... 72
3.1.
Drainage system………….............................................................................. 72
3.2.
Soil and land use…………….......................................................................... 74
3.3.
Spatial hydrological input and output............................................................. 75
4.
Model application……………………………………………........................ 76
4.1.
Watershed description and data availability.................................................... 76
4.2.
Model calibration............................................................................................ 78
4.3.
Model application using the historical and IDF data...................................... 82
5.
Discussion and conclusions............................................................................. 85
vi
Development and application of a GIS-based hydrological model
References ...................................................................................................... 87
Chapter V:
Assessing land use impacts on flood processes using a GIS
modelling approach....................................................................................... 91
Abstract .......................................................................................................... 91
1.
Introduction .................................................................................................... 91
2.
Methodology…………................................................................................... 94
2.1.
Description of the WetSpa model................................................................... 94
2.2.
Description of the study area........................................................................... 96
2.3.
Data collection………………......................................................................... 98
2.4.
Model calibration and verification................................................................ 100
2.5.
Model evaluation........................................................................................... 103
3.
Results and discussion……………….......................................................... 105
3.1.
Evaluating runoff partitions from different land use classes......................... 105
3.2.
Assessing the impact of land use changes on flood...................................... 112
4.
Conclusions…………………………………………………....................... 116
References .................................................................................................... 117
Chapter VI: Assessing the effects of river restoration on the reduction of
floods in a river basin.................................................................................. 120
Abstract ........................................................................................................ 120
1.
Introduction .................................................................................................. 120
2.
Methodology…………................................................................................. 124
2.1.
Model description.......................................................................................... 124
2.2.
Description of the study area......................................................................... 124
2.3.
Stream classification ………........................................................................ 124
2.4.
Modelling approach………………............................................................... 126
3.
Results and discussion................................................................................... 129
3.1.
Model calibration and evaluation.................................................................. 129
3.2.
Model prediction........................................................................................... 131
3.3.
Evaluation of a future flood scenario............................................................ 134
4.
Conclusions………………………………………….…........................ 136
References .................................................................................................... 137
vii
Table of contents
Chapter VII: Flow simulation in a Carpathian catchment accounting for
topographic controls.................................................................................... 139
Abstract ........................................................................................................ 139
1.
Introduction .................................................................................................. 139
2.
Methodology…………................................................................................. 141
2.1.
Description of the study area and data available........................................... 141
2.2.
Modelling snowmelt...................................................................................... 145
2.3.
Topographic adjustment for the input variable............................................. 146
2.3.1. Adjustment for temperature........................................................................... 147
2.3.2. Adjustment for precipitation......................................................................... 148
2.3.3. Adjustment for PET....................................................................................... 150
2.3.4. Topographic correction................................................................................. 151
3.
Model simulation........................................................................................... 151
3.1.
Parameter identification................................................................................ 152
3.2.
Automated calibration................................................................................... 154
3.3.
Modelling results........................................................................................... 156
5.
Discussion and conclusions.......................................................................... 160
References .................................................................................................... 162
Chapter VIII: Integrating GIS and hydrological process modelling in medium
and large watersheds................................................................................... 165
Abstract ........................................................................................................ 165
1.
Introduction .................................................................................................. 165
2.
Study area and data availability..................................................................... 168
3.
Effects of grid size on runoff and flow responses......................................... 170
4.
Transforming WetSpa into a semi-distributed model................................... 173
5.
Results and discussion................................................................................... 178
6.
Conclusions................................................................................................... 183
References .................................................................................................... 185
Chapter IX: Summary and conclusions.............................................................. 189
1.
General summary.......................................................................................... 189
1.1.
Model development....................................................................................... 189
viii
Development and application of a GIS-based hydrological model
1.2.
Model applications........................................................................................ 192
1.3.
Model limitations……….............................................................................. 195
2.
Future perspectives........................................................................................ 197
Appendix A: WetSpa Extension: A GIS-based hydrological model for flood
prediction and watershed management
Documentation and User Manual.............................................................. 201
1.
Model description.......................................................................................... 201
1.1.
Model construction........................................................................................ 202
1.1.1. Model objectives........................................................................................... 202
1.1.2. Model structure.............................................................................................. 203
1.1.3. Model assumptions........................................................................................ 205
1.2.
Data preparation............................................................................................ 205
1.2.1. Digital data.................................................................................................... 206
1.2.2. Hydro-meteorological data............................................................................ 208
2.
Model formulation......................................................................................... 210
2.1.
Precipitation................................................................................................... 211
2.2.
Interception.................................................................................................... 212
2.3.
Snowmelt....................................................................................................... 214
2.4.
Rainfall excess and infiltration...................................................................... 215
2.5.
Depression and overland flow....................................................................... 217
2.5.1. Formulation of depression storage................................................................ 218
2.5.2. Mass balance of depression storage.............................................................. 219
2.5.3. Formulation of overland flow........................................................................ 220
2.6.
Water balance in the root zone...................................................................... 221
2.7.
Evapotranspiration from soil......................................................................... 222
2.7.1. Potential evapotranspiration.......................................................................... 222
2.7.2. Actual evapotranspiration.............................................................................. 225
2.8.
Percolation and interflow.............................................................................. 226
2.9.
Groundwater storage and baseflow............................................................... 229
2.10.
Overland flow and channel flow routing....................................................... 231
2.10.1. Flow response at a cell level.......................................................................... 231
2.10.2. Flow response at a flow path level................................................................ 233
2.10.3. Flow response of the catchment.................................................................... 235
ix
Table of contents
2.11.
Subcatchment integration.............................................................................. 235
2.12.
Catchment water balance............................................................................... 237
3.
Parameter identification and model evaluation............................................. 239
3.1.
Default model parameters............................................................................. 239
3.1.1. Parameters characterizing soil texture classes............................................... 239
3.1.2. Parameters characterizing land use classes................................................... 240
3.1.3. Potential runoff coefficient............................................................................ 243
3.1.4. Depression storage capacity.......................................................................... 247
3.2.
Global parameters.......................................................................................... 250
3.3.
Model evaluation........................................................................................... 255
4.
Model operation............................................................................................ 258
4.1.
Program installation...................................................................................... 258
4.2.
Program description...................................................................................... 260
4.2.1. Avenue scripts and their tasks....................................................................... 260
4.2.2. Lookup tables................................................................................................ 261
4.2.3. FORTRAN programs and their tasks............................................................ 261
4.2.4. PEST files and their tasks.............................................................................. 262
4.3.
GIS pre-processing........................................................................................ 262
4.3.1. Surface grid preparation................................................................................ 262
4.3.2. Soil based grid preparation............................................................................ 266
4.3.3. Land use based grid preparation.................................................................... 267
4.3.4. Potential runoff coefficient and depression storage capacity........................ 268
4.3.5. Flow routing parameters................................................................................ 269
4.3.6. Thiessen polygon........................................................................................... 270
4.3.7. Drainage systems for a complex terrain........................................................ 271
4.4.
Creation of input files.................................................................................... 272
4.4.1. Input file of time series.................................................................................. 272
4.4.2. Global parameters and spatial output specifications..................................... 275
4.5.
Model calibration and verification................................................................ 278
4.5.1. Calibration and verification processes.......................................................... 278
4.5.2. Manual parameter adjustment....................................................................... 282
4.5.3. Parameter sensitivity..................................................................................... 283
4.6.
Model output................................................................................................. 285
4.6.1. Intermediate output........................................................................................ 285
x
Development and application of a GIS-based hydrological model
4.6.2. Final output.................................................................................................... 287
4.6.3. Post processing of model outputs.................................................................. 291
5.
Case study...................................................................................................... 291
5.1.
Description of the study area......................................................................... 291
5.2.
Data availability............................................................................................ 293
5.3.
Basin delineation and parameter determination............................................ 297
5.4.
Model calibration and validation................................................................... 299
5.5.
Discussion..................................................................................................... 304
6.
Concluding remarks...................................................................................... 306
References..................................................................................................... 307
xi
List of figures
II-1: GIS–Hydrological modelling integration methods............................................. 19
II-2: Hydrological processes considered in the original WetSpa model..................... 24
III-1: (a) Unit response functions for an expected travel time of 3600 s and
different standard deviations, and (b) Unit response functions for an
expected standard deviation of 3600 s and different travel times................... 41
III-2: Location plan showing the study area, the Attert and Alzette river basin…... 44
III-3: DEM of the study area..................................................................................... 44
III-4: Land use map of the study area....................................................................... 44
III-5: Distribution of potential runoff coefficient..................................................... 45
III-6: Distribution of hydraulic radius for a flood with a 2-year return period......... 45
III-7: (a) Average flow time to the basin outlet and (b) its standard deviation........ 47
III-8: Observed and predicted stream flow and baseflow at Ell station.................... 49
III-9: Measured vs. simulated peak direct discharges............................................... 49
III-10: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of hydraulic radius with expected flood frequency, p….. 51
III-11: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of channel Manning’s roughness coefficient, n................ 52
III-12: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of the threshold of minimum slope, Smin.......................... 53
III-13: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of cell number threshold, Cn, in delineating channel
networks.......................................................................................................... 54
IV-1: Location of the Barebeek catchment................................................................. 77
IV-2: Drainage system of the Barebeek catchment..................................................... 77
IV-3: Land use map of the Barebeek catchment......................................................... 77
IV-4: Distribution of potential runoff coefficient...................................................... 79
IV-5: Distribution of average flow time to the catchment outlet................................ 79
IV-6: Observed Vs calculated discharges at MO6...................................................... 80
IV-7: Observed Vs calculated discharges at MO3...................................................... 80
IV-8: Observed Vs calculated flow hydrographs at MO6 for the period of Sept.
1998 to Dec. 1999............................................................................................ 80
List of Figures
IV-9: Simulated distribution of relative soil wetness on 8/10/1999, 4:00................... 82
IV-10: Simulated distribution of surface runoff on 8/10/1999, 4:00-5:00.................. 82
IV-11: Design summer and winter storms with 100-year return period..................... 83
IV-12: Simulated floods for the 100-year design storms............................................ 83
IV-13: Comparison of the design peak flow discharges............................................. 84
IV-14: Simulated maximum flood at the watershed outlet......................................... 84
V-1:
Location of the Alzette basin and Steinsel sub-basin...................................... 97
V-2:
Topography and gauging network of the Steinsel sub-basin.......................... 97
V-3:
Soil type map of the Steinsel sub-basin........................................................... 99
V-4:
Land use map of the Steinsel sub-basin.......................................................... 99
V-5:
Observed Vs calculated flow at Steinsel for the floods in Feb. 1997........... 102
V-6:
Observed and calculated daily flow at Steinsel for the year 2000................ 102
V-7:
Storm runoff partitions at Steinsel for the flood events in Feb. 1997........... 105
V-8:
Storm runoff contributions at Steinsel for the flood events in Apr. 1999..... 106
V-9:
Plot of event to event variations of the different runoff contributions (a),
normalized relative runoff contribution from urban (b), cropland (c),
grassland (d), woodland (e), and other areas (f), and error in flood volume (g)
and error in peak discharge with respect to the flow coefficient………….109
V-10: Contributions of monthly flow at Steinsel from different land use classes... 111
V-11: Land use change scenarios for the Steinsel sub-basin................................... 113
V-12: (a) Simulated surface runoff distribution under present land use condition
for the storm on Feb. 24-26, 1997, and (b) Simulated surface runoff
distribution after urbanization for the same storm event............................... 114
V-13: Simulated hydrographs for each scenario for a storm in Dec. 1999............. 115
V-14: Peak discharges for each scenario over the simulation period...................... 115
VI-1: (a) Stream orders and their drained area, and (b) percentage of
stream length, percentage of drained area and average slope
for different order streams............................................................................. 125
VI-2: Observed and simulated flow hydrographs for the flood events in Oct.
and Nov. 1998............................................................................................... 130
VI-3: Observed versus simulated peak flows for the simulation period................. 130
VI-4: (a) Average flow travel time to the sub-basin outlet for the present condition,
and (b) Increases in flow travel time after river restoration.......................... 132
VI-5: Flood events showing the effect of natural river restoration......................... 133
xiv
Development and application of a GIS-based hydrological model
VI-6: Present versus restored simulated peak discharges for the simulation period
indicating a 14% reduction in average after river restoration....................... 133
VI-7: Simulated hydrograph under present condition and after river restoration for
a future storm scenario.................................................................................. 135
VII-1: Location of the Margecany catchment.......................................................... 142
VII-2: Monthly temperature, precipitation and PET at Spisske Vlachy.................. 142
VII-3: Land use map of the Margecany catchment.................................................. 142
VII-4: Soil textural map of the Margecany catchment............................................. 144
VII-5: Topographical map of the Margecany catchment......................................... 144
VII-6: Gauging sites and Thiessen polygons for the Margecany catchment........... 144
VII-7: Lapse rates for mean monthly temperature……………………................... 147
VII-8: Distribution of yearly precipitation over the Hornad River basin................. 149
VII-9: Vertical gradient of yearly precipitation with elevation................................ 149
VII-10: Vertical gradient of monthly PET with elevation........................................ 151
VII-11: Potential runoff coefficient for the Margecany catchment........................... 153
VII-12: Mean travel time to the basin outlet at Margecany...................................... 154
VII-13: Observed and calculated daily flow at Margecany for the year 1997.......... 157
VII-14: Variation of precipitation, temperature, evapotranspiration, and relative
soil saturation for the Margecany catchment during the year 1997.............. 159
VII-15: Distribution of surface runoff for the storm event 1/8-6/8, 1997................. 160
VII-16: Observed and simulated mean daily PET at Spisske Vlachy....................... 161
VIII-1: Study area and observation network............................................................. 168
VIII-2: Land use of the Alzette River basin.............................................................. 168
VIII-3: Mean parameters obtained from DEMs with grid sizes: (a) flow length,
flow time and its standard deviation, (b) slope, curvature and depression
capacity, (c) runoff coefficient, velocity and hydraulic radius, (d) IUHs
for the entire catchment................................................................................. 171
VIII-4: Comparison of flow hydrographs at Ettelbruck calculated from DEMs with
different grid size for a flood event in Dec. 1999......................................... 172
VIII-5: Comparison of surface flow hydrographs at Ettelbruck calculated from DEMs
with different grid size for a flood event in Dec. 1999................................. 173
VIII-6: Mean travel time to the basin outlet.............................................................. 179
VIII-7: River reaches and divided subwatersheds..................................................... 179
VIII-8: Calculated Vs observed flows at Ettelbruck for the floods in Feb. 1997...... 181
xv
List of Figures
VIII-9: Simulated Vs observed daily flows at Ettelbruck for the year 1999............. 182
A-1.1: Model structure of WetSpa Extension at a pixel cell level........................... 204
A-2.1: Annual variation of grass interception storage capacity............................... 214
A-2.2: Relationship between rainfall excess coefficient and soil moisture.............. 217
A-2.3: Sketch of depression storage as a function of excess rainfall....................... 219
A-2.4: Graphical presentation of excess rainfall and overland flow........................ 220
A-2.5: Graphical presentation of soil water balance................................................ 221
A-2.6: Observed and simulated daily EP at Ukkel for the year 1997....................... 224
A-2.7: Simulated hourly EP at Ukkel with EPd = 3mm........................................... 224
A-2.8: Graphical presentation of soil evapotranspiration......................................... 226
A-2.9: Effective hydraulic conductivity as a function of moisture content.............. 227
A-2.10: Flow path response functions with different ti and σi2................................. 234
A-3.1: Potential runoff coefficient vs. slope for forest and different soil types....... 245
A-3.2: Depression storage capacities vs. slope for grass and different soil types.... 249
A-4.1: Schematic view of the model’s project folders............................................. 259
A-4.2: Screenshort of surface menu......................................................................... 263
A-4.3: Screenshort of parameter menu..................................................................... 267
A-5.1: Location of the Bissen catchment................................................................. 292
A-5.2: Topography map of Bissen............................................................................ 293
A-5.3: Land use map of Bissen................................................................................. 293
A-5.4: Soil type map of Bissen................................................................................. 293
A-5.5: River network and Thiessen polygons of Bissen………………….…........ 293
A-5.6: Hydraulic radius of Bissen............................................................................ 298
A-5.7: Runoff coefficient of Bissen.......................................................................... 298
A-5.8: Mean travel time to the basin outlet of Bissen.............................................. 299
A-5.9: Standard deviation of flow time to the basin outlet …………...................... 299
A-5.10: Observed and calculated flow at Bissen for the floods in Dec. 1999.......... 301
A-5.11: Observed and calculated hourly flow at Bissen for the year 1999............... 303
A-5.12: Peak Qm Vs Peak Qc selected from the whole simulation period................ 303
A-5.13: Observed and calculated hourly flow frequency curves at Bissen............... 304
xvi
List of tables
II-1:
Primary topographic attributes that can be computed by terrain analysis
from DEM Data............................................................................................... 12
II-2:
Samples of popular distributed and semi-distributed hydrological models.... 22
V-1:
Description of the area, slope and main soil types for each land use class..... 98
V-2:
Evaluation criteria for the assessment of model performance...................... 104
V-3:
Watershed characteristics and model performance....................................... 104
V-4:
Simulated runoff contributions from different land use classes.................... 107
V-5:
Land use change scenarios compared with the present situation.................. 113
VII-1: Information of weather stations in the Margecany catchment...................... 143
VII-2: Regression analysis between monthly temperature and elevation................ 148
VII-3: PET stations used for regression analysis..................................................... 150
VII-4: Regression analysis between PET and elevation.......................................... 151
VII-5: Parameters and their ranges in the PEST control file..................................... 155
VII-6: List of input parameter values, water balance, and evaluation results.......... 157
VIII-1: Mean parameter values calculated from maps with different grid size....... 170
VIII-2: Flood characteristics estimated from maps with different grid size…..... 173
VIII-3: Subwatershed characteristics and model performance………………….. 183
A-3.1: Default parameters characterizing soil textural classes................................. 240
A-3.2: Default parameters characterizing land use classes...................................... 241
A-3.3: Potential runoff coefficient for different land use, soil type and slope......... 243
A-3.4: Slope constant S0 for determining potential runoff coefficient.................... 244
A-3.5: Impervious percentages associated with selected land use classes............... 246
A-3.6: Depression storage capacity for different land use, soil type and slope........ 248
A-4.1: Sample file of precipitation series p.txt......................................................... 273
A-4.2: Sample file of potential evapotranspiration series pet.txt............................. 274
A-4.3: Sample file of temperature series t.txt........................................................... 274
A-4.4: Sample file of discharge series q.txt.............................................................. 275
A-4.5: Template of global model parameters........................................................... 275
A-4.6: Template of spatial output specifications...................................................... 276
A-4.7: Parameter sensitivity for model calibration................................................... 284
A-4.8: Sample output file of mean.txt...................................................................... 285
List of Tables
A-4.9: Parts of output file uh_cell_h.txt.................................................................. 286
A-4.10: Sample output file of q_tot.txt..................................................................... 287
A-4.11: Sample output file of q_sub.txt.................................................................... 288
A-4.12: Sample output file of balance.txt................................................................. 289
A-4.13: Parts of the output file runoff.asc................................................................. 289
A-4.14: Model evaluation result evaluation .txt........................................................ 290
A-5.1: Default parameter values in the PET formula for different land uses........... 296
A-5.2: Data available and characteristics of the Bissen catchment........................... 297
A-5.3: Statistics and model performance for the calibration/validation period........ 302
A-5.4: Water balance estimation at Bissen for the whole simulation period............ 305
xviii
List of publications
Liu, Y.B., Gebremeskel. S., De Smedt, F., Hoffmann, L. and Pfister, L., A diffusive
transport approach for flow routing in GIS-based flood modeling, Journal of
Hydrology, 283, 91-106, 2003.
Liu, Y.B., De Smedt, F., Hoffmann, L. and Pfister, L., Assessing land use impact on
flood processes in complex terrain by using GIS and Modeling approach,
Environmental Modeling and Assessment, 2004 (in press).
Liu, Y.B. and De Smedt, F., Flood modeling for complex terrain using GIS and
remote sensed information, Water Resources Management, 2004 (accepted).
Liu, Y.B., Gebremeskel, S., De Smedt, F., Hoffmann, L. and Pfister, L., Predicting
storm runoff from different land use classes using a GIS-based distributed model,
Hydrological Processes, 2004 (accepted).
Liu, Y.B., Gebremeskel, S., De Smedt, F., Hoffmann, L. and Pfister, L., Simulation of
flood reduction by natural river rehabilitation using a distributed hydrological
model, Hydrology and Earth System Sciences, 2004 (accepted).
Liu Y.B., De Smedt F, Hoffmann L. and Pfister L., Parameterization using ArcView
GIS in medium and large watershed modeling, in Chen, Y.B., Takara, K.,
Cluckie, I. and De Smedt, F. (eds.), GIS and Remote Sensing in Hydrology,
Water Resources and Environment, IAHS Publ. 289, 50-58, 2004.
Liu, Y.B., Batelaan, O., Huong, N.T., Tam, V.T. and De Smedt, F., Flood prediction
in the karstic Suoimuoi catchment, Vietnam, in Batelaan, O., Dusar, M.,
Masschelein, J., Tam, V.T., Van, T.T. and Khien, N.X. (eds.), Trans-KARST,
Proceedings of the International Transdisciplinary Conference on Development
and Conservation of Karst Regions, Hanoi, Vietnam, 139-144, 2004.
Liu, Y.B., Gebremeskel. S., De Smedt, F. and Pfister, L., Flood prediction with the
WetSpa model on catchment scale, in Wu, B.S., Wang, Z.Y., Wang, Q., Huang,
G.H., Fang, W. and Huang, J.C. (eds.), Flood Defence ‘2002, 499-507, Science
Press, New York Ltd, 2002.
De Smedt, F., Liu, Y.B., Gebremeskel, S., Hoffmann, L. and Pfister, L., Application
of GIS and remote sensing in flood modeling for complex terrain, in Chen, Y.B.,
Takara, K., Cluckie, I. and De Smedt, F. (eds.), GIS and Remote Sensing in
Hydrology, Water Resources and Environment, IAHS Publ. 289, 23-32, 2004
Listof publications
De Smedt, F., Liu, Y.B., and Qiao, Y., Prediction of floods with the WetSpa model,
Annals of Warsaw Agricultural University – SGGW, Land Reclamation, 33: 7180, 2002.
De Smedt, F., Liu, Y.B. and Gebremeskel, S., Hydrologic modeling on a catchment
scale using GIS and remote sensed land use information, in Brebbia, C.A. (ed.),
Risk Analysis II, 295-304, WTI press, Southampton, Boston, 2000.
De Smedt, F., Liu, Y.B. and Gebremeskel, S., Integrated Hydrologic Modeling on a
Catchment Scale for Prediction of Floods, in Hoeben, R., Herpe, Y.V. and De
Troch, F.P. (eds.), ERB 2000 Proceedings on CDROM, 11pp, Ghent, Belgium,
September 27-29, 2000.
Gebremeskel S., Liu, Y.B., De Smedt, F. and Pfister, L., 2002. GIS based distributed
modelling for flood simulation. J. A. Ramirez (ed), Proceedings of the Twenty
Second Annual American Geoplhysical Union Hydrology Days, Fort Collins,
Colorado: 98-109.
Liu, Y.B., De Smedt, F., Hoffmann, L. and Pfister, L., Integrating GIS and process
modeling for runoff prediction in medium and large watersheds, 2004
(submitted to Journal of Spatial Hydrology).
Liu, Y.B., Yi, Y., Batelaan, O. and De Smedt, F., Assessing grid size effects on runoff
and flow response using a GIS-based hydrologic model, 2004 (submitted to
Environmental Modeling and Assessment).
Liu, Y.B., Batelaan, O., De Smedt, F., Poorova, J. and Velcicka, L., Automated
calibration applied to a GIS-based flood simulation model using PEST, 2005 (to
be submitted to the Third International Symposium on Flood Defence, 25-27,
May, 2005, Nijmegen, the Netherlands).
Liu, Y.B., Corluy, J., Bahremand, A., De Smedt, F., Poorova, J. and Velcicka, L.,
Estimation of runoff and phosphorus loading for the Margecany catchment,
Hornad, Slovakia, 2005 (to be submitted to the International Symposium on
Wetland Pollutant Dynamics and Control, 4-8 September 2005, Ghent, Belgium).
xx
Chapter I
General introduction
1.
Background and significance
Due to the increased water resources demand, there is a growing requirement to
predict their natural processes in order to address the environmental problems today
and in the future. A hydrological model is a simplified representation of the natural
hydrological system, and represents different physical processes at a wide range of
time and space scales. This has generally been associated with an increase in model
complexity, a lack of appropriate observational data to constrain model states, and an
increasing number of model outputs (Wagener et al., 2001). In particular, distributed
hydrological models allow for detailed description of the hydrological and energy
cycle and provide opportunities for dealing with forcing variables that fluctuate in
space and time. Hydrologists are therefore trying to implement these models
increasingly as a means to capture the state of knowledge on basins of interest, and
provide valuable information regarding hydrological state variables and potentially
important distributed information on existing and future streamflow conditions.
Flood prediction and control is one of the greatest challenges facing the world today,
which have become more frequent and severe due to the effects of global climate
change and human alterations of the natural environment. As the watershed becomes
more developed, it also becomes more hydrologically active, changing the stream’s
flow components as well as the origin of flow. In turn, flood flows that once occurred
infrequently during pre-development periods have now become more frequent and
more severe due to the transformation of the watershed from rural to urban land uses
(Boyle et al., 1997; Weng, 2001). Consequently, the extent of the floodplain also is
altered and the risk of flooding imposed on surrounding areas is increased. The
forecast of flooding would benefit greatly from the use of hydrological models, which
are designed to simulate the processes of surface or subsurface water flow. Because
the flow processes are spatially distributed, a great amount of spatially related
physical data needs to be prepared and analyzed in order to construct an adequate
Chapter I
simulation model, including variables related to the water, the air, the landscape, the
soil, the plant, and all of the geophysical and environmental constituents. Therefore,
in order to successfully manage natural hydrological systems, one must have a
thorough understanding of these variables with regard to their characteristic temporal
and spatial scale.
Modern geographic information systems (GIS) offer new opportunities for the
collection, storage, analysis, and display of spatially distributed meteorological and
geophysical data (Goodchild et al., 1992). The use of GIS enables one to implement
geographic data more efficiently for hydrological monitoring, analyzing, planning and
management. More specifically, the use of a GIS in combination with hydrological
models allows one to perform multi-objective analyses incorporating a wide range of
geographical information and data in an accurate and efficient manner (Babd &
Moore, 1995; McDonnell, 1996). Despite the advent of recent integrated approaches
to watershed planning and development, as well as the large research effort to
enhance the interface between GIS technology and hydrological models, a need
remains to make the GIS-based hydrological models more reliable, effective and easy
to implement for research and engineering purposes. In addition, a GIS methodology
for predicting runoff and flood risks spatially within the corresponding watershed
needs to be developed. These applications of GIS for flood prediction and watershed
management would greatly improve the capabilities of the hydrological modelling and
risk assessment, offering users a powerful capability to analyze and visually express
the spatially distributed hydrological variables, and therefore, assess the impacts of
land use and climate change on hydrological responses of the river basin.
The purpose of this research is to develop and test a GIS-based flow and water
balance simulation model, WetSpa (Water and Energy Transfer between Soil, Plant
and Atmosphere) Extension, based on the pre-proposed WetSpa model (Wang et al.,
1997). The model uses the spatial information of a digital elevation model (DEM),
land use and soil to derive all necessary spatially distributed model parameters within
a GIS framework. Hydrological computations are performed for each grid cell or
small subwatershed realized by incorporating with a tightly-coupled hydrological
model. The maps and databases are integrated using GIS data management tools, and
the data sets and programs are integrated by applying the concepts of object-oriented
2
General Introduction
programming (OOP). ArcView is selected as the host environment because it provides
both spatial database management and OOP capabilities, while a procedural
programming language, FORTRAN, is used to construct the hydrological model.
Three study catchments with distinct basin characteristics are selected to investigate
the applicability and adaptability of the model. They are: (1) Barebeek, a 67.8 km2
suburban plain watershed of the Dijle River basin situated northeast of Brussels,
Belgium; (2) Steinsel, a 407 km² highly urbanized hilly watershed located in the
upstream part of the Alzette River basin, Grand Duchy of Luxembourg; and (3)
Margecany, a 1133 km2 upland mountainous watershed situated in the upstream part
of the Hornad River basin, Slovakia. Model applications are illustrated in the above
study areas with an interest in flood forecasting, water balance simulation, the impact
of land use change and natural river restoration on flooding behaviours, and so on.
2.
Objectives of the research
The overall goal of this research is to develop and apply a WetSpa Extension, which
is a long-term, continuous simulation, physically-based, distributed parameter
watershed model for flood prediction and watershed management. The specific
objectives of this research regarding model development are to:
•
Develop a comprehensive GIS-based modelling approach being compatible with
GIS technology and remote sensing information, and by using the spatial
information associated with the DEM, land use and soil type of the river basin for
flood prediction and watershed management;
•
Create a software package by integrating GIS with hydrological modelling, which
contains a user-friendly interface allowing the model to operate in a GIS ArcView
framework, a modelling database containing all lookup tables for determining
model parameters, model programs, and other necessary components;
•
Develop a practical method for flow routing in GIS-based modelling that enables
to calculate response functions between any start and end point, depending upon
slope, flow velocity and dissipation characteristics along the flow lines;
•
Enable the use of the model for simulation of flow hydrographs at any location in
the stream network and the spatial distribution of hydrological processes, such as
runoff, soil moisture, evapotranspiration, groundwater recharge, etc.;
3
Chapter I
•
Investigate the sensitivity of model predictions to identify those model parameters
requiring the most careful estimation, and establish effective model evaluation
criteria for assessing the model performance;
•
Provide for a distributed model that can operate on a different spatial and temporal
scale, and enable the use of the model for assessing the impacts of land use change,
climate change, natural river restoration, etc., on the basin hydrological processes;
•
Provide a platform on which the future water quality and soil erosion models can
be developed at multiple scales.
To demonstrate the use of the model for flood prediction and watershed management,
the following specific objectives are addressed in different chapters:
•
Simulate flood hydrographs and water balance on complex terrain;
•
Estimate storm runoff contributions from different land use areas;
•
Assess the impacts of land use change on flood behaviours;
•
Assess the impacts of river restoration on the reduction of downstream flooding;
•
Apply the model in a mountainous catchment accounting for snow and
topographic adjustment for the input weather data.
3.
Outline of the dissertation
In the following chapters, the targets listed above are achieved by incorporating case
studies to each of the specific subjects. The main model equations are presented in
Chapter III and Chapter IV, while these equations are omitted in the following
chapters to avoid unnecessary repetition. The detailed descriptions of the model,
including model structure, formulation, data preparation, parameter identification,
model calibration and evaluation, etc. are presented in Appendix A: Documentation
and user manual of WetSpa Extension. A CD-ROM is prepared to install the full
package of the WetSpa Extension operating under ArcView environment, which
contains the sample project, Avenue scripts, lookup tables, help files, FORTRAN
programs, and essential testing data.
In Chapter II, a general literature review is conducted on the subject of GIS-based
hydrological modelling. It begins with a brief review of the lumped and distributed
4
General Introduction
hydrological modelling and the advantages of one type of modelling over the other
are given. Next, the influences of watershed characteristics, i.e. topography, soil type
and land use on runoff generation and flow routing are discussed, in order to stress the
importance and necessity of distributed hydrological modelling. The application of
GIS in hydrological modelling is highlighted including the application in watershed
description, watershed interpretation, and the integration with hydrological models. A
short description about some popular distributed and semi-distributed hydrological
models linked with GIS is also given in this chapter. At the end, an overview of the
WetSpa model is presented including the model history, assumptions and the
improvement made for the WetSpa Extension.
In Chapter III, a GIS-based diffusive transport approach for the determination of
rainfall runoff response and flood routing through a catchment is developed. In the
mean time, the sensitivity analysis for the effects of hydraulic radius, channel
roughness, minimum slope, area-threshold in delineating channel networks, etc., on
the flow response is discussed in this chapter.
In Chapter IV, the application of WetSpa for the flood simulation in the Barebeek
catchment, Belgium, is presented. This chapter gives a brief introduction at first about
the concepts of the WetSpa model and the procedures of GIS implementation to
derive model parameters for a complex terrain. Calibration and simulation results
using the measured and the intensity-duration-frequency (IDF) data based on the
analysis of historical records are presented afterwards.
In Chapter V, an assessment of land use impacts on flood processes in a complex
terrain is conducted for the Steinsel sub-basin of Alzette River basin, Grand-Duchy of
Luxembourg. The assessment focuses on the runoff contributions from different land
use classes and the potential impact of land use changes on runoff generation. Three
types of possible land-use scenarios are developed and their effect on flood processes
is investigated using the WetSpa distributed hydrology model.
In Chapter VI, a flood reduction method by using conceptual river restoration is
proposed. The scenarios are constructed considering the effects of increasing the flow
resistance and re-meandering of the first and second order streams of the Alzette
5
Chapter I
River basin, Grand-Duchy of Luxembourg, upstream of the Steinsel station. WetSpa
model is applied to estimate in a scientific way the possible beneficial effect of river
restoration on flood reduction in the main channels.
In Chapter VII, the WetSpa model is applied to an 1133 km2 Carpathian watershed,
Margecany, situated in the upstream part of the Hornad River basin, Slovakia. A
simple snowmelt model is developed and embedded with the WetSpa model running
on a daily scale. In addition, an automated calibration procedure by incorporating a
model independent parameter estimator PEST is developed serving as an optimization
algorithm to estimate the model parameters. Moreover, the topographic adjustment of
input data, i.e. temperature, precipitation and potential evapotranspiration (PET), in a
mountainous catchment is discussed.
In Chapter VIII, a method of integrating GIS and process modelling for runoff
prediction in medium and large river basins is presented based on a case study for the
Alzette River basin, Grand-Duchy of Luxembourg. The chapter starts with a
discussion of the grid size effects on runoff and flow responses. Next, the approach of
transforming WetSpa into a semi-distributed model is proposed, and the procedures to
derive model parameters together with the simulation results are presented.
In Chapter IX, the summary and conclusions of this research are provided, in which
the technique developed and knowledge acquired from this research are described and
evaluated together with some comments regarding model limitations and some
possible future researches of the model.
6
General Introduction
References
Babd, L.E. & Moore, I.D., Landscape attribute and Geographical information Systems.
In: Scale Issues in Hydrological Modelling, eds., J.D. Kalma and M. Sivapalan,
159-180, John Willey & Sons., 1995.
Boyle, C.A., Lavkulich, L., Schreier, H., & Kiss, E., Changing in land cover and
subsequent effects on lower Fraser basin ecosystems from 1827 to 1990,
Environ. Manage., 21(2), 185-196, 1997.
Goodchild, M.F., Haining, R.P., Wise, S. & 12 others, Integrating GIS and spatial
data analysis: problems and possibilities, Int. J. Geogr. Inf. Syst. 6(5), 407–423,
1992.
McDonnell, R.A., Including the spatial dimension: Using geographical information
systems in hydrology, Prog. Physical Geography, 20(2), 159-177, 1996.
Wagener, T., Boyle, D.P., Lees, M.J, Wheater, H.S., Gupta, H.V., & Sorooshian, S.,
A framework for development and application of hydrological models, Hydrol.
Earth Syst. Sc., 5(1), 13-26, 2001.
Wang, Z., Batelaan, O. & De Smedt, F., A distributed model for water and energy
transfer between soil, plants and atmosphere (WetSpa), Phys. Chem. Earth,
21(3), 189-193, 1997.
Weng, Q., Modelling urban growth effects on surface runoff with integration of
remote sensing and GIS, Environ. Manage., 28(6), 737-748, 2001.
7
Chapter II
GIS-based hydrological modelling and watershed analysis
Abstract
GIS with its upcoming advanced technology has been a great asset to the hydrological
modelling and watershed analysis. In particular, digital elevation models together with
soil and land use mapping are used in a number of sub-domains in hydrology. Many
hydrological models developed in the past which were useful individually and can be
combined in various applications. The goal of this chapter is to provide a brief review
of the extensive literature that exists in the area of GIS-based hydrological modelling;
to address the potential impacts of watershed characteristics, such as topography, soil
type and land use, on runoff generation and flow response that can be assessed by
using GIS; to outline the rational basis for the linkage between GIS and hydrological
modelling; and to indicate the type of model that could be incorporated within GIS
and which are best left as independent analytical tools linked to GIS for data input and
display of results. Finally, an overview of the WetSpa model and its extension is
presented at the end of this chapter.
1.
Introduction
Over the past decades, extensive studies have been carried out with the aim of
analyzing and modelling the natural systems in respect to the processes of runoff
generation as well as the related transport of water, solutes and sediments. However,
all these studies have different temporal and spatial scales from single events in
micro-scaled sub-catchments. Chow et al. (1988) offered a taxonomy of hydrological
models based on the randomness (deterministic/stochastic), spatial variation
(lumped/distributed; space-independent/space-dependent) and time variation (steady
flow/unsteady flow; time independent/time correlated) thereby drawing the attention
to the pivotal position of the spatial dimension explored by the several possible
applications of linking GIS with the hydrological models. The aim of these studies is
mostly the same, i.e. to represent the natural system in a more or less sophisticated
Chapter II
mathematical description in order to match the observed system outputs. The problem
hereby is to find the right model, which is appropriate for the particular scale and aim
of the study. There exists a distinct disagreement in the scientific community on
which kind of model is more appropriate for the simulation of natural processes. It is
widely recognized that the natural systems are extremely complex and the inherent
processes are non-linearly connected and sometimes even characterized as being a
chaotic system.
Simple lumped models treat the hydrological system as spatially averaged and
homogeneous in space with a small amount of calibration parameters for adapting the
model. These models have only in part the possibility or very little opportunity for
parameterization with respect to basin characteristics. Therefore measurements of the
system output for an adequate period are a prerequisite for their application. However,
lumped models have the disadvantage that the possibility of forecast simulations for
un-gauged sites is limited and no learning effect of the inherent processes of the
catchment is achieved. On the other hand, physically-based distributed models are
used to offset the mentioned disadvantage of the simple models. The process
description is derived from process studies at the scale of elementary spatial unit, such
that the whole basin is partitioned into smaller cell elements. For each model cell the
hydrological parameters and processes are assumed to be homogenous. One of the
drawbacks of spatially distributed hydrological models is their requirement of detailed
spatial data of the basin and of the climate. However, the availability of spatially
distributed data sets (DEM, land use, soil, etc.) in the present time coupled with recent
advances in computer hardwares and GIS software allows the spatial variation of
model parameters and processes to be considered at a detailed resolution.
Additionally, the spatio-temporal scales are also key considerations in selecting the
model and in modelling the hydrological processes. The spatial scale for which a
model is designed can play a significant role in how specific processes are treated.
Therefore, it is an important criterion in the selection of a model because the storage
characteristics may vary at different watershed scales, that is, large watersheds have
well developed channel networks and channel phase, and thus, channel storage is
dominant. Such watersheds are less sensitive to short duration, high intensity rainfalls.
On the other hand, small watersheds are dominated by the land phase and overland
10
GIS-based hydrological modelling and watershed analysis
flow, have relatively less conspicuous channel phase, and are highly sensitive to high
intensity, short duration rainfalls. The temporal scale is important for modelling that
operates from event to daily or even longer time scales. At the event time scale,
models typically do not compute inter-storm soil moisture conditions and therefore
this information must be provided as an initial condition to initiate the model run. On
the other hand, continuous-time hydrological models can simulate the processes of
precipitation, surface storage, snowmelt, evapotranspiration, soil moisture, and
infiltration in a seasonal framework. These models typically operate on a time interval
ranging from a fraction of an hour to a day. One of the advantages of continuous
modelling is that it can provide a long-term simulation of the hydrological processes
variability.
2.
Effects of watershed characteristics on runoff
Runoff is generated by precipitation during storm events and by groundwater entering
surface channels. During dry periods, streamflows are sustained by groundwater
discharges. Relations between precipitation and runoff are very complex, being
influenced by many factors, such as interception, depression storage, infiltration, and
evapotranspiration. Moreover, the quality and quantity of streamflow are strongly
affected by its basin’s physical, vegetative, and land use features. Thus, basin and
runoff are inter-related. These basin features are spatially distributed, and as a result
there is a need for physically-based distributed hydrological models that are
applicable to these environments. However, the robustness of such models would be
enhanced if they were developed from a conceptual framework based on the physics
of the dominant runoff processes.
2.1.
Effects of topography
Topographic features such as slope, curvature, and degree of convergence have an
important impact on runoff production and the nature and strength of the flow
connectivity.
For instance, as the mean slope length becomes shorter, the time
required to reach an effective channel decreases, leading to a steeper rising
hydrograph limb and a higher peak discharge. Primary terrain attributes include slope,
aspect, plan and profile curvature, flow-path length, and upslope contributing area.
11
Chapter II
Table II-1: Primary topographic attributes that can be computed by terrain analysis
from DEM data (Moore et al., 1991)
Attribute
Definition
Significance
Altitude
Elevation
Climate, vegetation, potential energy
Upslope height
Mean height of upslope area
Potential energy
Aspect
Slope azimuth
Solar isolation, evapotranspiration, flora
and fauna distribution and abundance
Slope
Gradient
Overland and subsurface flow, velocity and
runoff rate, precipitation, soil water content,
vegetation, geomorphology, land capability
Upslope slope
Mean slope of upslope area
Runoff velocity
Dispersal slope
Mean slope of dispersal area
Rate of soil drainage
Catchment slope
Mean slope of the watershed
Time of concentration
Upslope area
Catchment area above a
Runoff volume, steady-state runoff rate
short length of contour
Dispersal area
Area downslope from a
Soil drainage rate
short length of contour
Catchment area
Area draining to the
Runoff volume
catchment outlet
Specific drainage area
Flow path length
Upslope area per unit width
Runoff volume, steady-state runoff rate,
of contour
soil-water content, geomorphology
Maximum distance of water
Erosion rates, sediment yield, time of
flow to a point in the
concentration
catchment
Upslope length
Mean length of flow paths
Flow acceleration, erosion rates
to a point in the catchment
Dispersal length
Distance from a point in the
Impedance of soil drainage
catchment to the outlet
Catchment length
Distance from highest point
Overland flow attenuation
to the basin outlet
Profile curvature
Slope profile curvature
Flow acceleration, erosion and deposition
rate, geomorphology
Plan curvature
Contour curvature
Converging/diverging flow, soil water
content, soil characteristics
Tangential curvature
Elevation percentile
Plan curvature multiplied by
Provides alternative measure of local flow
slope
convergence and divergence
Proportion of cells in a user-
Relative landscape position, flora and fauna
defined circle lower than the
distribution and abundance
centre cell
12
GIS-based hydrological modelling and watershed analysis
Most of these topographic attributes can be calculated from the directional derivatives
of a topographic surface. The primary topographic attributes that can be computed by
terrain analysis from DEM data and their significance are listed in Table II-1 (Moore
et al., 1991). The secondary attributes that are computed from two or more primary
attributes, e.g. the topographic wetness indices (TWI), the stream power indices and
the radiation indices, are important because they offer an opportunity to describe
pattern as a function of process. Those attributes that quantify the role played by
topography in redistributing water in the landscape and in modifying the amount of
solar radiation received at the surface have important hydrological, geomorphologic,
and ecological consequences in many landscapes. These attributes may affect soil
characteristics, distribution and abundance of soil water, susceptibility of landscapes
to erosion by water, and the distribution and abundance of flora and fauna. These
topographic indices are used frequently in many topography-based hydrological
models, as for example the TOPMODEL (Beven & Kirkby, 1979), where TWI is
applied to characterize the spatial distribution and extent of zones of saturation and
variable source areas for runoff generation.
2.2.
Effects of soil type
The ability of the soil to transmit and retain water influences the rate of runoff during
a storm and the rate at which the soil dries out between storms. For example, sandy
soils allow for more infiltration of rain water than do heavier clay soils. Therefore, the
soil constituents are important to the accurate modelling of runoff, as well as soil
erosion and pollutant transport. Meanwhile, the states of surface and root zone soil
moisture reservoirs are key variables controlling surface water and energy balances.
Soil moisture plays an important role in various hydrological processes acting over a
range of spatio-temporal scales, like partitioning of rainfall into infiltration and runoff,
partitioning of net radiation into sensible and latent heat. Exchange of moisture flux
between land surface and atmosphere in the form of evapotranspiration is the major
link of interaction between hydrological and atmospheric processes. Hence there is a
need for accurate spatio-temporal representation soil moisture in the modelling of
atmospheric and hydrological processes.
13
Chapter II
The evolution and variability of soil moisture are affected by various factors, such as
soil properties, vegetation, solar radiation, atmospheric condition, prevailing
topography and general geomorphologic conditions. Numerical modelling of soil
moisture is usually based on highly nonlinear Richard’s equation. For stability
consideration most of the existing approaches solve the equation with a fully implicit
approach and use pressure head that is continuous in both saturated and unsaturated
zones as primary variable. However, soil water balance models are usually used to
keep track of water content changes in the soil zone, which treats the soil zone as a
control volume. This approach provides a consistent means for applying physical laws
to hydrological systems (Chow et al., 1988). Using this approach, direct runoff,
evaporation, and percolation are treated as losses from the hydrological system.
In hydrological modelling, soil texture is often used as a descriptor of soil physical
properties such as porosity, saturated hydraulic conductivity, soil matric potential, and
pore size distribution index (Cosby et al., 1984). Conventionally, the textural
classification of a soil is determined as a function of the mass ratios of the three
textural separates, namely sand, silt, and clay. Within the USDA soil textural
classification, soils with different percentages of sand, silt, and clay are assigned to 12
different classes. Although other descriptors such as horizon and structural size
certainly influence the hydraulic parameters of soils, Cosby et al. (1984) perform a
two-way analysis of variance of nine descriptors to conclude that soil texture alone
can account for most of the discernible patterns in porosity, saturated hydraulic
conductivity, soil matric potential, and pore size distribution index. Under given
climatic and vegetation conditions the above soil-texture-dependent physical
properties, through their influence on soil water movement and the energy state of the
water in the soil column, determine the soil wetness values which in turn establish the
water condition of the plant (Fernandez-Illescas, 2001).
2.3.
Effects of land use
The patterns of vegetation on land surface give areas with different runoff generating
characteristics. The vegetation cover density and the spatial configuration will both
affect the discharge from the hill slope. As the vegetation density increases, the
average infiltration rate will increase, thus leading to a reduction in discharge.
14
GIS-based hydrological modelling and watershed analysis
However, as the cover becomes more fragmented, there are a greater number of
pathways from the runoff source areas to the channel base. This increases in
connectivity and consequently increases hill slope discharges. Moreover, different
land use types have different evapotranspiration rates, because different plants have
different vegetation cover, leaf area indices, root depths and albedo. During storms,
interception rates are different for different land use types. Although it is recognized,
that interception losses represent a significant net addition to catchment evaporative
losses (Ward & Robinson, 1990), the influence of interception is noticeable only
during small storms and influences only surface runoff rates. For largest storm and
flood events, the interception losses are of minor importance (Calder, 1993). Land use
also influences the infiltration and soil water redistribution process, because
especially saturated hydraulic conductivity is influenced by plant roots and pores
resulting from soil fauna (Ragab & Cooper, 1993). An extreme example is the
influence of build up areas and roads on overland flow. Finally, land use and land
management influences surface roughness, either by the land use type itself or by its
management, which affects the overland flow velocity and floodplain flow rate.
The hydrological effects of land use changes have been thoroughly described by Ward
and Robinson (1990) and Calder (1993). The major changes in land use that affect
hydrology are afforestation and deforestation, the intensification of agriculture, the
drainage of wetlands, road construction, and urbanization. Of all the land use
modifications, urbanization is by far the most forceful, by which land is transformed
from its natural state or from agricultural use to an economically developed or
populating region. This process can take many forms including irrigation, drainage,
deforestation and logging, and urban development, all which result in numerous
adverse effects on the water quality and quantity of surrounding terrestrial and aquatic
ecosystems. The most significant of these effects is the alteration of the hydrological
cycle and rainfall-runoff transformation of the watershed, including (1) changes in
peak flow characteristics, (2) changes in total runoff, (3) changes in quality of water,
and (4) changes in the hydrological amenities (Leopold, 1968). As the watershed
becomes more developed, it also becomes more hydrologically active, changing the
stream’s flow components as well as the origin of flow. Additionally, urbanization
tends to increase both the flood volume and the flood peak.
15
Chapter II
3.
GIS applications in watershed modelling
GIS is a software and hardware tool applied to geographical data for integration of
collection, storing, retrieving, transforming and displaying spatial data for solving
complex planning and management problems. It integrates common database
operations including (1) database and data management operations, (2) time and
spatial analysis functions, (3) image elaboration and filtering possibilities, (4) data
merging and informative layers management, (5) cartographic and display functions,
and (6) map realization and data presentation. GIS has the advantage of handling
attribute data in conjunction with spatial features, which was totally impossible with
manual cartographic analysis. The availability of GIS technology greatly enhances the
capabilities for land description and interpretation by means of powerful distributes
indicators, and therefore has allowed, and sometimes imposed, significant changes in
the general approach to hydrological investigation and to operative hydrology since
its development.
3.1.
Watershed description
Watershed characteristics relevant to hydrological investigations can be easily stored
and handled by GIS, adding layers such as soil type and land use to the topographic
database. The GIS produces a digital model of the basin, as detailed as required,
which is easily readable by means of the appropriate software. Thus, the hydrologist
can account for not only the land characteristics but also their distribution and
individual localization in space. The input digital data are normally retrieved from
external sources such as numerical cartography, aerial photography, satellite images,
and digitalization of maps. The hydrologist usually deals with distributed objects as
land use, soil type, hydrographical network, and hydraulic infrastructures. Once the
databases of geo-referenced objects are setup the work begins by analyzing data,
extracting information, producing synthetic maps by logical and algebraic operations,
and running distributed models.
The terrain complexity can be better represented by means of vectorial information,
using points, polylines and polygons. Nevertheless, dealing with such geometry is still
often too difficult when overlying or elaborating maps. So it is usually preferable to
16
GIS-based hydrological modelling and watershed analysis
use raster maps in the analysis operations, which is rougher but easy to manage.
However, an excellent degree of precision can be achieved by simply reducing the
pixel dimension within reasonable levels. The morphological maps of elevation, slope
and aspect are the basic informative layers, especially when dealing with mountain
basins where the morphology plays a crucial role in hydrological response. Many
algorithms exist to transform elevation contours into a raster DEM. The capability of
DEM in term of land description is not limited to the elementary topographic attribute.
A good DEM makes it possible to recognize the channel network by means of
software, providing a suitable framework for routing modelling approach. The
distinction between slope and channel paths can even be achieved simply by fixing a
threshold drainage area for which the flow concentration is sufficient to initiate a
channel (Tarboton et al., 1991; Da Ros & Borga, 1997).
The use of soil and land use maps is generalized as both soil and land use strongly
affects the hydrological behaviour of a single land unit, and specifically it is an
effective indicator of potential direct flow generation. The land use map can be
derived from remotely sensed imagery, or generated by an aerial view, particularly in
terms of number of classes. The soil map, when not available, should be realized by
expensive field techniques. However, in most cases the local land use, sometimes
combined with a geologic map, can suggest some indications on soil characteristics.
3.2.
Hydrological parameter determination
A very active area of research is the use of GIS for model parameter estimation, in
which local interpretations of the phenomena that exhibit over a watershed are
provided by means of simple lookup tables or complex algorithms in combination
with different kind of digital information. This role of GIS can be very beneficial for
distributed parameter models which require large amounts of data. Special tools added
to any commercial GIS software are able to compute powerful distributed indicators.
The well-known Curve Number of the U.S. Soil Conservation Service, whose values
are based on land use and soil permeability maps, is actually an indicator of potential
direct flow generation. Specifically, primary terrain attributes like elevation, slope,
aspect, shape of profile, upslope drained area, can be combined to give compound
attributes, giving the dominant role of topography in hydrological processes control
17
Chapter II
and landscape evolution. A well-known compound indicator is the topographic steady
state wetness index (WI), defined, for each pixel, as the logarithm of the rate between
the upslope drained area and the local slope (Western et al., 1999). Studies have
shown the capabilities of slope and contributing drainage area to account topographic
control for potential erosion/deposition in complex terrain (Mitasova et. al., 1996; De
Roo, 1998). The drainage contributing area reflects the occurrence of flow
concentration. The local slope gives account for the action of gravity force and so
directly affects the flow velocity and the shear stress exerted by water on soil surface.
Energy for surface processes as evapotranspiration and snow melt is provided by solar
radiation, which is affected by local terrain morphology. With the model of the terrain
surface provided by the GIS, Cazorzi and Dalla (1996) proposed a method to produce
a potential energy distribution map, representing an indicator of the maximum solar
radiation that can reach each pixel of the surface in a given time interval, without
regard to weather conditions. Moreover, studies have shown the success of estimating
SCS curve numbers using GIS by incorporating the land use and soil type data layers
with the DEM (Hjelmfelt, 1991). Likewise, a potential runoff coefficient map can be
generated based on the digital information of slope, soil type and land use (De Smedt
et al., 2000; Liu et al., 2002). Maidment (1993) suggested a unit hydrograph technique
that could combine the advantages of distributed modelling with the power of GIS. In
his study, the time-area curve method was used to develop the synthetic unit
hydrograph, while the travel time from each cell to the watershed outlet was
calculated by dividing each flow length by a constant velocity. Liu et al. (2003)
proposed a diffusive transport approach for flow routing in GIS-based watershed
modelling, in which the unit response function of the grid cell is calculated based on
the spatially distributed travel time and its standard deviation. Differing from the
method of isochronal lines based only on the distance from the watershed outlet, these
GIS models can route the runoff over the elevation surface and account for
differences in runoff velocity due to changing slope, land use, and surface conditions.
3.3.
Integration with hydrological models
The ongoing development of GIS and associated databases offers the opportunity to
simulate hydrological processes on a watershed scale using more physically based
18
GIS-based hydrological modelling and watershed analysis
approaches than in the past. Three approaches exist for integrating hydrological
modelling with GIS environment (Figure II-1): un-coupled integration, loosely
coupled integration and tightly coupled integration (Kopp, 1996). In un-coupled
integration, the GIS are used to process the spatial data into the desired model inputfile format and post-processing the model output. In loosely coupled integration,
model input and output can be addressed directly by the GIS. Finally, in tightly
coupled integration the model is written in an integrated programming language such
as ArcView avenue language and Arc/Info AML language.
Figure II-1: GIS–Hydrological modelling integration methods (Matson, et al., 1995)
Parameters calculation for traditional lumped or semi-distributed models, when linked
to a GIS, becomes much quicker and easy to change and test for a better solution. This
kind of deterministic conceptual models is still very used in operative hydrology, as
their behaviour is almost well known and, in most cases, they provide sufficient
results. In this case the model and the GIS are essentially autonomous, and although
the GIS potentiality is far to be completely exploited, it offers undoubtedly a good
value added. The distributed models normally deal with square elementary land units,
corresponding to raster pixels, and parameter computation, for each land unit, can be
practically done through coupling with a GIS (Maidment, 1993, Wimgosta et al.,
1994). Some of these models have already shown to be very important in the
19
Chapter II
evolution of hydrological sciences, either for their conceptual structure, like for
instance the physically based SHE (Abbott et al., 1986a, b), or for their convenience
and ease of use, as for instance the TOPMODEL (Beven & Kirkby, 1979).
Recent research developments brought to fully distributed hydrological models
embedded into a GIS. In these cases a single database is used rather than two separate
ones and the user interacts solely with the GIS, as the model is seen as a GIS function
and is driven by a more or less customizable GIS menu. The leading idea of
embedded models is to keep the model simple while exploiting the GIS power. An
example is the LISFLOOD model, which is programmed in a dynamic GIS language
called PC Raster used to simulate floods in large European drainage basins (De Roo et
al., 2000). The model is defined by a regular horizontal grid of user-defined size
typically varying between a few hundred meters for smaller catchment or subcatchment simulations and 5 km for simulations on European scale. Embedded
models in a GIS environment have many advantages over traditional loosely GIScoupled models. However, current GIS is lacking of tools for developing physicallybased models. Especially simulating transport of water and pollutants through
landscapes is a problem in a GIS environment. The development of GIS systems to
handle all calculations will be an important step in hydrology, for which all aspects
related to hydrological modelling can be integrated into a comprehensive GIS system,
so that better simulations can be obtained, and therefore better management can be
achieved. Unfortunately this approach currently remains out of reach for most
practical applications due to data limitations and the lack of proven software.
4.
Modelling of watershed hydrology
Hydrological models are integral components of water management and monitoring
strategies. In particular, distributed hydrological models allow for detailed description
of the hydrological and energy cycle and provide opportunities for dealing with
forcing variables that fluctuate strongly in space and time, such as precipitation.
Hydrologists increasingly implement these models as a means to apply the state of
knowledge on basins of interest, and provide valuable information regarding
hydrological state variables and potentially important distributed information on
existing and future streamflow conditions. Also, there is increasing interest in using
20
GIS-based hydrological modelling and watershed analysis
spatially distributed meteorological data from diverse sources such as environmental
satellite and weather radar. GIS provides representations of these spatial features of
the Earth, while hydrological modelling is concerned with the flow of water and its
constituents over the land surface and in the subsurface environment. Singh and
Woolhiser (2002) provide a general review of mathematical modelling of watershed
hydrology. Vieux (1991) presents a review of water quantity and quality modelling
with GIS and, as an application example, employed the kinematic wave method to an
overland flow problem.
4.1.
Popular GIS-based hydrological models
The employment of GIS and remotely sensed data in watershed modelling is one of
the most important recent advances in hydrology. Over the last decade, there has been
tremendous development in hydrological modelling using GIS. Most of the
hydrological models are mathematically based, where they integrate existing
knowledge into a logical framework of rules and relationships. GIS technology has
been integrated with these surface or subsurface hydrological models emphasizing the
utility and significance of topographic attributes of the terrain for various hydrological
applications. The reason of adopting GIS technology is because it allows the spatial
information to be displaced in integrative ways that are readily comprehensible and
visual. The spatial information collected is further subjected to continuous GIS
analysis, providing the opportunity for realistic representation of the natural
landscapes under the constraints of maintaining physical consistency.
Hydrological models with a spatial structure are being increasingly based on DEM or
DTM (Moore et al., 1991). Many of the existing models, such as SHE, TOPMODEL,
etc., have been adapted to the new type of data that can be processed by GIS software.
Integration of hydrological models with remotely sensed, GIS, and DEM-based data
has started to occur. Examples of newly developed or adapted models are those by
Fortin et al. (2001a,b), Wigmosta et al. (1994), Julien et al. (1995), Desconnets et al.
(1996), Olivera and Maidment (1999) and De Roo et al. (2000). Table II-2 lists some
samples of popular distributed and semi-distributed hydrological models that support
GIS and remote sensing applications.
21
Chapter II
Table II-2: Samples of popular distributed and semi-distributed hydrological models
Model name
Author(s)
Remarks
Hydrological Engineering Centre, Hydrolo- Feldman
Physically-based, semidistributed, event-
gical Modelling System (HEC-HMS)
based, runoff simulation model
Semi-distributed Land Use-based Runoff
Processes (SLURP)
(1981)
Kite (1998)
Process-oriented, semidistributed,
continuous stormflow simulation model
Systeme Hydrologique Europeen/Systeme
Abbott et al.
Physically based, distributed, continuous
Hydrologique Europeen Sediment (SHE)
(1986a,b)
flow and sediment simulation model
Institute of Hydrology Distributed Model
Calver &
Physically based, distributed, continuous
(IHDM)
Wood (1995) rainfall-runoff modelling system
Physically Based Runoff Production Model Beven &
Physically based, distributed, continuous
(TOPMODEL)
Kirkby (1979) hydrological simulation model
Kinematic Runoff and Erosion Model
Smith et al.
Physically based, semidistributed, event-
(KINEROS)
(1995)
based, runoff and water quality model
Generalized River Modelling Package, Sys- Refsgaard &
Physically based, distributed, continuous,
teme Hydroloque Europeen (MIKE-SHE)
Storm (1995) hydrological & hydraulic model
Waterloo Flood System
Kouwen
Process-oriented, semidistributed
(WATFLOOD)
(1988)
continuous flow simulation model
Dynamic Watershed Simulation Model
Borah et al.
Process-oriented, event-based, runoff and
(DWSM)
(2002)
water quality simulation model
Hydrological Model System (HMS)
Yu et al.
Physically based, distributed, continuous
(1999)
hydrological simulation system
Hydrological Modelling System
Pfützner &
Process-oriented, distributed, continuous
(ARC/EGMO)
Becker (1995) simulation system
Lindström et
Process-oriented, distributed, continuous
al. (1997)
streamflow simulation model
Distributed Hydrology Soil Vegetation
Wigmosta et
Distributed, physically based, continuous
Model (DHSVM)
al. (1994)
hydrological simulation model
Hydrological Simulation (HBV) Model
Systeme Hydrologique Europeen Transport Ewen et al.
Physically based, distributed, water
(SHETRA)
quantity and quality simulation model
(2000)
Cascade two dimensional Model (CASC2D) Julien et al.
Physically based, distributed, event-based
(1995)
runoff simulation model
Geomorphology-Based Hydrology
Yang et al.
Physically based, distributed, continuous
Simulation Model (GBHM)
(1998)
hydrological simulation model
Physically-Based River Basin Modelling
De Roo et al.
Physically based, distributed, continuous
System (LISFLOOD)
(2000)
runoff simulation model on large scale
Distributed Hydrological Model
Fortin et al.
Physically based, distributed, continuous
(HYDROTEL)
(2001a, b)
hydrological simulation model
Arnold et al.
Distributed, conceptual, continuous
(1998)
simulation model
Soil Water Assessment Tool (SWAT)
22
GIS-based hydrological modelling and watershed analysis
4.2.
Assessment of future scenarios
The understanding of global climate systems has considerably increased in recent
years, as well as human concern about future global climatic changes. Along with
these changes important consequences are expected in regional hydrological cycles
and subsequent effects on regional water resources. Since hydrological processes
directly depend on climate conditions, influences of possible climatic changes on
these processes will differ from region to region. The magnitude and spatial
distribution of the climatic changes in combination with hydrological characteristics
of the study region determine which effects will be most relevant on the regional scale.
Though the direction or magnitude of many important changes are not yet fully clear,
studies in the last years have shown important regional vulnerabilities against changes
of both temperature and precipitation patterns. They suggest that climatic changes will
alter basic components of the hydrological cycle like soil moisture, groundwater
availability, magnitude and timing of runoff, and water quality, which would induce
dramatic environmental dislocations and widespread implications for future water
resources planning and management (Lahmer et al., 2001).
Land use change has been identified as a major driving force for global change, which
may induce comparable effects on water quantity and quality. These changes are the
result of natural processes as well as anthropogenic influences, which include such
processes as vegetation dynamics, erosion, acidification, salinization, overgrazing,
desertification, mining, urban and industrial development, conversion of lands into
agriculture, and deforestation, etc. it is desirable that the hydrological modelling
describes the spatio-temporal variability of land use effects so that the assessment
could reflect the variability of the hydrological parameter at the required scales
(Parkin et al., 1996). Though the problems and consequences resulting from land use
change are clearly defined, clear solutions and practical applications are still
challenging to the hydrologist. One of the most important reasons is the difficulty of
parameterization of the physiographic properties and state variables of a basin into a
model (Naef et al., 2002).
In recent years, river restoration, rehabilitation and other environmentally preferable
methods have become important issues in river engineering practice. The goal of
23
Chapter II
stream restoration is to restore the stream to a more natural form to create
environmentally favourable conditions, which do not necessarily imply that the
stream will be restored to its pre-settlement condition (Morris, 1995). Besides the
benefits on the ecology and morphology of a river basin, river restoration activities in
the headwater streams may have a positive effect on flood reduction for the main river
channels in the river basin. In this respect, distributed hydrological models based on
GIS techniques have advantages in modelling and assessing the effects of river
restoration on flooding dynamics based on reliable restoration scenarios.
5.
WetSpa model overview
5.1.
Model history
WetSpa is a physically based distributed hydrological model for predicting the Water
and Energy Transfer between Soil, Plants and Atmosphere on regional or basin scale
proposed by Wang et al. (1997). The model conceptualizes a basin hydrological
system being composed of atmosphere, canopy, root zone, transmission zone and
saturation zone. The basin is divided into a number of grid cells in order to deal with
the heterogeneity of catchment characteristics. Each cell is further divided into a bare
soil and vegetated part, for which the water and energy balance are maintained. Figure
II-2 shows schematically the considered hydrological processes for a grid cell.
precipitation
evapotranspiration
surface runoff
latent
heat
bare
soil
heat to ground
z
ot
ro
infiltration
percolation
recharge
e
on
on
e
sensible
heat
short and long
w ave radiation
ca tra
pil
lar ns im
y
f ri iss
ng ion
e
z
long w ave
radiation
r
tu
sa
ion
at
groundw ater
flow
ne
zo
Figure II-2: Hydrological processes considered in the original WetSpa model
24
GIS-based hydrological modelling and watershed analysis
Water movement in the soil is simplified as one-dimensional vertical flow, including
surface infiltration, percolation and capillary rise in the unsaturated zone and recharge
to groundwater. The model was designed to simulate the Hortonian overland flow and
the variable source area concept of runoff generation. In order to have a more realistic
representation of the interaction between surface runoff and groundwater storage, a
groundwater flow model is integrated, for which the groundwater balance in the
saturated zone is described by the two-dimensional Dupuit-Forchheimer horizontal
flow equation. Under appropriate boundary conditions the water table position is
determined with a finite difference scheme for each grid cell, and explicitly for each
time step. The model was designed for scientific research with time resolution of
minutes. Due to the complex model structure and the limit of available data, the
model is difficult to be implemented for an engineering purpose.
For the estimation of long-term spatial patterns of the groundwater recharge, that
could be used as input in regional groundwater flow models and for the analysis of
regional groundwater flow systems, a simplified model WetSpass was developed by
Batelaan & De Smedt (2001) based on WetSpa. WetSpass stands for Water and
Energy Transfer between Soil, Plants and Atmosphere under quasi-Steady State
conditions, which is GIS based, spatially distributed hydrological model for
calculating the spatially distributed yearly and seasonal evapotranspiration, surface
runoff, and groundwater recharge. The model accounts for the spatial variation in the
groundwater recharge, which is the result of distributed land use, soil type, and slope,
etc. The total water balance for a cell in a spatially distributed grid is split up in
independent water balances for vegetated, bare-soil, open-water and impervious parts
of the grid cell. This allows accounting for the non-uniformity of the land use
depending on the resolution of the grid cell. WetSpass model operates on a seasonal
basis, and the flow processes are not included.
5.2.
WetSpa Extension
The WetSpa Extension, developed during my PhD research, is a physically-based
distributed, continuous hydrological model compatible with remote sensing and GIS
data, which is capable of predicting outflow hydrographs at basin outlet or any
converging point in a watershed with a variable time steps (De Smedt et al., 2000; Liu
25
Chapter II
et al., 1999, 2002, 2003). The model aims not only at predicting flood, but also
investigating the reasons behind it, especially the spatial distribution of topography,
land use and soil type. Compared with the originally proposed WetSpa model, major
changes involved in this extension are:
1) The time resolution of simulated hydrological processes is changed to a variable
time scale (minutely, hourly, daily, etc.). The spatial resolution is also variable to
allow adequate interpretation of the landscape. The spatio-temporal scales of the
model are determined according to the project purpose, the size and complexity of
the catchment, data available, and computer speed and memory.
2) The Thiessen polygon method is applied to address the spatial distribution of input
time series, i.e. precipitation, temperature and PET, for the current version.
Topographical corrections for the input time series are considered in modelling a
mountainous catchment if the necessary data are available.
3) A moisture-related runoff coefficient method is developed for calculating surface
runoff in each grid cell, which allows the actual runoff coefficient to vary in time,
and in function of rainfall intensity, rainfall duration and cell characteristics (slope,
soil type and land use), giving an approximation to the surface runoff volume at
each time step.
4) The modelling of snow accumulation and snowmelt is added in the WetSpa model
capable of predicting snowmelt flood by a simple degree-day approach, in which
the temperature lapse rate for each grid cell is determined based on the DEM and
the elevation of reference station.
5) The hydrological processes of interception and depression storage are considered
in the WetSpa model allowing the estimation of initial abstraction for a storm
event. The parameter of interception storage capacity is determined based on the
land use map and varies with season, while the depression storage capacity is
determined based on the cell’s slope, soil type and land use.
6) The process of shallow subsurface lateral flow is considered in the WetSpa model
allowing the simulation of interflow and return flow from adjacent upslope cells
by the method of Darcy's law and kinematic approximation. The subsurface lateral
flow is assumed to occur when soil moisture is higher than field capacity and join
the overland flow at each grid cell. However, the routing of subsurface lateral
flow to the downhill neighbours is not performed for model simplicity.
26
GIS-based hydrological modelling and watershed analysis
7) An effective hydraulic conductivity of the soil is specified based on the soil
texture class, which limits the rate at which water can percolate out of the root
zone. The percolated water is assumed to recharge the groundwater reservoir
within the same time step.
8) Evapotranspiration from root zone is calculated for each cell as a function of PET
and moisture content in the cell. A part of water is extracted for transpiration from
groundwater storage when PET exceeds the evapotranspiration from soil
depending upon the amount of groundwater storage. Actual evapotranspiration is
then the sum of the evaporation from interception and depression storage and the
evapotranspiration from soil and groundwater storage.
9) The simulation of groundwater balance and baseflow is performed on small
subcatchment scale by the linear or non-linear reservoir method for the
simplification of model parameterization. Baseflow is added to the streamflow
producing a total-runoff hydrograph at the subcatchment outlet.
10) A flow routing model for both overland flow and channel flow is incorporated in
the WetSpa model using the method of linear diffusive wave approximation. The
unit response function for each grid cell is calculated based on the mean and
variance of the flow time distribution, which is derived from the advectiondispersion transport equation. The flow velocity is location dependent and
calculated for each cell by the Manning equation based on the local slope,
roughness coefficient and hydraulic radius. The hydraulic radius is determined
according to the geophysical properties of the river basin and the flood frequency.
11) An automated calibration procedure is applied to the WetSpa model by
incorporating a model-independent parameter estimator PEST (Doherty &
Johnston, 2003) to estimate the most sensitive parameters of the model with
observed flow hydrographs as the calibration target. This scheme serves as an
optimization algorithm to estimate the model parameters.
12) 5 criteria are set up for statistically evaluating the model performance, namely
model bias, model confidential coefficient, Nash-Sutcliffe efficiency (Nash &
Sutcliffe, 1970), logarithmic transformed Nash-Sutcliffe efficiency for low flow
evaluation (Smakhtin et al., 1998), and an adapted version of Nash-Sutcliffe
efficiency for high flow evaluation (Guex, 2001).
13) Some model formulas are modified in order to make the model more physically
based and capable of using readily available data, for instance the equation to
27
Chapter II
calculate water percolation out of the root zone and the equation to calculate
evapotranspiration from soil layer. Besides, all default parameter values in the
model lookup tables are recalibrated based on the literature review and practical
case studies, and some new lookup tables are established, such as hydraulic radius,
interception and depression storage capacity, etc.
14) Model programs are developed, which make use of spatial inputs and give spatial
outputs as well. The GIS part of the model is processed using ArcView Avenue
script together with functions in the ArcView Spatial Analyst extension. The
programming of hydrological simulation is developed using FORTRAN language.
A user friendly ArcView interface which integrates GIS with hydrological
modelling is also developed.
6.
Summary
The rainfall-runoff relationship is one of the most complex hydrological phenomena
due to the tremendous spatio-temporal variability of the watershed characteristics and
unpredictable rainfall pattern. However, to address the effects of spatial variability of
model parameters such as land-use changes, distributed hydrological models have the
advantage as they can explicitly consider spatial variability of parameters. With the
development of GIS and remote sensing techniques, the hydrological catchment
models have been more physically based and distributed to enumerate various
interactive hydrological processes considering spatial heterogeneity.
A GIS-based hydrological model, WetSpa Extension, has been developed for use in
flood prediction and watershed analysis. It accounts for the effects of topography, soil
and land use on runoff in a spatial way operates within a GIS framework. The model
automates the process of converting commonly available GIS data to input parameter
files for the hydrological modelling extension. Spatial results from the model, such as
runoff, groundwater recharge, soil moisture, etc., can be imported into GIS and
investigated using ArcView visualization tools. Since the models operate at different
spatial and temporal scales, it provides the capability to assess the spatial distribution
of the impacts of catchment characteristics, such as land use and land cover change,
on watershed hydrological responses.
28
GIS-based hydrological modelling and watershed analysis
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33
Chapter III
Development of a diffusive transport approach for flow routing in
GIS-based watershed modelling
Abstract
A GIS-based diffusive transport approach for the determination of rainfall runoff
response and flood routing through a catchment is developed. The watershed is
represented as a grid cell mesh, and routing of runoff from each cell to the basin outlet
is accomplished using the first passage time response function based on the mean and
variance of the flow time distribution, which is derived from the advection-dispersion
transport equation. The flow velocity is location dependent and calculated for each
cell by the Manning equation based on the local slope, roughness coefficient and
hydraulic radius. The hydraulic radius is determined according to the geophysical
properties of the river basin and the flood frequency. The total direct runoff at the
basin outlet is obtained by superimposing all contributions from every grid cell. The
model is tested on the Attert catchment in Luxembourg with 30 months of observed
hourly rainfall and discharge data, and the results are in good agreement with the
measured hydrograph at the basin outlet. Sensitivity analysis shows that parameters of
flood frequency and the channel roughness coefficient have large influences on the
outflow hydrograph and the calculated watershed unit hydrograph, while the threshold
of minimum slope and the threshold of drainage area in delineating channel networks
have a marginal effect.
1.
Introduction
Flood prediction and catchment modelling are main topics facing the hydrologist
dealing with processes of transforming rainfall into a flood hydrograph and the
translation of hydrographs throughout a watershed. The theory of the unit hydrograph
for the prediction of stream flow in a basin has played a prominent role in hydrology
for several decades since its development. This system response theory assumes that
the basin response to a rainfall input is linear and time invariant. The discharge at the
Chapter III
outlet of the basin is given by the convolution of the rainfall input and the
instantaneous unit hydrograph (IUH) (Dooge, 1959). In engineering practice, the unit
hydrograph is often determined by numerical deconvolution techniques (Chow et al.,
1988) using observed stream flow and rainfall data.
Since the characteristics of hydrological systems, as for instance precipitation and the
generation of runoff, are extremely variable in space and time, the response of the
system, i.e. the flow of water over the land surface and the river channels, is a
distributed process in which the characteristics of the flow change both in time and
space. This limits the use of the unit hydrograph model. Consequently, in trying to
relax the unit hydrograph assumptions of uniform and constant rainfall, and to
account for spatial variability of the catchment, considerable research has been
conducted in recent years, and many articles dealing with these topics can be found in
the literature.
In an attempt to find a physical basis for the IUH, Rodriguez-Iturbe and Valdes (1979)
introduced the concept of a geomorphologic instantaneous unit hydrograph (GIUH),
which relates the geomorphologic structure of a basin to the IUH using probabilistic
arguments. This theory was later generalized by Gupta et al. (1980) and Gupta and
Waymire (1983). In their paper, Horton's empirical laws, i.e. law of stream numbers,
lengths and areas, are used to describe the geomorphology of the system. The IUH is
defined as the probability density function (PDF) of the droplet travel time from the
source to the basin outlet, in which the time spent in each state (order of the stream in
which the drop is located) is taken as a random variable with an exponential PDF. The
model is relatively parsimonious in data requirements and most parameters can be
obtained from DEM data. Consequently, this theory has undergone several
noteworthy developments over the last two decades. Mesa and Mifflin (1986)
obtained their GIUH by means of the width function and the inverse Gaussian PDF.
The width function is the frequency distribution of channels with respect to flow
distance from the outlet. It is an approximate representation of the “area function”
under the assumption of a uniform constant of channel maintenance throughout the
drainage basin. Similar methodologies were presented by Naden (1992) and Troch et
al. (1994). Sivapalan et al. (1990) incorporated the effect of partial contributing areas,
which recognizes that during a rainfall event, droplets contributing to the runoff are
36
Development of diffusive transport approach for flow routing
not uniformly distributed throughout the basin but are more likely to come from areas
that are saturated close to stream channels. The saturated areas can be identified
through topographic indices (Beven & Kirkby, 1979), which can be easily obtained
from DEM data. Van Der Tak and Bras (1990) incorporated hillslope effects in the
basic formulation of GIUH by using a gamma distribution for the travel time
distributions through the flow pathways and introducing a hillslope velocity term.
Using the method of moments, they found that hillslope velocities are two orders of
magnitude smaller than channel velocities, which has a significant impact on the
GIUH. To describe the flow through individual streams, Rinaldo et al. (1991) used an
advection-dispersion equation, which is obtained by introducing a diffusion term in
the kinematic wave equation. They showed that not only is there a dispersion effect in
the individual channels, but that the stream network structure itself causes dispersion,
which is described as geomorphologic dispersion. Snell and Sivapalan (1994) showed
that the geomorphologic dispersion coefficient depends on the first two moments of
the flow path lengths, with the assumption of a constant flow velocity and
longitudinal dispersion throughout the catchment. Lee and Yen (1997) introduced the
kinematic wave theory to determine the travel times of overland and channel flows,
thus relaxing the linearity restriction of the unit hydrograph theory.
Maidment (1993) proposed the promising concept of using GIS to derive a spatially
distributed unit hydrograph (SDUH) that reflects the spatially distributed flow
characteristics of the watershed. The SDUH is similar to GIUH, except that it uses a
GIS to describe the connectivity of the links and the watershed flow network instead
of probability arguments. The travel time from each cell to the watershed outlet is
calculated by dividing each flow length by a constant velocity. Subsequently, a timearea diagram based on the travel time from each grid cell is developed. A more
elaborate flow model, which accounts for both translation and storage effects in the
watershed, is presented by Maidment et al. (1996). In his paper, the watershed
response is calculated as the sum of the responses of each individual grid cell, which
is determined as a combined process of channel flow followed by a linear reservoir
routing.
Olivera and Maidment (1999) proposed a method for routing spatially
distributed excess precipitation over a watershed using response functions derived
from a digital terrain model. The routing of water from one cell to the next is
accomplished by using the first-passage-time response function, which is derived
37
Chapter III
from the advection-dispersion equation of flow routing. The parameters of the flow
path response function are related to the flow velocity and the dispersion coefficient.
The watershed response is obtained as the sum of the flow path response to spatially
distributed precipitation excess. De Smedt et al. (2000) proposed a flow routing
method, in which the runoff is routed through the basin along flow paths determined
by the topography using a diffusive wave transfer model, that enables to calculate
response functions between any start and end point, depending upon slope, flow
velocity and dissipation characteristics along the flow lines, and all the calculations
performed with standard GIS tools.
In this study, a diffusive transport approach for flow routing in GIS-based flood
modelling is presented. A response function is determined for each grid cell
depending upon two parameters, the average flow time and the variance of the flow
time. The flow time and its variance are further determined by the local slope, surface
roughness and the hydraulic radius. The flow path response function at the outlet of
the catchment or any other downstream convergence point is calculated by
convoluting the responses of all cells located within the drainage area in the form of
the PDF of the first passage time distribution. This routing response serves as an
instantaneous unit hydrograph and the total discharge is obtained by convolution of
the flow response from all spatially distributed precipitation excess. The model is
applied to the Attert basin in the Grand-duchy of Luxembourg, for which topography
and soil data are available in GIS form, and land use data is obtained from remote
sensed images. River discharges are estimated on hourly basis from October 1998 to
March 2001. Consequently, a sensitivity analysis is conducted to study the effect on
the IUH and the predicted hydrograph at the basin outlet such as the hydraulic radius,
the channel roughness coefficient, the threshold of minimum slope, and the area
threshold of delineating permanent channel networks. The parameters, which
significantly affect the IUH and the general applicability of the model, are also
discussed.
2.
Methodology
Starting from the continuity equation and the St. Venant momentum equation,
assuming one-dimensional unsteady flow, and neglecting the inertial terms and the
38
Development of diffusive transport approach for flow routing
lateral inflow to the flow element, the flow process can be modelled by the diffusive
wave equation (Cunge et al., 1980):
∂ 2Q
∂Q
∂Q
−D 2 =0
+c
∂x
∂x
∂t
(3.1)
where Q [L³T-1] is the discharge at time t and location x, t [T] is the time, x [L] is the
distance along the flow direction, c [LT-1] is the kinematic wave celerity and is
interpreted as the velocity by which a disturbance travels along the flow path, and D
[L²T-1] is the dispersion coefficient, which measures the tendency of the disturbance
to disperse longitudinally as it travels downstream. Such dispersion is induced by
turbulence initiated from the shearing effects of channel boundaries (Mesa & Mifflin,
1986; Rinaldo et al., 1991). Assuming that the bottom slope remains constant and the
hydraulic radius approaches the average flow depth for overland flow and
watercourses, c and D can be estimated using the relation of Manning, by c = (5/3)v,
and D=(vR)/(2S) (Henderson, 1966), where v is the flow velocity, R the hydraulic
radius and S the bed slope. Parameters c and D are assumed to be independent of the
discharge, Q. Hence, the partial differential equation (3.1) becomes parabolic, having
only one dependent variable, Q(x, t).
Considering a system bounded by a transmitting barrier upstream and an adsorbing
barrier downstream, the solution of (1) at the cell outlet with cell size of l [L], can be
obtained using Laplace transforms for a unit impulse input (Eagleson, 1970), which
results in a PDF of the first passage time distribution as:
⎡ (ct − l )2 ⎤
u (t ) =
exp ⎢−
⎥
4 Dt ⎦
2 πDt 3
⎣
l
(3.2)
where u(t) [T-1] is the cell response function, and is equal to the PDF of the travel time
spent in a flow element, X [T], which is considered to be a random variable
independent of those in the other flow elements. From a physical point of view, the
independence of flow elements implies that the travel time a water particle spends in a
grid cell is not related to the time spent in any other cells, and the transport dynamics
depend solely on local variables and parameters and not on the conditions in the
39
Chapter III
surrounding cells (Maidment et al., 1996). Consequently, the first three moments can
be derived from the moment generating function of the first passage time distribution
(DeGroot, 1986, p. 201) as E(X)=l/c, Var(X)=2Dl/c3, Skw(X)=12D2l/c5, where E(X),
Var(X) and Skw(X) are the mean, variance and skewness of the random variable X.
Since the total time spent in the flow path, Y [T], is equal to the sum of the times
spent in each of its components along the flow path, Y is also a random variable
independent of those in the other flow paths. In probability theory, the PDF of the
sum of a finite number of random variables is defined as the sequential convolution of
their probability density functions. Therefore, the flow path redistribution function,
which is equal to the PDF of the random variable Y, can be obtained through the
sequential convolution of the PDF’s of the random variable X within the flow path.
Mathematically, this convolution can be performed only by numerical integration and
therefore has no analytical representation (Olivera & Maidment, 1999). For a flow
path consisting of N elements, N-1 convolutions have to be performed in order to get
the flow path redistribution function. Furthermore, this process has to be worked out
for each flow path in the watershed. Due to the enormous amount of calculations that
have to be performed, the method of numerical integration is not feasible and difficult
to realize in the hydrological models. Hence, an approximate numerical solution is
preferable in finding the PDF of Y, given that the probability density functions of all
X in the flow path are known. Although it is not possible to obtain an exact solution to
the sequential convolution, the moments of the sequential convolution can be
determined using the probability theory. DeGroot (1986, p. 188, p. 197) proves that
the expected value and the variance of the sum of the random variables are equal to
the sum of their expected values and variances. For a first passage time distribution,
the equations can be expressed as:
1
E (Y ) = t0 = ∫ dx
c
Var (Y ) = σ 2 = 2 ∫
40
(3.3)
D
dx
c3
(3.4)
Development of diffusive transport approach for flow routing
where t0 [T] is the travel time from the cell to the basin outlet along the flow path, and
σ2 [T²] is the variance of the flow time. Likewise, it can be proven that the skewness
of the sum of the independent variables is equal to the sum of their skewnesses.
Skw(Y ) = 12 ∫
D2
dx
c5
(3.5)
An approximate solution of the flow path response function is then obtained in the
form of a first passage time distribution, which satisfies the statistical requirement of
the first three moments as described above. The equation is written as:
U (t ) =
⎡ (t − t 0 ) 2 ⎤
exp⎢−
⎥
2
σ 2πt 3 t 03
⎣ 2σ t / t 0 ⎦
1
(3.6)
where U(t) [T-1] is the flow path unit response function, and σ [T] is the standard
deviation of the flow time. The parameters t0 and σ in equation (3.6) are spatially
distributed, so that each flow path has different parameters depending on the length of
the flow path and the physical characteristics of the flow path elements. From a
hydraulic point of view, Equation (3.6) describes an elementary wave serving as an
IUH of the flow path. Examples of such IUH at the end of the flow path are presented
in Figure III-1a and III-1b as a function of time. It is seen that the IUH is asymmetric
with respect to time caused by the wave attenuation.
(a)
(b) 0.0008
0.0008
7200 ss
σ == 7200
d
d
t0 == 7200
5400ss
d
3600 ss
σ = 3600
0.0006
d
t0 == 3600
3600ss
0.0006
d
1800 ss
σ = 1800
t0 == 1800
2700ss
d
U (s )
2300
t0 == 600
d
ss
-1
-1
U (s )
d
600ss
σ = 600
0.0004
0.0002
0.0004
0.0002
0.0000
0.0000
0
1800
3600
5400
7200
t (s)
0
1800
3600
5400
7200
t (s)
Figure III-1: (a) Unit response functions for an expected travel time of 3600 s and
different standard deviations, and (b) Unit response functions for an expected standard
deviation of 3600 s and different travel times
41
Chapter III
Figure III-1a and III-1b show that the approximate solution of the diffusive wave
equation satisfies the general characteristics of longitudinal wave dispersion along a
flow path, i.e. for a given variance of the flow time, more travel time results in less
wave attenuation, and for a given average travel time, more variance of the flow time
results in more wave attenuation. The IUH tends to a normal distribution when σ2 is
small and the wave propagates as a pure translation at the limit σ²→0. Olivera and
Maidment (1999) compare the goodness of the approximation of three probability
distributions: normal, gamma and first-passage-time, with the exact numerical integral
solution of the sequential convolution. They conclude that no statistical reasons make
one function better than the others. The first passage time distribution is chosen in this
study, because the two parameters t0 and σ2 are physically based and can be estimated
conveniently by using standard GIS functions, e.g. Equations (3.3) and (3.4) can be
calculated with the weighted flow length function, included in all commercially
available GIS software that operates on raster data. Moreover, the first passage time
distribution has been used in other studies (Mesa & Mifflin, 1986; Naden, 1992;
Troch et al., 1994; Olivera & Maidment, 1999) for modelling the time spent by water
in hydrological systems. The total flow hydrograph at the basin outlet can be obtained
by a convolution integral of the flow response from all grid cells.
Q (t ) =
∫ ∫ I (τ )U (t − τ )dτdA
t
A
0
(3.7)
where Q(t) [L³T-1] is the outlet flow hydrograph, I(t) [LT-1] is the excess precipitation
in a grid cell, τ [T] is the time delay and A [L²] is the drainage area of the watershed.
For the purpose of model parameter optimization and sensitivity analysis, a watershed
unit response function is proposed in this study based on the flow path redistribution
function described above. The watershed IUH differs from the traditional GIUH,
which uses the drainage basin hillslope function weighted by the channel network
width function (Troch et al., 1994), because it integrates the flow path response
functions in the basin weighted by the spatially distributed runoff coefficient
42
Development of diffusive transport approach for flow routing
UH (t ) =
∫
A
CU (t )dA
∫
A
(3.8)
CdA
where UH(t) [T-1] is the IUH of the catchment or subcatchment, and C [-] is the
default runoff coefficient of the grid cell, which is assumed to depend upon slope, soil
type and land use. Values of the default runoff coefficient can be collected from the
literature (Kirkby, 1978; Chow et al., 1988; Browne, 1990; Mallants & Feyen, 1990;
Pilgrim & Cordery, 1993) The numerator on the right hand side of Equation (3.8)
serves as the direct runoff hydrograph at the outlet resulting from a unit volume of
rainfall but spatially distributed surface runoff, while the denominator is the total
volume of the runoff. The watershed IUH described in Equation (3.8) can also be
used in lumped or semi-lumped rainfall runoff models to predict outlet hydrographs
with an average excess precipitation input on subcatchment or catchment scale.
3.
Application
The diffusive flow routing model was tested on a subcatchment with outlet at Ell in
the Attert basin, which is a main tributary of the Alzette river in the Grand-Duchy of
Luxembourg (Figure III-2). The topography and soil data of the catchment are
available in GIS form, and land use data was obtained from remote sensed images.
The elevation in the 96.8 km² watershed ranges from 273 to 530 m above mean sea
level, with an average basin slope of 9.6%. Figure III-3 shows the topographic
elevation map of the Attert subcatchment upstream of Ell gauging station, and Figure
III-4 shows the land use map of the study area. This subcatchment is partly located in
Belgium and partly in the Grand-Duchy of Luxembourg. Deciduous shrub and forest
are the dominant land use types of the watershed (41.1%); other land use types are
agriculture (21.4%), grassland (34.1%) and urban areas (3.4%). Left-bank tributaries
of the Attert are located on schistous substratum, characteristic of the Ardennes
massif, whereas right-bank tributaries are located on marls and sandstone, belonging
to the Paris Basin Mesozoic deposits. A very small area is covered by marshes. The
dominant soil textures are loam (67.6%) and sandy loam (29.8%), while the rest is
sand, loamy sand and sandy clay loam, which are scattered near the basin outlet.
43
Chapter III
#
#
BELGIUM
#
Towns
Rivers
Clervaux
Alzette basin
GERMANY
Wiltz
Grand-Duchy of Luxembourg
Study area
#
Ettelbruck
#
rt
Atte
#
Ell
Echternach
Mersch
N
W
Alzette
#
S
#
Luxembourg-city
#
#
E
Remich
0
10
20 km
Esch/Alzette
FRANCE
Figure III-2: Location plan showing the study area, the Attert and Alzette river basin
Elevation (m)
( )
270 - 300
300 - 330
330 - 360
360 - 390
390 - 420
420 - 450
450 - 480
480 - 510
510 - 540
Land use
crop
grass
marsh
shrub
forest
urban
N
N
W
W
E
S
S
0
1
Figure III-3: DEM of the study area
E
2 km
0
1
2 km
Figure III-4: Land use map of the study area
The climate in the region has a northern humid oceanic regime. Rainfall is the main
source of runoff and is relatively uniformly distributed over the year. High runoff
occurs in winter and low runoff in summer due to the higher evapotranspiration.
Winter storms are strongly influenced by the westerly atmospheric fluxes that bring
humid air masses from the Atlantic Ocean (Pfister et al., 2000) and floods happen
frequently because of saturated soils and low evapotranspiration. The average annual
precipitation in the region varies between 800 mm and 1000 mm, and the annual
potential evapotranspiration is around 570 mm. Precipitation generally exceeds
potential evapotranspiration except for four months in summer. A total of 30 months
of hourly precipitation, discharge and potential evapotranspiration data are available
44
Development of diffusive transport approach for flow routing
at Ell station. The average flow during the monitoring period is 2.41 m³/s with flows
ranging from 0.4 to 29.8 m³/s.
Model parameters are identified using GIS tools and lookup tables, which relate
default model parameters to the base maps, or a combination of the base maps.
Starting from the 50 by 50 m pixel resolution digital elevation map, hydrological
features including surface slope, flow direction, flow accumulation, flow length,
stream network, drainage area and sub-basins are delineated. The threshold for
delineating the stream network is set to 10, i.e. the cell is considered being drained by
ditches or streams when the drained area becomes greater than 25,000 m². A map of
Manning’s roughness coefficients is derived from the land use map, and a map of
potential runoff coefficients (Figure III-5) is calculated from the slope, soil type and
land use class combinations (Liu et al., 2000). Due to the 50 m grid size, urban cells
may not be 100% impervious in reality. In this study, the percentage of impervious
area in a grid cell is computed based on land use classes, with 30% for residential area,
70% for commercial and industrial area and 100% for open water areas (lakes and
ponds). Default potential runoff coefficients for these areas are calculated by adding
the impervious percentage with a grass runoff coefficient multiplied by the remaining
area. This results in runoff coefficients of 40 to 100% in urban areas, while other
areas have much smaller values, down to 5% for forests in valleys with practically
zero slopes.
(a)
(b)
Runoff coefficient
0.0 - 0.1
0.1 - 0.2
0.2 - 0.3
0.3 - 0.4
0.4 - 0.5
0.5 - 0.6
0.6 - 1.0
Hydraulic
radius (m)
y
( )
0.005 - 0.01
0.1 - 0.05
0.05 - 0.1
0.1 - 0.2
0.2 - 0.3
0.3 - 0.5
0.5 - 1.0
N
W
N
E
W
S
S
0
1
E
2 km
0
1
2 km
Figure III-5: Distribution of potential
Figure III-6: Distribution of hydraulic radius
runoff coefficient
for a flood with a 2-year return period
45
Chapter III
For calculation of the spatially distributed flow velocity and dispersion coefficient,
both parameters are assumed to depend on local slope, hydraulic radius and
vegetation type. This differs from previous work, where the flow velocity and
dispersion coefficient are considered to be uniform distributed over the hillslope and
the channel networks and estimated by model calibration (Van Der Tak & Bras, 1990;
Troch et al., 1994; Gyasi-Agyei et al., 1996; Olivera and Maidment, 1999). In this
study, the roughness coefficients for river courses and different land uses are obtained
from literature (Chow, 1964; Yen, 1991; Ferguson, 1998), while the hydraulic radius
is determined by a power law relationship with an exceeding probability (Molnar &
Ramirez, 1998), which relates hydraulic radius to the drained area and is seen as a
representation of the average behaviour of the cell and the channel geometry, i.e.
Rp = a ( Ad ) b
(3.9)
Where Rp [L] is the hydraulic radius with exceeding probability p, Ad [L²] is the
drained area upstream of the cell, which can be easily determined by the flow
accumulation routine in standard GIS, a [-] is a network constant and b [-] a geometry
scaling exponent both depending on the discharge frequency. In determining the
parameters a and b for a fixed flood frequency, the minimum and maximum hydraulic
radius, corresponding to a drained area of a single cell and the whole catchment, are
determined firstly based on basin characteristics or estimated when catchment
geohydrological data is available. By substituting these values into Equation (3.9), a
and b can be determined. Consequently, the hydraulic radius for each grid cell in the
basin is calculated with Equation (3.9). In this study, the exceeding probability p is
set to a 2-year return period for normal floods with corresponding a and b values of
0.10 and 0.50. This causes the minimum hydraulic radius for overland flow to be
0.005 m and the maximum hydraulic radius for channel flow 1 m at the basin outlet.
The values of a and b can be increased for more extreme floods. Figure III-6 shows
the spatial distribution of the hydraulic radius for a flood with a 2-year return period.
46
Development of diffusive transport approach for flow routing
Because the local slope in some cells derived from the DEM can be very small and
even can reach zero particularly in the river valleys in the flood plain area, the
calculated flow time and its variance become very large and the computed flow path
IUH is unrealistic. Therefore, a threshold for the minimum slope should be fixed, in
order to make the flow path IUH more reasonable. In this study, the threshold of the
minimum slope is set to 0.05%, i.e. the local slope is considered to be at least 0.05%.
Thereafter, by combining the maps of the hydraulic radius, Manning’s roughness
coefficient, and surface slope, the average flow velocity in each grid cell can be
calculated using Manning’s equation, which results in velocities in the order of 0.005
m/s for overland flow on upland areas in the watershed, and up to 2 m/s for some
parts of the main river. The contributing area is then determined from topographic
data for a particular downstream convergence point, normally the cells corresponding
to the main river or the basin outlet. Figure III-7a shows the spatial distribution of the
average flow time to the basin outlet from each grid cell, and Figure III-7b shows the
spatial distribution of the standard deviation of the flow time. The average flow time
is less than 4 h for the main river and up to 15 h for the most remote areas, and the
standard deviation increases with flow length up to 5 h for the most remote cells. With
the above information, the flow path unit response functions are calculated for each
grid cell to the basin outlet using Equation (3.6), and the watershed unit response
function can be calculated using Equation (3.8), weighted by the spatially distributed
runoff coefficient. The calculated watershed IUH is shown in Figure III-10b.
(a)
b)(b)
Flow time
( ) (h)
Standard deviation (h)
0-1
1-2
2-3
3-4
4-5
5-8
8 - 12
> 12
00.0 - 1.0
1.0 - 1.5
31.5 - 2.0
2.0 - 2.5
2.5 - 3.0
3.0 - 3.5
23.5 - 4.0
> 4.0
N
N
W
W
E
E
S
S
0
1
2 km
0
1
2 km
Figure III-7: (a) Average flow time to the basin outlet and (b) its standard deviation
47
Chapter III
The generation of surface runoff is performed using the WetSpa (Water and Energy
Transfer between Soil, Plants and Atmosphere) model developed by Wang et al.,
(1997), De Smedt et al., (2000), and Liu et al., (2002), in which the runoff production
in the cell is calculated by the method of default runoff coefficients and controlled by
the rainfall intensity and the soil moisture content. A linear relationship is assumed
between the actual surface runoff and the soil moisture content in the root zone, where
wet soils tend to generate more runoff and dry soils tend to generate less or even no
runoff. The soil moisture content for each cell is simulated on the basis of a soil water
balance on hourly time scale, which relies on the rate of the infiltration, percolation,
interflow and evapotranspiration in and out of the root zone. Finally, the hydrograph
at the basin outlet is obtained by the convolution integral of the excess precipitation
and the flow path IUH from all cells in the watershed with Equation (3.7).
In order to evaluate the performance of the diffusive wave approximation method for
the routing of surface runoff, 30 months observed hourly discharge data at the Ell
station in the Attert catchment are selected for the model verification. The baseflow is
separated from the total hydrograph by the nonlinear reservoir algorithm (Wittenberg
& Sivapalan, 1999), in which the baseflow is assumed to be proportional to the square
of the groundwater storage as:
Qg = kS 2
(3.10)
where Qg [L³T-1] is the baseflow, S [L] is the groundwater storage, and k [LT-1] is a
reservoir recession coefficient, which is related to the area, shape, pore volume and
transmissivity of the watershed, and can be derived from the analysis of the recession
curves. Combined with the soil water balance equation, the groundwater storage can
be determined and used for baseflow separation with Equation (3.10). It turns out that
the computed surface runoff hydrographs compared very well with the observations.
As a typical example, we show the results for a flood event that occurred from
October 23 to November 13, 1998, shown in Figure III-8, where the baseflow volume
takes about 69% of the total flood volume, and the direct flow about 31%. The
diffusive flow routing model is then applied with spatially distributed excess rainfall
as input and the hydrograph at the basin outlet as output. The predicted direct flow
48
Development of diffusive transport approach for flow routing
plus baseflow versus observed hydrograph is shown in Figure III-8 for the same
period. The maximum recorded rainfall intensity during this period is 12 mm/h,
yielding an observed peak discharge of 29.8 m3/s, while the simulated peak flow is
31.4 m3/s. As can be seen in the figure, the predicted hydrograph is in good agreement
Rainfall
3
Q (m /s)
30
Predicted
10
Baseflow
20
20
30
10
0
23/10
40
26/10
29/10
1/11
4/11
7/11
10/11
P (mm/h)
Observed
25
3
0
40
Simulated direct discharge (m /s)
with the observations.
20
15
10
5
0
0
5
10
15
20
25
3
Time (d/m)
Measured direct discharge (m /s)
Figure III-8: Observed and predicted stream
Figure III-9: Measured vs. simulated
flow and baseflow at Ell station
peak direct discharges
The results for other periods of the 30 months observation series are similar. A scatter
plot of observed versus simulated peak direct discharges of the 24 largest storm
events that occurred during the 30 months simulation period are presented in Figure
III-9, in which the measured peak direct discharge is given as the observed peak
discharge minus the baseflow. As can be seen in the figure, peak floods are
reproduced fairly well, while the low floods tend to be somewhat overestimated by
the model. This is because the frequency used to estimate the hydraulic radius in the
model is a 2-year return period, which may not be correct for simulating more
frequent flood events. For assessing the model performance, 3 evaluation criteria were
applied to the simulation results for the whole simulation period: (1) the model
reproduces the volume of surface runoff with 8% under estimation, (2) the model
Nash-Sutcliffe efficiency (Nash & Sutcliffe, 1970) for reproducing the direct
discharges is 83%, and (3) the average correlation coefficient between the measured
and predicted hydrograph is 76%. Also, the prediction errors of the time to the peak of
the 24 flood events are within 3 hours, which proves that the diffusive transport model
is very well suited for flood prediction in the Attert basin.
49
Chapter III
4.
Sensitivity analysis
The basic purpose of the sensitivity analysis is to determine differences in the model
responses as a result of changes in the values of specific parameters. In the present
study, a sensitivity analysis was conducted for the hydraulic radius, the channel
roughness coefficient, the threshold for minimum slope, and the area threshold in
delineating channel networks. The sensitivity results are, however, site specific and
may vary with locations of different catchment size, soils, land use, and slope
configurations. The effect of each parameter is studied by varying its value while
keeping other parameters constant. In all cases, the predicted hydrograph for a flood
event in October 1998 is considered as references. The calculated watershed IUH by
Equation (3.8) is also presented to give a graphical view of the effect on the mean,
variance and skewness of the average travel time, even though it is not used to
calculate the outlet hydrograph.
4.1.
Effect of hydraulic radius
Instead of using a constant hillslope velocity and channel flow velocity to calculate
the flow path response and watershed response as in many of the previous works, the
concept of minimum energy expenditure is applied here to derive the hydraulic radius.
The flow velocity is considered to be location dependent relying on the roughness
coefficient, the local slope, and the hydraulic radius. The average hydraulic radius is
obtained by the power law relationship given by Equation (3.9) (Molnar & Ramirez,
1998), which is assumed to be constant for a flood event, but may vary from event to
event according to the flood frequency.
Three flood frequencies, namely 0.1, 0.5 and 2.0, were considered to study their
influence on the runoff hydrograph at the outlet and the watershed IUH, while
keeping other parameters constant. The frequencies, 0.1, 0.5 and 2.0, correspond to
return periods of 10, 2 and 0.5 years respectively. The corresponding values of
calculated hydraulic radius at the basin outlet are about 1.5, 1.0 and 0.5 m
respectively, while the minimum value of the hydraulic radius remain constant at 5
mm for surface runoff in the upstream part of the catchment. It is found from Figure
50
Development of diffusive transport approach for flow routing
III-10a that a change in the flood frequency causes a considerable alteration in the
peak value of the simulated direct hydrographs and the catchment IUH. The peak
discharge increases from 16.7 m³/s to 17.8 ³/s and shifts one hour ahead as the flood
frequency decreases from 0.5 to 0.1, and decreases to 14.7 m³/s with one hour time
delay as the flood frequency increases to 2.0. This is logical because big storms lead
to higher peak discharges and shorter travel times. Figure III-10b shows the effect of
the hydraulic radius on the calculated watershed IUH. The mean, variance and the
skewness of the travel time are decreasing with increased flood frequency, because
these parameters are inversely depending on the celerity, as can be seen from
Equations (3.3), (3.4) and (3.5), and any increase in hydraulic radius will result in less
damping and faster response of the flood wave.
(b)
25
0.25
Watershed IUH (h )
p= 0.1
20
3
p= 0.5
p= 2.0
15
10
5
0
24/10 19
p= 0.1
0.20
-1
D irect discharge (m /s)
(a)
p= 0.5
p= 2.0
0.15
0.10
0.05
0.00
25/10 3
25/10 12
25/10 20
26/10 4
26/10 13
Time (d/m h)
0
5
10
15
20
Time (h)
Figure III-10: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of hydraulic radius with expected flood frequency, P
4.2.
Effect of channel roughness
Since surface runoff from each grid cell will contribute to the stream flow, the
roughness coefficient has a direct impact on the travel time and amount of dissipation
that will occur when routing a flood hydrograph through a river basin. Roughness
coefficients for hydrological routing models are typically in the form of Manning’s n
values, and estimated based on the channel geometry. Generally, the roughness
coefficient is higher for upstream channels, and decreases with stream order when the
channel slope becomes small. For the convenience of model computation and result
comparison, the channel roughness coefficient is considered to be constant in this
example regardless of the effect of stream order. Figure III-11a shows the simulated
51
Chapter III
direct runoff hydrographs and the calculated watershed IUH with three different
values of Manning’s roughness coefficient. The value 0.03 corresponds to clean and
straight streams without riffles or deep pools, 0.04 to clean and winding streams with
some pools and shoals, and 0.05 to clean and winding streams with stones (Chow,
1964). It is found that the peak discharge decreases from 16.7 to 14.3 m³/s and is
somewhat delayed as the roughness coefficient increases from 0.04 to 0.05, and
increases to 20.2 m³/s with one hour shifting ahead as the roughness coefficient
decreases to 0.03. Since the total runoff volume remains constant, reduction in peak
discharge and delay in peak time are compensated by prolonged flow recession, and
vice versa. This is also reflected in the calculated watershed IUH as shown in Figure
III-11b. The mean, variance and the skewness of the travel time are increasing with
increasing roughness, due to the fact that any increase in roughness coefficient results
in higher shear stresses, causing more damping and slowing down of the flood wave.
(b) 0.25
n = 0.03
n = 0.03
Watershed IUH (h )
20
n = 0.05
15
10
5
0
24/10 19
0.20
n = 0.04
-1
n = 0.04
3
Direct discharge (m /s)
(a) 25
n = 0.05
0.15
0.10
0.05
0.00
25/10 3
25/10 12
25/10 20
26/10 4
Time (d/m h)
26/10 13
0
5
10
15
20
Time (h)
Figure III-11: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of channel Manning’s roughness coefficient, n
4.3.
Effect of minimum slope
The present approach considers the changes in velocity with respect to distance, but
ignores the changes in velocity with respect to time. Therefore, it can be used to route
slow rising floodwaves through very flat slopes, but errors in the amount of damping
will occur when routing rapidly rising flood waves through extremely flat channel
slopes, because the inertia terms are not included in the diffusion wave method. In
GIS, the slope of the cell is derived from the DEM and calculated from the 3x3
neighbourhood using the average maximum technique. Inevitably, nearly zero slopes
52
Development of diffusive transport approach for flow routing
may occur in some areas, especially in the river valleys in the flood plain area,
resulting in nearly infinity travel time and damping. To mitigate the impact of the
extremely flat slopes on the flow path function, it is necessary to import a threshold
for minimum slope, i.e. the cell slope is put equal to the threshold value when the
calculated slope is smaller than the threshold.
Keeping all other parameters constant, three values of minimum slope, namely,
0.01%, 0.05% and 0.1% are considered to study the effect of the threshold value on
the outflow hydrograph and the calculated watershed IUH. Results are shown in
Figure III-12a and 12b. It is found that the peak discharge and the time to the peak of
the watershed IUH decrease slightly with a smaller threshold for minimum slope. This
is because a decrease in slope will reduce the flood wave celerity, and therefore
increase the travel time and the amount of hydrograph attenuation. Since the number
of cells with a slope lower than the thresholds is small in this catchment, the influence
of the minimum slope is not very significant. However, the minimum slope may have
a large influence on the outflow hydrograph for catchments with flatter slopes.
(b)
0.25
Smin
0.1%
Smin == 0.1%
15
Watershed IUH (h )
Smin
0.05%
Smin == 0.05%
Smin
0.1%
Smin ==0.1%
0.20
Smin
0.05%
Smin ==0.05%
-1
3
Direct discharge (m /s)
(a) 20
Smin
Smin == 0.01%
0.01%
10
5
Smin
Smin ==0.01%
0.01%
0.15
0.10
0.05
0
24/10 19
0.00
25/10 3
25/10 12
25/10 20
26/10 4
26/10 13
0
5
Time (d/m h)
10
15
20
Time (h)
Figure III-12: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of the threshold of minimum slope, Smin
4.4.
Effect of area threshold in delineating channel networks
In standard GIS applications, such as ArcInfo and ArcView, watershed channels are
delineated based on the upstream area of each cell. It is assumed that any upstream
area smaller than the threshold value does not produce enough runoff to support a
53
Chapter III
channel. The area required to develop a channel depends on regional and watershed
characteristics such as climatic conditions, soil properties, surface cover, and slope
characteristics (Martz & Garbrecht, 1992). In cells that are not part of the stream
network, overland flow occurs. Therefore, with a small area threshold value, GIS
derived stream networks are more meticulous and may represent ephemeral and
intermittent streams that are too small to be represented on topographical maps.
The effect of the area threshold in delineating channel networks on the outflow
hydrograph and the calculated watershed IUH is investigated by varying the cell
number threshold, namely 5, 10 and 50, which corresponds to draining areas of
respectively 12500, 25000 and 125000 m², while keeping other model parameters
constant. It can be seen from Figure III-13a and III-13b, that there is no significant
effect on the peak discharge and the calculated watershed IUH in this catchment. This
is due to the fact that changes in the threshold area will result in expansion or
shrinking of the stream network with lengths that are however relatively short
compared to the whole flow paths. Hence, the impact will only become significant
when using large threshold values, because in this case hillslope effects become
important due to their high overland flow roughness, which will result in a longer
flow time, and a prolonged flow response at the end of the flow path.
(b)
25
Watershed IUH (h )
0.20
Cn
Cn = 10
-1
Cn
= 10
10
C
n =
Cn
C
= 50
50
n =
15
10
5
0
24/10 19
0.25
Cn
Cn = 5
Cn
= 55
C
n =
20
3
Direct discharge (m /s)
(a)
Cn
Cn = 50
0.15
0.10
0.05
0.00
25/10 3
25/10 12
25/10 20
Time (d/m h)
26/10 4
26/10 13
0
5
10
15
20
Time (h)
Figure III-13: (a) Simulated direct hydrographs and (b) calculated watershed IUH
showing the effect of cell number threshold, Cn, in delineating channel networks
54
Development of diffusive transport approach for flow routing
4.5.
Other effects
In addition to the effects discussed above, the variation of channel geometry and the
temporal and spatial resolutions of the model will also have considerable influence on
the outflow hydrograph and the watershed IUH. In this study, flow is routed using a
velocity calculated for each land use category both for overland flow and channel
flow. The velocity is determined from Manning’s equation by assuming that the
hydraulic radius equals the average flow depth without considering the effect of
channel width and type. This assumption is warranted if the width of the river is much
larger than its depth for a flood event. However, as the width of a channel decreases,
the hydraulic radius does not tend towards the average flow depth. Also, the effect of
flood plains on the propagation of a floodwave can be very significant, when water
overflows the riverbanks. It is expected that an expanded channel width will slow
down the flow velocity and therefore reduce the peak discharge and delay the
resulting runoff hydrograph. Hence, more reliable results can be obtained when
calculating the hydraulic radius combined with measured or estimated channel width.
The time and space scale of the model not only influence on rainfall intensity and the
surface runoff distribution, but they also have impacts on the watershed IUH derived
from the diffusive transport method. Errors may arise when modelling flash flood for
a small catchment with a long time scale. This is because floodwater can flow out of
the catchment within the first time step, which the IUH cannot calculate accordingly.
Therefore, a higher time resolution is necessary in this case. However, when
modelling floods in a large catchment with relatively long concentration times, the
effect of time scale is not important. On the other hand, changes in spatial resolution
of the model will lead to variations of the GIS derived slope, flow direction, and
spatial distribution of the flow paths. In general, higher spatial resolution tends to
generate longer flow paths, and hence increases the hydrodynamic and the
geomorphologic attenuation of the flood wave. The first is due to increased flow time,
and the second to increased variability of the flow paths. Both impacts will play an
important role in the prediction of transport phenomena, especially in large basins
(Rinaldo et al., 1991). It is expected that reduction in spatial resolution will result in a
decrease of peak discharge and prolonged time to flood peaks, and vice versa.
55
Chapter III
As pointed out by Horritt and Bates (2001), a high-resolution model is advantageous
when small scale processes have a significant effect on model predictions, but have to
be balanced against the increased computation onus. Predictions with a low-resolution
may also give an essentially correct result in many cases. In practice, determination of
temporal and spatial resolution of the model should rely on the data available, the
catchment characteristics and the model accuracy requirement. However, quantitative
analysis of these effects on the outflow hydrograph and the watershed IUH in GIS
flood modelling is beyond the scope of this study.
5.
Conclusions
A physically based distributed unit hydrograph method derived from the diffusive
transport approach is presented in this study for GIS based modelling on catchment
scale. The method differs from the previous work in that it is based on a location
dependent velocity field. The basic modelling approach is to use raster GIS functions
to calculate the travel time from each point in the watershed to the outlet by
determining the flow path and the travel time through each cell along the path. The
flow velocity in each grid cell is calculated by the Manning equation, which depends
upon the local slope, roughness coefficient and hydraulic radius. The travel time
through each individual cell along the flow path is integrated to obtain the cumulative
travel time to the outlet. Based on the mean and the variance of the flow time, the first
passage time distribution density function is applied as a flow response function.
Runoff is routed over the surface flow path, and accounts for the differences in runoff
amount and velocity, due to changing slope, land use, soil type and other surface
conditions. Finally, the total direct discharge at the downstream convergence point is
obtained by superimposing all contributions from every grid cell. The watershed IUH
is calculated based on the flow path functions and the spatially distributed runoff
coefficient, and can be used for model parameter sensitivity analysis or as the IUH for
lumped prediction models. Model parameters based on surface slope, land use, soil
type and their combinations are collected from literature, and can be prepared easily
using standard GIS techniques.
The model was tested on the Attert catchment in Luxembourg with 30 months of
observed hourly rainfall and discharge data, where the spatial distributed surface
56
Development of diffusive transport approach for flow routing
runoff was generated by the WetSpa model. The results show an excellent agreement
with the measured hydrograph at the basin outlet. Consequently, a sensitivity analysis
was conducted to study the effect of the hydraulic radius, the channel roughness
coefficient, the threshold for minimum slope, and the area threshold in delineating
channel networks on the outflow hydrograph and the calculated watershed IUH. It
was found that the hydraulic radius and channel roughness coefficient are the most
sensitive parameters. The hydraulic radius corresponding to a 2-year return period can
meet the requirements of flood prediction for normal floods, but should be increased
for more extreme flood. Also, the channel roughness coefficient shows a strong
impact on the model output. More reliable results are expected when the channel
roughness is determined according to the stream order. The thresholds of minimum
slope and the area in delineating channel networks have only marginal effects on the
outflow hydrograph and the calculated watershed IUH. However, all these parameters
should be chosen properly when applying the model in practice.
The diffusive wave transport approach assumes a unique relationship between flow
and stage at each point for both overland flow and channel flow, and so does not
require the specification of a downstream stage. It also generally operates
satisfactorily with less detailed ditch and channel geometry information than required
by dynamic wave models and is much more stable and easy to use in GIS based flood
modelling. Moreover, this approach allows the spatially distributed excess
precipitation and hydrological parameters of the terrain to be used as inputs to the
model, and is especially useful to analyze the effects of topography, and land use or
soil cover on the hydrological behaviour of a river basin. The method is worth to be
applied in flood modelling for a wide range of slopes from flood plains to the hilly
areas. However, accuracy of the diffusive wave approach increases with increasing
slope, and it cannot be used in situations where flow reversals occur. Application of
the methodology suggests that simulations of the hydrological response based on
diffusive wave approximation and GIS specification of the topographical network are
validated in the study area. This is sustained by a proper adjustment of the parameter
values characterizing the flow travel time and its variance, which is deemed to cover
most cases of engineering interest.
57
Chapter III
References
Beven, K.J. & Kirkby, M.J., A physically based variable contributing area model of
basin hydrology, Hydrol. Sci. Bull., 24(1), 43-59, 1979.
Browne, F.X., Stormwater Management, Standard Handbook of Environmental
Engineering, ed., R.A. Corbitt, McGraw-Hill, New York, 7.1-7.135, 1990.
Chow, V.T., Handbook of Applied Hydrology, 7-25, McGraw-Hill Book Company,
New York, 1964.
Chow, V.T., Maidment, D.R. & Mays, L.W., Applied Hydrology, McGraw-Hill, New
York, 1988.
Cunge, J. A., Holly, F.M. & Verwey, A., Practical Aspects of Computational River
Hydraulics, p. 45, Pitman Publ. Ltd, London, GB, 1980.
DeGroot M.H., 1986, Probability and Statistics, Addison-Wesley, Reading, MA, USA.
De Smedt, F., Liu, Y.B. & Gebremeskel, S., Hydrological modelling on a catchment
scale using GIS and remote sensed land use information, In: Risk Analysis II,
ed., C.A. Brebbia, 295-304, WTI press, Southampton, Boston, 2000.
Dooge, J.C.I., A general theory of the unit hydrograph, J. Geophys. Res., 64, 241-256,
1959.
Eagleson, P.S., Dynamic Hydrology, 364, McGraw-Hill Pub., 1970.
Ferguson, B.K., Introduction to Stormwater, Concept, Purpose and Design, 111, John
Wiley & Sons, Inc., 1998.
Gupta, V.K. & Waymire, E., On the formulation of an analytical approach to
hydrological response and similarity at the basin scale, J. Hydrol., 65, 95-123,
1983.
Gupta, V.K., Waymire, E., & Wang, C.T., A representation of an instantaneous unit
hydrograph from geomorphology, Water Resour. Res., 16(5), 855-862, 1980.
Gyasi-Agyei, Y., De Troch, F.P. & Troch, P.A., A dynamic hillslope response model
in a geomorphology based rainfall-runoff model, J. Hydrol., 178, 1-18, 1996.
Henderson, F.M., Open Channel Flow, 522, McMillan, New York, 1966.
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Development of diffusive transport approach for flow routing
Horritt, M.S. & Bates, P.D., Effect of spatial resolution on a raster based model of
flood flow, J. Hydrol., 253, 239-2498, 2001.
Kirkby, M.J., Hill-slope Hydrology, 235, John Wiley & Sons, Ltd., 1978.
Lee, K.T. & Yen, B.C., A geomorphology and kinematic-wave-based hydrograph
derivation, J. Hydraulic Eng., ASCE, 123(1), 73-80, 1997.
Liu, Y.B., Gebremeskel, S., De Smedt, F., and Pfister, L., Flood prediction with the
WetSpa model on catchment scale, In; Flood Defence ‘2002, ed., Wu et al., 499507, Science Press, New York Ltd, 2002.
Maidment, D.R., Developing a spatially distributed unit hydrograph by using GIS, In
HydroGIS 93: Application of Geographic Information Systems in Hydrology
and Water Resources, Proceedings of the Vienna Conference, eds., K. Dovar
and H. P. Natchnebel, 181-192, Vienna: Int. Assoc. of Hydrol. Sci., 1993.
Maidment, D.R., Olivera, J.F., Calver, A., Eatherral, A. & Fraczek, W., A unit
hydrograph derived from a spatially distributed velocity field, Hydrol. Process,
10(6), 831-844, 1996.
Mallants, D. & Feyen, J., Kwantitatieve en kwalitatieve aspecten van oppervlakte en
grondwaterstroming (in Dutch), 96, Volume 2, KUL, 1990.
Martz, L.W. & Garbrecht, J., Numerical definition of drainage network and
subcatchment areas from digital elevation models, Computers and Geosciences,
18(6), 747-761, 1992.
Mesa, O.J. & Mifflin, E.R., On the relative role of hillslope and network geometry in
hydrological response, in Scale Problems in Hydrology, eds., V.K. Gupta, I.
Rodriguez-Iturbe, and E.F. Wood, 1-17, D. Reidel, Norwell Mass, 1986.
Molnar, P. & Ramirez, J.A., Energy dissipation theories and optimal channel
characteristics of river networks, Water Resour. Res., 34(7), 1809-1818, 1998.
Naden, P.S., Spatial variability in flood estimation for large catchments: The
exploitation of channel network structure, J. of Hydrol. Sci., 37, 53-71, 1992.
Nash, J.E. & Sutcliffe, J.V., River flow forecasting through conceptual models, J.
Hydrol. 10, 282-290, 1970.
Olivera, F. & Maidment, D.R., Geographic information system (GIS)-based spatially
distributed model for runoff routing, Water Resour. Res., 35(4), 1155-1164,
1999.
59
Chapter III
Pfister, L., Humbert, J. & Hoffmann, L., Recent trends in rainfall-runoff
characteristics in the Alzette river basin, Luxembourg, Climate Change, 45(2),
323-337, 2000.
Pilgrim, D.H. & Cordery, I., Flood runoff, in Handbook of Hydrology, ed., D. R.
Maidment, 9.1-9.42, McGraw-Hill, New York, 1993.
Rinaldo, A., Marani, A. & Rigon, R., Geomorphological dispersion, Water Resour.
Res., 27(4), 513-525, 1991.
Rodriguez-Iturbe, I. & Valdes, J.B., The geomorphologic structure of hydrological
response, Water Resour. Res., 15(6), 1409-1420, 1979.
Sivapalan, M., Wood, E.F. & Beven, K., On hydrological similarity: 3. A
dimensionless flood frequency model using a generalized geomorphologic unit
hydrograph and partial area runoff generation, Water Resour. Res., 26(1), 43-58,
1990.
Snell, J.D. & Sivapalan, M., On geomorphologic dispersion in natural catchments and
the geomorphologic unit hydrograph, Water Resour. Res., 30(7), 2311-2323,
1994.
Troch, P.A., Smith, J.A., Wood, E.F. & de Troch, F.P., Hydrological controls of large
floods in a small basin, J. Hydrol., 156, 285-309, 1994.
Van Der Tak, L.D. & Bras, R.L., Incorporating hillslope effects into the
geomorphologic Instantaneous Unite Hydrograph, Water Resour. Res., 26(1),
2393-2400, 1990.
Wang, Z., Batelaan, O. & De Smedt, F., A distributed model for Water and Energy
Transfer between Soil, Plants and Atmosphere (WetSpa), Phys. Chem. Earth,
21(3), 189-193, 1997.
Wittenberg, H. & Sivapalan, M., Watershed groundwater balance estimation using
streamflow recession analysis and baseflow separation, J. Hydrol., 219, 20-33,
1999.
Yen, B.C., Channel Flow Resistance: Centennial of Manning's Formula, p. 43, Water
Resources Publications, Littleton, CO., 1991.
60
Chapter IV
Flood modelling for complex terrain using GIS and remote sensed
information
Abstract
A spatially distributed hydrological model, WetSpa (Water and Energy Transfer
between Soil, Plants and Atmosphere) Extension, working on an hourly time scale is
presented in this chapter. The model combines elevation, soil, and land use data, and
predicts flood hydrograph and the spatial distribution of hydrological characteristics
in a watershed. The model is tested on a small catchment in Belgium for which
topography and soil data are available in GIS form, while the land use and soil cover
is obtained from remote sensed images. The resulting calculated discharges compare
favourably with the field measurements. Next a 102-year series of measured hourly
precipitation data is processed with the model and the resulting hydrographs are
analyzed statistically to determine the characteristics of extreme floods. Finally, the
simulated extreme peak discharges are compared to the results calculated with design
storms. Comparison of the two methods shows that the model is capable to predict
both normal and extreme floods in a complex terrain.
1.
Introduction
Flood is a natural phenomenon that poses serious challenges to many countries and
regions in the world. It is among the most severe risks on human lives and properties,
as well as economical development. The forecast and simulation of floods is therefore
essential for planning and operation of civil protection measures and for early flood
warning. In applied hydrology, the prediction of peak flow and the simulation of flood
hydrographs in a stream or river is a very complex process, because the hydrological
variables vary both in space and time as a function of the meteorological inputs, and
the spatial variability of topography, land use and soil types.
Chapter IV
In contrast to lumped models, distributed models attempt to account for the spatial
variability of basin parameters, as well as their physical significance. In flood
prediction and rainfall-runoff computation, physically based distributed hydrological
models have become a more feasible approach in recent years. In addition to the
development of improved computational capabilities, DEMs, digital data of soil type
and land use, as well as the tools of GIS, give new possibilities for hydrological
research in understanding the fundamental physical processes underlying the
hydrological cycle and the solution of mathematical equations representing those
processes. In a distributed model, the watershed is subdivided into a grid of cells, and
model parameters are assigned to each grid cell based on the physical land, soil and
vegetation characteristics that exist in that cell. Precipitation and other meteorological
data are then applied over each cell in the watershed, and the runoff is computed and
routed along its flow direction to the collecting channel. In such a way, distributed
models are able to account for the spatial variability of hydrological processes within
a watershed. In addition, the model parameters of this approach are largely physically
based and the spatial information of the land, soil, vegetation and precipitation can be
captured with much greater detail than the lumped watershed modelling. This gives
the advantage for the model to be used in complex terrains and ungauged river basins
without model optimization.
Recently, many hydrological models with a flood prediction component using
information on topography available from DEM have been developed (Moore, 1991;
Palacios-Vélez & Cuevas-Renaud, 1992; Robson et al., 1993; Garrote & Bras, 1995),
whereas models like SHE and TOPMODEL were adapted to a new type of data which
can benefit from the GIS techniques (Quinn et al., 1991; Ewen et al., 2000). At the
same time, hydrological models compatible with remotely sensed data and GIS have
been developed or updated from their previous version, such as the model DHSVM
(Wigmosta et al., 1994), CASC2D (Julien et al., 1995), DWSM (Borah et al., 2002),
HYDROTEL (Fortin et al., 2001), and so on. These models are either loosely or
tightly coupled with the GIS and remote sensed data. Along with the rapid
development of GIS technology and remote sensing techniques, especially the
concomitant availability of high resolution DEM and the advances in integrating GIS
with hydrological modelling, flood prediction with distributed models tends to be
more advantageous and competent by linking GIS with hydrological modelling.
62
Flood modelling for complex terrain using GIS and Remote sensed information
In this chapter, a physically based distributed hydrological model, WetSpa Extension,
is presented, which is tightly coupled with GIS technology and remote sensed
information. The model takes into account the detailed basin characteristics to predict
flood hydrographs and other spatially distributed hydrological variables on catchment
scale. The parameters of the model are derived from DEM, land use and soil maps in
raster format. The model is validated by comparing calculated and observed hourly
discharges for a 16 months period in a small watershed, Barebeek, located northeast
of Brussels, Belgium, where the topography and soil data are available in GIS form,
and land use data was obtained from remote sensed images. The utility of the model is
demonstrated by forecasting peak discharges resulting from an observed 102-year
precipitation series. The simulation results are then compared with the results
computed from design storms.
2.
The WetSpa model
The WetSpa model is a grid-based distributed hydrological model for Water and
Energy Transfer between Soil, Plants and Atmosphere, which was originally proposed
by Wang et al. (1997) and adopted for flood prediction on hourly and daily time step
by De Smedt et al. (2000) and Liu et al. (2002, 2003). For each grid cell, four layers
are considered in the vertical direction as vegetation zone, root zone, transmission
zone and saturated zone. The hydrological processes considered in the model are
precipitation, interception, depression, surface runoff, infiltration, evapotranspiration,
percolation, interflow, ground water flow, and water balance in the root zone and the
saturated zone. The total water balance for a raster cell is composed of the water
balance for the vegetated, bare-soil, open water and impervious parts of each cell.
This allows accounting for the non-uniformity of the land use per cell, which is
dependent on the resolution of the grid. The processes in each grid cell are set in a
cascading way, which means that an order of occurrence of the processes is assumed
after a precipitation event. A mixture of physical and empirical relationships is used to
describe the hydrological processes in the model. The model predicts peak discharges
and hydrographs, which can be defined for any numbers and locations in the channel
network, and can simulate the spatial distribution of catchment hydrological
characteristics.
63
Chapter IV
2.1.
Runoff production
Three runoff components, surface runoff, interflow and groundwater flow, are
considered in the model. The model takes Hortonian flow as the main overland flow
process, which occurs when rainfall intensity exceeds the infiltrability of soil.
However, for a complex terrain, particularly suburban and urban areas, precise
estimation of infiltration parameters is rather difficult due to the high heterogeneity of
the land and soil characteristics. Hence, simplified methods are still widely used by
the hydrologists for surface runoff estimation in water resources planning, design and
practices, for instance the rational method and the soil conservation service (SCS)
method. The rational formula is the most commonly used method of determining peak
discharge from small drainage areas since it was developed in the late nineteenth
century (Kuichling, 1889). This method is traditionally applied to design storm
sewers, channels, and other drainage structures by making use of intensity-durationfrequency (IDF) curves, which are statistical summaries of the historical precipitation
records. Since the method does not produce a hydrograph, and does not account for
the change of time dependent conditions such as soil moisture or rainfall intensity, it
is in general incapable to predict floods that result from individual predefined runoff
events (Singh, 1992). The SCS method is an empirical approach to estimate
infiltration within a watershed, in which the runoff depth is calculated as a function of
the rainfall and the SCS retention factor, which is estimated from the land surface
properties using an empirical relationship depending upon a curve number (Maidment,
1993). The excess rainfall is then available for runoff routing over the watershed
surface and through the stream network. The SCS method is widely used for
estimating floods in small to medium-sized ungauged catchments in the US. However,
intensive calibrations need to be performed for the model parameters against local
conditions when applying this method to other areas.
In this study, a moisture-related runoff coefficient method is proposed for calculating
surface runoff in each grid cell, which allows the actual runoff coefficient to vary in
time, and in function of rainfall intensity, rainfall duration and cell characteristics,
giving an approximation to the surface runoff volume at each time step. The initial
losses due to interception and depression are considered separately in the formula:
64
Flood modelling for complex terrain using GIS and Remote sensed information
V = c s c r (P − I a ) − D a
(4.1)
where V [LT-1] is the surface runoff in depth over the time, P [LT-1] is the rainfall
intensity, Ia [LT-1] is the interception loss, Da [LT-1] is the depression loss, cs [-] is a
moisture related coefficient relying on the relative soil moisture content of the root
zone, and cr [-] is the potential runoff coefficient, which is assumed to depend upon
slope, soil type, land use and the proportions of bare soil and impervious areas in a
grid cell. The values of default runoff coefficients are taken from literature references
(Kirkby, 1978; Chow et al., 1988; Browne, 1990; Mallants and Feyen, 1990; Pilgrim
and Cordery, 1993) and a table was generated, linking values of the runoff coefficient
to slope, soil type and land use classes. The potential runoff coefficient is then the
area-weighted average of the land use classes within the grid cell. The moisture
related coefficient cs is time dependent and calculated as a function of the soil
moisture and rainfall intensity as:
cs =(θ t θ s )α
(4.2)
where θt [L3L-3] is the soil moisture content at time t [T], θs [L3L-3] is the soil porosity,
and α [-] is an exponent variable reflecting the effect of rainfall intensity and the
modelling time step on the volume of surface runoff, which can be expressed as:
⎡
α = Min ⎢1, α 0 +
⎣
1−α0 ⎤
P⎥
Pm
⎦
(4.3)
in which α0 [-] is the exponent at a near zero rainfall intensity, α0 ≥ 1, and Pm [LT-1] is
the rainfall intensity, over which α equals 1 and the volume of surface runoff will not
be affected by the rainfall intensity. Normally, α0 approaches to 1 for a short time
interval, and increases when the time scale is enlarged. These two parameters mainly
affect the amount of surface runoff for small storms so that more water will infiltrate
into the soil. Pm has no sense if α0 is set to 1 for which a linear relationship is assumed
between the surface runoff and the soil moisture content. Equation (4.1) reveals that
the surface runoff achieves its potential rate when the soil is saturated, and approaches
65
Chapter IV
to zero as the soil dries out. This is logical from a hydrological point of view that wet
soil tends to produce more surface runoff, and dry soil tends to give more infiltration.
The first term on the right side of Equation (1) is the excess rainfall calculated with
the net precipitation (P - Ia) multiplied by a potential runoff coefficient and a moisture
related coefficient. The difference between net precipitation and excess rainfall is the
amount of infiltration into the soil. Surface runoff that is available for runoff routing
is then computed with the excess rainfall subtracted by the depression losses. The
coefficient cs is determined based on the intermediate soil moisture of the time step. A
first trial is performed using cs of the last step to estimate excess rainfall and
infiltration, and soil moisture at the end of this time step is calculated by means of
water balance of the cell. The intermediate soil moisture is then estimated as the
arithmetic mean of the moisture content at the end of last step and the result of the
first trial. Thereafter, excess rainfall and soil moisture content at the end of the time
step are recalculated using cs computed from the intermediate soil moisture. In such a
way, cs is controlled not only by the antecedent soil moisture, but also by the rainfall
intensity and rainfall duration. Hence, high rainfall intensity or rainfall with long
duration tends to give higher percentage of runoff. The product of cs and cf forms the
actual runoff coefficient, which varies both with time and rainfall intensity depending
upon the soil moisture content, and allows computing excess rainfall for each time
step during the model simulation. The actual runoff coefficient is set to one under the
condition where saturation happens from below and groundwater resurgence occurs.
The sum of interception and depression losses forms the initial abstraction, which
does not contribute to runoff. In studies of major storm events, the interception loss is
generally neglected. However, it may be a very significant factor for small or medium
storms, and water balance computations would be significantly in error if evaporative
losses of intercepted moisture were not included (Singh & Szeicz, 1979). Interception
is a complicated process, which is mainly a function of the storm characteristics, the
season, and the species, age and density of plants. In this study, interception loss is
evaluated using a simple reservoir model, in which the rainfall rate is reduced until its
storage capacity is achieved. If the total rainfall during the first time increment is
greater than the interception storage capacity, the rainfall rate is reduced by the
capacity. Otherwise, all rainfall is intercepted in the canopy, and the remainder of
66
Flood modelling for complex terrain using GIS and Remote sensed information
interception is removed from the rainfall in the following time increments. Typical
interception capacity values can be found in the literature (Lull, 1964; Zinke, 1967;
Rowe, 1983). A lookup table of maximum and minimum interception storage capacity
corresponding to the extreme points during summer and winter periods is established
linking values of interception storage capacity to different land use classes. Thereafter,
a simple sine-shaped variation curve was proposed allowing the interception storage
capacity to vary continuously with time. The intercepted water in the canopy is lost by
evaporation and returns to the hydrological cycle with a potential evaporation rate.
Depression storage may have a considerable magnitude and plays an important role in
flood modelling for small or medium storms. The rainfall excess begins to fill
depressions once rainfall intensity exceeds the local infiltration capacity. Due to the
extreme variability of these characteristics, it is very difficult to specify a general
relationship for the losses due to depression storage. In this study, a simple empirical
equation suggested by Linsley (1982) is used to calculate depression loss, in which
the depression storage is assumed to be a function of depression storage capacity and
increases exponentially with rainfall intensity up to the point where depression
storage capacity is reached. This allows overland flow and depression storage to occur
simultaneously. The depression storage capacity is a function of landform, soil type
and vegetation. Based upon the typical values found in the literature (ASCE, 1969;
SINCE, 1972; Sheaffer et al., 1982), a lookup table of default depression storage
capacity is set up according to the category classes of slope, land use and soil type.
Water held in depressions at the end of a rainfall event depletes either by evaporation
with a potential evaporation rate or contributes to the soil moisture. With the
component of depression storage, the model can handle surface runoff production
more properly. For instance, the depression storage capacity in forest areas is much
higher than that of other land use areas. Hence, there will be no or little surface runoff
generated in those areas during the initial phase of a storm or for a small rainfall,
because most of the produced excess rainfall will contribute to the depression storage.
In this case, dominant surface runoff comes from impervious area or areas with high
runoff coefficient and low depression storage capacity.
67
Chapter IV
2.2.
Water balance
WetSpa has four water stores, i.e. the plant canopy, land surface, root zone and
saturated zone, for each of which the water balance is maintained. The water balance
in the root zone is the most important one, as it controls the amount of surface runoff,
interflow, evapotranspiration and groundwater recharge. Assuming that the
groundwater table is below the root zone, the water balance in the root zone can be
modelled continuously for each grid cell by equating inputs and outputs:
D
∆θ
= P − I −V − E − R − F
∆t
(4.4)
where D [L] is the root depth, ∆θ [L3L-3] is the change in soil moisture, ∆t [T] is the
time interval, I = Ia+Da, [LT-1], is the initial abstracts including interception and
depression storage within time ∆t, E [LT-1] is the actual evapotranspiration from soil,
R [LT-1] is the percolation out of the root zone, and F [LT-1] is the amount of
interflow in depth over the time.
Evapotranspiration from soil and vegetation is calculated based on the relationship
developed by Thornthwaite and Mather (1955) as a function of potential
evapotranspiration, vegetation type, stage of growth and soil moisture content
E=0
⎛ θ −θw ⎞
⎟
E = (c v E p − E i − E d )⎜ t
⎜θ −θ ⎟
w ⎠
⎝ f
E = cv E p − Ei − E d
for θ t < θ w
for θ w ≤ θ t < θ f
(4.5)
for θ t ≥ θ f
where cv [-] is a vegetation coefficient, which varies throughout the year depending on
growing stage and vegetation type, Ep [LT-1] is the potential evapotranspiration, Ei
[LT-1] and Ed [LT-1] are evaporations from interception storage and depression storage,
θw [L3L-3] is the moisture content at permanent wilting point, and θf [L3L-3] is the
moisture content at field capacity. The soil evapotranspiration varies linearly with Ep,
when the soil moisture content is above the permanent wilting point, and zero, when
the soil moisture is below the permanent wilting point. Potential evapotranspiration
68
Flood modelling for complex terrain using GIS and Remote sensed information
data can be obtained from field measurements, estimated from the historical records
through statistical analysis, or calculated with Penman-Monteith equation when
hourly meteorological data of net radiation, air temperature, relative humidity and
wind speed are available. The process of evapotranspiration is assumed to occur in an
order from interception storage, depression storage and soil subsequently. If the water
content of interception storage and depression storage is equal to or greater than the
potential evapotranspiration, all the evapotranspiration comes from those storages.
Otherwise, the difference is calculated with Equation (4.5) from the soil water. For the
surface layer, actual evapotranspiration is computed as the area-weighted mean of the
land use composition, for which transpiration happens from the vegetated parts,
evaporation happens from the bare soil, and there is no evaporation from impervious
areas. Finally, the total evapotranspiration is calculated as the sum of evaporation
from interception storage, depression storage and the actual evapotranspiration from
the soil and a part from the groundwater storage.
Percolation and interflow are important components in the root zone water balance.
Both processes are assumed to be gravity driven. The rate of percolation or
groundwater recharge is determined by Darcy’s law (Hillel, 1980) in function of the
hydraulic conductivity and the gradient of hydraulic potential. When an assumption is
made that the pressure potential only varies slightly in the soil, its gradient can be
approximated to zero, such that the percolation is controlled by gravity alone
(Famiglietti & Wood, 1994). Therefore, the percolation out of root zone is simply the
hydraulic conductivity corresponding to the moisture content in the soil layer. The
Brooks and Corey relationship between hydraulic conductivity and moisture content
is used to define percolation, which is simply (Eagleson, 1978):
( 2+3B) B
⎛ θ −θr ⎞
⎟⎟
R = K(θ ) = Ks ⎜⎜
⎝ θs −θr ⎠
(4.6)
where K(θ) [LT-1] is the unsaturated hydraulic conductivity, Ks [LT-1] is the saturated
hydraulic conductivity, θs [L3L-3] is the soil porosity, θr [L3L-3] is the residual moisture
content, and B [-] is the soil pore size distribution index. The vertical transport of
water through the unsaturated soil matrix is slow. It generally takes days or months
69
Chapter IV
before the percolating water reaches the saturated zone. Nevertheless, precipitation is
followed by an almost immediate rise of the groundwater table owing to a rapid
transfer of increased soil-water pressure through the unsaturated zone (Myrabo, 1997).
In addition, macropores in the subsurface layers resulting from root and fauna activity
may allow rapid bypassing of the unsaturated zone when the rate of precipitation is
high (Beven, 1982). The model assumes that percolation input affects the
groundwater table within one time step.
Interflow is assumed to occur in the root zone after percolation and becomes
significant only when the soil moisture is higher than field capacity. Darcy’s law and
kinematic approximation are used to estimate the amount of interflow generated from
each cell, in function of hydraulic conductivity, the moisture content, the slope angle,
and the root depth
F = c f DS0 K(θ ) W
(4.7)
where S0 [LL-1] is the surface slope, W [L] is the cell width, and cf [-] is a scaling
parameter depending on land use, used to consider river density and the effects of
organic matter on the horizontal hydraulic conductivity in the top soil layer.
Apparently, with Equation (4.7), rapid interflow will be generated in areas with high
moisture, steep slope and well vegetation. For other areas, little interflow will be
produced. Since little is known about the hydro-geological conditions in the saturated
layer at the cell level, the groundwater storage is simulated with a semi-distributed
model for simplicity, in which the groundwater balance is maintained in a small
subcatchment scale with input of average groundwater recharge and output of average
evapotranspiration and groundwater discharge at the subcatchment outlet.
2.3.
Flow routing
The routing of overland flow and channel flow is implemented by the method of the
diffusive wave approximation, which has been described in detail in chapter III. A
two-parameter response function, based on the average flow time and its standard
deviation of the flow time, is applied for routing both overland flow and channel flow.
70
Flood modelling for complex terrain using GIS and Remote sensed information
The flow time and its standard deviation are determined by the local slope, surface
roughness and the hydraulic radius for each grid cell. The flow path response function
at the outlet of the catchment or any other downstream convergence point is
calculated by convoluting the responses of all cells located within the drainage area in
the form of the probability density function (PDF) of the first passage time
distribution. This routing response serves as an instantaneous unit hydrograph and the
total discharge is obtained by a convolution integral of the flow response from all
generated spatially distributed runoff. Interflow is assumed to contribute to the surface
runoff at the outlet of each cell, and routed to the catchment outlet together with
surface runoff without redistribution among downslope cells for simplicity.
Groundwater flow is modelled with a linear reservoir method on small subcatchment
scale, while a non-linear reservoir method is optional in the model with storage
exponent of 2 (Wittenberg & Sivapalan, 1999). The groundwater outflow is added to
any runoff generated at the subcatchment outlet to produce the total streamflow. The
general groundwater flow equation can be expressed as:
G(t ) = kSm
(4.8)
where G [L3T-1] is the groundwater flow of the subcatchment at time t [T], S [L3] is
the groundwater storage, m [-] is an exponent, m=1 for linear reservoir and m = 2 for
non-linear reservoir which is the same as Equation 3.10, k is a baseflow recession
constant, has a dimension of [T-1] for a linear reservoir and [L-3T-1] for a non-linear
reservoir, which is related primarily to area, shape, pore volume and transmissivity of
the subcatchment. The groundwater storage in each subcatchment is obtained by
equating the water balance of the saturated zone as:
∆S
= RdA−G − Eg As
∆t ∫As
(4.9)
where As [L2] is the subcatchment area, and Eg [LT-1] is the average transpiration
from groundwater storage giving the effect of a steeper recession during dry period.
71
Chapter IV
Eg is assumed to occur only when the PET is higher than soil evapotranspiration, and
equated as a function of PET and groundwater storage:
E g = (cv E p − Ei − Ed − E )
G
Gm
(4.10)
where Gm is the maximum active groundwater storage of the subwatershed [L]. Hence,
the flow routing consists of tracking runoff along its topographic determined flow
path, and evaluating groundwater flow for each small subcatchment. In order to
consider the damping effect of the river, overland flow and interflow are routed firstly
from each grid cell to the main channel, and joined with groundwater flow at the
subcatchment outlet. Then the total hydrograph is routed to the outlet of the catchment
by the channel response function derived from Equation (3.6). The total discharge is
the sum of the overland flow, interflow and groundwater flow.
3.
GIS implementation
WetSpa operates within a GIS framework. Input maps to the model include DEM, soil
type and land use. Besides, the digital information of gauging sites, watershed
boundary and river network, sewer systems, main hydraulic and civil infrastructures
are necessary geo-referenced data for a complex terrain. Once the project database is
setup, the work begins by analyzing data, extracting information, producing parameter
maps, and running the distributed model. GIS functions greatly enhance the
capabilities for watershed description and interpretation by means of powerful
distributed indicators, which account not only for the watershed characteristics but
also for their distribution and individual localization in space.
3.1.
Drainage system
Elevation data in the form of a DEM are the principle digital data source for acquiring
watershed properties in the GIS-based WetSpa model. The raster-type DEM has to be
compatible with remotely sensed data layers such as land use and soil type. Based on
the digital elevation model, hydrological GIS tools are used to extract information on
the watershed boundaries, such as slope, flow length, flow direction and accumulation,
72
Flood modelling for complex terrain using GIS and Remote sensed information
configuration of stream network, subwatershed, etc., providing a suitable framework
for the modelling approach. The flow accumulation map is used for synthetic network
extraction, where each pixel is associated to an upstream drainage area. The
distinction between hill slopes and channel paths can be achieved simply by fixing a
threshold drainage area for which the flow concentration is sufficient to initiate a
channel.
For a small and steep watershed, processing a DEM is relatively straightforward.
After filtering the initial data to detect and remove erroneous extreme values, the
slope and aspect of each cell are determined and the flow direction can be obtained
allowing water flowing to the basin outlet from each grid cell. However, in flat areas
that are often present in large watersheds or floodplains, a raster cell within a DEM
may not have neighbouring cells with a lower elevation, and thus has no down-slope
exit. Such features could occur due to insufficient data, data noise, or interpolation
errors during DEM production. As a result, a channel network cannot be captured
from the raster DEM. A practical way to solve this problem is by the method of filling
sinks (Band, 1986), in which the elevation of sink cells is increased until a downslope path to a neighbouring cell becomes available, under the constraint that the flow
is not directed to another depression cell. Caution should be paid when using this
method in the presence of a large water surfaces, such as lakes, reservoirs, ponds, etc.,
and large plains with little or no elevation variation. Additionally, difficulties may
arise in delineating meandering rivers or actual watershed boundaries in flat areas. To
account for these cases, data from the hydrographical layer of a digitized map can be
used in combination with the DEM to identify output cells and revise flow directions,
in order to produce realistic and topographically consistent drainage patterns.
In a natural drainage basin with very little or no human interactions, aspect
information obtained from a DEM alone is a good indication of flow direction, and
the derived internal drainage structure of a watershed can be a perfect reflection of the
natural reality. However, in complex terrain, such as urban or suburban watersheds,
sewer systems, roads, artificial channels, etc., are important elements in drainage
structure configuration, and often govern the flow direction more strongly than the
derived slopes at local scale. Since most of these features are not sufficiently
represented in a DEM, additional procedures for deriving more realistic flow direction
73
Chapter IV
map have to be performed using GIS overlaying techniques. A general flow direction
map can be generated using geographic data alone. Thereafter, direction maps of
sewer areas, main water routes and a fine river network can be created separately
based on the DEM and available coverage maps. Finally, the general flow direction
map can be overlaid by the flow direction map of sewers, drain ditches, and streams
subsequently. In such a way, normal flow directions are altered fundamentally by the
presence of artificial drainage systems. The derived flow direction map is then used
for further drainage structure delineation.
Local slopes are normally derived from a DEM and calculated from the 3x3
neighbourhood using the average maximum technique with GIS. These are used in
several fundamental equations that form the foundation of the model. Among them,
the channel slope is most important, because all water from individual cells
contributes to the river flow. The slope of a channel cell is determined by the
elevation difference and distance between the upward and downward cells along a
streamline. Therefore, the channel slope should be calculated separately from the
general slope map in the model using the available DEM data and stream network
information.
3.2.
Soil and land use
In addition to the topography, soil and land use properties are utilized in the WetSpa
model to specify the land surface characteristics that determine the partitioning of
incident rainfall into infiltration and runoff, as well as the simulation of subsurface
flow and the vertical water and energy budget. Parameters, which depend upon soil
type and land use, are incorporated in the model as attribute tables of the land use and
soil type maps. The soil texture is classified based on the US Department of
Agriculture (Soil Survey Staff, 1951) classification in the model for the identification
of soil dependent parameters, such as porosity, field capacity, permanent wilting point,
residual moisture content, pore size distribution index, saturated hydraulic
conductivity, etc. An assumption made in the model is that soil hydraulic properties
remain constant throughout the root zone for each grid cell. Default values are
available in the model, but can be adjusted by the user to more appropriate values in
case more specific information is available.
74
Flood modelling for complex terrain using GIS and Remote sensed information
The digital land use map is normally obtained from a high-resolution remotely sensed
image. Fourteen land use classes are identified in the WetSpa model, which are
significantly different from each other on the basis of their effects on hydrological
processes. Each of these classes is characterized by quantitative attributes, as for
instance, canopy resistance, albedo, root depth, interception capacity, Manning’s
roughness coefficient, etc. The proportion of impervious area and bare soil are
considered separately for setting up the overall land use dependent parameters for
each grid cell. Using the roughness map derived from the land use, combined with the
slope map and hydraulic radius map derived from the DEM, the average flow velocity,
celerity and dispersion coefficient can be calculated for each cell. Consequently, the
average travel time and standard deviation are obtained using the weighted GIS flow
length routine, and used for determining flow response function for each grid cell.
Afterwards, the land use is regrouped into six classes, namely forest, pasture, crop,
bare soil, urban and open water surface, for deriving potential runoff coefficient and
depression storage capacity in combination with slope and soil texture classes.
3.3.
Spatial hydrological input and output
Rainfall and potential evapotranspiration are the two meteorological variables needed
for the WetSpa model. If the Penman-Monteith equation is used for estimating
potential evapotranspiration, the data of net radiation, air temperature, relative
humidity, and wind speed are required. The method of Thiessen polygons is applied
to interpolate precipitation and other meteorological variables observed at different
meteorological stations. This implies that the rainfall or other meteorological
variables of each grid cell is set to the value recorded at the nearest gauging site. The
average rainfall and potential evapotranspiration for each subwatershed can be
estimated by integration of the values on the cells belonging to that subwatershed.
For long-term flood simulation in a watershed, the initial soil moisture content
distribution is less important, as it affects runoff production only in the initial part of
the simulation. However, for short-term flood prediction or event based flood
simulation, the antecedent soil moisture condition is one of the most important factors
in storm-runoff generation. The concept of topographic wetness index (TWI) (Beven
75
Chapter IV
& Kirkby, 1979) is introduced to the model to evaluate antecedent moisture condition
in a watershed with TWI = ln(A/S), where A [L2] is the upslope drained area, and S [-]
the local slope. The TWI distribution can be easily obtained from a high resolution
DEM. Those cells with high TWI values have larger upslope contributing areas or
smaller element slopes or a combination of the two properties that lead to
accumulation of soil moisture. The antecedent moisture distribution can be obtained
by simply relating moisture content to the TWI values. Cells with very high TWI
values are assumed saturated and are generally distributed along the main river or in
the depression areas of the watershed.
WetSpa model computes and generates time series of flow hydrographs at selected
stations in a watershed and maps of spatial outputs. These maps include interception,
surface runoff, infiltration, soil moisture, actual evapotranspiration, percolation,
interflow, as well as the gross and net rainfall distribution. For each of these, maps in
GIS format can be saved at a specified time increment, which can be used for
graphical presentation to see the complete temporal and spatial variation of each of
the above state variables during a model simulation.
4.
Model application
4.1.
Watershed description and data availability
The model is tested on a 67.8 km2 catchment, Barebeek, which is located in the
downstream part of the Dijle River basin, Belgium. It is a typical suburban area
situated northeast of Brussels (Figure IV-1). The Brussels international airport is
located in the upper area of the catchment. Four main traffic lines cross the watershed
in different directions, and many country roads crisscross the area from one village to
another. The Leuven canal passes through the area in the north. A small lake covering
about 0.55 km² is located near the basin outlet. Several residential areas with sewer
systems exist in the watershed occupying about 28% of the total area. The watershed
drainage system, together with the main civil infrastructures and measuring stations
are presented in Figure IV-2.
76
Flood modelling for complex terrain using GIS and Remote sensed information
#
Netherlands
Netherlands
Barebeek
Barebeek
Flanders
Flanders
Antwerp
North Sea
City
City
River
River
N
Brugge
Gent
Mechelen
Brussel
W
Leuven
E
S
France
0
20
40 km
Wallonia (South-Belgium)
Figure IV-1: Location of the Barebeek catchment
# Rain gauge
MO6
$
$ P1
$
#
$
$ MO1
MO2
$
MO3
Stream gauge
River
Canal
High way
Sewer area
Boundary
Land use
Crop
P1
Grass
Forest
Urban
Water
N
N
$
$
#MO4
MO5
P2
W
E
W
S
0
2
E
S
4 km
0
2
4 km
0
Figure IV-2: Drainage system of the
Barebeek catchment
Figure IV-3: Land use map of the
Barebeek catchment
The study area is discretized into grid cells of 50 m by 50 m. The topography is
digitalized from 1/10,000 maps and the soil types are obtained from the physical
system map of Flanders. The catchment is rather low and flat with average basin slope
of 0.63%. Elevation differences are small with extreme values ranging from 5 to 68 m.
The dominant soil types are sandy loam (66.2%) and loamy sand (29.8%), while the
rests are sand, loam, silt loam and clay scatted around the catchment. The soil cover is
obtained from the digital land use map of Flanders, which is based on remote sensed
data of 1995. The resampled land use map for use in the model is presented in Figure
IV-3. The study area is well vegetated. Forest (16.8%) is predominant in the river
valleys, while the higher terrains consist of agricultural areas, with pasture (24.7%)
and crops (36.9%), strongly intermixed with urban areas (16.2%), as villages, roads
and Brussels international airport in the south.
77
Chapter IV
The study area has a maritime temperate climate with no proper distinction between
rainy and dry seasons. Rainfall is relatively uniformly distributed through out the year,
but storms have low intensities and long durations in winter, and are intense and of
short duration in summer. High runoff occurs in winter and low runoff in summer due
to dry soils and high evapotranspiration. Heavy storms usually last 2 to 3 days with
peak rainfalls concentrated into 3 to 6 hours. The average annual precipitation in the
region is about 800 mm, and the annual potential evaporation from free water surface
is around 650 mm. During the period of Dec. 1998 to Feb. 1999, an intensive
hydrological research was carried out to study the water quantity and quality in the
Barebeek watershed. Two temporary rainfall gauges and five stream gauges were set
up, MO1 to MO5, as shown in Figure IV-2. MO6 is a regular flow monitoring station
located in the downstream part of the river with a relatively long discharge record.
The main meteorological station is situated at Ukkel, located south of Brussels about
12 km away from the catchment. At this station, a very long meteorological record
starting from the year 1898 is available, which can be used for model simulation.
4.2.
Model calibration
Calibration of the model was performed using the measured precipitation and
discharge data during the period of Dec. 1998 to Feb. 1999. The PET data was
obtained from Ukkel station. Predicted hydrographs were compared with the
measured streamflows at each stream gauge. Model calibration was performed at the
most down gauging site MO6, while simulation results at other stream gauging sites
can be seen as model verifications. Further verification was carried out at MO6 for the
period of Sept. 1998 to Dec. 1999, considering the seasonal parameter verification
and using the available precipitation and PET data of Ukkel.
Figure IV-4 shows the distribution of potential runoff coefficients that result from the
different slope, soil type and land use class combinations. The watershed is covered
by either dense plants or impervious areas. Impervious areas have a significant
influence on runoff production, because they can generate direct runoff even during
small storms. Due to the model grid size, cells may not be 100% impervious in reality.
In this study, the percentage of impervious area in a grid cell is computed based on
78
Flood modelling for complex terrain using GIS and Remote sensed information
land use classes, with 30% for residential areas, 70% for commercial and industrial
areas and 100% for streams, lakes and roads. Default runoff coefficients for these
areas are calculated by adding the impervious percentage with a grass runoff
coefficient multiplied by the remaining percentage. This results in potential runoff
coefficients of 40 to 100% in urban areas, while other areas have much smaller values,
down to 3% for forests in valleys with practically zero slopes.
Flow time (h)
Runoff coefficient
&$
%
0.0 – 0.1
0.1 – 0.2
0.2 – 0.3
0.3 – 0.4
0.4 – 0.5
0.5 – 1.0
0–5
5 – 10
10 – 15
15 – 20
20 – 25
25 – 30
30 – 40
&
N
W
N
E
W
S
0
2
Figure IV-4: Distribution of potential
runoff coefficient
E
S
4 km
0
2
4 km
Figure IV-5: Distribution of average flow
time to the catchment outlet
A flow direction map is generated considering the effect of sewer systems. The
average hydraulic radius is computed for normal floods, i.e. with a return period of 2
years. The parameters of network constant and the geometry scaling exponent are set
to 0.07 and 0.43 respectively resulting in a minimum hydraulic radius for overland
flow of 0.005 m and a maximum hydraulic radius for channel flow of 0.5 m at the
watershed outlet. These two parameters can be increased for more extreme floods.
Next, the overland flow velocity is calculated using Manning’s equation. The urban
areas have a remarkable influence, due to the artificial drainage facilities as sewer
systems that result in flow velocities of order 0.5 m/s or more. On the other hand, the
overland flow velocity in valley areas is very small, due to the high resistance of the
soil cover, being mostly forest, and the very faint slopes. With this information the
flow path response functions are calculated for each cell using the diffusive wave
approximation. The exponent α in Equation 4.2 is set to 1 after model calibration.
79
Chapter IV
This is possible because that there are no extreme rainfalls during the simulation
period. Figure IV-5 shows the resulting average flow time from each grid cell to the
outlet of the watershed, in which the average flow time is less than 10 hours for the
main river and up to 40 hours for the most remote areas. A comparison of calculated
and observed discharges at the most downstream measuring station MO6 is presented
in Figure IV-6. A comparison at an internal site MO3 for the same period is shown in
Figure IV-7. The simulation results for other measuring stations are similar. Six
storms occurred during this calibration period, with quite small rainfall intensities
lower than 3 mm/h, but lasting for relatively long periods, i.e. 2 to 5 days for each.
Flow volumes are mainly determined by the baseflow, about 82% for MO6 and 71%
for MO3. Peak discharges result from surface runoff during each flood, and are
1.0
0
4
2
0.8
2
Precipitation
Measured
Calculated
4
2
6
1
8
0
12/20/98 12/30/98
1/9/99
1/19/99
1/29/99
10
2/8/99
Figure IV-6: Observed Vs calculated
0.6
Precipitation
Measured
Calculated
4
0.4
6
0.2
8
0.0
12/20/98 12/30/98 1/9/99
1/19/99 1/29/99
Figure IV-7: Observed Vs calculated
discharges at MO6
discharges at MO3
0
5
5
4
Discharge (m³/s)
10
2/8/99
Precipitation
Measured
3
Calculated
10
2
15
1
20
0
9/1/98
10/19/98
12/6/98
1/23/99
3/12/99
4/29/99
6/16/99
8/3/99
9/20/99
11/7/99
Precipitation (mm/h)
3
Precipitation (mm/h)
0
Discharge (m³/s)
5
Precipitation (mm/h)
Discharge (m³/s)
mainly generated in urban areas.
25
12/25/99
Figure IV-8: Observed Vs calculated flow hydrographs at MO6 for the period of Sept.
1998 to Dec. 1999
80
Flood modelling for complex terrain using GIS and Remote sensed information
A comparison at MO6 for the period of Sept. 1998 to Dec. 1999 is presented in Figure
IV-8. One can notice a reasonable agreement between the simulation results and the
observed hydrograph. Peaks in the hydrograph are rather well simulated, as well as
for their shape and time of occurrence. From the 16 months simulation results, about
11% of the total rainfall is lost by interception, 53% of the total rainfall returns to the
atmosphere as evapotranspiration, and 32% is recharged to the groundwater, which
mainly happens during the winter season. The simulated flow volume is composed of
surface runoff (28%), groundwater flow (70%), and Interflow (2%). Interflow is not
an important flow component in this study area, due to the fact that the slope is too
small to generate lateral flow in the unsaturated zone. Infiltrated water either stays in
the soil and is lost as evapotranspiration, or is recharged to the saturation zone for
generation of baseflow. Floods occur frequently in the winter season, because of
saturated soils and high baseflow, even though the storms were not very intensive.
The largest storm occurred on August 10, 1999, with maximum rainfall intensity of
15 mm/h, and the accumulative rainfall was 39 mm within 15 hours. This storm did
not result in a severe flood, since the antecedent soil moisture of the watershed was
much lower than the field capacity, thus leading to very high infiltration and storage
in the soil. Additionally, a large amount of rainfall was lost by interception and
depression storage during the initial phase. The measured peak discharge was 1.43
m³/s, and the calculated peak discharge was 1.82 m³/s. Figure IV-9 shows the
simulated spatial distribution of relative soil wetness (θ/θs) on Oct. 8, 1999, before the
main storm. It is found that higher soil wetness was present in river valleys and lower
wetness in the upper areas. In general, the soil moisture content is quite small in the
watershed due to little precipitation and high evapotranspiration in the previous month.
Additionally, it is seen from the figure that the relative soil wetness in the downstream
areas close to the river outlet was much lower than that in other areas. This is because
the area is covered by sandy soils with rather small water holding capacity, and most
soil water contributed to the evapotranspiration and percolation. Figure IV-10 gives
the simulated surface runoff produced in the following hour. High surface runoff was
mainly generated from the impervious areas and open water surfaces, while surface
runoff for other areas was rather small, especially for the areas covered by forest and
sandy soils.
81
Chapter IV
Relative saturation
0.1 – 0.2
0.2 – 0.3
0.3 – 0.4
0.4 – 0.5
0.5 – 0.6
0.6 – 0.7
0.7 – 0.8
0.8 – 0.9
0.9 – 1.0
Surface runoff (mm)
0.0 – 1.0
1.0 – 2.0
2.0 – 3.0
3.0 – 4.0
4.0 – 5.0
5.0 – 6.0
6.0 – 7.0
7.0 – 8.0
8.0 – 15
N
W
N
E
W
S
0
2
E
S
4 km
0
2
4 km
Figure IV-9: Simulated distribution of
Figure IV-10: Simulated distribution of
relative soil wetness on 8/10/1999, 4:00
surface runoff on 8/10/1999, 4:00-5:00
The model performed well with the Nash-Sutcliffe efficiency criteria for the
calibration period, with water volume under estimated by 2%, the efficiency for
reproducing river discharges by 72.4%, and the ability to reproduce low flow and high
flow by 83.8% and 76.8% respectively. This indicates that the model is suitable for
both peak flow prediction and hydrograph simulation in this watershed.
4.3
Model application using the historical and IDF data
To demonstrate the usefulness and performance of the model, a historical 102-year
series of precipitation data from Ukkel was processed under the present land use
condition. The daily and hourly potential evapotranspiration was estimated from the
historical records of Ukkel through statistical analysis. The resulting hydrographs for
the whole catchment were then analyzed statistically to determine the characteristics
of peak discharges.
Also, hourly design storms developed by Willems (2000) were introduced as rainfall
input to the model for calculating corresponding design floods to compare with the
modelling results of the 102-year rainfall series. The IDF relationships were
established based on the long rain gauge record of 10-min precipitation depths for the
period 1967-1993 at Ukkel, which is the same rainfall station for the model simulation
82
Flood modelling for complex terrain using GIS and Remote sensed information
of the Barebeek. Storms of two different types, air mass thunderstorms and
cyclonic/frontal storms, are separated based on their distribution of peak-overthreshold intensity. This is done for each of the durations in the range of 10 min to 15
days, using a two-component exponential distribution. Different mixtures of the two
type storms are estimated for summer and winter conditions.
100
10
Summer
10
1
Summer
8
Discharge (m³/s)
P (mm/h)
Winter
Winter
6
4
2
0
0
0
48
96
144
192
240
288
336
T (h)
Figure IV-11: Design summer and winter
storms with 100-year return period
0
48
96
144
192
240
288
336
Time (h)
Figure IV-12: Simulated floods for the
100-year design storms
The hourly design summer and winter storms with 15 days duration and 100 year
return period are shown in Figure IV-11, in which the peak storm intensities are 36.3
mm/h and 13.1 mm/h respectively for summer and winter design storms, while the
storm volumes are the same, i.e. 174 mm. Summer design storms are more intensive
corresponding mostly to air mass thunderstorms, and winter design storms are less
intensive corresponding mostly to cyclonic/frontal storms. The resulting flood
hydrographs from the 100-year design storms were simulated with the WetSpa model,
as shown in Figure IV-12, resulting in peak discharges of 8.55 m³/s and 5.96 m³/s
respectively for the design summer and winter storms. The winter floods were
simulated with the assumption that the initial soil moisture content was equal to the
field capacity, while for summer design floods, the initial soil moisture content was
assumed to be half of the field capacity. Figure 12 shows clearly that the design
summer storm produces higher peak discharge and lower flood volume compared
with that induced from the design winter storm due to the high rainfall intensity, high
evapotranspiration rate, and low antecedent soil moisture. These results reflect the
typical pattern of summer and winter floods of the catchment on one hand and the
importance of soil moisture in controlling the runoff production on the other hand.
83
Chapter IV
The comparison of design peak flows for the two methods is presented in Figure IV13. For each return period, the design winter peak flow is smaller than the design
summer peak flow, but is getting closer with each other for short return periods. The
statistical result of the 102-year series model simulation is very close to the result
calculated from the summer design storms. This is because the annual maximum
flood occurs mostly in the summer season.
10
Discharge (m³/s)
Discharge (m³/s)
Summer
Winter
Model
8
6
4
2
0
1
10
100
Return period (y)
Figure IV-13: Comparison of the design
peak flow discharges
0
Precipitation
Discharge
8
4
6
8
4
12
2
16
0
8/23/96 8/25/96
8/28/96 8/31/96
9/3/96
Precipitation (mm/h)
10
20
9/6/96
Time (m/d/y)
Figure IV-14: Simulated maximum flood
at the watershed outlet
The simulated largest flood at the watershed outlet on Aug. 30, 1996 is presented in
Figure IV-14. It shows a typical pattern that is present in most of the precipitation
events in the study area that lead to flood discharges. The actual storm was preceded
by another storm 5 days before the main event. The simulated antecedent soil
moisture was very low at that moment with average moisture content around 43% of
the saturation capacity. This resulted in a very small actual runoff coefficient for
pervious soils, and the surface runoff was mainly produced from the impervious areas.
This storm did not lead to flooding, but increased the root zone average soil moisture
to field capacity, or about 54% of the saturation capacity. On Aug. 29, 1996, a storm
event with 108 mm fell on the entire catchment, causing a severe flood in the
watershed. The calculated surface runoff was generated from every grid cell of the
catchment. Complete saturation of the root zone occurred in the river valleys and the
areas with sandy soils, forest cover and very flat slopes, but not on the entire
watershed. The average moisture content of the watershed was 70% of the saturation
capacity after the storm event. This information, together with the simulated stream
84
Flood modelling for complex terrain using GIS and Remote sensed information
flow hydrographs, gives a more complete view of the hydrological behaviour and
allows a better understanding of the hydrological processes.
5.
Discussion and Conclusion
A physically based distributed hydrological model compatible with remote sensing
and GIS is presented for simulating the hydrological behaviour of a watershed. The
generation of runoff depends upon rainfall intensity and soil moisture status and is
calculated in function of slope, land use and soil type. The runoff is subsequently
routed through the watershed along flow paths determined by the topography using a
diffusive wave transfer model that leads to response functions between any start and
end point, depending upon slope, flow velocity and dissipation characteristics along
the flow paths. The model can predict not only the flood hydrograph at any
controlling point of the river, but also the spatially distributed hydrological processes,
such as surface runoff, soil moisture, interflow, groundwater recharge, actual
evapotranspiration and so on, at each time step during a simulation.
The modified runoff coefficient for surface runoff production is no longer the
conventional runoff coefficient used in the rational method, but a measure of rainfall
partitioning capacity, which allows varying with time, rainfall intensity, rainfall
duration and the cell geophysical characteristics. With such improvements, the model
can be used for the computation of storm hydrographs for any size watershed.
Processes in water and energy transfer between soil, plant and atmosphere are
simulated using simplified equations for each grid cell. Among these, water balance in
the root zone is important, as the moisture in the root zone is a key factor to control
the amount of surface runoff, interflow, actual evapotranspiration and groundwater
recharge. All model parameters can be obtained from DEM, land use and soil type
data of the watershed or combinations of these three fundamental maps. The spatial
distribution of rainfall intensity, potential runoff coefficient and the antecedent soil
moisture content are governing factors of the flood volume, while the hydraulic radius
and the channel roughness coefficient are sensitive for flow routing simulations.
GIS provides a powerful platform for developing the model, calibrating parameters
and displaying model results in a spatial way, so that it is possible to capture local
85
Chapter IV
complexities of a watershed and compare model results to the field measurements.
The model was validated on a small watershed in Belgium for which topography and
soil data are available in GIS form, while the land use and soil cover was obtained
from remote sensed images. The resulting calculated hydrographs compare favourably
with measurements. The usefulness and utility of the model are subsequently
demonstrated by forecasting peak discharges resulting from an observed 102 years
precipitation series. The resulting discharges were analyzed statistically to determine
the characteristics of extreme flood events and compared with the results computed
from design storms. Comparison of the two methods shows that the model is capable
to predict both normal and extreme floods.
For flood modelling on a large catchment scale, computing with small grid size leads
to huge memory cost and is time consuming. To solve this problem, the model can be
easily converted to a semi-distributed model, where water and energy budget are
maintained for each very small subwatershed derived from the high resolution DEM,
hydrographs at each subwatershed outlet are firstly calculated using GIS derived
subwatershed response function and then routed to the basin outlet using the channel
response function. Model parameters and meteorological data input for each
subwatershed can be obtained by integration of the values from all cells of that
subwatershed. This has the advantage of maintaining the correct internal drainage
structure within each subwatershed, which could not be the case with a distributed
model with larger grid cells. However, division of the catchment should be done with
caution in order to take care of the spatial variability of the hydrological processes.
The model makes full use of the remote sensed data and calculations are for the most
part performed by standard GIS tools, such that the model is especially useful for
flood prediction on complex terrain and analyzing the effects of topography, soil type,
and land use or soil cover on the flood. Additionally, the model can be easily coupled
with other water quality and soil erosion models, and used for simulating spatial
hydrological behaviour of a river basin.
86
Flood modelling for complex terrain using GIS and Remote sensed information
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Horritt, M.S. & Bates, P.D., Effect of spatial resolution on a raster based model of
flood flow, J. Hydrol., 253, 239-249, 2001.
Julien, P.Y., Saghafian, B. & Ogden, F.L., Raster-based hydrological modelling of
spatially-varied surface runoff, Water Resour. Bull., 31, 523-536, 1995.
Kirkby, M.J., Hill-slope Hydrology, 235, John Wiley & Sons, Ltd., 1978.
Kuichling, E., The relation between rainfall and the discharge in sewers in populous
district, Trans., AECE, No 20, 1889.
Linsley, Ray K., Jr., Kohler, M.A. & Joseph Paulhus, L.H., Hydrology for Engineers,
237, McGraw-Hill, New York, 1982.
Liu, Y.B., Gebremeskel, S., De Smedt, F. & Pfister, L., Flood prediction with the
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283, 91-106, 2003.
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Mallants, D. & Feyen, J., Kwantitatieve en kwalitatieve aspecten van oppervlakte en
grondwaterstroming (in Dutch), 96, Vol. 2, KUL, 1990.
Moore, I.D., Grayson, R.B. & Ladson, A.R., Digital terrain modelling: a review of
hydrological, geomorphologic, and biological applications, Hydrol. Process., 5,
3-30, 1991.
Myrobo, S., Tempral and spatial scale of response area and groundwater variation in
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Palacios-Velez, O.L. & Cuevas-Renaud, B., SHIFT: A distributed runoff model using
irregular triangular facets, J. Hydrol., 134, 35-55, 1992.
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Hydrology, 9.1-9.42, McGraw-Hill, New York, 1993.
Quinn, P., Beven, K., Chevallier, P. & Planchon, O., The prediction of hillslope flow
paths for distributed hydrological modelling using digital terrain models, Hydrol.
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27, 513-525, 1991.
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Flood modelling for complex terrain using GIS and Remote sensed information
Robson, A.J., Whitehead, P.G. & Johnson, R.C., An application of a physically based
semi-distributed model to the Balquhidder catchments, J. Hydrol., 145, 357-370,
1993.
Rowe, L.K., Rainfall interception by an evergreen beech forest, Nelson, New Zealand,
J. Hydrol., 66, 143-158, 1983.
Sheaffer, J.R., Wright, K.R., Taggart, W.C. & Wright, R.M., Urban Storm Drainage
Management, Marcel Kekker, New York, 1982.
SINCE, WatfloodSPL8, Flood forecasting system, developed for surveys and
information branch ecosystem science and evaluation directorate, Environment
Canada, 1972.
Singh, B. & Szeicz, G., The effect of intercepted rainfall on the water balance of a
hardwood forest, Water Resour. Res., 15, 131-138, 1979.
Singh, V.P., Elementary Hydrology, Prentice Hall, Englewood Cliffs, New Jersey,
1992.
Soil Survey Staff, Soil Survey Manual, Handbook, No. 18, US Department of
Agriculture, 1951.
Thornthwaite, C.W. & Mather, J.R., The Water Balance, Laboratory of Climatology,
Publ. No. 8, Centerton NJ., 1955.
Wang, Z., Batelaan, O. & De Smedt, F., A distributed model for Water and Energy
Transfer between Soil, Plants and Atmosphere (WetSpa), Phys. Chem. Earth, 21,
189-193, 1997.
Wigmosta, M.S., Vail, L.W. & Lettenmaier, D.P., A distributed hydrology vegetation
model for complex terrain, Water Resour. Res., 30(6), 1665-1679, 1994.
Willems, P., Compound intensity/duration/frequency-relationships of extreme
precipitation for two seasons and two storm types, J. Hydrol., 233, 189-205,
2000.
Wittenberg, H. & Sivapalan, M., Watershed groundwater balance estimation using
streamflow recession analysis and baseflow separation, J. Hydrol., 219, 20-33,
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H.W., International Symposium on Forest Hydrology, 137-161, Pergamon Press,
Oxford, 1967.
89
Chapter V
Assessing land use impacts on flood processes using a GIS modelling
approach
Abstract
A distributed hydrological modelling and GIS approach is applied for the assessment
of land use impact in the Steinsel sub-basin, Alzette, Grand-Duchy of Luxembourg.
The assessment focuses on the runoff contributions from different land use classes
and the potential impact of land use changes on runoff generation and flow responses.
The results show that the direct runoff from urban areas is dominant for a flood event
compared with runoff from other land use areas in this catchment, and tends to
increase for small floods and for the dry season floods, whereas the interflow from
forested, pasture and agricultural field areas contributes to the recession flow. For
assessing the hydrological effects of land use changes, three scenarios, urbanization,
deforestation and afforestation, are established and investigated. Significant variations
in flood volume, peak discharge, time to the peak, etc., are found from the model
simulation based on the three hypothetical land use change scenarios.
1.
Introduction
Flood risk is among the most severe risks on human lives and properties, and has
become more frequent and severe along with local economical development. As the
earth’s population has been growing rapidly and more stress is put on the land to
support the increased population, hydrological resources are affected both on local
and global scale. One of the recent thrusts in hydrological modelling is the assessment
of the effects of land use and land cover changes on water resources, and the influence
on storm runoff generation is one of the main research topics in the last decade.
The influence of land use on storm runoff generation is very complex as land use and
soil cover have an effect on interception, surface retention, evapotranspiration, and
resistance to overland flow. For instance, cropland and urban land yield more flood
Chapter V
volumes, higher peak discharges and shorter flow travel times than grassland or
woodland. Increased runoff from cropland is mainly due to the removal of native
vegetation and soil compaction, which decrease soil infiltration capacity. Increased
runoff from urban areas results from impervious surfaces that prevent infiltration of
water into soils. Urban land uses also reduce the surface roughness and therefore
shorten the overland flow retention time. In contrast, less runoff is produced from
undisturbed grassland and woodland areas. This is due to factors such as interception
of precipitation by the vegetation canopy, the dense network of roots that increase
infiltration capacity and soil porosity, as well as the accumulated organic debris on the
surface that increases depression storage capacity and overland flow retention time.
Moreover, dense vegetation causes higher evapotranspiration and affects the longterm water and energy balance. Evidently, areas with a high percentage of cropland or
urban land use yield more storm runoff than the areas of similar soils and topography
with grassland or woodland.
Land uses generally do not affect the slope and soil composition. Although certain
practices such as terraced agriculture, mining, and residential landscaping can
potentially have drastic effects on the slope and the physical properties of the soil.
Land use can have a big effect on the water quality of rivers, lakes and estuaries, since
land reclamation, cultivation, deforestation and urbanization influence the water
environment by non-point source pollution, soil erosion, sedimentation, etc. Bultot et
al. (1990) employed a conceptual hydrological model on a small catchment in
Belgium to assess the impacts of possible land use changes on the water balance. The
study was carried out by converting the present diversified vegetation cover for the
un-built areas into a single vegetation species, and simulation results showed that
minimum streamflow occurs for a coniferous cover and maximum streamflow for
pasture. Nandakumar and Mein (1997) combined a Monte-Carlo simulation method
with a conceptual rainfall-runoff model to examine the effect of random errors in land
use model parameters on flood predictions. One of their conclusions is that small
changes in catchment land use may cause changes in runoff, which cannot be detected
statistically from the output errors with a lumped model. Lorup et al. (1998) adopted a
methodology combining common statistical methods with conceptual hydrological
modelling to distinguish between the effects of climate variability and the effects of
land use for six semi-arid catchments in Africa. Their analysis indicated a decrease in
92
Assessing land use impacts on flood processes using a GIS modelling approach
the low flow for most of the testing catchments, with the largest changes occurring for
catchments located within communal land, where large increases in population and
agricultural intensity have taken place. Karvonen et al. (1999) developed a semilumped model to study the influence of land use on catchment runoff. The modelling
is based on the subdivision of the catchment into smaller units, which aggregate areas
of hydrologically similar behaviour, e.g., land use, soil, slope, and vegetation, and
allows calculating runoff from different land use areas separately. In their model, a
characteristic profile was used as a basic component to represent various sizes of
homogenous land use areas and the hydraulic properties were defined at the profile
scale and were applied as such for areas of different sizes. In general, conceptual
rainfall-runoff models usually consider the entire catchment or sub-catchment as one
unit, and describe the transformation of rainfall to runoff with simple concepts. Due to
limitations in the model conceptualizations of the hydrological processes involved,
lumped catchment models must be used carefully in predicting the impacts of land use
change on catchment runoff (Kuczera et al., 1993).
In this type of analysis, it is desirable that the hydrological modelling describes the
spatio-temporal variability of anthropogenic effects so that the assessment could
reflect the variability of the hydrological parameter at the required scales. These kinds
of hydrological models have the advantage of reflecting the effects of spatially
distributed model parameters such as land use on stream flows. As for instance,
Niehoff et al (2002) combined spatially distributed land use scenarios and a processoriented hydrological model to study land use impacts on storm runoff generation in a
meso-scale catchment in SW-Germany. The simulation results showed that the
influence of land use conditions on storm runoff production depends largely on the
rainfall event characteristics and on the related spatial scale. However, distributed
physically-based rainfall-runoff models use a high number of parameters which are
difficult to determine, and are usually accompanied by a high degree of data and
parameter uncertainty, which impose limitations to the prediction of land use impacts
on the hydrological behaviour. Along with the rapid development of GIS technology
and remote sensing techniques, especially the concomitant availability of high
resolution DEM and the advances in integrating GIS with hydrological modelling,
hydrological assessment with distributed models tends to be more advantageous and
competent by linking GIS with hydrological modelling.
93
Chapter V
In this chapter, a GIS modelling approach for predicting flood hydrograph and runoff
contribution from different land use areas and assessing the land use change on flood
processes is presented. The model takes into account the spatial heterogeneity of the
basin parameters to predict flood hydrographs and spatially distributed hydrological
characteristics in a watershed, and therefore making it suitable for analysis of the
effect of land use change on stream flows. The input of the model includes observed
data of precipitation and evaporation together with parameters derived from a
combination of a DEM, land-use and soil map in raster format. The model is validated
by comparing calculated and observed hourly discharges for a 52 months period at
four stream flow stations in the Steinsel watershed, located in the upstream part of the
Alzette River basin, Grand-Duchy of Luxembourg. Three land use scenarios,
urbanization, deforestation and afforestation, are considered for assessing the effects
of land use change on runoff and flow processes in the Steinsel catchment.
2.
Methodology
2.1.
Description of the WetSpa model
WetSpa is a grid-based distributed hydrological model for water and energy transfer
between soil, plants and atmosphere, which was originally proposed by Wang et al.
(1997) and adopted for flood prediction on a variable time step by De Smedt et al.
(2000), and Liu et al. (2002, 2003). The detailed theory and formulation of the
WetSpa model have been described in chapter III and IV. For each grid cell, four
layers are considered in the vertical direction as vegetation zone, root zone,
transmission zone and saturated zone. The hydrological processes considered in the
model are precipitation, interception, depression, surface runoff, infiltration,
evapotranspiration, percolation, interflow, ground water flow, and water balance in
the root zone and the saturated zone. The total water balance for a raster cell is
composed of the water balance for the vegetated, bare-soil, open water and
impervious parts of each cell. This allows accounting for the non-uniformity of the
land use per cell, which is dependent on the resolution of the grid. The processes in
each grid cell are set in a cascading way, which means that an order of occurrence of
the processes is assumed after a precipitation event. A mixture of physical and
94
Assessing land use impacts on flood processes using a GIS modelling approach
empirical relationships is used to describe the hydrological processes in the model.
The model predicts peak discharges and hydrographs, which can be defined for any
numbers and locations in the channel network, and can simulate the spatial
distribution of catchment hydrological characteristics.
The simulated hydrological system consists of four control stores: the plant canopy,
the soil surface, the root zone, and the saturated groundwater aquifer. Among the
process variables, soil moisture content is a crucial factor in the model as it affects the
hydrological processes of surface runoff, actual evapotranspiration, interflow and
percolation out of the root zone. The precipitation that falls from the atmosphere
before it reaches the ground surface is abstracted by canopy interception storage. The
remaining rainfall reaching to the ground is separated into rainfall excess and
infiltration. Rainfall excess is calculated using a moisture-related modified rational
method with potential runoff coefficient depending on the land cover, soil type, slope,
the magnitude of rainfall, and the antecedent moisture content of the soil. The
calculated rainfall excess fills the depression storage at the initial stage and runs off
the land surface simultaneously as overland flow (Linsley, 1982). The infiltrated part
of the rainfall may stay as soil moisture in the root zone, move laterally as interflow
or percolate as groundwater recharge depending on the moisture content of the soil.
Both percolation and interflow are assumed to be gravity driven (Famiglietti & Wood,
1994) in the model. Percolation out of the root zone is equated as the hydraulic
conductivity corresponding to the moisture content as a function of the soil pore size
distribution index (Eagleson, 1978). Interflow is assumed to occur in the root zone
after percolation and becomes significant only when the soil moisture is higher than
field capacity. Darcy’s law and a kinematic approximation are used to estimate the
amount of interflow generated from each cell, in function of hydraulic conductivity,
the moisture content, slope angle, and the root depth. The actual evapotranspiration
from soil and plant is calculated for each grid cell using the relationship developed by
Thornthwaite and Mather (1955) as a function of potential evapotranspiration,
vegetation and stage of growth, and moisture content in the cell. A percentage of the
remaining potential evapotranspiration is taken out from the water content in the
groundwater reservoir as a function of the maximum reservoir storage, giving the
effect of a steeper baseflow recession during dry period. The total evapotranspiration
is the sum of evaporation from intercepted water, depressed water and the bare soil
95
Chapter V
surface, and the transpiration from plants through the root system and a small part
from the groundwater storage.
A simple structure is used in the model because the emphasis here is on developing
and testing parameterizations for the root zone. Excess runoff, infiltration,
evapotranspiration, interflow and percolation estimates are point calculations.
Different slope, land use and soil properties in different grid cells of a watershed
result in different amounts of excess runoff when subjected to the same amount of
rainfall. Runoff from different cells in the watershed is routed to the watershed outlet
depending upon flow velocity and wave damping coefficient by using the diffusive
wave approximation method. A two parameter, mean travel time and its variance,
approximate solution proposed by De Smedt et al. (2000) in the form of an
instantaneous unit hydrograph (IUH) was used in the model relating the discharge at
the end of a flow path to the available runoff at the start of the flow path. The mean
travel time and its variance for each grid cell are spatially distributed, and can be
obtained by integration along the topographic determined flow paths as a function of
flow celerity and dispersion coefficient. Although the spatial variability of land use,
soil and topographic properties within a watershed are considered in the model, the
groundwater response is modelled on small GIS-derived subcatchment scale due to
the fact that groundwater flow is much slower than surface flow and little is known
about the bedrock. The simple concept of a linear reservoir is used to estimate
groundwater discharge on a small subwatershed scale, while a non-linear reservoir
method is optional in the model with storage exponent of 2 (Wittenberg & Sivapalan,
1999). The groundwater outflow is added to any runoff generated to produce the total
streamflow at the subwatershed outlet. All model equations are specifically chosen to
maintain a physical basis and well supported by previous studies.
2.2.
Description of the study area
The Steinsel watershed covers approximately 407 km² and is located in the upstream
part of the Alzette river basin. The study area is situated in the southern part of the
Grand Duchy of Luxembourg, with a small part in the south located in France, as
shown in Figure V-1. The elevations in the watershed range from 450.0 m to a low
elevation of 225.5 m at the watershed outlet, with an average basin slope of 7%.
96
Assessing land use impacts on flood processes using a GIS modelling approach
Figure V-2 shows the topographic elevation map and measuring stations in the
watershed. The local topography is characterized by a natural sandstone bottleneck,
located near Luxembourg-city. The valley is up to 2.5 km wide upstream of the
bottleneck, and only 75 m in the Luxembourg sandstone, which extends
approximately 80 m into the ground (Pfister et al., 2000).
Stei nsel
Loren tzweiler#
Waldhaff
Mull endo rf #
#
Mamer
#
River
Rive
r
Boundary
Bou
nd ary
Ele
Elevation
vatio n (m)
( m)
225
225- 2- 70
270
m
Hesperange Contem
#
270
270- 3- 15
315
315
315- 3- 60
360
360
4
05
360 - 405
405 - 4 50
Pfaffe nthal
Be a
l ir
#
Reckan ge/Mess
#
Streamgau
Streamg au
Raingauge
# Raingauge
#
#Fin del
405 - 450
Livange
Ro eser #
Belvaux
#
N
Schifflan ge
#
W
E
S
0
Figure V-1: Location of the Alzette basin
and Steinsel sub-basin
5
10 k
Figure V-2: Topography and gauging
network of the Steinsel sub-basin
The dominant soil types are loamy sand (29.1%) and silt (37.7%) distributed in the
higher terrains, while the rests are silt clay loam (13.3%), sandy clay loam (10.2%)
and clay loam (9.5%) mainly in the river valleys, and other soil types covering very
small areas scattered around the catchment as shown in Figure V-3. The watershed
has undergone rapid urbanization and extensive cultivation since the 1950s. Urban
areas cover about 20.5% of the watershed with Luxembourg-city in the downstream
and Esch-Alzette city in the upstream part. Cultivated lands occupy about 22.1% of
the total area distributed beside the river valleys with main crop types of maize and
wheat. Forest (28.9%) and grass (24.4%) are predominant in the river valleys and the
high terrain, intermixed with urban areas and cultivated lands. There are also some
former mining areas located in the high terrain of the upstream watershed covering
about 2.5% of the total area, where surface runoff is seldom generated. The watershed
is well drained with a dense stream network, open water occupies about 1.6% of the
total area. Table V-1 gives a general description of the area, average slope and main
soil types for each land use class.
97
Chapter V
Table V-1: Description of the area, slope and main soil types for each land use class
Land use
Area
(km²)
Cropland
94.0
23.1
5.77
Silt, loamy sand
Grassland
97.3
23.9
4.73
Silt, clay loam, sandy clay loam
Woodland
115.6
28.4
10.10
Silt, loamy sand, silt clay loam
Mining area
10.2
2.5
11.50
Loamy sand
Urban
83.4
20.5
5.93
Silt, silt clay loam
6.5
1.6
1.31
Clay loam, silt clay loam
407.0
100.0
7.01
Silt, loamy sand, silt clay loam
Water surface
Total
Relative
area (%)
Average
slope (%)
Main soil types
The climate in the region has a northern temperate humid oceanic regime without
extremes. The mean annual temperature is around 10°C, with average temperature of
0.7°C in January and 17.3°C in July (Pfister et al., 2002). Rainfall has a relatively
uniform distribution throughout the year. High runoff occurs in winter and low runoff
in summer due to the higher evapotranspiration. Winter storms are strongly influenced
by the westerly atmospheric fluxes that bring humid air masses from the Atlantic
Ocean (Pfister et al., 2000), and floods happen frequently because of the saturated
soils and low evapotranspiration. The average annual precipitation in the region varies
between 800 mm to 1,000 mm. Precipitation generally exceeds potential
evapotranspiration except for four months in the growing season.
2.3.
Data collection
Three digital base maps are prerequisite in the model to define the watershed drainage
work and derive spatial model parameters, i.e. DEM, soil type and land use. A DEM
with 50×50 m grid size for the watershed was constructed using 2-meter resolution
elevation contours and the official river network. Information of soil types was
obtained from the digital 1:100,000 Soil Map of the European Communities, and
converted to 12 USDA soil texture classes based on textural properties. The land use
information was obtained from the digital land use map of Luxembourg and France
derived from remote sensed image with respect to the watershed condition in the year
1995. The original land use map was classified to fourteen classes for use in the
WetSpa model, and reclassified to five hydrological land use classes for simulation of
98
Assessing land use impacts on flood processes using a GIS modelling approach
storm runoff partitions from different land use areas, i.e., crops, grassland, forest,
urban areas, surface water, and mining areas, as shown in Figure V-4.
Crop
Grass
Forest
Mining
Urban
Water
Sand
Sand
Loamy
san
Loamy sand
Silt
Silt
Sandy
Sandy clay
clay
Silt
Silt clay
clay loa
Clay
Clay loam
coam
N
W
N
E
W
E
S
0
5
Figure V-3: Soil type map of the
Steinsel sub-basin
S
10
0
5
10 km
Figure V-4: Land use map of the Steinsel
sub-basin
A dense hydrological observation network has been set up in the Alzette river basin,
as shown in Figure V-2, where 4 stream gauges, namely Steinsel, Pfaffenthal,
Hesperange and Livange, are located in the study area and recording water levels at a
15-minute time step, and 10 rain gauges are located in and around the watershed
recording at an hourly or daily time step. Daily rainfall was disaggregated into hourly
rainfall series according to the nearest hourly reference rain gauges for being used in
the model. Potential evapotranspiration was estimated using the Penman-Monteith
formula (Monteith & Unsworth, 1990) with daily meteorological data measured at the
Luxembourg airport, and extended to each rainfall Thiessen polygon based on the
proportions of different land use type over the polygon (Drogue et al., 2002). A total
of 52 months of hourly rainfall, discharge and potential evapotranspiration data from
December 1996 to March 2001 are available for model application. The average flow
at Steinsel during the monitoring period is 5.6 m³/s, with flows ranging from 0.07 to
40.7 m³/s, and the measured maximum hourly rainfall intensity is 23 mm/h, which
occurred on July 2, 2000.
99
Chapter V
2.4.
Model calibration and verification
The application procedures for WetSpa include database development, watershed
segmentation, model calibration and validation. Model parameters are identified
firstly using GIS tools and lookup tables, which relate default model parameters to the
base maps, or the combination of these base maps. Starting from a 50 by 50 m pixel
resolution digital elevation map of the Steinsel catchment, hydrological features
including surface slope, flow direction, flow accumulation, flow length, stream
network and drainage area are delineated. Maps of porosity, field capacity, wilting
point, residual moisture content, saturated hydraulic conductivity and pore size
distribution index are obtained from the soil type map. Maps of root depth, Manning’s
roughness coefficient and interception storage capacity are derived from the land use
map. Maps of potential runoff coefficient and depression storage capacity are
obtained from the slope, soil type and land use combinations. Impervious areas have
significant influence on runoff production in a watershed, because they can generate
direct runoff even during small storms. Due to the model grid size, cells may not be
100% impervious in urban areas. In practice, the percentage of impervious area in a
grid cell is computed based on land use classes, with 30% for residential area, 70%
for commercial and industrial area and 100% for streams, lakes and bare exposed rock.
Default potential runoff coefficients for these areas are calculated by adding the
impervious percentage with a grass runoff coefficient multiplied by the remaining
percentage. This leads to runoff coefficients of 40 to 100% in urban areas, while other
areas have much smaller values, down to 5% for forests in valleys with practically
zero slopes.
The model was calibrated against hourly streamflow measurements at the four
stations for the time period of December 1996 to December 1999, while the period of
January 2000 to March 2001 was used for model validation. The calibration was not
carried out for all model parameters, but for some global parameters only, including
the evapotranspiration correction factor in controlling water balance, the interflow
scaling factor in controlling the amount of interflow, and the groundwater flow
recession coefficient governing the routing process of baseflow. Other parameters,
such as potential runoff coefficient, soil properties, overland flow roughness
coefficient, interception and depression storage capacity, etc., were set to values
100
Assessing land use impacts on flood processes using a GIS modelling approach
obtained from the literature, which have shown to yield reliable results in previous
model applications on different basin (De Smedt et al. 2000; Liu et al. 2003).
Calibration of the evapotranspiration factor can be performed independently by
comparing the calculated and observed flow volume for a long time series. The
interflow scaling factor is calibrated by matching the computed discharge with the
observed discharge for the recession part of the flood hydrograph. Groundwater flow
recession coefficient can be obtained by the analysis of recession curves at discharge
gauging stations. Refinement of this coefficient is necessary to get a better fit for the
low flows.
Inputs to the model are spatially distributed precipitation interpolated by the method
of Thiessen polygon and potential evapotranspiration, while the outputs are
hydrographs at each gauging site and the simulated spatial distribution of hydrological
characteristics. Model performance for calibration and validation were evaluated
through qualitative and quantitative measures, involving both graphical comparisons
and statistical analysis for hourly, daily and monthly values. In addition to the above
comparisons, the water balance components for individual land uses were reviewed
by displaying model results including precipitation, surface runoff, interflow,
baseflow, actual evapotranspiration and groundwater recharge. Although observed
values were not available for each of the water balance components listed above, the
average annual values must be consistent with expected values for the region,
depending upon the individual land use categories. This is a separate consistency
check with data independent of the modelling to ensure that land use categories and
overall water balance reflect local conditions. Finally, the spatial outputs of simulated
hydrological variables were used to assess the reasonability of hydrological processes
distribution, where the processes of surface runoff, soil moisture, interflow, and
percolation etc. would be spatially distributed depending upon the cell’s physical
characteristics.
Figure V-5 gives a graphical comparison between simulated and observed hourly
streamflows at Steinsel for a sequence of floods that occurred in February and March
1997. The total rainfall was 184.3 mm with measured runoff of 107.8 mm and
simulated runoff of 111.0 mm. A small flood happened in early February, followed by
three large floods successively. The simulated hydrographs of surface runoff,
101
Chapter V
interflow and baseflow correspond to respectively 38%, 27% and 35% of the
predicted total flood volume, which were obtained by summation of flow responses
from all contributing cells. The figure shows a very good agreement between the
predicted and measured hydrograph, in which the rising and high water limb are
dominated by surface runoff, while interflow is a few hours delayed and mainly
contributes to recession flow. Groundwater discharge forms the baseflow of the total
hydrograph. Due to the high antecedent soil moisture content and groundwater storage,
the amount of interflow and groundwater flow is abundant in these flood events, being
62% in total of the whole flood volume.
Figure V-5: Observed Vs calculated flow at Steinsel for the floods in Feb. 1997
0
30
30
Precipitation
Measured
Calculated
20
60
10
90
0
1/00
120
2/00
3/00
4/00
5/00
6/00
7/00
8/00
9/00
10/00
11/00
12/00
Figure V-6: Observed and calculated daily flow at Steinsel for the year 2000
102
Daily precipitation (mm/d)
Daily discharge (m³/s)
40
Assessing land use impacts on flood processes using a GIS modelling approach
Figure V-6 presents a graphical comparison of calculated and observed daily flows at
Steinsel for the validation year 2000. The year 2000 was a very high flow year in the
region with an annual precipitation of 1004 mm and an annual mean discharge of 6.61
m³/s at Steinsel, which is 1.4 times the average flow for the previous 3 years. Floods
happened both in winters due to the saturated soils and high groundwater storage, and
in summer due to intensive rainfall intensity. With the initial hydrological condition at
the end of the simulation period, the validation results for the year 2000 are in a good
agreement with the measured daily discharges. This indicates that a fairly high degree
of model precision is obtained, and the general hydrological trends are well captured
by the model.
2.5.
Model evaluation
For the assessment of the model performance and model efficiency for the simulation
period, 5 evaluation criteria were selected as listed in Table V-2. In all equations, Qs
and Qo are the simulated and observed streamflows at time step i, Qo is the mean
observed streamflow over the simulation period, and N is the number of time steps.
CR1 is the model bias, for which the value 0 represents a perfect simulation of the
flow volume. CR2 is a model determination coefficient representing the proportion of
the variance in the observed discharges that are explained by the simulated discharges
with the best value of 1. The Model efficiency is measured by the Nash-Sutcliffe
coefficient (Nash & Sutcliffe, 1970) expressed as CR3. A CR3 of 1 indicates a perfect
fit, while a negative CR3 means that the prediction is worse than simply using the
observed mean. CR4 is a logarithmic transformed Nash-Sutcliffe criterion, giving
emphasize for evaluating the quality of low-flow simulations (Smakhtin et al., 1998).
An arbitrarily small value may be introduced to the discharges in case of zero flows
for which the logarithm does not exist. Moreover, an adapted version of the NashSutcliffe criterion CR5 is proposed, which is in fact a combination between the
calibration criteria used by Guex (2001) for the hydrological study on the Alzette
river basin and the HEC-1 objective function (USACE, 1998). As seen in the formula,
more weight is given to high discharges, and therefore, the criterion CR5 can be used
for evaluating model efficiency for high flows.
103
Chapter V
Table V-2: Evaluation criteria for the assessment of model performance
Code Criteria
Description
N
N
CR1
∑ Qs ∑ Qo
CR2
∑ (Qs
i
i =1
i =1
N
i =1
i
− Qo
Model bias for evaluating the ability of
−1
i
reproducing water balance
) ∑ (Qo
N
2
i =1
N
2
CR3 1 − ∑ (Qs i − Qoi )
i =1
i
∑ (Qo
− Qo
N
i =1
i
N
2
CR4 1 − ∑ [ln (Qs i ) − ln (Qo i )]
i =1
)
Determination coefficient representing
2
− Qo
the simulation variance
)
Model efficiency for evaluating the
2
ability of reproducing streamflows
∑ [ln (Qo ) − ln (Qo )]
N
i =1
2
CR5 1 − ∑ (Qoi + Qo )(Qsi − Qoi )
N
i =1
Model efficiency for evaluating the
2
i
∑ (Qo
N
i =1
i
)(
ability of reproducing low flows
+ Qo Qoi − Qo
)
2
Model efficiency for evaluating the
ability of reproducing of high flows
The model performance was evaluated both qualitatively by visual comparison of the
simulated and observed hydrographs and quantitatively using the above statistical
indexes at Steinsel and other three stations inside the catchment. The model
performance is found to be satisfactory as illustrated in Table V-3, which shows the
subcatchment area, the percentage of main land use classes, and the results of the five
assessment criteria for both calibration and validation periods on hourly scale. Model
biases are within the range of -0.04 to 0.02, and the mean value is 0.81, 0.80 and 0.85
respectively for the three efficiency criteria, which indicate that the model has a high
confidence and can give a fair representation of both low-flow and high-flow
hydrographs for the study catchment.
Table V-3: Watershed characteristics and model performance
Station
Livange
Area Urban Crop Grass Forest
(km²) (%)
(%)
(%)
(%)
233
18.6
28.9
22.9
24.7
Hesperange 291
17.8
27.4
25.3
25.4
Pfaffenthal
350
19.2
25.4
26.8
25.2
Steinsel
407
20.5
23.2
24.3
29.0
104
Period
CR1
CR2
CR3
CR4
CR5
Calibration -0.02 0.76 0.78 0.83
0.82
Validation -0.04 0.79 0.75 0.78
0.80
Calibration -0.03 0.81 0.83 0.78
0.87
Validation -0.02 0.75 0.79 0.81
0.84
Calibration 0.02 0.80 0.81 0.82
0.92
Validation -0.03 0.82 0.80 0.76
0.87
Calibration 0.01 0.87 0.85 0.83
0.85
Validation -0.03 0.83 0.84 0.82
0.86
Assessing land use impacts on flood processes using a GIS modelling approach
3. Results and discussion
3.1.
Evaluating runoff partitions from different land use classes
Since the WetSpa model calculates runoff and flow path response in a spatial way for
each grid cell, it is capable of evaluating storm runoff partitions from different land
use areas. By convolution of the flow responses from the cells belonging to a certain
land use category, runoff partition to the flood hydrograph from this land use category
can be estimated. The total flow hydrograph at the watershed outlet is obtained by the
sum of runoff partitions from different land use areas in the watershed. For assessing
runoff partitions from different land use areas of the catchment, the calibrated WetSpa
model is run for the whole simulation period, and the flow components for different
land use classes are calculated at each time step. Figure V-7 gives a graphical
presentation for the same flood event used in the model calibration but shows storm
runoff contributions from different land use classes. Clearly, surface runoffs from
urban areas, cropland and grassland form the high water peak of the hydrograph,
representing 39.1%, 11.6% and 9.0% respectively of the storm runoff (excluding
baseflow). Interflow from woodland, grassland and cropland yields 16.7%, 8.8% and
7.5% of the storm runoff. Other storm runoff components in the figure are mainly
surface runoff from water surfaces and forested areas, accounting to about 7.2% of the
storm runoff, while surface runoff and interflow from mining areas and interflow
from urban areas are negligible for this flood event.
Figure V-7: Storm runoff partitions at Steinsel for the flood events in Feb. 1997
105
Chapter V
Another simulated partitioning of hourly outflow at Steinsel for a flood event, that
occurred in April 1999, is given in Figure V-8, for which the runoff contribution from
urban, forested, pasture, agricultural, water surface and mining areas are identified
separately. The total rainfall is 49.7 mm with a measured runoff of 21.3 mm and a
calculated runoff of 19.9 mm. Runoff from urban areas, being 35.4% of the total flood
volume (including baseflow), dominates the high water flow in this flood event. A
part of rainfall infiltrates in urban areas in gardens and parks, and is used mainly for
evapotranspiration. Therefore, interflow and groundwater recharge in urban areas are
very small and contribute very little to the total runoff. Runoff from woodland
(16.4%), grassland (23.2%) and cropland (22.3%) are basic components of the flood
hydrograph, contributing to the flow in the period of peak flow and recession, as well
as baseflow. The interflow and baseflow contribution from forested areas is the
highest compared to other land use areas, because it is one of the most common land
types in the catchment, and moreover, most rainfall falling on woodland infiltrates
into the soil and contributes to interflow in areas with steep slopes or otherwise to
groundwater recharge. Note that a small flood occurred 2 days before the main flood,
for which runoff from urban areas was dominant, being 58% of the flood volume,
while other runoff contributions were relatively small compared to the main flood.
Other runoff contributions for this flood event are direct flows from water surfaces
(3.5%), and groundwater drainage from mining areas (1.3%). Surface runoff and
interflow from mining areas are negligible in the catchment.
Figure V-8: Storm runoff contributions at Steinsel for the flood events in Apr. 1999
106
Assessing land use impacts on flood processes using a GIS modelling approach
In order to analyze the controlling factors on runoff at the basin outlet from different
land use classes, 18 flood hydrographs with peak discharges higher than 20 m³/s
within the simulation period are selected, and the partitions as well as the flow
coefficient for the flood event and relative errors in flood volume and peak discharges
are calculated individually. Table V-4 contains the simulated runoff partitions for the
selected storm events occurring at Steinsel and the statistics of the simulation errors
for each flood event.
Precipitation
(mm)
Urban
contribution (%)
Cropland
contribution (%)
Grassland
contribution (%)
Woodland
contribution (%)
Other
contributions (%)
Observed flood
volume (mm)
Error in flood
volume (%)
Flow coefficient
(-)
Observed peak
discharge (m³/s)
Error in peak
discharge (%)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Flood period
(d/m-d/m y)
No.
Table V-4: Simulated runoff contributions from different land use classes
10/02-06/03 97
17/12-24/12 97
01/01-12/01 98
15/01-24/01 98
23/10-07/11 98
12/04-18/04 99
10/12-17/12 99
23/12-02/01 00
03/03-06/03 00
09/07-12/07 00
13/07-19/07 00
24/07-31/07 00
18/08-23/08 00
08/10-14/10 00
06/11-11/11 00
21/11-30/11 00
01/01-10/01 01
21/01-31/01 01
Average
156.0
43.2
56.7
35.0
174.7
48.4
79.4
67.0
19.4
25.3
41.6
63.3
43.4
42.0
37.5
49.4
70.3
63.3
62.0
34.1
32.0
22.6
22.2
29.3
39.9
35.1
22.9
23.8
42.0
38.3
35.2
53.7
35.7
26.9
22.7
24.0
22.7
31.3
20.9
22.0
21.7
23.1
22.8
23.7
24.1
22.3
23.0
24.1
22.9
23.7
22.4
23.5
22.6
22.6
22.5
23.4
22.8
23.8
22.1
25.1
25.2
22.1
18.7
22.1
24.2
25.5
22.7
19.3
22.4
11.8
22.1
24.3
24.8
23.9
24.6
22.5
16.1
19.0
26.2
25.1
20.8
12.7
13.5
25.8
23.1
6.0
14.3
13.7
5.9
14.0
21.6
25.4
25.1
24.8
18.5
5.1
4.9
4.5
4.4
4.9
5.1
5.1
4.8
4.6
5.1
5.2
4.9
6.3
4.6
4.6
4.4
4.6
4.5
4.9
82.2
25.6
43.5
28.7
73.7
19.2
30.4
47.4
15.4
9.8
12.3
19.3
8.3
17.6
19.6
29.0
38.3
39.7
31.1
1.6
-9.4
-10.0
-17.8
6.0
-10.6
1.0
-18.1
-13.2
-10.8
18.1
13.5
18.6
-9.3
-5.9
2.7
5.0
-1.5
-2.3
0.55
0.61
0.80
0.85
0.44
0.41
0.40
0.73
0.82
0.40
0.31
0.32
0.20
0.43
0.54
0.61
0.56
0.65
0.53
40.2
27.5
33.9
31.5
40.5
32.9
38.9
39.9
32.6
24.8
21.4
23.8
24.3
25.8
26.1
28.6
40.7
32.6
31.4
12.7
-7.9
-8.7
-12.4
15.7
-15.2
16.7
-6.0
-10.2
-14.8
16.4
16.6
-1.8
-5.1
-17.9
-7.5
14.1
-11.8
-2.0
The flow coefficient for a storm event defined in Table V-4 is the ratio of the outflow
water volume at the catchment outlet to the volume of water precipitated over the
catchment during this event. The simulated flow coefficients can be computed in a
similar manner by incorporating the simulated flow volume at the basin outlet and
107
Chapter V
should be close to those of the observed flow coefficient. As can be seen in the table,
both flow coefficient and runoff partitions from different land use areas vary from one
storm event to another, because they depend upon antecedent soil moisture,
groundwater storage and storm behaviour. The WetSpa model takes the soil moisture
content and rainfall intensity into account, and makes it possible to better explain
these variations.
Variations in runoff contribution and runoff partition are directly tied to soil moisture
and groundwater storage. Among the 18 storm events listed in the table, 13 occurred
during the winter season, and 5 events between April and November. Winter storms
are usually characterized by high flow coefficients, due to the high soil moisture
content and high groundwater storage, causing high baseflow, interflow and saturation
overland flow. Under such conditions, an amount of the river discharges is generated
from natural areas. This can be illustrated by the two flood events which occurred in
January 1998 and one flood in March 2000, in which flow coefficients were higher
than 0.80, and the runoff partitions from urban, agricultural, pasture and forested areas
were of the same magnitude. This indicates that groundwater drainage plays an
important role in the winter season, which is mostly produced by previous storms. For
instance, the simulated baseflow accounts to 30% of the total volume for the flood
event in March 2000, and 38% for the flood in January 1998. However, the urban
contribution increases greatly if we consider only the storm runoff excluding baseflow.
For instance, the simulated urban contribution increases from 22.6% of the total
runoff to 31.2% of the storm runoff for the first flood in January 1998, and from
22.2% to 36.5% for the second flood in the same month. On the contrary, summer
storms usually have low flow coefficients, due to the low soil moisture content and
low groundwater storage. Runoff from urban areas is dominant in all flood
hydrographs of this catchment, while other contributions are relatively small,
especially the runoff from forested areas. An extreme example is the storm event,
which occurred in August 2000, for which the total rainfall was 43.3 mm, causing a
peak discharge of 24.3 m³/s at Steinsel and a flood volume of 8.3 mm with a flow
coefficient of 20%. The calculated runoffs from urban, agricultural, pasture and
forested areas were 53.7%, 22.4%, 11.8% and 5.9% respectively. The soil was very
dry before the storm, and most rainfall infiltrated in the soil resulting in rather small
runoff contributions to the flood event.
108
Assessing land use impacts on flood processes using a GIS modelling approach
(a) Land-use classes contributions
60
Urban
Grassland
Others
40
(b) Urban relative contribution
2.5
Cropland
Woodland
2.0
1.5
1.0
20
0.5
0
0.0
1
5
9
13
17
0.0
0.2
Event
2.5
(c) Cropland relative contribution
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.6
0.8
1.0
(d) Grassland relative contribution
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Flow coefficient
2.5
0.4
Flow coefficient
0.4
0.6
0.8
1.0
Flow coefficient
(e) Woodland relative contribution
(f) Other relative contribitions
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
0.0
0.2
0.4
0.6
0.8
0.0
1.0
0.2
(g) Error on flood volume
20
0.4
0.6
0.8
1.0
Flow coefficient
Flow coefficient
(h) Error on peak discharge
20
10
10
0
0
-10
-10
-20
-20
0.0
0.2
0.4
0.6
0.8
1.0
Flow coefficient
0.0
0.2
0.4
0.6
0.8
1.0
Flow coefficient
Figure V-8: Plot of event to event variations of the different runoff contributions (a),
normalized relative runoff contribution from urban (b), cropland (c), grassland (d),
woodland (e), and other areas (f), and error in flood volume (g) and error in peak
discharge with respect to the flow coefficient
109
Chapter V
Storm characteristics, such as volume, duration, intensity and shape, have a big
influence on the flow coefficient and the runoff contributions from different land use
areas. Large storms with long duration and high intensity produce more runoff under
similar antecedent soil moisture conditions, but the flow coefficient may not response
positively due to the lower baseflow. For small rainfall events, most runoff is
generated from impermeable areas and open water surfaces, while runoff from natural
areas can be ignored. For the three storm events in July 2000 for example, the rainfall
volume for each storm event was 25.3 mm, 41.6 mm and 63.3 mm, resulting in urban
runoff of 42.0%, 38.3% and 35.2 respectively, while the contributions from other
natural land use classes increased with storm volume accordingly. In addition, runoff
varies also with time and storm shapes. The flow at the start of the flood stems
exclusively from direct runoff from urban areas and water surfaces because of the
quick response and short travel times. Other runoff contributions join the flow
afterwards, but the magnitude of which is strongly depending upon soil moisture
conditions. For instance, for the flood in April 1999, shown in Figure V-8, a
considerable rainfall occurred 2 days before the main storm, causing a small flood in
which urban runoff was dominant. However, this was no longer the case for the main
flood, because the first storm also increased the soil wetness, such that runoff from
agricultural, pasture and forested areas was strongly increased for the main flood.
A series of plots based on the resules in Table V-4 is presented in Figure V-8 showing
the event to event variations of the different runoff contributions, the evolution of
each contribution normalized by the percentage of its land-use class area, the error on
flood volume and the error on peak discharge with respect to the flow coefficient. As
can be seen V-8a, both flow coefficient and runoff partitioning from different landuse areas vary from one storm event to another, which demonstrates the effects of
antecedent soil moisture, storm characteristic and groundwater storage on the flood
behaviour of the catchment. Urban contribution to storm runoff decreases with the
flow coefficient with mean of 1.53 and standard deviation of 0.43 (Figure V-8b). The
relative contribution value is larger than one indicating its contribution being higher
than its percentage of land-use class area of the catchment. Cropland relative
contribution is almost constant for different storms with mean of 0.99 and standard
deviation of 0.04 (Figure V-8c), which indicates its contribution being more or less
110
Assessing land use impacts on flood processes using a GIS modelling approach
equal to the cropland percentage of the catchment. The relative contribution from
grassland increases slightly with the flow coefficient with mean of 0.94 and standard
deviation of 0.14 (Figure V-8d). The relative contribution from woodland areas
increases significantly with the flow coefficient with mean of 0.64 and standard
deviation of 0.24 (Figure V-8e). The relative contribution values from grass and forest
land-use class areas are less than one indicating their contributions being less than the
percentage of their land-use class areas. Other contributions (mining plus water
surface) decrease with the flow coefficient with mean of 1.19 and standard deviation
of 0.11 (Figure V-8f), which is mainly due to the change of runoff contribution from
water surface. The relative error on the flood volume strongly decreases with the flow
coefficient (Figure V-8g). This indicates that the Thiessen polygon method may not
give a precise estimate of the rainfall distribution for small and large storms, or may
because of the model deficiency itself. The relative error on the peak discharge is
presented in Figure V-8h with mean of -1.5 m3/s and standard deviation of 12.8 m3/s,
which indicates that the model gives a fairly good prediction of the flood peaks.
Figure V-10: Contributions of monthly flow at Steinsel from different land use classes
Figure V-10 shows the simulated contributions to the monthly flow at Steinsel from
different land use classes from December 1996 to March 2001. The runoff
contributions from urban (29.3%), agricultural (22.8%), pasture (22.2%), forested
(21.5%), mining (1.5%) and water surfaces (2.7%) are indicated separately. The
runoff contribution from urban areas is the highest, contributing mainly to direct flow.
111
Chapter V
Contributions from agricultural, pasture and forested areas are more or less equal,
contributing to surface runoff, interflow and baseflow, while the contribution from
mining areas is the smallest contributing only to baseflow.
3.2.
Assessing the impact of land use changes on flood
Changes in land use may have significant effects on infiltration rates, on the water
retention capacity of soils, on sub-surface transmissivity and thus on the runoff
production. It is evident that the Alzette watershed has undergone rapid urbanization
since 1950. In general, the flood potential of a catchment significantly increases by
urbanization. The introduction of impervious surfaces and good drainage systems
increases the volume of runoff and results in flood hydrographs which are faster to
peak, faster to recede, and of increased peak discharge (Crooks, 2000). As the WetSpa
model accounts for spatially distributed hydrological and geophysical characteristics
of the watershed, it is suitable for assessing the impact of land use changes on
hydrological behaviours in a complex terrain with reliable land use change scenarios.
A realistic set up of land use scenarios requires scenarios of future regional
development. Land use decision-making is strongly influenced by socio-economic
factors. As these particular future land use policies are complicated, three distinct
scenarios are considered in the Steinsel sub-basin of the Alzette (Figure V-11), where
urban areas are increased at the expense of crops and grassland for urbanization, all
forests are converted into crops or grassland for deforestation, and forests are
increased at the expense of crops and grassland for afforestation. The urbanisation
scenario was elaborated on the basis of information regarding the changes in land use
planned by the government. The afforestation scenario was meant to recreate in a
simple manner the conditions that might have prevailed some 200 years ago when the
Grand-Duchy of Luxembourg was largely covered by forests. The deforestation
scenario was more or less chosen to evaluate what the behaviour of the basin would
be without this important forest cover. Starting from the land use map with respect to
the 1995 watershed situation, the first scenario increases urban areas by 31.8%, and
decreases agricultural and grasslands by 11.7% and 15.4% respectively. The second
scenario reduces forested areas by almost 100%, and expands agricultural and
grasslands by 108% and 16% accordingly. The third scenario increases forested areas
112
Assessing land use impacts on flood processes using a GIS modelling approach
by 52.6% and decreases agricultural and grasslands by 48.8% and 16% with respect to
the present land use situation (Table V-5).
Table V-5: Land use change scenarios compared with the present situation
Scenarios
Present
Urbanization
Deforestation
Afforestation
Urban areas
20.5
27.0
20.5
20.5
Grass (%)
24.3
20.5
28.2
20.4
Grassland
Forest
Forest (%)
29.0
29.0
0.0
44.2
Others (%)
3.0
3.0
3.0
3.0
Afforestation
Deforestation
Urbanization
Crops
Crops (%)
23.2
20.5
48.3
11.9
Urban areas
Surface water
Mining
Figure V-11: Land use change scenarios for the Steinsel sub-basin
Based on these land use change scenarios, model parameters were recalculated and
the model was run to deliver the modified runoff and streamflows. Figure V-12(a)
shows the simulated surface runoff distribution for the storm of Feb. 24-26, 1997
under the present land use condition, corresponding to the fourth flood in Figure V-5.
The total storm rainfall was 63 mm with a calculated average surface runoff volume
of 12.8 mm. Due to the very high antecedent soil moisture content of this storm event,
almost all areas contribute to the storm runoff but with different volumes according to
their land use types. As can be seen from the map, high surface runoff was produced
on surface water and urban areas, while low surface runoff occurred in the areas with
forest cover and sandy soils. There was very little surface runoff generated from the
former mining areas because of its specific surface characteristics, and most water in
these areas recharged to the groundwater reservoir. Figure V-12(b) presents the
simulated surface runoff distribution for the same storm event after urbanization. The
113
Chapter V
calculated average surface runoff volume becomes 17.0 mm, being increased 32.8%
compared with the result under present land use condition.
(a)
(b)
Surface runoff (mm)
0- 5
5 - 10
10 - 20
20 - 30
30 - 40
> 40
N
W
E
S
0
5
10 km
Figure V-12: (a) Simulated surface runoff distribution under present land use
condition for the storm on Feb. 24-26, 1997, and (b) Simulated surface runoff
distribution after urbanization for the same storm event
Figure V-13 gives the simulated flood hydrographs for the present and three land use
scenarios at Steinsel for a flood event that occurred on December 12, 1999. The
results indicate that the urbanization scenario produces the highest peak flow,
followed by the deforestation and afforestation scenario. The rainfall originated from
slow moving westerly atmospheric fluxes with long duration and low intensity. The 2day rainfall was 65 mm, but the highest rainfall intensity was only 4.6 mm/h. The
simulated peak discharge for the present land use is 45.3 m3/s, for the urbanization
scenario 61.7 m3/s, the deforestation 50.6 m3/s and the afforestation 41.7 m3/s.
Accordingly, the urbanization scenario increases the peak discharge for this storm by
36%, the deforestation scenario increases the peak discharge by 12%, while the
afforestation scenario decreases the peak discharge by 8%. In addition to the
difference in the magnitude of the simulated peak discharges, differences in time to
peak of the modelled discharges are also observed. The peak discharge occurred
around 3 hours after the main rainfall for the present condition, after 2 hours for the
urbanization and deforestation scenarios, and 3 hours for afforestation scenario.
114
Assessing land use impacts on flood processes using a GIS modelling approach
80
40
5
20
3
10
15
Urbanisation
Deforestation
Afforestaion
Present
60
Qscenario (m /s)
Rainfall
Urbanisation
Deforestation
Present
Afforestation
70
P (mm/h)
3
Q (m /s)
60
0
50
40
20
25
0
30
11/12/99 12/12/99 13/12/99 14/12/99 15/12/99
Time (d/m/y)
30
20
20
30
40
50
60
70
3
Qpresent (m /s)
Figure V-13: Simulated hydrographs for
Figure V-14: Peak discharges for each
each scenario for a storm in Dec. 1999
scenario over the simulation period
Figure V-14 gives the present versus the scenario peak discharges selected from the
whole simulation period. It shows that afforestation has a mild positive effect in
reducing the peak discharge in comparison to the present situation. On the contrary,
urbanization and deforestation lead to an increase of the simulated peak discharges. In
addition to the effects of land use change on flood volume, runoff composition,
evapotranspiration and soil moisture were also evaluated quantitatively from the
model results. It was found that urbanization and deforestation result in increasing the
flood volume and the amount of surface runoff, but decreasing the amount of
interflow and baseflow, as well as soil moisture and the amount of evapotranspiration
from a long term simulation, while this is the contrary for afforestation. The
magnitudes of changes, however, differed from one storm to another depending upon
the antecedent soil moisture content. This can be explained by the fact that a change
in land cover will alter the leaf area index, the interception storage capacity, the soil
infiltration capacity and thus the evolution of soil moisture. High soil moisture leads
to more evapotranspiration, groundwater recharge and interflow, and vice versa.
Investigation of low flows indicates that the effect on baseflow is not pronounced in
summer, due to the fact that most soil water is used for evapotranspiration, and the
baseflow is very small for all the three scenarios. However, considerable differences
in baseflow are found in winter with the afforestation scenario producing the highest
baseflow, while the urbanization scenario producing the lowest baseflow.
115
Chapter V
4. Conclusions
Distributed models have proven to be useful in such kind of analyses because of their
ability to predict the effect of spatially changing variables, like land-use change. In
this chapter, a spatially distributed continuous simulation model, WetSpa, running on
hourly time scale and compatible with GIS and remote sensed information, is applied
to assess the land use impacts on flood processes in the Steinsel sub-basin, Alzette,
Grand-Duchy of Luxembourg. Model calibration and validation have shown the
model’s level of representativeness to be quite satisfactory. The outflow at the
catchment outlet has been especially well reproduced. 5 criteria are used to evaluate
the model performance. The model bias is between the range of -0.04 to -0.02 for the
four gauging stations over the simulation period, and model determination coefficient
from 0.75 to 0.87, Nash- Sutcliffe efficiency from 0.75 to 0.85, and the adapted NashSutcliffe efficiency for low flow and high flow from 0.76 to 0.83 and from 0.80 to
0.92 respectively.
It is demonstrated from the model simulation that the land use composition and soil
moisture condition play an important role in generating flood hydrographs at basin
outlet. Simulation results show that the important runoff processes, which contribute
to storm runoff, are mainly surface runoff from urban areas and partly from cropland,
grassland for big storms. Interflow from woodland, grassland and cropland forms the
recession of the flood hydrograph, but also contributes considerably to the peak
discharges for the floods in the wet season. Other areas with high infiltration and
storage capacity contribute very little to the storm runoff. Simulations show that the
flow coefficient and the runoff partitions from different land use classes vary from
one storm event to the other due to differences in soil moisture and storm behaviour.
The relative runoff contribution from urban areas decreases with the flow coefficient.
Cropland relative runoff contribution tends to be a constant being more or less equal
to the cropland area percentage of the catchment. The relative runoff contributions
from grassland and woodland increase with flow coefficient, and toward their
percentage of land-use class areas of the catchment for large storms. It can be
concluded that the runoff from urban areas is dominant for a flood event compared to
other land use classes in this catchment, and tends to increase for small floods and for
116
Assessing land use impacts on flood processes using a GIS modelling approach
flood events with low antecedent soil moisture. Other runoff contributions tend to
increase for large storms and for storm events with high antecedent soil moisture.
Interflow and baseflow from natural areas are important during the wet season but not
for small floods during the dry season.
For assessing the hydrological effects of land use changes on floods, three
hypothetical scenarios, namely urbanization, deforestation and afforestation scenario,
were considered based on the present land use configuration and possible land use
trends in the study area. It is found from the model simulation that the urbanization
scenario has a large impact on increasing peak discharge and flood volume, as well as
time to the peak. Likewise, deforestation has a fair negative impact, while
afforestation has a moderate positive impact on the floods. Investigation of the peak
flow shows that land-use changes can have remarkable effects on peak discharges in
comparison to the present land use condition. The urbanization and deforestation
scenarios increase the peak discharges by 26% and 9.1% in average, respectively,
while afforestation has a positive impact, decreasing the peak flow by -5.3% in
average. The model can also be used for the assessment of the land use change
impacts on other hydrological processes, such as interception, depression, soil
moisture, evapotranspiration, low flow, etc. in a river basin. However, since this
research focuses on the estimation of flow contributions from different land use
classes and the assessment of land use change effects on the floods processes, detailed
discussions of these effects are not given in this report.
References
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on the water balance - A case study for Belgium, J. Hydrol., 114, 327-348, 1990.
Crooks, S., Davies, H. & Goodsell, G., Rainfall runoff modelling and the impact of
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Potsdam, Germany, 2000.
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Chapter V
De Smedt, F., Liu, Y.B. & Gebremeskel, S., Hydrological modelling on a catchment
scale using GIS and remote sensed land use information, In: Risk Analysis II,
ed., Brebbia, C.A., 295-304, WTI press, Southampton, Boston, 2000.
Drogue, G., Leviandier, T., Pfister, L., El Idrissi, A., Iffly, J.F., Hoffmann, L., Guex,
F., Hingray, B. & Humbert, J., The applicability of a parsimonious model for
local and regional prediction of runoff, Hydrol. Sci. J., 47, 905-920, 2002.
Eagleson, P.S., Climate, Soil, and Vegetation, a simplified model of soil moisture
movement in liquid phase, Water Resour. Res., 14(5), 722-730, 1978.
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energy balance processes, Water Resour. Res., 30(11), 3061-3078, 1994.
Guex, F., Modélisation hydrologique dans le bassin versant de l’Alzette
(Luxembourg), Régionalisation des paramètres d’un modèle global. Travail
pratique de Diplôme, EPFL/CRP-GL, Luxembourg, 2001.
Karvonen, T., Koivusalo, H., Jauhiainen, M., Palko, J. & Weppling, K., A
hydrological model for predicting runoff from different land use areas. J.
Hydrol., 217, 253-265, 1999.
Kuczera, G., Raper, G.P., Brah, N.S. & Jayasuriya, M.D.A., Modelling yield changes
following strip thinning in a mountain ash catchment: An exercise in catchment
model validation, J. Hydrol., 150, 433-457, 1993.
Linsley, Ray K., Jr., Kohler, M.A. & Joseph Paulhus, L.H., Hydrology for Engineers,
237, McGraw-Hill, New York, 1982.
Liu, Y.B., Gebremeskel, S., De Smedt, F. & Pfister, L., Flood prediction with the
WetSpa model on catchment scale, In; Flood Defence ‘2002, eds., Wu et al, pp.
499-507, Science Press, New York Ltd., 2002.
Liu, Y.B., Gebremeskel, S., De Smedt, F., Hoffmann, L. & Pfister, L., A diffusive
transport approach for flow routing in GIS-based flood modelling, J. Hydrol.,
283, 91-106, 2003.
Lorup, J.P., Refsgaard, J.C. & Mazvimavi, D., Assessing the effect of land use change
on catchment runoff by combined use of statistical tests and hydrological
modelling: Case studies from Zimbabwe, J. Hydrol., 205,147-163, 1998.
Monteith, J.L. & Unsworth, M., Principles of Environmental Physics, 291, London,
Edward Arnold, 1990.
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Nandakumar, N. & Mein, R.G., Uncertainty In rainfall runoff model simulations and
the implications for predicting the hydrological effects of land use change, J.
Hydrol., 192, 211-232, 1997.
Nash, J.E. & Sutcliffe, J.V., River flow forecasting through conceptual model, J.
Hydrol., 10, 282–290, 1970.
Niehoff, D., Fritsch, U. & Bronstert, A., Land use impacts on storm-runoff generation:
Scenarios of land use change and simulation of hydrological response in a mesoscale catchment in SW-Germany, J. Hydrol., 267, 80-93, 2002.
Pfister, L. & Hoffmann, L., Experimental hydro-climatological atlas of the Alzette
river basin, Grand-Duchy of Luxembourg, Centre de Recherche Public, Gabriel
Lippmann, 2002.
Pfister, L., Humbert, J. & Hoffmann, L., Recent trends in rainfall-runoff
characteristics in the Alzette river basin, Luxembourg, Climate Change, 45(2),
323-337, 2000.
Smakhtin, V.Y., Sami, K. & Hughes, D.A., Evaluating the performance of a
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transfer between soil, plants and atmosphere (WetSpa), Phys. Chem. Earth, 21(3),
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119
Chapter VI
Assessing the effects of river restoration on the reduction of floods in
a river basin
Abstract
This chapter discusses the effects of river restoration on flood reduction in the
Steinsel sub-basin of the Alzette River basin, the Grand-Duchy of Luxembourg. The
basic approach of restoration is carried out firstly by classifying the streams into
different orders and by assessing the response of stream channels to the resistance or
obstruction of flows, and the river re-meandering in the headwater streams. Based on
this assessment, the roughness to the flow in the first and second order streams is
adjusted for the river restoration while the roughness of downstream higher order
channels is kept unchanged. An increase of 10% of channel sinuosity is proposed in
this study to account for possible future activities in river re-meandering. The
hydrological analysis is performed using the WetSpa distributed hydrological model
based on the spatial information of topography, soil type, and land use. Flow delay as
a result of increased channel roughness offered by obstruction of the flow from the
headwater channels results in a reduced peak discharge at the outlet of the basin. The
model simulation indicates that peak flow can be reduced by as much as 14% and
delay the time of concentration by as much as 2 hours after river restoration.
1.
Introduction
The Alzette River basin has encountered a series of serious floods since the early
1990’s. For instance, floods in 1993, 1995 and 1998, caused a lot of damage to
properties within municipal areas in the river basin. In addition to the positive trend
noticed in winter rainfall totals due to an increase in westerly atmospheric fluxes since
1970’s (Pfister et al., 2000), the change of land-use pattern in the Alzette River basin
is a major reason causing rapid runoff into channelized streams, which may increase
flood frequency and enhance downstream peaks in flood hydrographs. The proportion
of urban areas in the Alzette River basin had increased by 30% between 1954 and
Chapter VI
1979, and by 15% between 1979 and 1995. Major changes in the future land-use are
also anticipated.
The changes in land-use pattern within a watershed and especially adjacent to rivers
and streams have a great influence on the river hydrological processes. For instance,
cropland increases runoff due to the removal of native vegetation and soil compaction,
which decreases the soil infiltration capacity. Urbanization increases runoff even
more due to impervious areas, reduced vegetation cover and depression storage, and
by concentrating and accumulating runoff by sewer systems. Such impacts result in
increasing the volume of surface runoff, increasing the velocity and concentration
time of storm runoff, reducing infiltration into the soil and ultimately reducing
baseflow (Schueler, 1994). Urbanization can also change the balance of forces in the
stream towards channel incision. In addition to the aforementioned effects,
urbanization can damage the zone surrounding the channel that influences the
hydrology and ecology. Trees and vegetation along the bed of the riverbank play an
important role in the hydrodynamic behaviour and the ecological equilibrium of a
river. Therefore, urbanization reduces the amount of wood and vegetation that enter
into the river and can deprive the stream of stabilizing elements that help to dissipate
the flow energy (Booth, 1991).
The valleys of the upper Alzette River have been densely populated for centuries.
Modification of rivers and their riparian areas has been undertaken considerably.
Physical degradation has been particularly great since 1950’s as a result of artificial
drainage, and flood defence structures. Such changes also occurred in the headwater
areas of the river basin. Many stream reaches were straightened and channelized, and
the landscape formerly covered by forest is converted into farmland. As pointed out
by Nienhuis and Leuven (2001), such practices may lead to irreversible changes, not
only in riverine habitats caused by the disruption of the natural evolution of
backwaters, but also in the disappearance of aquatic-terrestrial transition zones.
Because of the change in the response to rainfall of a basin following urbanization,
peak flows become higher causing more flood damage compared to the predevelopment stage. Previous studies have shown the local negative effect of heavily
urbanized areas on peak runoff in small streams in the vicinity of the city of
Luxembourg (Pfister et al., 2002).
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Assessing the effects of river restoration on the reduction of floods in a river basin
Channelization is one of the common approaches to reduce floods caused by
urbanization of a basin. However, flood conveyance benefits of channelization are
often offset by ecological losses resulting in an increased stream velocity and reduced
habitat diversity. Channelization by creating smoother and faster flow also increases
the risk of flooding in downstream areas. Because of these negative effects, there is a
trend to restore streams to their pristine conditions to minimize similar flood
repercussions in the future. Riparian plants, which influence strongly the headwater
streams, play a key role to dam up the stream water and have major impacts on
lowland stream ecosystems. Increasing the capacity of high water retention in noncritical areas may reduce the extent of flooding in the downstream inhabited areas,
and improve the ecological stabilization of the watercourse with reinforcement of
natural metabolisms. Currently, stream restoration programs are seeking to improve
aquatic habitats and regulate stream flows by natural means. The goal of stream
restoration is to restore the stream to a more natural form to create environmentally
favourable conditions, which do not necessarily imply that the stream will be restored
to its pre-settlement condition (Morris, 1995). The effects will be reduction of damage
to property, risk of accident, making water flow rates favourable to the development
of aquatic life and avoiding damage due to destructive erosion.
The purpose of this study is to investigate the effect of a conceptual headwater
restoration on flooding in the Steinsel sub-basin of the Alzette River basin mainly
located in Luxembourg. The restoration is considered for first and second-order
streams, characterized by moderate steep slopes, flowing through forest and grassland
intermixed with agricultural and urban areas, and therefore potentially suitable for
river restoration. The simulation results illustrate the importance of headwater
restoration on the reduction of flood peak discharge for the downstream main
channels. The analysis is performed with the WetSpa model, which is a GIS-based
distributed runoff and flow routing model calculating hourly runoff occurring at any
point in a watershed and providing spatially distributed hydrological characteristics in
the river basin. The study is not intended to address the biological and ecological
value of river restoration, nor does it focus on the planning and design of future river
restoration activities.
123
Chapter VI
2.
Methodology
2.1.
Model description
The WetSpa model is used to assess the possible effects of river restoration on flood
reduction in a river basin. The model is a grid-based distributed hydrological model
for water and energy transfer between soil, plants, and atmosphere. The model was
originally developed by Wang et al. (1997) and adapted for flood prediction by De
Smedt et al. (2000) and Liu et al. (2003). The theory and formulas of the model have
been described in detail in chapter III and chapter IV, and will not be discussed
repeatedly in this chapter.
2.2.
Description of the study area
A case study is performed in the 407 km2 Steinsel sub-basin, Alzette, Grand Duchy of
Luxembourg, as shown in Figure V-1. Detailed descriptions about the topography,
soil type, land use, climate, geology, hydrology, gauging network, and data available
of the study area have been provided in chapter V, and will not be addressed
repeatedly in this chapter.
According to Pfister et al. (2002), the maximum stormflow coefficient, which is the
maximum slope of the double-mass curve of rainfall and stormflow, is stable for each
subcatchment of the Steinsel sub-basin from one winter to the next in recent years.
The maximum stormflow coefficient for the upper part of the basin (sandy soils,
deciduous shrub mixed with agricultural land) is 0.29, whereas the lower part has a
maximum stormflow coefficient of up to 0.64, due to the extensive sewage system of
Luxembourg City. The average stormflow coefficient is 0.37 for the entire Steinsel
sub-basin. The maximum stormflow coefficient is strongly related to the basin
characteristics as shape of drainage area, topography, soil type, land-use, etc.
2.3.
Stream classification
The classification of stream channels can be helpful in the interpretation and
assessment of the response of stream channels to the resistance or obstruction of flow.
124
Assessing the effects of river restoration on the reduction of floods in a river basin
Based on this assessment and interpretation a decision can be made on which section
of the basin to focus in order to restore streams. There are different methods of
classifying streams depending on the intended use. Morphologically described stream
types (Rosgen, 1994) are delineated by slope, channel materials, width/depth ratio,
sinuosity, and entrenchment ratio. This classification system has been widely used in
stream restoration and mitigation, because it allows for predicting the behaviour of the
system, extrapolating knowledge of one system to another, and provides a consistent
frame of reference for communication among those interested in these systems.
Usually streams are classified according to their number of tributaries and
confluences. Smaller tributaries are assigned the lowest order and main rivers are
assigned the highest order. One of the most popular methods for assigning stream
orders was proposed by Strahler (1957). The uppermost channels in a catchment with
no upstream tributaries are first order. The confluence of two first-ordered streams
gives a second-order stream, and so on, but the confluence of a channel with another
channel of lower order does not raise the order of the stream after the confluence. The
main purpose in classifying the streams of the Steinsel basin is to make a sound
judgement about the areas of the basin that can be restored to mitigate floods. Figure
VI-1 shows the different stream orders and their specific characteristics of the Steinsel
basin according to Strahler’s method of ordering that is extracted from a 50m by 50m
resolution DEM of the basin.
N
W
E
S
0
5
10 km
Stream length
Drained area
Average slope
4
60
3
40
2
20
1
0
0
Slope (%)
Drained area
1st order
2nd order
3rd order
4th order
5th order
Percentage (%)
(b) 80
(a)
1
2
3
4
5
Stream order
Figure VI-1: (a) Stream orders and their drained area, and (b) percentage of stream
length, percentage of drained area and average slope for different order streams
125
Chapter VI
The streams of the study area are ordered from first to fifth order corresponding to the
threshold value of 100 cells when delineating the stream network based on the flow
accumulation theme. This implies that the flow concentration is sufficient to initiate a
channel if the drainage area is greater than 0.25 km2. Figure VI-1a represents the area
of the sub-basin that is drained by different order streams. Among them, the first and
second order streams drain about 322 km2 area representing 79% of the total study
area (Figure VI-1b). In addition the length of the first and second order stream
constitutes 425 km and around 76% of the total length of the GIS extracted stream
network of the Steinsel sub-basin (Figure VI-1b). Headwater streams are
predominantly accumulators, processors, and transporters of materials from the
terrestrial system. Therefore, restoring these stream channels can have significant
implications in the reduction of downstream floods in the river basin. Overlapping of
the stream order and the land-use of the Steinsel sub-basin shows that the first and
second order streams are channels that usually pass through forest and grassland.
These stream channels have a moderate gradient with calculated average slopes of
0.013 and 0.016 for the first and second streams respectively (Figure VI-1b). In
addition, the characteristics of these streams are much more influenced by riparian
vegetation and geomorphology than the downstream higher order channels.
2.4.
Modelling approach
Environmentally acceptable river restoration prefers features such as non-uniform
cross-sectional profiles, vegetation, meanders, islands, riffles and pools, in order to
have diverse habitats (Hansen, 1996). In addition, allowing nature restoration by
wood and debris to fall in streams for regulating river flows is becoming an important
component of current stream and river restoration (Larson et al., 2001). However, one
of the difficult tasks is to predict the amount and distribution of flow obstacles in the
streams, which is not uniform throughout the whole stream network and depends on
the morphology of the river system and the dynamics of the flow. Generally, small
channels tend to contain abundant wood and debris that is distributed randomly, and
affected by the density and species composition of the riparian area. Due to variable
roughness and extra turbulence, estimation of flow behaviour after restoration is
rather difficult.
126
Assessing the effects of river restoration on the reduction of floods in a river basin
Because of the lack of prior detailed studies in the Alzette headwater streams about
the channel morphology and the distribution of woods and vegetation in the streams
and their movement during and after floods, a conceptual river restoration is proposed
based on some facts of the basin. In the study area, the small streams originate
upstream on the plateaus with channel riparian areas mainly characterised by forest
land-use, while much of the downstream area is characterised by urban settlement.
The first and second order streams have steeper slopes than that of higher order
streams (Figure VI-1b), which have a potential of eroding and entraining the riparian
vegetation. The mean bank-full width of these streams is generally less than 2 m, and
the mean bank-full depth smaller than 0.5 m, which are favourable conditions to
collect woody debris that can form obstacles and increase the resistance to the flow.
Moreover, first and second order streams flow through forest areas enabling woods
being entrained into the stream. Based on these facts, natural restoration of the first
and second order streams is proposed in order to mitigate floods in the downstream
main channels of the sub-basin. Riparian and stream strategies may include increasing
desired vegetation, decreasing invasive species, and increasing stream sinuosity.
Following factors before and after river restoration are therefore considered in the
modelling approach.
(1) Change of flow resistance: Change in stream flows is linked directly to the change
of flow resistance of the streams. Such resistance to flow reflects the rate of
energy dissipation and incorporates resistance offered by in-stream vegetation and
natural obstruction as wood and debris accumulation. The effect of vegetation and
natural obstructions in the stream channels is estimated in terms of the Manning
roughness coefficient. Literature indicates that the Manning roughness coefficient
can increase by as much as three times compared to without in-stream woods
vegetation (Shields & Gippel, 1995). Therefore, an increase of the Manning
roughness coefficient from the value of 0.04 to 0.1 m-1/3s is proposed for the first
and second stream orders, while the Manning coefficient of the higher order
streams remains unchanged.
(2) Stream re-meandering: Stream re-meandering is one of the major measures for
river rehabilitation and restoration. Re-meandering of a watercourse can remedy
127
Chapter VI
some of the consequences of former channelization and improve the interplay
between watercourses and their river valley. Moreover, it can have a positive
influence on water quality, not just in the watercourse itself, but also in other
aquatic areas. Typical examples were given by Hansen (1996), who described the
river restoration projects in Denmark involving re-meandering and increased
inundation of the floodplain during the recent two decades. More specifically, a
positive response was monitored in their study for an upper reach, which was remeandered from a 2.7 km straight and channelized channel into a new 3.2 km
meandering course. Considering the non-uniformity of the stream meandering for
the Alzette headwater streams, an increase of 10% of channel sinuosity is
proposed, which will increase 42.5 km in total length for the first and second
order streams.
(3) Change of stream slope: The longitudinal stream slope after restoration is reduced
due to the effect of stream re-meandering. 10% increase of channel sinuosity
results in a same ratio of decrease, i.e. 0.0012, of the average channel slope of the
first and second order streams. Changes in slope may also be associated with
changes in channel material and in-stream vegetation, which slow down the flow
velocity and induce more sediment deposit along the river channel. However, only
the slope change caused by stream re-meandering is considered in this study.
(4) Hydraulic radius: Hydraulic radius is a measure of the relative channel shape,
which is governed by the channel cross section and a particular flow level. It is
often approximated by flow depth for broad and shallow channels. Therefore, a
consistent way would be to model the dynamic interaction between water level
and channel flows from the characteristic profiles. This interaction cannot be
modelled unless detailed information is available about the hydraulic properties of
the entire channel network. As such information does not exist for the Steinsel
sub-basin, a diffusive wave approximation routing procedure was adopted in the
model. This method assumes time-independent flow velocities parameterized as a
function of the topographic gradient, which is commonly used in the GIS-based
flow routing schemes (Lee & Yen, 1997; Olivera & Maidment, 1999). The model
determines the hydraulic radius by a power law relationship with an exceedance
probability (Molnar & Ramirez, 1998), which relates hydraulic radius to the
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Assessing the effects of river restoration on the reduction of floods in a river basin
drained area and is seen as a representation of the average behaviour of the cell
and the channel geometry. Due to the increased flow resistance, more water would
be retained in the headwater streams during the rising stage of a flood event.
However, this extra flood volume may partly be compensated by the extended
river reaches after stream re-meandering. Accordingly, the estimation scheme for
hydraulic radius remains unchanged in this study.
3.
Results and discussion
3.1.
Model calibration and evaluation
The model was verified for the present situation before being applied for analysis of
the effects of river restoration to mitigate flooding of the study area. The procedures
of model parameterization and calibration results have been provided in chapter V.
Normally, the model improvement and calibration proceed in three phases, focusing
on different flow conditions. Initially, the volume of precipitation, evapotranspiration
and outflow is examined at each flow station, for which the correction factor of
potential evapotranspiration can be determined. Next, the interflow and groundwater
flow recession coefficients are adjusted by comparing the low flow and the recession
part of flood hydrographs. The third phase of model calibration focused on improving
the timing, magnitude and hydrograph shape of various flood pulses. In conjunction
with this, major parameters, including channel roughness coefficient and hydraulic
radius, are adjusted in order to achieve the best agreement with the measurements. A
value of 0.04 m-1/3s is obtained as a proper stream’s Manning roughness coefficient
for the present situation by model calibration, which is typical for clear streams
without vegetation, or any other major obstructions. The calibrated minimum
hydraulic radius for overland flow is 0.005 m, and maximum 1.2 m for channel flow
at the sub-basin outlet for a normal flood corresponding to a 2-year return period.
These values can be increased for extreme floods. Observed hourly time series of
streamflow are used to verify the model’s performance and to adjust model
parameters. Based on graphical and numerical evaluation of the results, model
parameters are adjusted, and the model is re-run until a good match between the
observed and simulated hydrographs is obtained.
129
Chapter VI
50
0
Observed
Simulated
30
10
20
15
10
20
0
23/10
Precipitation (mm/h)
5
3
Discharge (m /s)
40
25
25/10
27/10
29/10
31/10
2/11
4/11
6/11
8/11
10/11
12/11
14/11
Time (d/m)
Figure VI-2: Observed and simulated flow hydrographs for the flood events in Oct.
and Nov. 1998
45
3
Simulated (m /s)
40
1:1
35
30
25
20
15
15
20
25
30
35
40
45
3
Observed (m /s)
Figure VI-3: Observed versus simulated peak flows for the simulation period
Specifically, Figure VI-2 presents an observed and simulated hydrograph for a
compound flood at Steinsel, which is the largest flood during the simulation period
that occurred in October and November 1998. As can be seen from the figure, the
general evolution of the observed hydrograph is reproduced rather well. The total
rainfall was 193.2 mm with a measured runoff of 87.6 mm and a simulated runoff of
84.3 mm. A small flood occurred on October 24, followed by three large successive
floods with observed peak discharges of 33.3, 38.8 and 40.5 m3/s. The predicted peak
discharges are 34.3, 42.7 and 38.4 m3/s with relative errors of 3.0%, 10.0% and -5.2%
130
Assessing the effects of river restoration on the reduction of floods in a river basin
respectively. Figure VI-3 gives the observed versus simulated peak flows selected
from 60 independent storm events that occurred throughout the simulation period. The
high peak discharges are reproduced reasonably well, while the estimations are
slightly poorer for small floods. Some points are far from the 1:1 line, which might be
caused by small scale thunderstorms for which the spatial distribution of rainfall was
not well captured by the rainfall stations (Drogue et al., 2002).
Five evaluation criteria are applied for the assessment of the model performance for
both calibration and validation period at the four flow stations. They are model bias,
model determination coefficient, Nash-Sutcliffe efficiency, and adapted NashSutcliffe efficiency for evaluating high flow and low flow, as have been described in
chapter V. A good model performance, especially for the high flow, has been obtained
after model calibration, which indicates that the model is suitable to predict runoff and
flow responses for the study area.
3.2.
Model prediction
Once the model is verified for the present conditions, it can be applied for the
simulation of the effect of river restoration in first and second-order streams in the
study area. The modelling approach includes: (1) increasing the roughness coefficient
by 250% to account for the effect of in-stream vegetation and natural obstructions as
wood and debris accumulation after river restoration, (2) extending the channel length
for the first and second order streams by 10% as a consequence of increasing channel
sinuosity, and (3) reducing the average stream slope by 10% as a result of river remeandering. Since the detailed information of the hydraulic properties is not available
for the entire channel network, the changes in flow resistance, flow length and stream
slope are assumed to be uniformly distributed over the headwater streams. By
applying these changes, a new roughness coefficient grid and a new channel slope
grid of the first and second order streams are constructed, for which the Manning’s
coefficient is increased from 0.04 to 0.1 m-1/3s, and the slope is reduced by 0.0012 for
each channel cell. The new grids are then merged by the previous roughness
coefficient and slope map of the sub-basin. The new grids of average flow time and its
standard deviation are obtained using the weighted GIS FLOWLENGTH routine,
giving an extra weight of 1.1 for the first and second order streams to account for the
131
Chapter VI
increase of flow length for each channel cell, while the grid of flow direction and flow
accumulation is kept unchanged. In this way, the flow response function for each grid
cell after river restoration can be obtained.
The immediate effect of these changes in the first and second order streams is to
decrease the flow velocity in these channels. However, there is no change in velocity
once the flow enters in the main channel. The lower velocities in the first and second
order streams result in a prolonged travel time from the headwater areas to the subbasin outlet. Figure VI-4a gives the average flow travel time to the sub-basin outlet in
hours for the present condition, in which the flow time is less than 10 hours for the
main river and up to 35 hours for the most remote areas. Figure VI-4b shows the
increase in average flow travel time after river restoration, in which the travel time of
areas of the sub-basin that are drained by first and second order streams is delayed by
several hours, while the flow time of areas drained by high order streams remains
unchanged.
(a)
(b)
Time (h)
(h)
Time
00 - 51
2
51 - 10
2 - -315
10
3 - -420
15
4 - -525
20
>> 525
Time (h)
0-1
1-2
2-3
3-4
4-5
>5
N
N
W
NN
E
W
WW
S
EE
WW
S
S
NN
EE
S
S
E
S
0
5 5
10 km
10 km
0
5 5
10 km
10km
0
5
10km
0
5
10km
Figure VI-4: (a) Average flow travel time to the sub-basin outlet for the present
condition, and (b) Increases in flow travel time after river restoration
The changes of stream features after river restoration result not only in a time delay
from the headwater streams to the downstream main river, but also in a reduction of
peak flows at the outlet of the sub-basin. Figure VI-5 shows the impact of river
restoration on peak discharges for the compound flood event in October and
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Assessing the effects of river restoration on the reduction of floods in a river basin
November 1998, which was described in the model calibration. Under the proposed
conceptual mitigation plan, the peak discharges are reduced to 29.8, 38.2 and 35.1
m3/s, indicating a 13%, 10% and 9% reduction respectively in calculated peak
discharge after river restoration. The reduction in the discharge occurs in the rising
stage of the flood hydrograph and continues until reaching the peak value. During the
recession limb, the runoff becomes larger in the river restoration case compared to the
present situation. This shows that the flow is retarded and stored in the headwater
streams, and later released during the recession stage of the flood. Figure VI-5 also
indicates that the travel time of the peak discharges are shifted by 1, to 2 hours by the
water flow delaying effect.
3
Discharge (m /s)
Present condition
After restoration
Depletion
Accumulation
40
5
10
30
15
20
20
10
23/10
Precipitation (mm/h)
0
50
25
25/10
27/10
29/10
31/10
2/11
4/11
6 /11
8/11
Time (d/m)
Figure VI-5: Flood events showing the effect of natural river restoration
45
3
After restoration (m /s)
1:1
40
35
30
25
20
15
15
20
25
30
3
35
40
45
Present (m /s)
Figure VI-6: Present versus restored simulated peak discharges for the simulation
period indicating a 14% reduction in average after river restoration
133
Chapter VI
The effect of river restoration is also evident in Figure VI-6, which gives a general
overview of reduction in peak discharges. This figure shows the calculated peak flows
before and after river restoration for the 60 independent storm events that occurred
during the entire simulation period. This result shows that peak flows are reduced for
all storms by an average of about 14%. Hence, the reduction is substantial and can
contribute in a significant way to the mitigation of floods in the downstream rivers.
3.3.
Evaluation of a future flood scenario
Studies have shown that there has been a marked increase in the contribution of the
westerly component of atmospheric circulation to rainfall in the Alzette River basin
since the 1970s (Pfister et al., 2000). These changes in atmospheric circulation are
usually accompanied with an increase in rainfall intensity and duration, which result
in a significant increase in the winter maximum daily storm and river flow. Therefore,
the model approach can be used to investigate the consequences of future climate
change and the potential effect of river restoration for a given storm scenario under
present land-use conditions.
Future regional climate scenarios are firstly constructed by using the outputs from
HadCM3, which is the third generation coupled atmosphere-ocean general circulation
model developed by the U.K. Meteorological office, Hadley centre (Gordon et al.,
2000). The atmospheric component of HadCM3 has 19 levels with a horizontal
resolution of 2.5o latitude by 3.75o longitude, which produces a global grid of 96 by
73 cells that is equivalent of about 417 km by 278 km at the Equator. Future time
series of precipitation and temperature are synthesised, the latter to estimate the
potential evaporation, and together with precipitation to be used as input to the
WetSpa model. The downscaling of precipitation and temperature for the study area is
performed with the Statistical Downscaling Model (SDSM) (Wilby et al., 2002). First,
a daily statistical relationship is established between surface and upper-atmospheric
circulation variables with locally observed precipitation and temperature data for the
period from 1961 to 1990. Next, the SDSM model is calibrated using observed
precipitation and temperature data of the baseline period and the selected predictor
variables, namely, the geopotential height and relative humidity at 500 hPa, the
134
Assessing the effects of river restoration on the reduction of floods in a river basin
geopotential height and relative humidity at 850 hPa, the near surface specific
humidity, the westerly wind component at 10 m elevation, and the maximum
temperature at 2 m height (Gebremeskel, 2003). Hourly precipitation and temperature
series are simply extracted from the daily SDSM predictions by amplification of the
hourly baseline series.
A worst simulated storm scenario in February, 2050 is selected from the SDSM
predictions to study the potential effect of river restoration on flood shape at the subbasin outlet as shown in Figure VI-7. The total rainfall is 72.5 mm within 18 hours
with a maximum rainfall intensity of 11.3 mm/h, corresponding to a winter storm with
a frequency of 2% (Gebremeskel, 2003). A new grid of hydraulic radius is generated
by the model with an exceedance probability of 50-year return period, which results in
a maximum value of 2 m at the basin outlet, which is nearly the double of values
obtained for a normal flood with a 2-year return period. Thereafter, the grids of flow
velocity, average travel time and its standard deviation are created. By keeping other
parameter maps as used in model calibration and prediction, the outflow hydrograph
at Steinsel is estimated by the WetSpa model using the input data from the selected
scenario. The calculated peak discharge for this flood under the present condition is
70.1 m3/s. The estimated peak discharge after river restoration is 59.5 m3/s and the
peak time is delayed by 2 hours. The peak discharge at Steinsel is reduced by 10.6
m3/s indicating a 15% reduction after river restoration.
0
80
60
6
3
Discharge (m /s)
After restoration
12
40
18
20
Depletion
Accumulation
Precipitation (mm/h)
Present condition
Reduced peak
24
0
1
25
49
73
97
121
Time (h)
Figure VI-7: Simulated hydrograph under present condition and after river restoration
for a future storm scenario
135
Chapter VI
Considering the water volume for this scenario flood, about 1 million m3 of water is
retained during the first two days and released thereafter during the next four days.
This water volume is stored in the first and second order riverbeds, which may induce
a considerable increase of water depth in these watercourses. As a result, river
restoration may cause local flooding, which however will be less damaging and
dangerous than flooding of the downstream urban areas.
3.4.
Discussion
In this study, an increase of roughness coefficient by 150% is assumed for the first
and second order streams after river rehabilitation. This increase is associated to the
rehabilitation measures on the headwater streams and their riparian areas. Typical
Manning’s roughness coefficient values are with the range 0.08-0.12 m-1/3s for minor
streams with dense vegetation and irregular alignment and cross section (Chow, 1959).
Much higher values have been reported in some recent river rehabilitation studies in
Europe, e.g. Helmiö & Järvelä (1998) and Seara & Newsonb (2004). The Manning’s
coefficient value of 1.0 m-1/3s is therefore feasible reflecting the stream condition after
rehabilitation. However, Manning’s roughness coefficient are site-specific, depending
on the channel surface roughness, irregularity, shape variation, obstructions, type and
density of vegetation, degree of meandering, flow depth, seasonal changes in
vegetation, and so on. These factors are unique to each stream reach and change in
space and time. Using a unique roughness coefficient value and applying it to the
entire headwater streams in this study may misrepresent site conditions and add
uncertainty to the simulation results.
The flow routing in this study is modelled by a linear approximation of the diffusive
wave equation. This method assumes that flood waves propagate at a constant
velocity on a river reach. WetSpa model calculates flow velocity at each grid cell
using Manning’s equation as a function of roughness coefficient, slope and hydraulic
radius. The hydraulic radius is estimated as a power function of the upstream drainage
area of the cell and varies with flood frequencies. Parameters controlling the
distribution of hydraulic radius for different flood magnitudes are adjusted at each
gauging station using historical records during model calibration. Consequently, the
136
Assessing the effects of river restoration on the reduction of floods in a river basin
average travel time and its standard deviation to the basin outlet can be obtained,
which are location dependent and vary with floods frequencies. Since there is no
detailed channel geometric data available for this study, the effects of overbank flow
and flood plain storage are accounted for in the model by cautiously setting the
hydraulic radius parameters for extreme flood. The resulting values are compared
with the measurement at different stations and adjusted through model calibration.
However, such simplification may not represent precisely the real situations under
heavy flooding, and may reduce the value of model validation.
In addition to the rehabilitation measure of increasing natural storage capacities in
lowland areas downstream of the river segment, flood mitigation strategies in
upstream areas are also important (WWF, 2002). The main purposes of these
measures as described in this study are to reduce rapid runoff on upland and riparian
areas, to retain more floodwater in the upstream tributaries, and consequently to
mitigate the flood risk in the downstream areas. Compared with other flood control
measures, river rehabilitation, as means of increasing channel resistance in headwaters,
also provide a wide range of additional benefits in the form of reducing soil erosion,
increasing water quality, maintaining biodiversity and areas for recreation, and so on.
These strategies are therefore essential for the integrated river basin management. The
rehabilitation measures are, however, feasible for a long time period, which can be
realized by stopping deforestation, using buffer zoning and strips, planting of tree
species alongside the river channel, providing tree barriers and other engineering
measures, etc.
This study focuses on the possible river rehabilitation effects on the Steinsel sub-basin.
It covers an area of 34.7% of the Alzette River basin (1175 km2), and is only 0.22% of
the Rhine River basin (185000 km2). Simulation results of this study show that the
natural river rehabilitation in the headwater areas can produce a prolonged flow time,
and result in a remarkable reduction in the flood peaks in the downstream main
channels. Considering the vast headwater areas of the Rhine River basin, these
measures may significantly mitigate the flood risk on the main river channels. This is
especially important for the downstream delta, which strongly depends on the flood
defence strategies for the entire river basin and the time of peaks of all tributaries.
However, the impact of river rehabilitation of headwater areas can not be assessed by
137
Chapter VI
simply amplifying the results obtained from a small subcatchment. Collection of
detailed data and studies on the complex flow systems are required in this respect.
4.
Concluding remarks
In this chapter, the effects of river restoration on flood reduction in the Steinsel subbasin of the Alzette River basin Grand-Duchy of Luxembourg is presented. A
conceptual method is proposed to account for the effect of in-stream vegetation and
channel re-meandering after river restoration. The restoration is focused on the first
and second order streams ordered according to Strahler’s method. The
implementation is performed using the WetSpa model, applied in a GIS environment.
The simulation results indicate a significant decrease in peak discharge and a delay of
flood peak occurrence after river restoration. The reduction of peak discharge is as
much as 14% on average compared to the present situation, and the time delay of
flood peak can be as much as 2 hours. A reduction in the discharge occurs during the
rising limb of the flood hydrograph, while the discharge increases during the falling
limb of the hydrograph, which results in longer sustained flows than in the present
conditions. However, while large floods in the main stream channels are reduced or
avoided, a local flooding may occur in the headwater stream areas due to river
restoration. It can be concluded that river restoration in such a way as to increase flow
resistance, restore more natural conditions, and enable watercourse locally to flow
their meadows, has a positive influence on reducing the risk of flooding further
downstream, where the consequences can be more severe due to the size of river basin
and the magnitude of the discharge. This work focused on the beneficiary effects of
river restoration for flood reduction in the Steinsel sub-basin. However, it is clear that
river restoration can have additional beneficiary as well as adverse effects on the
ecology and morphology of river basins that are not covered in this study.
References:
Booth, D.B., Urbanization and the natural drainage system-impacts, solutions and
prognosis, Northwest Environ. J., 7, 93-118, 1999.
Chow, V.T., Open-Channel Hydraulics, New York, McGraw-Hill, 680 pp., 1959.
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De Smedt, F., Liu, Y.B. & Gebremeskel, S., Hydrologic modelling on a catchment
scale using GIS and remote sensed land-use information, In: Risk Analysis II,
ed., C. A. Brebbia, 295-304, WTI press, Southampton, Boston, 2000.
Drogue, G., Leviandier, T., Pfister, L., El Idrissi, A., Iffly, J.F., Hoffmann, L., Guex,
F., Hingray, B. & Humbert, J., The applicability of a parsimonious model for
local and regional prediction of runoff, Hydrol. Sci. J., 47, 905-920, 2002.
Gebremeskel, S., Modelling the effect of climate and land-use changes on
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Gordon, C., Cooper, C., Senior, C.A., Banks, H., Gregory, J.M., Johns, T.C., Mitchell,
J.F.B. & Wood, R.A., The simulation of SST, sea ice extents and ocean heat
transports in a version of the Hadley Centre coupled model without flux
adjustments, Clim. Dynamics 16, 147-168, 2000.
Hansen, H.O., River Restoration, Danish experience and examples, 99, National
Environmental Research Institute, Denmark, 1996.
Helmiö, T. & Järvelä, J., Assessing the hydraulic performance in river rehabilitation
projects - Myllypuro Brook case study, In: Kajander, J. (ed.), XX Nordic
Hydrological Conference, Helsinki, Finland, 357–364, 1998.
Larson, M.G., Booth, D.B. & Morley, S.A., Effectiveness of large woody debris in
stream rehabilitation projects in urban basins, Ecol. Eng., 18, 211–226, 2001.
Lee, K.T. & Yen, B.C., A geomorphology and kinematic-wavebased hydrograph
derivation, J. Hydraulic Eng., ASCE 123(1), 73–80, 1997.
Liu, Y.B., Gebremeskel, S., De Smedt, F., Hoffmann, L. & Pfister, L., A diffusive
transport approach for flow routing in GIS-based flood modelling, J. Hydrol.,
283, 91-106, 2003.
Molnar, P. & Ramirez, J., Energy dissipation theories and optimal channel
characteristics of river networks, Water Resour. Res., 34(7), 1809-1818, 1998.
Morris, S.E., Geomorphic aspects of stream-restoration, Phys. Geogr. 16(5), 444-459,
1995.
Nienhuis, P.H. & Leuven, R.S.E.W., River restoration and flood protection:
controversy and synergism, Hydrobiologia, 444, 85-99, 2001.
Olivera, F. & Maidment, D.R., Geographic information system (GIS)-based spatially
distributed model for runoff routing, Water Resour. Res. 35(4), 1155–1164,
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Chapter VI
Pfister, L., Humbert, J, Iffly, J.F. & Hoffmann, L., Use of regionalised stormflow
coefficients in view of hydro-climatological hazard mapping, Hydrol. Sci. J.,
47(3), 479-491, 2002.
Pfister, L., Humbert, J. & Hoffmann, L., Recent trends in rainfall-runoff
characteristics in the Alzette river basin, Luxembourg, Climate Change 45,
323-337, 2000.
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Seara, D.A. & Newsonb, M.D., The hydraulic impact and performance of a lowland
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140
Chapter VII
Flow simulation in a Carpathian catchment accounting for
topographic controls
Abstract
An application of the WetSpa model based on GIS and remote sensing is presented
for hydrological modelling of a Carpathian catchment on daily scale. This is the
Hornad River catchment upstream of the Ruzin reservoir in the eastern Slovak
Republic, which is characterised by mountainous terrain and altitudinal variation is an
important determinant of the local climate and soil characteristics in all the state. It is
required to develop further the WetSpa model to account for these terrain features,
which includes the snow accumulation and snowmelt processes in order to predict
spring flood. Particular attention is devoted to the analysis of the temporal and spatial
distribution of temperature, PET and precipitation within the catchment. The
derivation of distributed model’s parameters is based on an extensive database of
catchment characteristics available for the region, including a 100 m resolution DEM,
and digital maps of soil type and land use. An automated calibration scheme is
employed to the WetSpa model in this study serving as an optimization algorithm to
estimate the model parameters. The encouraging results in spite of the highly complex
catchment morphology underline the importance of the availability of spatially
distributed data to be used for model identification and parameterisation. However, as
expected, the model is strongly sensitive to the parameters describing the runoff
generation processes and the routing of water in surface, subsurface and groundwater
reservoirs. The study concludes about the evident need for enlarging data availability
or, alternatively, in developing a robust parameter calibration method, which rely on
data that are generally available.
1.
Introduction
In March 1999 and April 2000, major flood events occurred in Slovakia affecting
most regions of the Hornad River basin. These events were caused by incessant heavy
Chapter VII
rainfall, preceded by a considerable snowmelt over a large area of the region,
particularly in the Margecany catchment upstream of the Ruzin reservoir, due to
particularly mild weather conditions at the end of an extremely snow-rich winter.
Because of the complexity of the regulation of the lakes in relation to the downstream
flood conveyance capacity, it is of interest to understand the dynamics of the events
and investigating the long-term vulnerability of the basin to similar circumstances.
Furthermore, the basin is highly complex in terms of topography, geology,
climatology, and soil properties. Floods occur both in springs due to snowmelt, and in
summers due to heavy rainfall. Snow accumulation in winter and snowmelt in spring
and early summer represent a significant component of the hydrological cycle and
play an important role in generating floods.
Reliable estimates of meteorological inputs like precipitation, temperature and PET
are key elements to hydrological models, particularly when modelling a mountainous
catchment. The analyses of spatial variability of hydrological processes in general and
precipitation processes in particular have been of interest to water resources planners
and managers for quite some time (Tabios and Salas, 1985). Such analyses have
applications in such studies as determination of water budget at different spatial and
temporal scales, validation of different hydrological models and recently global
climate change impact studies (Nijssen et al., 2001; Arnell, 1999). A number of
techniques for the spatial interpolation of long-term mean precipitation for the whole
territory of Slovakia have been tested with acceptable results (Parajka, 1999). The
importance of spatial variability in temperature and PET to the hydrological
modelling has been addressed in many publications (Shevenell, 1999; Xu and Li,
2003). Distributed models have the advantage to estimate the evapotranspiration in a
spatial way in combination with the measured meteorological and land-use data
(Flerchinger et al., 1996). In this study, a simple linear regression method is used for
the spatial interpretation of precipitation, temperature and PET inputs based on
measured meteorological data. Further physically-based studies on the spatial
variability of meteorological variables are necessary once additional data are available.
The investigation of all of these aspects requires the availability of a tool that allows a
robust simulation of the hydrological processes. Therefore, the WetSpa model,
working on a daily basis, is applied to simulate both spring and summer floods for the
142
Flow simulation in a Carpathian catchment accounting for topographic controls
Margecany
catchment
accounting
for
topographic
controls
on
the
input
meteorological variables. Some developments of the original formulation of the
model are illustrated in order to account for peculiarities of the mountainous
environment. A preliminary set of results is illustrated, and the adequacy of the
WetSpa model to represent the response of mountainous catchments is also discussed.
2.
Methodology
2.1.
Description of the study area and data available
The Margecany catchment covers the upper Hornad River basin upstream of the
Ruzin reservoir in the eastern Slovak Republic (Figure VII-1), with elevation ranging
from 333 m a.s.l. near Margecany to 1556 m a.s.l. The Ruzin reservoir has several
other tributary streams, like the Hnilec River, entering the reservoir, which were not
evaluated in this study. The total watershed size of Ruzín Reservoir is 1929 km2,
where the Margecany catchment accounts for 1130 km2 (58.6%) of that area.
The basin has a northern temperate mountainous climate with four distinct seasons.
January is the coldest month and July is the warmest month of the year. The highest
amount of precipitation occurs in the period from May to August and the least is in
January and February. The mean annual precipitation ranges from about 640 mm in
the valley to more than 1000 mm in the vicinity of the water divide from the analysis
of the Slovak hydrometeorological institute, Bratislava, Slovakia. Based on the
statistical analysis of the 10-year (1991-2000) weather data observed at Spisske
Vlachy, located in the downstream reach of the Margecany catchment at an elevation
of 382 m a.s.l., the annual precipitation ranges from 453 mm to 745 mm with mean of
610 mm, in which about 10% of the total in annual precipitation is snowfall mainly
concentrated in December, January and February. The average annual temperature at
Spisske Vlachy is 7.2 °C with a monthly minimum temperature of –8.0 °C in
December and an average monthly maximum temperature of 19.9 °C in August. The
average annual PET measured at Spisske Vlachy is 518 mm with a monthly minimum
PET of zero mm in December and January, and an average monthly maximum PET of
96 mm in July and August. Figure VII-2 shows the average monthly distribution of
143
Chapter VII
temperature, precipitation and PET at Spisske Vlachy based on the 10-year measured
weather data.
Figure VII-1: Location of the Margecany catchment
Temperature
80
Precipitation
Potential evaporation
60
40
20
o
T ( c) and P, PET, (mm)
100
0
-20
1
2
3
4
5
6
7
8
9
10
11
12
Month
Figure VII-2: Monthly temperature, precipitation and PET at Spisske Vlachy
The daily precipitation, temperature and discharge data are obtained from SHMU, the
Slovak Hydrometeorological Institute, whereas the PET data are obtained from
VUVH, the Water Research Institute of Slovakia. The sets include daily precipitation
for 9 stations, temperature for two stations, PET at Spisske Vlachy, and discharge data
at Margecany from 1991 to 2000 (Table VII-1). Flow stations containing daily
discharge data at 8 locations are available within the catchment, but only the outlet
144
Flow simulation in a Carpathian catchment accounting for topographic controls
station, Margecany, is used for model calibration in this case study. The precipitation
in a given raster cell is obtained from the precipitation of the representative weather
station and is corrected for the altitude of that cell within its Thiessen polygon (Figure
VII-3) with the use of elevation data from the DEM. The same procedures are applied
for the temperature and PET for each raster cell.
Table VII-1: Information of weather stations in the Margecany catchment
Station
Number
Spisske Vlachy
Ganovce
Vikartovce
Hranovnica
Levoca
Rudnany
Spisske Podhradie
Krompachy
Mlynky
Margecany
Type
5
6
15
16
17
18
19
20
22
Elevation
(m)
382
691
752
613
577
546
427
366
1007
339
P, T, E
P, T
P
P
P
P
P
P
P
Q
X_coord
(m)
485522
450468
437883
449580
470566
477042
482033
490591
458204
498007
Y_coord
(m)
5421194
5431519
5427066
5426359
5430167
5413764
5427029
5418827
5416373
5417377
#
#
Vikartovce
#
Ganovce
$
Levoca
#
Spisske Podhradie
#
#
U
$
#
#
Hranovnica
$
$
Spisske
$ Vlachy
$
Mlynky
#
#
#
U
#
$U
#
$
Krompachy $
Rudnany
#
$
#
Evaporation station
Flow station
Precipitation station
Stream network
Thiessen polygon
Catchment boundary
$
#
Figure VII-3: Gauging sites and Thiessen polygons for the Margecany catchment
Land cover data were obtained from the third hierarchy CORINE geographic
information system coverage developed from the European PHARE Project. This land
cover information was reclassified into 14 categories and converted to a 100 m cell
size grid for use in the WetSpa model, and re-grouped into 5 classes for deriving
model parameters of potential runoff coefficient and depression storage capacity
(Figure VII-4). The soil information was provided by VUPU, the Soil Science and
Conservation Research Institute, Slovakia. A simple nearest neighbour interpolation
method was applied based on the point information. The map is further reclassified
145
Chapter VII
into 12 USDA soil texture classes based on their textural properties and converted to a
100 m cell size grid (Figure VII-5). The elevation data for the river basin was
obtained from SHMU, the Slovak Hydrometeorological Institute, digitized from an
elevation map. This elevation data was interpolated to construct a 100 m grid size
DEM, from which the drainage system and area were determined (Figure VII-6).
Landuse
Crop
Grass
Forest
Urban area
Open water
Figure VII-4: Land use map of the Margecany catchment
Figure VII-5: Soil textural map of the Margecany catchment
Figure VII-6: Topographical map of the Margecany catchment
146
Flow simulation in a Carpathian catchment accounting for topographic controls
2.2.
Modelling snowmelt
Physical processes within the snowpack and involved in snowmelt are very complex.
They involve mass and energy balances as well as heat and mass transport. Formation
of ice layers further complicates evolution of snowpack resulting in processes known
from soil physics like fingering or lateral flow (Parajka, 2001). Snowmelt is basically
an energy driven process. Incoming solar radiation, absorption and emission of long
wave radiation, turbulent transfers by sensible and latent heat fluxes, and energy
exchanges at snow-ground base are the main driving components.
The volume of water released by melting snow is a major state variable that
characterises the snowmelt processes. Numerous snowmelt models have been
developed to describe the evolution of this variable (Leavesley, 1989). Generally, they
can be divided into three groups: index models, energy based models and detailed
models using full solutions of the energy and mass flow equations. Energy based
models use more correct physical description of basic processes affecting snow
accumulation and melt. Detailed models based on energy and mass flow equations are
physically correct, but demand a lot of data that are not easily available.
The conceptual temperature index or degree-day method used in this study is a simple
method but has a strong physical foundation. The method replaces the full energy
balance with a term linked to air temperature. It is physically sound in the absence of
shortwave radiation when much of the energy supplied to the snowpack is
atmospheric long wave radiation. The equation can be expressed as:
M = Max[0, C snow (T − T0 ) + C rain P(T − T0 )]
(7.1)
where M [LT-1] is the daily snowmelt, T [°C] is the cell daily mean temperature, T0
[°C] is a threshold melt temperature, Csnow [L°C-1T-1] is a melt-rate factor, and Crain
[LL-1°C-1T-1] is a degree-day coefficient regarding to the heat contribution from
rainfall. The critical melt temperature, T0, is often intuitively set to 0ºC. The melt-rate
factor, Csnow, is an effective parameter and may vary with location and snow
147
Chapter VII
characteristics. However, this parameter is assumed as a constant in this study for
model simplicity.
Melt water reaching permeable surfaces can either infiltrate or flow overland
depending on soil structure, moisture and thermal status. Outside permafrost regions,
overland flow of melt water is rare in rural areas, especially in forests where the soil
cover is thick and permeable (Espeby, 1990). On the other hand, melt water from
snow overlying a saturated, frozen and compacted urban soil can flow overland,
particularly towards the end of the melt period (Bengtsson & Westerström, 1992). In
hydrological modelling, the infiltration of melt water into soil is usually modelled by
a coefficient and the ratio of water stored in the soil to the maximum storage (Mocko
& Sud, 2001; DHI, 1994). The HBV model, as another example, treats soil with a
bucket approach, for which rain and melt water infiltrate freely until the soil layer is
saturated (Lindström, 1997). In this study, the same scheme as for surface runoff from
rainfall is used to calculate the snowmelt runoff and its infiltration:
⎛θ
V = c r (M + P )⎜⎜
⎝θs
⎞
⎟⎟
⎠
α
(7.2)
where V [LT-1] is the surface runoff resulting from snowmelt and rainfall, cr is a
potential runoff coefficient depending on slope, soil type and land use, P [LT-1] is the
rainfall intensity, θ [L3L-3] is the soil moisture content, and θs [L3L-3] is the soil
porosity. The difference between snowmelt, rainfall and surface runoff (M + P - V) is
the snowmelt infiltration, which contributes further to the lateral subsurface flow,
evapotranspiration and percolation to the groundwater storage. The snowmelt surface
runoff, together with lateral subsurface flow and the groundwater flow at the
subcatchment out is routed along its flow path to the basin outlet using the diffusive
water approximation method as describe in chapter III.
2.3.
Topographic adjustment for the input variables
Reliable estimates of meteorological data such as temperature, precipitation and PET
are key elements to the hydrological modelling. The traditional approach is to use
148
Flow simulation in a Carpathian catchment accounting for topographic controls
observed values from nearby stations, which are usually located in the river valleys
and can not be representative for the high terrain areas. Since the study area is located
in a temperate, mountainous region, vertical variation of theses elements are of major
importance in hydrological modelling, such as snow accumulation and snowmelt,
runoff, evapotranspiration, soil moisture content, etc.
2.3.1. Adjustment for temperature
Air temperature is strongly related to altitude. In average the temperature decreases
with about 0.65-1.0 ºC/100m vertically in the free atmosphere. Close to the surface,
this vertical temperature gradient is different due to local and regional characteristics,
influenced by the local terrain, distance from sea, etc. 28 temperature stations with 10
years daily average temperature data (1991-2000) in and surrounding the Hornad
River basin are selected to study the vertical temperature gradient. Figure VII-7 shows
the lapse rates for the three mean monthly temperatures, as well as the yearly
temperature lapse rate.
14
February
Marc h
April
o
Temperature ( C)
10
Year
y = -0.0049x + 9.9263
R2 = 0.8561
y = -0.0064x + 11.045
R2 = 0.9058
6
2
y = -0.0055x + 4.7451
R2 = 0.8704
-2
y = -0.0032x - 0.2008
R2 = 0.7497
-6
0
500
1000
1500
2000
Elevation (m)
Figure VII-7: Lapse rates for mean monthly and yearly temperature
Table VII-2 gives a summary of monthly temperature characteristic values and the
regression relationships between monthly temperature and elevation, which shows a
very close correlation between mean monthly temperature and elevation with average
correlation coefficient of 0.83. The vertical temperature gradient varies considerably
with season with low slope in winter and steep slope in summer. The yearly
149
Chapter VII
regression slope is -0.50% (0.5oC/100 m) with correlation coefficient of 0.86, which
conforms to the normal lapse rate of the region. The air temperature from October to
March is important in controlling the snow accumulation in this catchment, whereas
the temperature in March and April is critical in controlling the snowmelt.
Table VII-2: Regression analysis between monthly temperature and elevation
Month
Mean (oC)
Max. (oC)
Min. (oC)
Slope (%)
Intercept (oC)
R2
Jan.
-2.50
2.45
-7.47
-0.21
-1.72
0.63
Feb.
-1.39
4.17
-8.39
-0.32
-0.20
0.75
Mar.
2.71
9.75
-5.91
-0.55
4.75
0.87
Apr.
8.72
14.48
-1.54
-0.64
11.05
0.91
May
13.73
19.51
4.33
-0.61
15.97
0.89
Jun.
17.26
20.84
10.54
-0.62
19.50
0.90
Jul.
18.66
24.16
10.88
-0.61
20.91
0.88
Aug.
18.38
24.82
9.12
-0.56
20.44
0.79
Sep.
13.21
19.00
4.00
-0.52
15.11
0.82
Oct.
8.22
13.75
-1.60
-0.44
9.84
0.82
Nov.
2.83
9.77
-7.05
-0.42
4.35
0.89
Dec.
-2.13
3.10
-8.02
-0.28
-1.11
0.77
Year
8.10
9.20
7.29
-0.50
9.93
0.86
2.3.2. Adjustment for precipitation
The increase of precipitation with altitude is well known, chiefly because landforms
obstruct the movement of air and cause it to rise.
The effects of altitude on
precipitation are very complex, including (1) forced ascent, (2) blocking or retardation
of storms, (3) lifting by landforms, (4) local convection, and (5) condensation
processes. Besides, the local variability of precipitation in a mountainous catchment
may be poorly cast with a function of topographic height along and it strongly
depends on other physiographical factors (slope, aspect, broad-scale topographic
environment), especially for a small-scale storm or precipitation within a short time
period. However, due to the lack of dense observation, linear precipitation-height
regression analysis over a larger region can be used to compensate for the local
variation of precipitation as a function of altitude. In this study, 44 precipitation
stations in and surrounding the Hornad River basin with elevation ranging from 105
to 1240 m and available daily precipitation data over the period of 1991 to 2000 were
150
Flow simulation in a Carpathian catchment accounting for topographic controls
selected to study the precipitation-height correlation. As illustrated in Figure VII-9
(hollow points), the annual precipitation is poorly correlated with its altitude.
Precipitation (mm/year)
590 - 630
630 - 660
660 - 700
700 - 740
740 - 780
780 - 820
820 - 870
880 - 930
930 - 1020
1020 - 1220
River network
N
W
E
S
0
10
20 km
Figure VII-8: Distribution of yearly precipitation over the Hornad River basin
1250
Precipitation (mm/year)
Obtained from the distribution map
Observed
1000
750
y = 0.3921x + 484.79
R2 = 0.9838
500
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Ele vation (m)
Figure VII-9: Vertical gradient of yearly precipitation with elevation
A spatial distribution of yearly precipitation with grid size of 1000×1000 m over the
Hornad River basin is given in Figure VII-8 provided by SHMU, in which the mean
annual precipitation was created based on the climatological and geophysical
information, taking account for the effects of altitude, slope and aspect. It gives a
highly satisfactory qualitative representation of the gross features over the river basin,
showing a continuous wet zone in the south-western mountain chain, high mean
151
Chapter VII
values along the mountain ridges, and low values in the broad river valleys. By
ordering the elevation for each cell and calculating the mean precipitation for each
100 m interval, the mean annual precipitation was found to have a close correlation
with elevation as shown in Figure VII-9 (solid points) with a slope of 0.39
mm/year/100m and a correlation coefficient of 0.98.
2.3.3. Adjustment for PET
To study the topographic effect on PET, 8 weather stations were selected in and
surrounding the Hornad River basin with elevation ranging from 239 to 904 m and
observation period from 10 to 40 years (Table VII-3). A linear regression analysis was
performed between average monthly measured PET and its altitude. All months show
a decrease in PET values with increasing elevation. Although these data are not
available over the entire range of elevations in the region, the data are sufficient to
demonstrate that PET decreases with increasing elevation, except the 5 winter months
in which the regression slope is close to zero, the intercept is more or less equal to the
monthly mean PET, and no correlations are found due to the low temperature (Table
VII-4). 4 typical regression lines between monthly PET and its elevation are shown
in Figure VII-10. However, the latitude, slope and aspect may cause a remarkable
variation in the angle at which solar radiation intersects a hill slope, and therefore
have considerable effects on the PET distribution. These adjustments on PET are not
performed in this study due to data limit.
Table VII-3: PET stations used for regression analysis
Station ID
Station name
11938
11934
11945
11963
11949
11955
11968
Telgart
Poprad
Svedlar
Jakubovany
Spisske Vlachy
Presov - vojsko
Kosice - letisko
152
Period
(year)
1961-2000
1961-2000
1961-2000
1963-2000
1965-2000
1991-2000
1961-2000
Altitude
(m)
904
695
475
398
382
295
239
X coordinate
(m)
440382.01
444753.06
477080.25
509890.95
485521.91
521340.24
516238.02
Y coordinate
(m)
5410897.25
5435331.20
5406705.20
5439402.77
5421193.81
5430299.31
5391001.42
Flow simulation in a Carpathian catchment accounting for topographic controls
Table VII-4: Regression analysis between PET and elevation
Month
Mean
(mm/d)
0.03
0.17
0.87
1.90
2.74
3.19
3.35
2.87
1.85
0.88
0.23
0.02
1.52
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
Year
Max.
(mm/d)
0.07
0.30
1.19
2.29
3.22
3.68
3.92
3.43
2.21
0.98
0.36
0.06
1.82
Min.
(mm/d)
0.00
0.03
0.48
1.55
2.34
2.70
2.87
2.49
1.61
0.78
0.08
0.00
1.27
Slope
(%)
0.00
0.00
-0.09
-0.09
-0.11
-0.13
-0.13
-0.11
-0.06
0.00
0.00
0.00
-0.06
R2
Intercept
(mm/d)
0.04
0.22
1.30
2.35
3.27
3.83
3.98
3.40
2.14
0.90
0.22
0.04
1.82
0.05
0.08
0.89
0.79
0.76
0.77
0.78
0.59
0.50
0.03
0.05
0.13
0.71
4.5
March
May
July
September
y = -0.0013x + 3.9764
PET(mm/d)
2
R = 0.7804
3.0
y = -0.0011x + 3.273
2
R = 0.7633
y = -0.0006x + 2.1444
1.5
2
R = 0.4972
y = -0.0009x + 1.3041
2
R = 0.8912
0.0
200
400
600
800
1000
1200
Elevation (m)
Figure VII-10: Vertical gradient of monthly PET with elevation
2.3.4. Topographic correction
Using GIS ArcView, knowing the coordinates of each weather station, the Thiessen
polygons for precipitation, temperature and PET can be created. Next, the daily mean
precipitation, temperature and PET are computed for each grid cell within its Thiessen
polygon by applying the regression expressions. The data used in the calculation are
measured daily series at the reference station, elevations of the grid cell and the
reference station, and the regression slope. For instance, the reference precipitation
153
Chapter VII
series can be adjusted for each grid cell or subcatchment in which the precipitation is
assumed to vary linearly with the elevation (Dingman et al., 1988):
Pi = Pref + Pref (H i − H ref )β
(7.3)
where Pi [LT-1] is the precipitation at cell i, Pref [LT-1] is the precipitation at the
reference precipitation station, Hi and Href are the height at cell i and at the reference
station, and β is the precipitation regression slope. Likewise, the temperature and PET
at each cell can be estimated based on the data series at reference station, lapse rate
and the elevation difference. These topographical adjusted spatially distributed
precipitation, temperature, and PET form the input to the WetSpa model. Using mean
monthly temperature, yearly precipitation and monthly PET to describe their spatial
distributions in a daily scale is under the assumption of linear relationship between
elevation and climate features. However it is not sufficient to describe conditions
strongly controlled by local terrain and climate features. Nevertheless, these
adjustments provide an estimate of temperature, precipitation and PET that account
for topographic effects obtained on a grid, and hence the model can account for the
spatial variations of these input datasets more properly than using a unique value
within each Thiessen polygon.
3.
Model Simulation
3.1.
Parameter identification
Once the required data are collected and processed for use in the WetSpa model,
identification of spatial model parameters is undertaken. Terrain features at each grid
cell including elevation, flow direction, flow accumulation, stream network, stream
link, stream order, slope, and hydraulic radius are firstly extracted from the 100×100
DEM. The grid of stream network is delineated by applying a threshold value to
subset cells with an accumulated flow, for which cells that have more than 10 cells
flowing into them corresponding to a drainage area of 0.1 km2 are assigned as stream
network. The threshold value for determining subcatchments is set to 100, on which
585 subcatchments are divided with average subcatchment area of 1.93 km2. When
154
Flow simulation in a Carpathian catchment accounting for topographic controls
creating the grid of surface slope, a minimum slope threshold of 0.01% is given in
order to keep water moving on those cells without extremely low velocity. The grid of
hydraulic radius is generated with an exceeding frequency of 0.5 (2-year return
period), for which the network constant ap and the geometry scaling exponent bp are
set to 0.05 and 0.48 resulting in average hydraulic radius of 0.005m for the upland
cells and up to 1.5 m at the outlet of the watershed.
Next, the grids of soil hydraulic conductivity, porosity, field capacity, residual
moisture, pore size distribution index, and plant wilting point are reclassified based on
the soil texture grid by means of its attribute lookup table. Similarly, the grids of root
depth, interception storage capacity, and Manning’s n are reclassified from the land
use grid. Specifically, the Manning’s n for stream channels is linearly interpolated
based on the stream order grid with 0.055 m-1/3s for the lowest order and 0.025 m-1/3s
for the highest order. The grids of potential runoff coefficient and depression storage
capacity are obtained by means of attribute table combining the grids of slope, soil
and land use, for which the percentage of impervious area in an urban cell is set to
30%. As can be seen in Figure VII-11, the non-afforested and steeper grid generates a
very high runoff coefficient, whereas the afforested and gentle grid generates less
surface runoff. The calculated average potential runoff coefficient is 0.43 for the
entire catchment.
Runoff Coefficient
0.071 - 0.174
0.174 - 0.278
0.278 - 0.381
0.381 - 0.484
0.484 - 0.587
0.587 - 0.69
0.69 - 0.794
0.794 - 0.897
0.897 - 1
Figure VII-11: Potential runoff coefficient for the Margecany catchment
The grids of Thiessen polygons for precipitation, temperature and PET are created
based on the geographical coordinates of each measuring station and the catchment
boundary using the Thiessen polygon extension of the ArcView Spatial Analyst.
155
Chapter VII
Finally, the grids of flow velocity, travel time to the basin outlet and to the main river,
as well as their standard deviation are generated, on which the IUH from each grid
cell to the basin outlet and the main river is calculated. Figure VII-12 shows the
estimated average flow time from each grid cell to the basin outlet. Flow time for the
main rivers is generally less than 20 hours, whereas the flow time for the most remote
area is around 2 days. The mean travel time for the entire catchment is 24 hours.
Flow time (h)
0-3
3-6
6-9
9 - 12
12 - 15
15 - 18
18 - 21
21 - 24
24 - 27
27 - 30
30 - 35
35 - 40
40 - 45
45 - 50
Figure VII-12: Mean travel time to the basin outlet for the Margecany catchment
3.2.
Automated calibration
Distributed models are generally parameterized by deriving estimates of parameters
from the topography and physical properties of the soils and land use of the basin. The
reliability of model predictions depends on how well the model structure is defined
and how well the model is parameterized. However, estimation of model parameters
is difficult due to the large uncertainties involved in determining the parameter values,
which can not be directly measured in the field. Therefore model calibration is
necessary to improve the model performance. Because of the large number of model
parameters and the complexity in simulating the hydrological response of a catchment,
automated calibration techniques are becoming popular methods to account for spatial
parameter variability, while reducing the model calibration effort.
An automated calibration procedure is applied to the WetSpa model by incorporating
a model-independent parameter estimator PEST (Doherty, 1994; Doherty & Johnston,
2003). The automated calibration approach is applied in this study to focusing only on
156
Flow simulation in a Carpathian catchment accounting for topographic controls
the global parameters of the WetSpa model with observed flow hydrographs at
selected stations as the calibration targets, including interflow scaling factor, baseflow
recession constant, evapotranspiration correction factor, initial soil moisture, initial
groundwater storage and maximum groundwater storage, three snowmelt parameters,
and two surface runoff parameters. The spatial model parameters calculated with GIS
tools are not calibrated in this study and remain as they are. Automated calibration of
these spatially distributed parameters with PEST is recommended for the following
research, for which more organization and computation efforts are needed.
To accomplish the automated calibration process, three input files must be prepared at
first, including an input template file, an output instruction file and a PEST control
file. The template file is one for each model input file on which parameters are
identified, and is needed only for those input files which contain parameters requiring
optimization. The instruction file is one for each model output file containing the
directions which PEST must follow in order to read or write that file. The PEST
control file supplies PEST with the names of all template and instruction files together
with the model input/output files to which they pertain. It also provides PEST with the
model name, parameter initial estimates, measurements to which model outcomes
must be matched, prior parameter information, and a number of PEST variables which
control the implementation of the optimization method. The above three input files
must be prepared before the model is run, and can be constructed using any text editor.
Table VII-5: Parameters and their ranges in the PEST control file
Parameter
Description
Ci
Interflow scaling factor (-)
-1
Initial
Minimum
Maximum
1.5
1.0
5
Cg
Baseflow recession constant (d )
0.01
0.001
0.1
K_ss
Initial soil moisture Vs field capacity (-)
1.0
0.8
1.2
K_ep
PET correction factor (-)
1.0
0.8
1.2
G0
Initial groundwater storage (mm)
10
5.0
150
G_max
Maximum groundwater storage (mm)
20
10
250
0.0
-0.5
1.0
2.0
0.0
5.0
T0
K_snow
o
Threshold melt temperature ( C)
o
-1 -1
Melt-rate factor (mm C d )
o
-1 -1
K_rain
Rainfall melt-rate factor ( C d )
0.0
0.0
0.02
K_run
Surface runoff exponent (-)
3.0
1.0
6.0
P_max
Maximum rainfall intensity (mm)
40
10
100
157
Chapter VII
Table VII-5 lists the parameters, their initial estimates and possible range during
automated model calibration. The best set of parameters is selected from within
reasonable ranges by adjusting values until the discrepancies between observed and
simulated hydrographs is reduced to a minimum in the weighted least squares sense.
This scheme serves as an optimization algorithm to estimate the model parameters. A
further manual calibration approach is implemented to avoid the ill-posed problems,
which is commonly associated with direct inverse procedures.
3.3.
Modelling results
10 years (1991-2000) measured daily precipitation, temperature, PET, and discharge
data as described in section 2.1 are used for both automated and manual model
calibration. The calibration processes are performed mainly for the global model
parameters, whereas the spatial model parameters are kept as they are. The initial
global model parameters are specifically chosen according to the basin characteristics
as discussed in chapter IV. The automated calibration procedures are firstly performed
to initially estimate global model parameters. Next, a manual calibration approach is
implemented for avoiding ill-posed problems and parameter optimization.
The simulation results are compared to the observed hydrograph at Margecany both
graphically and statistically. As for the first step, the parameters of base temperature
and degree-day coefficients are adjusted independently in order to get a proper fit of
snowmelt flood that occurred normally in late February and early March. The initial
groundwater flow recession coefficient is estimated by analyzing the baseflow, which
is separated from the observed hydrograph at Margecany. Adjustment of this
parameter is necessary in accordance with the fitting of baseflow and the total flow
volume. The interflow scaling factor is adjusted for the peak and recession part of the
flood hydrograph, which is sensitive for both high and low flow evaluation. The
additional two parameters controlling the amount of surface runoff, i.e. the surface
runoff exponent for a near zero rainfall intensity and the rainfall intensity
corresponding to a surface runoff exponent of 1, are adjusted mainly for small storms,
in which the actual runoff coefficients are small due to the low rainfall intensity. The
initial soil moisture and active groundwater storage are adjusted by comparison of the
hydrographs and water balance for the initial phase. The maximum active
158
Flow simulation in a Carpathian catchment accounting for topographic controls
groundwater storage controls the amount of vapour transpirated from the groundwater,
and therefore can be adjusted by comparison of the flow volume and low flow during
dry period. Figure VII-13 gives a graphical comparison between observed and
calculated daily flow at Margecany for the year 1997. The input global model
parameters after automated and manual calibration, the calculated water balance, and
the model evaluation results are listed in Table VII-6.
0
Precipitation
80
20
Observed
Calculated
60
40
40
60
20
80
0
Precipitation (m m/d)
Discharge (m 3/s)
100
100
1/1
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10 1/11 1/12
Date (d/m)
Figure VII-13: Observed and calculated daily flow at Margecany in 1997
Table VII-6: List of input parameter values, water balance, and evaluation results
1) Global model parameters
Ci
Cg
K_ss
K_ep
G0
G_max
T0
K_snow K_rain K_run P_max
2.0
0.0085 0.95
1.10
30.0
40.0
0.0
2.20
E
0.00
3.0
60.0
2) Calculated water balance
P
I
DS
F
Sum (mm) 7108
551
26.5
% of P
Mean
1.95
Perc
Rs
Ri
Rg
R
DG
6067 4947 2036
446
346
1310
2102
-2.25
7.75 0.37
85.3
69.6
28.6
6.3
4.9
18.4
29.6
-0.03
0.16 287
1.66
1.35
0.56
0.12
0.10
0.36
0.58
37.7
3) Model evaluation
C1
C2
0.05
0.919
C3
C4
C5
0.738
0.703
0.825
Figure VII-13 shows that both the spring and summer flood hydrographs are well
reproduced by the model. The simulation of snowmelt flood is important in this study
as it not only contributes to the results of model evaluation, but also provides reliable
soil moisture estimation at the end of snow melting period, which affects following
159
Chapter VII
rainfall runoff processes. The calibrated base temperature and degree-day coefficient
are 0oC and 2.2 mm/day/ oC, whereas the heat contribution from rainfall to the
snowmelt is not important for this case study. The calibrated groundwater flow
recession coefficient at Margecany is 0.0085 day-1, which coincides with the
calculated value (0.01 day-1), and gives a good estimation for the whole simulation
period. The peak discharges, concentration time, and flow volumes are especially well
predicted for the three summer floods in 1997, and similar simulation results are
obtained for other hydrological years. The model performance is satisfactory from the
statistical evaluation results, in which the flow volume is 5.0% over estimated, model
determination coefficient is 0.919, the Nash-Sutcliffe efficiency is 0.738 for the time
evolution of stream flows, and the modified Nash-Sutcliffe efficiency is 0.703 and
0.825 respectively for low and high flows. These indicate that the model is able to
consider the precipitation, antecedent moisture and runoff-generating processes in a
spatially realistic manner based on topography, land use and soil type, resulting in a
fairly high accuracy for both high and low flows, and the general hydrological trends
being well captured by the model.
The estimated annual precipitation after topographic correction is 710.8 mm/year over
the 10 years simulation period, which coincides with the result obtained from Figure
VII-8 for the Margecany catchment (704.8 mm/year). The estimated annual
precipitation without considering the topographic correction is only 662.1 mm/year,
which is much lower than the expected value, and may not reflect properly the spatial
precipitation distribution over the catchment. From the results of model simulation,
as shown in Table VII-6, 7.75% of the precipitation is intercepted by the plant canopy,
85.3% infiltrate to the soil, 69.6% evapotranspirates to the atmosphere, 28.6%
recharges to the groundwater reservoir, and 29.6% becomes runoff, of which direct
flow, interflow, and groundwater flow possesses 21.3%, 16.5%, and 62.2%
respectively. These values are reasonable in view of the catchment hydrological
characteristics. Figure VII-14 presents the simulated variation of precipitation,
temperature, evapotranspiration, and relative soil saturation for the Margecany
catchment during the year 1997. The precipitation series is decreased by 20 mm/d in
the figure in order to give a clear view from other three time series. Obviously, large
storms are concentrated in July and early August of the year. Mean temperature is
below freezing in December, January and February, and fluctuates around zero in
160
Flow simulation in a Carpathian catchment accounting for topographic controls
March, April, October and November. Accordingly, high evapotranspiration occurs
from May to August, and the value is zero during winter season. The simulated
average soil saturation varies accordingly, in which it remains stable during winter
season as there is no water movement into or out of the root zone, increases
temporarily in spring due to the infiltration taking place during snowmelt, and
decreases dramatically afterwards due to the high evapotranspiration. High soil
moisture is present in July and August as a result of intensive rainfall, while low
moisture is present in June and September duo to the intensive evapotranspiration and
the insufficient rainfall to recharge the soil moisture.
15
Relative saturation (%)
60
40
10
Evapotranspiration (mm/d)
20
5
0
o
Temperature ( C)
0
-5
Evapotranspiration
P, T, relative saturation
80
Precipitation-20 (mm/d)
-20
-10
1/1
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11 1/12
Date (d/m)
Figure VII-14: Variation of precipitation, temperature, evapotranspiration, and
relative soil saturation for the Margecany catchment in 1997
A spatial distribution of simulated surface runoff for the storm event occurred in early
August, 1997, is presented in Figure VII-15. One can see that the rainfall distribution
is highly variable over space and time. The average rainfall over the catchment is 70
mm with measured maximum storm volume over the 5 days of 101 mm at Spisske
Vlachy located in the downstream part, and the minimum storm volume of 50.2 mm
at Ganovce located near the north-western boundary of the catchment. The calculated
average surface runoff for this storm event over the catchment is 8.8 mm with surface
runoff coefficient of 0.126. Apparently, high runoff occurs in the areas with high
rainfall intensity, steep slope, clay soil and afforested land uses, while low runoff
occurs in the areas with low rainfall intensity, gentle slope, sandy soil and forest land
uses. The model can also produce other spatial output maps, such as soil moisture
161
Chapter VII
content, interflow, groundwater recharge, actual evapotranspiration, etc., in different
time scales, which are not presented here.
#
1/8/1997
- 5/8/1997
Surface runoff (mm)
0-5
5 - 10
Ch
10 - 15
15 - 20
20 - 30
30 - 40
> 40
#
50.2
Ganovce
#
Levoca
#
66
51.4
Vikartovce Hranovnica
#
#
55
#
Spisske#Vlachy
101 Krompachy
#
63.6
Mlynky
#
62.3
Rudnany
#
#
#
81.1
Spisske Podhradie
#
#
96.6
Mean = 8.8 mm
#
Figure VII-15: Distribution of surface runoff for the storm event 1/8-5/8, 1997
4. Discussion and conclusion
1) Spatial and temporal variability of input time series
The spatial and temporal variability of rainfall, temperature, PET, and snow
accumulation in the western mountains of the Hornad River basin is an important but
poorly documented phenomenon. It governs the hydrological processes such as runoff
generation, soil moisture condition, etc., and is one of the major uncertainties to the
modelling results. A linear topographical correction is applied in the WetSpa model to
compensate the elevation effects on the spatial distribution of input time series.
However, the regression is performed based on the monthly temperature, PET, and
yearly precipitation data, which is not sufficient to account for the nonlinearity of
daily variables. Moreover, local variability in input time series results from variations
in latitude, aspect, wind speed and direction, humidity, as well as sun radiation, is not
taken into account in this case study. In particular, the snow pack is assumed to be
accumulated from the solid precipitation without considering the wind-induced snow
drift. These local factors have considerable effects on the spatial distribution of input
time series and the modelling results as well when conducting water studies for a
large mountainous catchment. Further researches may be undertaken on this subject
once the relevant data are available.
162
Flow simulation in a Carpathian catchment accounting for topographic controls
In this case study, the WetSpa model is conducted using measured precipitation,
temperature and PET data on daily scale, which has shown success in the simulation
of flood hydrographs at Margecany. Due to the large time resolution of precipitation
time series, the effects introduced by the internal structure of rainfall are ignored. The
complex structure of rainfall has been found to exhibit a large degree of temporal
variability under natural conditions in the region (Kostka & Holko, 2002), which
substantially affects the processes of runoff production and the downward water
movement in the root zone. Studies have shown that accuracy of hydrological models
can be improved by using fine time step resolution of rainfall data in the
determination of infiltration excess runoff (Finnerty et. al., 1997). Therefore,
hyetographs with a fine time resolution are required to capture rainfall variability for
further research. The daily PET data observed at Spisske Vlachy is used as a reference
series in the model, on which the topographical corrections are conducted over the
catchment. As an alternative, an empirical sine curve as a function of date solely is
developed based on the 10 years daily observed PET data. This curve can be used as a
PET input for simulating future flood scenarios. The equations can be expressed as:
⎡
⎛ d − 90 ⎞⎤
EPd = − 0.12 + 1.31⎢1 + sin ⎜ 2π
⎟
365 ⎠⎥⎦
⎝
⎣
1.41
(7.4)
where EPd (mm/day) is the daily PET, d is the day of the year, starting from 1 for the
first of Jan. and ending with 365 for the 31st of Dec. Figure VII-16 gives a graphical
presentation between observed and simulated mean daily PET at Spisske Vlachy.
4.5
Observed mean
PET (mm/d)
Simulated
3.0
1.5
0.0
1
31
61
91
121
151
181
211
241
271
301
331
361
Date
Figure VII-16: Observed and simulated mean daily PET at Spisske Vlachy
163
Chapter VII
2) Operation of the model for real time forecasts
WetSpa has relatively modest requirements for input variables (temperature,
precipitation, and PET) and therefore it is possible to be used for real time forecasts
on hourly or daily basis. For short term forecasts, temperature and precipitation must
be forecasted or predetermined for the coming days and substituted into the model,
which are becoming increasingly available from meteorological services. For long
term forecasts, such as monthly or seasonal runoff volumes, the PET series is
becoming essential, which can be extracted from the mean PET curve or estimated
based on the predicted temperature series.
Differing from the conventional lumped model predictions, the distributed WetSpa
model can predict not only the flood hydrograph at the basin outlet, but also the
hydrographs at any selected stations inside the catchment, and the spatial distribution
of hydrological processes for a certain period as well. The advantage of this modelling
approach is to have the knowledge of how much, and where runoff will occur for a
real time prediction by combining terrestrial GIS/RS data with meteorological
information. In this respect, GIS techniques can be efficiently used to store, manage
and display the spatial distribution of real time variables, such as rainfall, snow cover,
runoff, soil moisture, as well as remotely sensed images, etc.
The model performance in the forecasting mode is naturally affected by the reduced
accuracy and reliability of temperature and precipitation forecasts. The propagation of
errors can be avoided by periodical updating. Therefore, further possibilities of
updating can be made available to users when more experience in real time situations
is accumulated, for instance, to adjust some parameters (e.g., the potential runoff
coefficient) in the progress of the forecast within hydrologically and physically
acceptable limits. In any case, false forecasts of temperature and precipitation should
be updated whenever a correction by new data is indicated.
References
Arnell, N.W., The effect of climate change on hydrological regimes in Europe: a
continental perspective, Glob. Environ. Change, 9, 5-23, 1999.
164
Flow simulation in a Carpathian catchment accounting for topographic controls
Bengtsson, L. & Westerström, G., Urban snowmelt and runoff in northern Sweden,
Hydrol. Sci. J., 37, 263-275, 1992.
Dingman, S.L., Barry, R.G. & Reynolds, R.C., Application of kriging to estimating
mean annual precipitation in a region of orographic influence, Water Resour.
Bull., 24, 329-339, 1988.
DHI, Danish Hydraulic Institute. MouseNAM Reference Manual 1.0, 1994.
Doherty, J. & Johnston, J.M., Methodologies for calibration and predictive analysis of
a watershed model, J. Am. Water Resour. Ass., 39(2), 251-265, 2003.
Doherty, J., PEST: a unique computer program for model-independent parameter
optimization, Watermark Computing, Washington, DC, 1994.
Espeby, B., Tracing the origin of natural waters in a glacial till slope during snowmelt,
J. Hydrol., 118, 107-127, 1990.
Finnerty, B., Smith, M., Seo, D.J., Koren, V. & Moglen, G., Space time scale
sensitivity of the Sacramento model to radar-gauge precipitation inputs, J.
Hydrol., 102, 69-92, 1997.
Flerchinger, G.N., Hanson, C.L. & Wight, J.R., Modelling evapotranspiration and
surface energy budgets across a catchment, Water Resour. Res., 32(8), 25392548, 1996.
Kostka, Z. & Holko, L., Analysis of rainfall-runoff events in the mountain catchment,
eds., Holko L., Miklánek P., Parajka J. & Kostka Z., ERB and NE FRIEND Proj.
5 Conf., Interdisciplinary approaches in small catchment hydrology: monitoring
and research, Slovak IHP UNESCO/IH SAS, 10-13, 2002.
Leavesley, G.H., Problems of snowmelt runoff modelling for a variety of
physiographic and climatic conditions, Hydrol. Sci. J., 34(6), 617-634, 1989.
Lindström, G., Johansson, B., Persson, M., Gardelin, M. & Bergström, S.,
Development and test of the distributed HBV-96 hydrological model, J. Hydrol.,
201, 272-288, 1997.
Mocko, D.M. & Sud, Y.C., Refinements to SSiB with an emphasis on snow physics:
Evaluation and validation using GSWP and Valdai data, Earth Interactions, 5, 131, 2001.
Nijssen, B., O’Donnell, G.M., Hamlet, A.F. & Lettenmaier, D.P., Hydrologic
sensitivity of global rivers to climate change, Climatic Change, 50, 143-175,
2001.
165
Chapter VII
Parajka, J., Mapping long-term mean annual precipitation in Slovakia using
geostatistical procedures. In: Problems in Fluid Mechanics and Hydrology,
Institute of Hydrodynamics, ASCR, Prague, 1999.
Parajka, J., Holko, L., Kostka, Z., Snowmelt modelling and GIS, GIS at Development
Magazine, 5(10), 23-27, 2001.
Shevenell, L., Regional potential evapotranspiration in arid climates based on
temperature, topography and calculated solar radiation, Hydrol. Process., 13,
577-596, 1999.
Tabios, G.Q. & Salas, J.D., A comparative analysis of techniques for spatial
interpolation of precipitation, Water Resour. Bull., 21(3), 365-380, 1985.
Xu, Z.X. & Li, J.Y., A distributed approach for estimating catchment
evapotranspiration: comparison of the combination equation and the
complementary relationship approaches, Hydrol. Process., 17, 1509-1523, 2003.
166
Chapter VIII
Integrating GIS and hydrological process modelling in medium and
large watersheds
Abstract
This chapter examines the effects of the DEM grid size on hydrological modelling by
comparing the resulting runoff and flow responses from different resolution DEMs
(50, 100, 200, 400, and 800 m) of the Alzette River basin, an 1176 km² medium-sized
watershed in the Grand-duchy of Luxembourg. Next, a comprehensive subwatershed
parameterization method is developed for modelling medium and large-scale
watersheds based on the distributed WetSpa model. A simplified approach is used in
order to take advantage of the existing spatial analysis function within ArcView GIS
and its Spatial Analyst and hydrological modelling extensions. The method of
diffusive wave approximation is applied in tracing water for both overland flow and
channel flow, while the water and energy budgets are maintained for each very small
subwatershed derived from the high resolution DEM. Hydrographs at each
subwatershed outlet are firstly calculated using the GIS derived subwatershed
response function and then routed to the basin outlet using the channel response
function. Model parameters and meteorological data input for each subwatershed are
obtained by integration of the values from all cells of that subwatershed, allowing for
the internal drainage structure within each subwatershed. Calibration and validation
are performed on hourly basis using observed rainfall and discharge data from Dec.
1996 to Dec. 2000. Good agreement between the predicted and measured hydrographs
has been achieved according to the graphical comparison and statistical assessment.
1.
Introduction
Watershed models have become useful tools in water resources planning and
management, allowing prediction of stream flow from measured meteorological data.
Evidently the spatial distribution of soil moisture and the production of runoff are
dependent on basin topography, soil and land use patterns, especially for medium and
Chapter VIII
large watersheds. Consequently, accounting for this spatial heterogeneity within
watershed, models has long been considered as a prerequisite for improving water and
energy flux predictions. Recent advances in computer hardware and software
including increased speed and storage, debugging tools, and GIS technology have
made possible the hydrological simulations of large catchments. The challenge then is
to develop a basin-scale model that is computationally efficient, capable of simulating
land management scenarios, allowing considerable spatial detail, requiring readily
available inputs, and giving reasonable results (Arnold et al., 1998).
Along with the rapid development of GIS technology and remote sensing techniques,
especially the concomitant availability of high resolution DEM and the advances in
integrating GIS with hydrological modelling, flood prediction with distributed models
tends to be more advantageous and competent. However, model simulation for long
time series on medium and large catchment scale with small grid size and short time
interval is tedious, costly, and time consuming. This is because the computation time
and the use of computer memory are affected by the number of cells involved in the
catchment. If the watershed is large or the cell dimension too small, the number of
cells increases so that the computation time increases and the free memory of the
computer is often insufficient, and therefore the simulation is sometimes difficult or
impossible to realize with a personal computer. One approach to cope with this
problem is to increase the cell size, which may introduce errors by aggregation of
spatial input data and misrepresentation of the true basin characteristics. For instance,
increasing grid size causes the information content of the slope gradient to decrease
slightly and the curvature of the landscape to decrease greatly. Studies have shown
that grid size has remarkable effects on the simulation results of both runoff
generation and flow routing. The coarser resolution results in a lower peak discharge
and earlier time-to-peak, especially for the storm events of short duration and lower
antecedent soil moisture condition (Braun et al., 1997; Molnar and Julien, 2000). This
is in agreement with the argument used by Beven (1995) that the aggregation
approach towards macro-scale hydrological modelling, using averaged parameter
values, is inadequate for representing hydrological processes at a large scale. In
addition, terrain information is lost as a result of data aggregation at a larger grid-cell
size, and the high-resolution data is not fully utilized in the watershed modelling.
168
Integrating GIS and hydrological process modelling in medium and large watersheds
It has been widely recognized that spatial scale, e.g. the size of grid cell or sub-basin,
generally lead to predictive uncertainty in distributed hydrological modelling (Blöschl
& Sivapalan, 1995). Although such difficult and serious scale problems are yet far
from any form of solution, many valuable ideas have been proposed to attempt to
solve it and hence improve model reliability. For example, the simple scaling and
multi-scaling frame (Gupta et al., 1994), the REA (Representing Element Area)
concept (Wood et al., 1988), the GLUE (Generalized Likelihood Uncertainty
Estimation) framework (Beven & Binley, 1992), the HRU (Hydrological Response
Units) concept (Flügel, 1995), as well as the basin-scale model equations (Kavvas et
al., 1998). In addition, many efforts have been focused on the effects of grid size on
model parameters and performances. For instance, Quinn et al. (1991), Zhang and
Montgomery (1994), Bruneau et al. (1995), and Wolock and Price (1994) looked at
how grid size affected the computed topographic characteristics, wetness index, and
outflow using TOPMODEL. In general, they found that the finer grid size gave more
accurate results. Similar results have been obtained in recent studies (Franchini et al.,
1996; Saulnier et al., 1997; Horritt & Bates, 2001; Moglen & Hartman, 2001).
In this study, an operational method for the automated physiographic parameterization
of a hydrological model is developed. The purpose is to provide an enabling
technology for GIS-based medium and large watershed modelling, utilizing highresolution information as much as possible. The automated model parameterization is
implemented using ArcView, which is a friendly desktop mapping and GIS tool that
enables users to quickly select and display different combinations of data for
creatively visualizing information. Moreover, the Avenue programming language and
the spatial extension of ArcView enable the modelling of water budgets on a grid cell
basis and the tightly integrating of GIS outputs with hydrological models. Using this
technique, it is possible to derive all necessary model parameters rapidly and
accurately, and at different discretizing levels by varying the number of GIS derived
subwatersheds. A case study in the Alzette river basin, located in the Grand-Duchy of
Luxembourg, is presented. The potential application, limitation and the major
influencing factors of this method with respect to watershed modelling for flood
prediction and water balance simulation on medium and large catchment scale are
also discussed.
169
Chapter VIII
2.
Study area and data availability
The analysis of grid size effects and the test of the modified WetSpa model are
performed on the Alzette river basin using available hydro-meteorological data from
Dec. 1996 to Dec. 2000. The topography and soil data are available in GIS form,
while the land use data is obtained from remote sensed images. The study area covers
an area of 1176 km2 and is located mostly in the Grand-duchy of Luxembourg. Highmagnitude floods occurred frequently and have caused important damages since the
early 1990’s. Figure VIII-1 shows the location of the study area, as well as the river
system and the monitoring network. The bedrock of the basin is of sedimentary origin,
consisting of flat fractured layers of marls, limestone, sandstone and schist (El Idrissi
et al., 2002).
# Et telbru ck
Ell
#
Mer s ch
#
Mining
Wate r
Crop
Grass
Forest
Urban
Luxembou rg-cit y
#
N
Esc h/Alzette
#
W
E
S
0
Figure VIII-1: Study area and observation
network
5
10 km
Figure VIII-2: Land use of the Alzette
River basin
The study area has generally a rolling topography, with elevation ranging from 195 to
545 m and an average basin slope of 8.7%. Most tributaries of the Alzette are leftbanked and located in the western part of the basin. The soil is mostly a
sandstone/limestone mixture with spots of clay and marl, and can be classified as
170
Integrating GIS and hydrological process modelling in medium and large watersheds
texture categories of loamy sand (16.7%), silt loam (8.1%), silt (21.4%), loam
(22.7%), sandy clay loam (10.9%), silt clay loam (15.4%) and clay loam (4.8%). The
soil geological formations partially condition the land use patterns. Thus, in general,
agricultural areas coincide with marls and forest areas with sandstones. The dominant
land use types in the catchment are deciduous shrub and forest (33.7%), grassland
(30.7%) and cropland (23.3). Because the study area is highly developed, urban area
(11.2%) is one of the major land use types in the river basin, including several towns
such as Ettelbruck, Mersch, Luxembourg-city, and Esch/Alzette (Figure VIII-2).
Other land use types are free water surface (0.2%), and former mining areas (0.9%),
which are located in the right bank tributaries of the upstream catchment and disturb
the local hydrological behaviour during storm events.
The climate in the region has a northern temperate humid oceanic regime without
extremes. Rainfall has a relatively uniform distribution over the year. High runoff
occurs in winter and low runoff in summer due to the higher evapotranspiration.
Winter storms are strongly influenced by the westerly atmospheric fluxes that bring
humid air masses from the Atlantic Ocean (Pfister et al., 2000), and floods happen
frequently because of the saturated soils and the low evapotranspiration. The average
annual precipitation in the region varies between 800 mm to 1000 mm. Precipitation
generally exceeds potential evapotranspiration except for the four months in the
growing season.
A dense rainfall and discharge monitoring network was set up to study the
hydrological behaviours of the river basin in 1995 as shown in Figure VIII-1. Water
levels are recorded at 16 streamgauges at a 15-minute time step, while rainfall is
collected via 19 daily raingauges and 4 hourly raingauges, covering the study area and
modelling period. To define the hourly rainfall distribution over the catchment, the
daily areal rainfall interpolated via Thiessen polygons is time disaggregated according
to the temporal structure of the 4 hourly reference raingauges (El Idrissi et al., 2002).
Potential evapotranspiration is estimated using the Penman-Monteith formula with
measured meteorological data at Luxembourg-city (Findel Airport), and extended to
each rainfall Thiessen polygon based on the proportions of different land use type
over the polygon (Drogue et al., 2002).
171
Chapter VIII
3.
Effects of grid size on runoff and flow responses
The 50 x 50 m maps of elevation, soil type, land use, and watershed boundaries for
the study area are aggregated to produce 5 sets of data with grid sizes of 50, 100, 200,
400, and 800 m. Due to the gentle relief for some areas along the catchment boundary,
DEM aggregation using a simple GIS resample command may cause divergence of
the stream lines, and hence can not represent properly the drainage system of the
catchment. To serve this problem, the ArcInfo’s TOPOGRID function is used to
create DEMs with different grid size based on the information of 2 m contour map,
the catchment boundary and the digitalized stream network. The digital land use and
soil type maps with the same cell size are resampled from the 50×50 m land use and
soil type grid by means of the nearest-neighbour assignment. The spatial analysis of
the physical elements of the catchment and the preparation of model parameters are
implemented using GIS ArcView.
Table VIII-1: Mean parameter values calculated from maps with different grid size
Parameters
Elevation
Flow length
Slope
RMS profile curvature
Hydraulic radius
Flow velocity
Flow time
Standard deviation
Urban percentage
Loam percentage
Potential runoff coefficient
Depression storage capacity
unit
(m)
(km)
(%)
(%m-1)
(m)
(m/s)
(h)
(h)
(%)
(%)
(-)
(mm)
50 m
332
37.9
8.18
12.4
0.017
0.08
22.4
6.71
11.3
22.6
0.426
2.01
100 m
332
36.2
6.41
6.26
0.022
0.11
20.5
6.26
11.3
22.6
0.410
2.24
200 m
332
33.7
4.41
3.12
0.038
0.14
18.9
6.20
11.1
22.6
0.389
2.59
400 m
333
31.8
2.68
1.28
0.066
0.18
16.8
5.59
11.3
22.6
0.369
2.97
800 m
333
30.1
1.64
0.45
0.112
0.27
11.2
4.40
12.0
22.6
0.359
3.27
The effects of grid size on parameters including elevation, flow length, slope,
curvature, hydraulic radius, flow velocity, flow time and its standard deviation, urban
and loam percentage, potential runoff coefficient and depression storage capacity, are
investigated as listed in Table VIII-1. The value of the model parameter derived from
the 50×50 m DEM is used as the reference value, with estimates of model parameters
for DEMs of coarser resolutions compared against it. It is found from the table that
the mean elevation, urban percentage and loam percentage remain more or less the
172
Integrating GIS and hydrological process modelling in medium and large watersheds
same for different grid size DEMs. As the resolution grows coarser, estimates of mean
flow length, slope, root mean square (RMS) profile curvature, potential runoff
coefficient, flow time and its standard deviation decrease consistently. On the other
hand, the mean hydraulic radius, flow velocity and depression storage capacity
increase consistently as the resolution grows coarser (Figure VIII-3). The decrease of
potential runoff coefficient and increase of depression storage capacity are mainly
caused by the decrease of the derived grid slope, while the decrease of flow time is
due to the decrease of flow length and the increase of flow velocity.
(a) 50
30
20
9
6
10
3
0
0
0
200
400
600
Slope (%)
RMS curvature (%m-1 )
Depression capacity (mm)
12
Para meter v alues .
40
Parameter values
(b) 15
Flow length (km)
Flow time (h)
Standard deviation (h)
0
800
200
Grid size (m)
800
(d) 0.08
(c) 0.6
Potential runo ff coefficien t
Flow velocity (m/s)
Hydraulic radius (m)
50 m
100 m
200 m
400 m
800 m
0.06
0.4
-1
IUH (h )
Para meter val ues .
400
600
Grid size (m)
0.04
0.2
0.02
0
0
0
200
400
600
Grid size (m)
800
0
10
20
30
Time (h)
40
50
Figure VIII-3: Mean parameters obtained from DEMs with grid sizes: (a) flow length,
flow time and its standard deviation, (b) slope, curvature and depression capacity, (c)
runoff coefficient, velocity and hydraulic radius, (d) IUHs for the entire catchment.
173
Chapter VIII
Figure VIII-3(d) presents the calculated catchment IUHs obtained from DEMs with
different grid sizes. Obviously, the IUH’s peak increases consistently with
considerably shorter times to its peak value as the resolution grows coarser. These
biases lead to a tendency to overestimate peak discharge for a certain amount of
runoff when coarser data are used. In addition, the calculated lateral interflow
decreases dramatically as the grid size increases due to the decreasing slope gradient.
Figure VIII-4 presents the hydrographs at Ettelbruck for a flood event in Dec. 1999
calculated from base maps with grid size of 50, 200 and 800 m. One can see that the
lag time decreases consistently with the increasing map resolution, but the flood
volume and peak discharge are decreasing on the contrary. These are due to the
decrease of estimated interflow as the resolution grows coarser (Table VIII-2). Figure
VIII-5 presents the surface runoff hydrographs independently calculated from maps
with grid size of 50, 200 and 800m, in which the peak discharge increases consistently
with the increasing grid size. The characteristics for the flood event in Dec. 1999
estimated from maps with different grid size are presented in Table VIII-2.
Apparently, the estimated surface runoff, interflow, total runoff, peak discharge and
its lag time decrease consistently with the increasing grid size, while the amount of
infiltration, percolation, groundwater flow, and soil moisture are increasing on the
contrary. The calculated groundwater flow is not important for this flood event. Water
percolated to the groundwater reservoir is released slowly feeding low flow and
further evapotranspiration from groundwater reservoir.
Precipitation
Q observed
Q 50 m
Q 200 m
Q 800 m
3
Discharge (m /s)
160
120
4
8
80
12
40
16
0
11/12
12/12
13/12
14/12
Time (d/m)
15/12
16/12
Precipitation (mm/h) .
0
200
20
17/12
Figure VIII-4: Comparison of flow hydrographs at Ettelbruck calculated from DEMs
with different grid size for a flood event in Dec. 1999
174
Integrating GIS and hydrological process modelling in medium and large watersheds
160
0
Precipitation
Q 800 m
80
10
40
15
0
11/12
12/12
13/12
14/12
Time (d/m)
15/12
16/12
Precipitation (mm/h) .
5
Q 200 m
3
Surfa ce flow (m /s)
Q 50 m
120
20
17/12
Figure VIII-5: Comparison of surface flow hydrographs at Ettelbruck calculated from
DEMs with different grid size for a flood event in Dec. 1999
Table VIII-2: Flood characteristics estimated from maps with different grid size
Characteristics
Surface runoff
Infiltration
Interflow
Percolation
Groundwater flow
Total runoff
Soil moisture on 13/12
Peak discharge
Lag-time
3.
unit
(mm)
(mm)
(mm)
(mm)
(mm)
(mm)
(m3/m3)
(m3/s)
(h)
50 m
18.1
64.8
16.2
34.1
2.2
36.5
0.606
176.5
11
100 m
17.6
65.4
14.3
35.2
2.4
34.3
0.617
164.3
8
200 m
17.2
65.8
10.4
36.3
2.6
30.2
0.629
158.5
6
400 m
16.8
66.1
7.9
39.2
2.8
26.5
0.642
153.8
5
800 m
16.1
66.7
4.1
41.3
3.0
23.2
0.654
151.0
4
Transforming WetSpa into a semi-distributed model
From the analysis above, it can be concluded that coarser grid size may result in
significant bias for model predictions. Therefore, flood modelling using a high
resolution DEM is preferred to improve model reliability. In order to deal with the
computing time and memory problem when applying the distributed WetSpa model to
a medium or large river basin with a fine grid size, the model is modified to a semidistributed pattern, where the water budget is computed for each very small
subwatershed, built up from high resolution DEM data, rather than large grid cells
with approximately the same area as the subwatershed. The GIS derived very small
175
Chapter VIII
subwatershed serves as a relatively homogeneous hydrological unit, with the same
precipitation and potential evapotranspiration. The advantage of this method is to
maintain the internal drainage structure of the subwatershed, for which surface runoff,
interflow and groundwater flow can be estimated at the subwatershed outlet, and the
respecting water and energy are balanced for each subwatershed. Simulations using
large grid cells do not have this advantage, because the cell boundary may not reflect
the true drainage boundary adequately. In the modified WetSpa model, the soil water
balance in the root zone layer for a controlling unit is described as:
D
∆θ
= P − I −V − E − R − F
∆t
(8.1)
in which ∆θ [LL-1] represents the change of average soil moisture of the subwatershed
during time ∆t [T] in the root zone layer with depth D [L]. The flow across the
controlling interface consists of infiltration, which is calculated by precipitation P
[LT-1] subtracted by the initial abstraction I [LT-1], including interception and
depression, and the surface runoff V [LT-1], evapotranspiration E [LT-1], percolation
out of root zone R [LT-1] and lateral interflow F [LT-1].
Using GIS ArcView, the meteorological and hydrometrical stations are georeferenced to the base map and a spatial analysis of the precipitation, and PET is
undertaken for the entire catchment with ArcView Thiessen Polygon extension. The
mean precipitation and PET for each subwatershed as inputs to the model are then
calculated by weighing the data of the neighbouring meteorological stations, for
which the weight of a given station is predetermined by its area percentage in the
subwatershed, using a high resolution base map and the ArcView Spatial Analyst
extension. In such a way, the spatial distribution of meteorological variables is fairly
taken into account in the model. Model parameters such as interception storage
capacity, depression storage capacity, potential runoff coefficient, overland roughness
coefficient, root depth, soil property parameters (saturation hydraulic conductivity,
porosity, field capacity, wilting point, residual moisture content, pore size distribution
index, etc.), average travel time to the outlet, dispersion coefficient and so on, are
firstly calculated for each grid cell using ArcView lookup tables and the high
resolution DEM, soil type and land use maps, or a combination of the three base maps.
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Integrating GIS and hydrological process modelling in medium and large watersheds
The mean parameters for each subwatershed are obtained by integrating the values
from all cells of that subwatershed. In such a way, the minority categories of land use
and soil type are taken into account in each subcatchment, and the flow time and
dispersion coefficient are calculated based on the high resolution DEM. These result
in a better estimation of the natural properties compared with the method using large
grid cells, since a unique value is assigned to each pixel for grid type data and
therefore the grid resample enumeration may cause errors in reflection of the cell
characteristics.
Using the predetermined parameters above for each subwatershed, the model is
operated within the ArcView interface and with the input meteorological data of
hourly precipitation and PET of different gauging stations. For continued simulation
purpose, the storages of the four stores are estimated for each control unit and for each
time step. The sum of the interception and depression storage forms the initial loss at
the beginning of a storm, and does not contribute to the storm flow. Typical
interception capacity values for different land use categories can be found in the
literature, and the mean value of the controlling unit is calculated accordingly.
Default values of depression storage capacity for different combinations of slope, land
use and soil type are interpolated based on the values found in the literature, and the
mean value of the controlling unit is obtained by means of weighting average for the
cells within the subwatershed weighted by the land use area and the corresponding
potential runoff coefficient. Water held in depressions at the end of rain depletes
either by evaporation with a potential evaporation rate or contributes to the soil
moisture with a linear decay function.
The modified coefficient method is used to estimate surface runoff in the model,
where the volume of surface runoff is a function of the potential runoff coefficient and
the average soil moisture of the simulation unit, so that the actual runoff coefficient
varies with time, rainfall intensity, rainfall duration and unit characteristics as
described in chapter IV, which gives an approximation to the surface runoff volume at
each time step. The potential runoff coefficient serves as a measure of rainfall
partitioning capacity under ideal soil moisture conditions, depending upon slope, soil
type, land use and the proportions of bare soil and impervious areas on the land
surface. Default runoff coefficients are interpolated from the values found in the
177
Chapter VIII
literature, and may be revised during calibration. The actual evapotranspiration in the
model includes evaporation from interception and depression storage, the
evapotranspiration from root zone limited by the PET rate and the soil moisture
content, and the evapotranspiration from groundwater storage. Water stored in
depressions evaporates with a potential rate, while a vegetation coefficient depending
on growing stage and vegetation type is multiplied for calculating evapotranspiration
from the soil. Deep evapotranspiration from groundwater storage is then calculated by
the residuals of the PET multiplied by a variable coefficient depending on the
groundwater storage and its capacity. The percolation out of the root zone is assumed
to be controlled by gravity alone, and is defined by the Brooks and Corey relationship
between hydraulic conductivity, effective saturation and soil pore size distribution
index (Eagleson, 1978). The amount of interflow generated in the subwatershed is
estimated based on Darcy’s law and the kinematic wave approximation, which is a
function of the subwatershed scale effective values of hydraulic conductivity, the
degree of soil saturation, the slope angle and the root depth. Interflow is assumed to
occur after percolation and becomes significant only when the water content of the
root zone soil is between field capacity and saturation. Finally, the groundwater flow
is estimated towards the subwatershed outlet, as a function of groundwater storage
and a recession coefficient, which can be computed, if measured stream flow data is
available, or adjusted by model calibration.
The routing of overland flow and channel flow is carried out using the method of
diffusive wave approximation of the continuity equation and the St. Venant
momentum equation by assuming one-dimensional unsteady flow, and neglecting the
inertial terms and the lateral inflow to the flow element. A linear approximate solution
proposed by De Smedt et al. (2000) is used to serve the equation in the form of a first
passage time distribution, relating the discharge at the end of a flow path to the
available runoff at the start of the flow path as described in chapter III. All routing
parameters are estimated firstly for each grid cell with a high resolution DEM. The
unit response functions for each simulation unit at their outlets are then obtained by
integration of the cell response functions within that subwatershed weighted by its
potential runoff coefficient, whereas the channel response functions from each
subwatershed outlet to the basin outlet are obtained by integration of the cell response
functions along the stream channel. If the discretization of the watershed is highly
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Integrating GIS and hydrological process modelling in medium and large watersheds
intensive, the water may flow out of the subwatershed within the first time step, and
the process of flow routing within each subwatershed can be omitted. However, this
process is maintained in the model in case of coarse discretization of the catchment or
very small time intervals of the model simulation.
With the above unit response functions defined for each simulation unit, stream flow
can be routed accumulatively downstream. Three options are considered in the
outflow hydrograph simulation. The first option is to compute and add interflow and
groundwater flow to surface runoff at the subwatershed outlet, and route the total flow
from each subwatershed accumulatively down to the watershed outlet. The second
option is to add interflow to groundwater, and route surface runoff and groundwater
downstream separately. The third option is to route all three components separately.
The last two options are not computationally efficient compared to the first option, but
can give a clear view of subsurface hydrological responses to the storm event and the
distribution of surface runoff, interflow and groundwater throughout the watershed.
The challenge in model calibration is that virtually no observed interflow and
groundwater flow data are acquirable for medium or large watersheds. A workable
solution might be to use the available baseflow separation models to separate
baseflow and interflow adequately from the measured outflow hydrographs, for
example the method developed by Wittenberg (1999).
All model parameters can be derived within GIS ArcView framework, using lookup
tables based on the three base maps. The hydrological data series needed for the input
of the model are hourly precipitation and PET at each measuring station, and the
outputs of the model are hydrographs at the basin outlet or any other flow measuring
point inside the catchment, the variation of basin mean hydrological variables, as well
as the distribution of hydrological characteristics for each subwatershed of the terrain.
The division of the watershed should be performed according to the project purpose
and of the terrain. Dividing the watershed into very small subwatersheds is necessary
in order to take care of the spatial variability of the hydrological processes. However,
for a medium sized plain watershed, if the project purpose is flood prediction only at
the outlet of the watershed, dividing that watershed into a few hundreds or even tens
of subwatersheds might be sufficient. Then, the modified WetSpa model could be
considered as becoming more and more semidistributed as the dimensions of the
179
Chapter VIII
subbasins increase. A few simulations are necessary to decide how many
subwatersheds are necessary to meet various objectives going from flow forecasting
at the basin outlet to detailed stream flow simulation at a number of points on the river
network, together with interest in the spatial variability of hydrological characteristics,
such as surface runoff, interflow, soil moisture, etc.
4.
Results and Discussion
Based on the point elevation measurements, a 50 by 50 m pixel resolution DEM is
generated. The digital land use and soil type map with the same cell size are converted
from the available land use and soil coverage. The cell-based parameters are then
identified using GIS tools and lookup tables, which relate default parameters to the
base maps, or the combination of base maps. Starting from the high resolution DEM,
hydrological features including aspect, surface slope, flow direction, flow
accumulation, flow length, stream network, and drainage area are delineated. Maps of
porosity, field capacity, wilting point, residual moisture, saturated hydraulic
conductivity, and pore size distribution index are obtained from the soil type map.
Maps of root depth, Manning’s roughness coefficient and interception storage
capacity are derived from the land use map. Maps of default runoff coefficient and
depression storage capacity are calculated from the slope, soil type and land use class
combinations. For the urban areas, due to the model grid size, cells may not be 100%
impervious in reality. In this study, the percentage of impervious area in the grid cell
is computed based on land use classes, with 30% for residential area, 70% for
commercial and industrial areas. Default runoff coefficients for these areas are
calculated by adding the impervious percentage with a grass runoff coefficient
multiplied by the remaining area. These result in runoff coefficients of 40 to 100% in
urban areas, while other areas have much smaller values, down to 3% for forests with
sandy soils and practically zero slopes. The average hydraulic radius for each grid cell
is calculated according to the controlling drained area using a power law relationship.
For normal floods, the estimated minimum hydraulic radius for overland flow was
0.005 m, and maximum 1.5 m for channel flow at the basin outlet. The values can be
increased for extreme floods. The channel roughness coefficients are set in the model
based on the stream orders with 0.025 m-1/3s for the highest order, 0.045 m-1/3s for the
lowest order, and linear interpolations in between, considering the effect of river bed
180
Integrating GIS and hydrological process modelling in medium and large watersheds
composition and geometry. By combining the maps of the average hydraulic radius,
the Manning’s roughness coefficient and the surface slope, average flow velocity in
each cell is calculated using Manning’s equation, which results in values of 0.005 m/s
for overland flow on upland areas in the watershed, and up to 2.7 m/s for some parts
of the main river. Next, the celerity and dispersion coefficients in each cell are
produced by the equations described in chapter III. The contributing area is then
determined from topographic data for a particular downstream convergence point, i.e.
normally the cells corresponding to the stream flow gauging sites and the basin outlet.
For each contributing grid cell, the flow time and its standard deviation are calculated
by integration along the flow paths, using the GIS’ FLOWLENGTH routine. A spatial
distribution of the average flow time to the basin outlet is shown in Figure VIII-6, in
which the average flow time is less than 10 h for the main river and up to 55 h for the
most remote areas.
5 - 10
10 - 20
20 - 30
30 - 40
40 - 50
> 50
h
h
h
h
h
h
N
N
W
W
E
S
S
0
5
E
10 km
Figure VIII-6: Mean travel time to the
basin outlet
0
5
10 km
Figure VIII-7: River reaches and divided
subwatersheds
For the simulation of hydrographs both at the basin outlet and the flow monitoring
points inside the catchment, and the interest in the spatial variability of hydrological
181
Chapter VIII
characteristics over the catchment, the basin is divided into 2276 subwatersheds, as
shown in Figure VIII-7, corresponding to the threshold value of 100 when delineating
the stream network based on the flow accumulation theme. The areas of the GIS
derived subwatersheds range from 0.025 to 3.8 km2 with average subwatershed area
of 0.52 km2 corresponding to a grid mesh with cell size of 720 m. The flow unit
response functions at each subwatershed outlet and from the subwatershed outlet to
any downstream converging point can be obtained by the method described in chapter
III. The flow routing within each subwatershed is not important if the GIS derived
subwatersheds are very small, as is the case in this study, since most excess water
may flow out of the subwatershed during the first time step with little damping effects.
Routing of the flow is therefore mainly governed by the channel geophysical
conditions. However, flow routing within each subwatershed becomes more and more
important along with the increasing subwatershed scale. In this study, stream net
delineating thresholds of 200, 300, 500, and 1000, resulting in the subwatershed
numbers of 1207, 797, 455 and 233, are also tested during model calibration, for
which the predicted hydrograph at the basin outlet did not change too much, but the
simulation results for the small watershed inside the catchment are affected
considerably.
Both automated and manual calibration of the model are realized at Ettelbruck for the
period of 1997-1998 and the model is validated using the available hourly
precipitation, PET and stream discharge data at different stations for the period of
1999-2000. The parameters that need to be adjusted during model calibration are
mainly interflow scaling factor, groundwater flow recession coefficient, plant
coefficient, the initial relative soil moisture and initial groundwater storage, while the
runoff exponent is set to one and other distributed model parameters are
predetermined using GIS tools before the model operation and normally remain
constant as they are. The predetermined distributed parameters of potential runoff
coefficient, hydraulic radius, Manning’s coefficient, etc., can also be adjusted during
calibration. The predicted hydrographs at other flow monitoring sites inside the
catchment can also be seen as model verifications, but only the simulation results at
Ettelbruck, the basin outlet, are presented here. Figure VIII-8 shows the observed
versus the simulated stream flow and the estimated base flow (interflow plus
groundwater drainage) at Ettelbruck for a compound flood event that occurred in Feb.
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Integrating GIS and hydrological process modelling in medium and large watersheds
and Mar. 1997. Three large storms happened successively during the period, and
caused serious floods over the catchment. The total recorded rainfall over the
catchment during the period was 147.8 mm, with 56.5, 22.8 and 67.4 mm for the three
storms respectively, corresponding to observed peak discharges of 115, 105 and 190
m3/s at Ettelbruck for each individual flood. As can be seen in the Figure, the
predicted hydrograph fits the measured hydrograph very well. The volume of surface
runoff takes about 53% of the total flood volume, while the interflow and
groundwater flow is about 47% of the total flood volume. The first storm did not
produce a relevant big flood compared with its storm volume, as a large quantity of
rainfall was used for saturating the soil, while the second and the third storm
generated a higher proportion of runoff. This was approved by the predicted
hydrograph, where the calculated surface runoff coefficient was 0.30, 0.35 and 0.39
for the three floods respectively.
250
0
200
Discharge (m 3/s)
Calculated outflow
150
Calculated baseflow
6
Observed outflow
100
9
50
12
0
10/2/97 13/2/97 16/2/97 19/2/97 22/2/97 25/2/97 28/2/97 3/3/97 6/3/97 9/3/97 12/3/97 15/3/97
15
Precipitation (mm /h)
3
Precipitation
Figure VIII-8: Calculated Vs observed flows at Ettelbruck for the floods in Feb. 1997
A graphical comparison between calculated and measured flows at Ettelbruck for the
validation year 1999 is presented in Figure VIII-9, in which the hourly precipitation
and discharges are integrated to a daily value, and the vertical axis is on a logarithmic
scale in order to give a clear distinction for the low flows. With the initial
hydrological condition at the end of calibration period, the validation results for the
year 1999 and 2000 are in fairly good agreement with the measured discharges. The
183
Chapter VIII
model can well reproduce high flows, but low flows are a little over estimated. This
may be because of the simplification of the groundwater component in the model, or
less accurate estimation of the evapotranspiration from groundwater storage during
dry periods. Similar simulation results can be obtained for other flow gauging sites
inside the catchment, but the model performance for the stations with small drained
area is not as good as the stations with large areas. However, by discretizing the large
catchment into very small subwatersheds, the model is able to consider the
precipitation, antecedent moisture and runoff-generating processes in a spatially
realistic manner based on topography, land use and soil type, resulting in a fairly high
accuracy for high flows, and the general hydrological trends being well captured by
0
1000
20
Discharge (m 3/s)
10000
Precipitation
Sim ulated
100
40
Observed
10
60
1
80
0.1
1/99
Precipitation (mm/d)
the model.
100
2/99
3/99
4/99
5/99
6/99
7/99
8/99
9/99
10/99
11/99 12/99
Figure VIII-9: Simulated Vs observed daily flows at Ettelbruck for the year 1999
Three model performance criteria, i.e. model bias, model confidential coefficient and
the Nash-Sutcliffe coefficient (Nash & Sutcliffe, 1970) as described in chapter V, are
performed to the simulation results simultaneously after the model run. The calculated
values of the three criteria at Ettelbruck are 0.06, 0.84 and 0.88 for the calibration
period, and 0.04, 0.81 and 0.85 respectively for the validation period, which are
satisfactory in the view of model assessment, and indicate that the modified WetSpa
model is able to provide good fits to the observed hydrographs at the basin outlet. The
model performance at Ettelbruck and other 15 flow stations inside the catchment
covered by the three assessment criteria for the whole simulation period on hourly
184
Integrating GIS and hydrological process modelling in medium and large watersheds
scale, together with the subwatershed characteristics, are presented in Table VIII-3.
Model biases are within the range of -0.08 to 0.05. The model confidential
coefficients are with the range of 0.53 to 0.84 with mean value of 0.73, and the NashSutcliffe coefficients are within the range of 0.47 to 0.87 with mean value of 0.74. It
is found that better performance exists for the watershed with large areas, while for
small watersheds the performance is less satisfactory. For example, the three
evaluation values at Huncherange, a 7.3 km² small watershed, are 0.05, 0.53 and 0.47,
and the outflow hydrograph is poorly predicted. This indicates that the modified
WetSpa model can give a good representation of flow hydrographs for larger
catchments. For a small watershed, a fully distributed model based on high resolution
DEM and with smaller time interval is preferred.
Table VIII-3: Subwatershed characteristics and model performance
River
Station
Alzette Ettelbruck
Alzette Mersch
Alzette Steinsel
Alzette Pfaffenthal
Alzette Hesperange
Alzette Livange
Attert
Bissen
Attert
Useldange
Attert
Ell
Roudbach Platen
Pall
Niederpallen
Eisch
Hunnebour
Eisch
Hagen
Mamer Schoenfels
Mamer Mamer
Mierbech Huncherange
5.
Area Slope Urban Crop Grass Forest Water
CR1
(km²) (%) (%) (%) (%) (%) (%)
CR2
CR3
1176 8.7
705 8.0
408 7.0
349 6.5
291 6.7
233 7.2
294 8.8
255 8.9
107 9.4
47.1 11.1
34.6 6.1
172 8.9
47.2 5.0
84.7 7.8
18.3 6.3
7.3
4.9
0.83
0.78
0.82
0.83
0.78
0.71
0.76
0.84
0.81
0.63
0.75
0.77
0.61
0.72
0.55
0.53
0.87
0.76
0.85
0.82
0.79
0.77
0.79
0.82
0.85
0.58
0.73
0.81
0.64
0.70
0.53
0.47
11.2
15.3
20.5
19.2
17.8
18.6
4.8
4.1
3.5
4.8
3.9
6.6
6.4
11.6
8.9
6.2
23.3
22.8
23.1
25.4
27.4
28.9
23.7
24.7
20.9
32.4
19.1
23.4
31.3
22.7
30.0
45.9
30.7
28.0
24.3
26.8
25.3
22.9
36.8
37.2
33.7
25.8
51.6
33.2
45.0
33.9
50.6
15.8
33.7
32.0
29.0
25.2
25.4
24.7
34.5
33.9
41.8
36.7
25.0
36.6
17.3
31.6
10.5
32.0
0.2
0.3
0.4
0.4
0.5
0.5
0.1
0.1
0.0
0.2
0.2
0.1
0.0
0.1
0.0
0.2
0.05
0.02
-0.01
-0.03
-0.05
-0.08
0.05
0.03
-0.01
-0.02
0.03
-0.04
-0.01
0.04
0.04
0.05
Conclusions
The effects of grid size on catchment characteristics, runoff and flow responses are
investigated in this chapter. It is concluded that significant bias in the modelling
results can be generated when using a coarse resolution data. On the other hand, the
computing time and memory problems arise when modelling a medium or large
185
Chapter VIII
catchment with a fine resolution data. To overcome these problems, a practical
approach by dividing a large catchment into very small subwatersheds based on highresolution digital graphic data is developed. The modified WetSpa model uses
elevation, soil and land use data in a simple way to estimate runoff and soil moisture
within root zone on the scale of GIS derived natural units, allowing for the internal
drainage structure of WetSpa for each small subwatershed. The discretization of the
catchment is implemented according to the model purpose, terrain complexity, and
the interest of spatial variable distributions. In case of fine discretization, channel
characteristics are more important in controlling the routing of stream flow, which
have to be determined properly. On the other hand, flow routing inside the
subwatershed has to be taken into account for coarse discretization, in order to predict
outflow hydrographs more accurately. The model has been applied to the 1176 km²
Alzette river basin in Luxembourg with 4 years observed hourly rainfall and stream
flow data. Results from the integrated output show that it adequately predicts stream
flow at the basin outlet and the flow gauging sites with relatively large drained area
inside the catchment. Working on a very small simulation unit, as illustrated in the
case study, the model is also capable of predicting spatial distributions of hydrological
variables on a natural unit scale.
Despite the good performance in the case study, the model suffers some limitations in
practice. Firstly, the model requires high resolution DEM, land use and soil type maps
as input, and continuous data of precipitation, PET, and discharge for model
calibration, which cannot be fully met for many watersheds. Secondly, the model
employs many default parameters, which are interpolated from the literature and used
over the entire catchment. Due to the large variation range, parameters such as
hydraulic conductivity, roughness coefficient, etc., may change greatly when applying
the model to other areas with quite different environment, and therefore model
calibration is necessary. In addition, the model generates runoff using a modified
coefficient method, which is empirical-based rather than on equations more closely
representing physical processes. Though definitely a limitation, the use of the method
has its advantages of closely relating runoff with cell characteristics such as slope,
land use, soil type and moisture content, and has the potential to predict the impact of
human activities on hydrological behaviours over the watershed.
186
Integrating GIS and hydrological process modelling in medium and large watersheds
The use of the modified WetSpa model with its physiographic parameters provided by
ArcView GIS has the attraction of reducing the cost and time required for
parameterization and model simulation. This advantage is more outstanding when
modelling a large watershed with long data series and short time intervals. Finally,
with its display options allowing monitoring of various variables for each simulation
unit during model operation, the model appears to be a good tool for understanding
and managing phenomena related to hydrological processes. The implementation of
the model entirely within ArcView using Avenue scripts along with the Spatial
Analyst and hydrological extensions enables the integration of modelling capabilities
within a GIS environment. The method makes full use of the spatially distributed
hydrological and geophysical characteristics of the catchment, and therefore is
suitable for stream flow forecasting and scenario simulations.
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189
Chapter IX
Summary and conclusions
1.
General summary
The core of the research in this PhD study is to develop a GIS-based continuous
hydrological model and to apply the model in the context of flood prediction and
watershed management in a river basin, for instance, the assessment of land use
change impacts on hydrological processes, the assessment of river restoration effects
on the flood reduction, etc. The model simulates water and its movement coming
from precipitation in the system of soil, plant and atmosphere within a GIS framework.
The areas of major emphasis in this study are: (1) to develop a practical method of
estimating runoff that relates the rainfall runoff relationship to basin characteristics, (2)
to develop a diffusive transport approach for flow routing in GIS-based watershed
modelling, (3) to develop efficient ArcView scripts and Fortran codes capable of
identifying spatial model parameters and hydrological computation, (4) to understand
the nature of hydrological interactions between soil, plant and atmosphere, (5) to
develop an approach by integrating GIS and hydrological process modelling in
medium and large watersheds, and (6) to demonstrate the applicability of the model
by applying the model in 3 watersheds with different characteristics.
1.1.
Model development
A GIS-based distributed-parameter model, WetSpa Extension, has been developed to
simulate runoff and flow responses in a river basin. The model conceptualizes a basin
hydrological system being composed of atmosphere, canopy, root zone, transmission
zone and saturation zone layers. The basin is divided into a number of grid cells, for
which the water and energy balance is maintained. The hydrological system consists
of four control stores: the interception storage of the plant canopy, the depression
storage on the soil surface, the soil moisture content of the root zone, and the active
groundwater storage of the saturated aquifer. The hydrological processes simulated by
the model include precipitation, interception, snow accumulation and melt, depression,
Chapter IX
infiltration, surface runoff, interflow, percolation, evapotranspiration, and the flow
routing on hillslopes and in stream channels.
A modified rational method is applied to estimate surface runoff and infiltration based
on rainfall intensity, soil moisture status and cell characteristics, i.e. slope, soil type
and land use. Interflow and percolation out of the root zone are simplified to be
gravity driven flows and simulated by Darcy’s law and kinematic approximation.
Actual evapotranspiration is limited by the potential evapotranspiration and calculated
from the available water in the interception storage, depression storage, root-zone soil
and groundwater storage. Flow routing is characterized by a two-parameter diffusive
wave approximation approach, for which the travel time and its standard deviation are
spatially distributed and calculated as a function of the cell’s roughness coefficient,
hydraulic radius and slope gradient. For model simplification, groundwater flow is
modelled using a reservoir method and on a small subcatchment scale. The model
requires three base maps, i.e. DEM, soil type and land use, to identify spatial model
parameters and process model simulations. The coverage maps of gauging site, stream
network and catchment boundary are necessary in order to delineate drainage network
more accurately and create Thiessen polygons. Site specific data input to the model
include precipitation, temperature and PET, while discharge data is optional for model
calibration. The model predicts flow hydrographs at the basin outlet or any
convergent point inside the catchment, and the spatial distribution of hydrological
characteristics at any time step over the catchment, such as surface runoff, interflow,
groundwater recharge, soil moisture, and actual evapotranspiration, etc. All
computational processes are implemented within a GIS ArcView framework.
The model results on free flow travel time and its standard deviation within a river
basin are very encouraging for handling overland and channel flow routing. As
discussed in chapter III, one of the primary assumptions of the method employed in
this research is a zero loss of water to storage during overland and channel flow.
Although this is not a trivial assumption, it is important to make the model
computationally efficient. Rather than calculating the inflow of water to and outflow
of water from each cell in the basin and then routing the outflow from each cell based
on its connectivity to its neighbouring cells, the two-parameter diffusive approach
cuts the calculations down to the assessment of inflow of water into a cell from
192
Summary and conclusions
precipitation and then travel time of the water to the outlet. Even if one only dealt
with cells in the basin that have non-zero inflow in the calculations, the complete
accounting and routing of water across a landscape is a computationally expensive
undertaking. This new method is able to provide satisfactory estimates of the flood
hydrographs and save computational cost greatly in a GIS-based hydrological
modelling system.
The raster-based approach as used in the WetSpa model is often simpler than other
finite difference and finite element approaches, which aim to discretize and solve the
equations governing fluid flow and energy dynamics, and thus may present a lesser
computational burden and development cost. Despite its crude representation of
hydrological processes, the model has shown to give good results in different
applications. Moreover, the raster-based model can benefit from GIS technology
greatly extracting hydrological features from the DEM and other digital maps. Once
the DEM, land-use and soil maps are prepared, model parameters in the form of raster
GIS maps are derived for each cell. In addition, the raster schematisation of the basin
enables one to consider spatial characteristics at a small scale with reasonable
accuracy. The fact that model parameters are derived from known basin
characteristics makes the model suitable for analysis of the effects of changes of
distributed model parameters, such as land-use changes.
In order to reduce the model calibration effort, an automated calibration procedure is
applied by incorporating a model-independent parameter estimator. This approach is
used in this study to estimate the most sensitive parameters of the WetSpa model with
observed flow hydrographs at selected stations as the calibration targets. The best set
of parameters is selected from within reasonable ranges by adjusting the values until
the discrepancies between observed and simulated hydrographs is reduced to a
minimum in the weighted least squares sense. This scheme serves as an optimization
algorithm to estimate the model parameters. A further manual calibration is necessary
to avoid the ill-posed problems. In addition to the evaluation based on a visual
comparison between calculated and observed hydrographs, five evaluation criteria are
selected for assessing the model performance including model bias, model
determination coefficient, the Nash--Sutcliffe efficiency, the logarithmic version of
Nash-Sutcliffe efficiency for low flow evaluation, and the adapted version of Nash193
Chapter IX
Sutcliffe efficiency for high flow evaluation. These statistical measures provide
quantitative estimates for the goodness of fit between observed and predicted values,
and are used as indicators of model performance.
In order to identify the input parameters that had the biggest impact on the WetSpa
model, a series of sensitivity analyses are performed. The potential runoff coefficient,
soil hydraulic conductivity, interflow scaling factor, soil moisture status, and the
runoff exponent have the biggest influence on the flood volume. The channel and
overland flow roughness, hydraulic radius, channel flow threshold, and rainfall excess
intensity have the biggest influence on the prediction of peak flow and the time to the
peak. The size of the grid cell may also have a great influence on derived catchment
characteristics, runoff and flow responses as described in chapter VIII. Generally, the
estimated surface runoff, interflow, total runoff, peak discharge and its lag time
decreases consistently with the increasing grid size, while the amount of infiltration,
percolation, groundwater flow, and soil moisture are increasing on the contrary.
Therefore, significant bias in the modelling results can be generated when using a
coarse resolution data. These problems are typically encountered when modelling a
large catchment. In this research, a practical approach by dividing a large catchment
into very small subwatersheds based on high-resolution digital graphic data is
developed, which allows for the internal drainage structure of WetSpa for each small
subwatershed. Encouraging results have been achieved through the model application
in the Alzette River basin located in the Grand-duchy of Luxembourg.
1.2.
Model applications
The WetSpa distributed hydrological model was initially developed and tested on a
small catchment, Barebeek, in Belgium for flood prediction and hydrological design
using long-term historical precipitation records and design storms. The study
catchment is very complex and highly urbanized with the Brussels international
airport located in the upper area of the catchment, four main traffic lines crossing the
watershed in different directions, and many country roads crisscrossing the area from
one village to another. Besides, a main canal passes through the area in the north, and
a small lake is situated near the watershed outlet. The residential areas with sewer
systems exist in the watershed occupying about 28% of the total area. Simulation
194
Summary and conclusions
results show that the model is capable of handling hydrological processes in a
complex terrain as for the case in the Barebeek catchment. The flood volume and its
peak discharge are especially well reproduced. In addition, GIS provides a powerful
tool for developing the model, calibrating parameters and displaying model results in
a spatial way, and the local complexities of the watershed can be well captured.
Next, the WetSpa model on hourly time scale was applied to the Alzette River basin,
located in the Grand-duchy of Luxembourg, to predict floods and assess the impacts
of land use change on flood behaviours. The study catchment has generally a rolling
topography, and is highly developed with several towns inside the catchment such as
Ettelbruck, Mersch, Luxembourg-city, and Esch/Alzette. Urban areas occupy 11.2%
of the total area and have a significant effect on runoff and flow responses of the river
basin. Good performance in predicting flow hydrographs and the spatial distribution
of hydrological variables over the catchment has been obtained by using the fully
distributed and the semi-distributed WetSpa model. The assessment of land use
impacts on flooding was performed in the Steinsel sub-basin situated in the upstream
area of the Alzette basin. Model simulation shows that (1) the runoff from urban areas
is dominant for a flood event compared to runoff from other land use areas in this
catchment, and its partition tends to increase for small floods and for the flood events
with low antecedent soil moisture, (2) other runoff contributions tend to increase for
large storms and for storm events with high antecedent soil moisture, (3) interflow
and baseflow from natural areas are important during wet season but not for small
floods during the dry season, and (4) the flow coefficient and the runoff partitions
from different land use classes vary from one storm event to the other due to the
difference in soil moisture and storm behaviours.
For assessing the hydrological effects of land use changes on floods, three
hypothetical scenarios, namely urbanization, deforestation and afforestation scenario,
were considered based on the present land use configurations in the Steinsel sub-basin.
The result of model simulation shows that that the urbanization scenario has a large
impact on increasing peak discharge and flood volume, as well as time to the peak
compared to the present land-use. The result from the simulation of deforestation
scenario shows the same trend as the result from the urbanisation scenario but with
reduced impact than the urbanisation scenario. Afforestation is found to increase the
195
Chapter IX
infiltration water and evapotranspiration while reduces the peak discharge and the
total runoff. Urbanisation with high proportion of impervious areas change the water
balance of the river basin towards increased surface runoff while forest areas by
allowing more water to pass through the soil surface change the water balance into
increased infiltration and subsequently increasing the groundwater recharge.
Investigation of the peak flow shows that land-use changes can have remarkable
effects on peak discharges in comparison to the present land use condition. The
urbanisation and deforestation scenarios may increase the peak discharges by 26%
and 9.1% in average, while afforestation has a positive impact, decreasing the peak
flow by –5.3% in average.
A conceptual flood reduction methodology by natural river restoration for the
headwater streams is evaluated for the Steinsel sub-basin, Alzette, the Grand-duchy of
Luxembourg. The streams are firstly classified into 5 orders, and the response of
stream channels to the resistance and the river re-meandering in the first and secondorder streams are assessed. These streams have deeper channel slopes, strongly
influenced by morphology, soils, and vegetation of their channels than downstream
higher order streams. Under natural conditions, these streams may have dense instream vegetation and low fluvial power, which eventually increase the flow
resistance. Accordingly, the roughness coefficient of these channels is increased for
simulating the effect on downstream flooding. The hydrological simulation indicates
that the reduction of peak discharge is as much as 14% on average compared to the
present situation, and the time delay of flood peak can be as much as 2 hours. A
reduction in the discharge occurs during the rising limb of the flood hydrograph,
while the discharge increases during the falling limb of the hydrograph, which results
in longer sustained flows than in the present conditions. However, while large floods
in the main stream channels are reduced or avoided, a local flooding may occur in the
headwater stream areas due to river restoration.
Finally, an application of the WetSpa model on daily scale based on GIS and remote
sensed land use information is performed for a Carpathian catchment, Margecany, in
the upstream part of the Hornad River basin, Slovak Republic. The study catchment is
characterised by mountainous terrain. Altitudinal variation is an important
determinant of the local climate and soil characteristics in all the state. Snowmelt is an
196
Summary and conclusions
important process in the river basin and forms the main source of the spring floods.
Model simulations indicate that both spring and summer floods are well reproduced,
and the model is suitable to be used in a mountainous catchment situated in the
temperate region. An analysis of the temporal and spatial distribution of temperature,
PET and precipitation over the catchment is implemented during the case study,
which illustrates the importance of capturing the spatial pattern of the input variables
in hydrological modelling. It is also concluded from the calibration and validation
processes that the model is strongly sensitive to the parameters describing the runoff
generation and the routing of water in surface, subsurface and groundwater reservoirs.
1.3.
Model limitations
Hydrological modelling is an attempt to simulate real hydrological processes through
the use of input data describing physical characteristics of the system, a set of
algorithms to transform input data to output of interest, and simplifying assumptions
to limit the scope of the model. Therefore, model limitations must be considered in
running the model and interpreting its output. Followings are major limitations
associated with the WetSpa model simulation.
1) WetSpa is a continuous simulation model. Therefore, the check of data continuity
and reliability must be carried out in the phase of data preparation. If missing data
exist in the precipitation or PET series, logical interpolation must be made for the
time period.
2) The land use categories are grouped, for which some of the categories might be
somewhat ambiguous. For instance, the category agriculture may include farmsteads,
lawns, disturbed areas, and other land uses that are not identifiable as one of the other
specified land use categories. Furthermore, the annual crop rotation is not taken into
account in the model. In addition, lower level highways and country roads are not
modelled uniquely, but are combined within the rural residential category. This may
reduce the amount of runoff and alter the flow direction expected from these areas.
3) Values assigned to any raster or grid cell represents an average value over the area
of each cell. The greater the variability over the cell, the greater will be the error
197
Chapter IX
induced through the use of an average value. Therefore, the grid size should be well
defined. A small grid size may better represent the variability of physical watershed
characteristics, but leads to more memory cost and time consumption during model
simulation, particularly when modelling a large watershed. Balance should be made
between the model accuracy and computer efficiency.
4) The time resolution should be well defined. As for instance, it is not feasible to
predict flood using hourly or daily scale for a very small watershed, since excess
water may flow out within the first time step without any flood wave attenuation. In
this case, a shorter time interval should be chosen if field measurements are available.
5) The snow accumulation and snowmelt are modelled in a simple way by the
degree-day coefficient method with a constant degree-day factor. Moreover, the
redistribution of snow pack and the effects of aspect, local slope, and land use, etc., on
snowmelt are not taken into account. These may reduce the reliability of model
performance in modelling snow processes.
6) WetSpa model generates runoff by an empirical-based modified coefficient
method rather than from equations more closely representing physical processes.
Therefore, calibration is necessary when the model is applied in a different
environment. Though definitely a limitation, the use of the method has its advantages
of closely linking runoff with rainfall intensity and cell characteristics such as slope,
land use, soil type and moisture content, and thus has a great potential to predict the
impact of land use change on hydrological behaviours in the watershed.
7) The impervious fractions for urban areas are set subjectively depending upon cell
size due to the lack of detailed measurements. For instance, for a 50×50 m grid, 30%
is set for residential area, 70% for commercial and industrial area and 100% for major
communication lines, parking lots, etc. This may not actually reflect the real world
and increase uncertainties to the model result.
8) WetSpa model employs many default parameters, which are interpolated from the
literature and used over the entire catchment. Due to the vast variation range,
parameters such as hydraulic conductivity, roughness coefficient, etc. may change
198
Summary and conclusions
greatly when applying the model to another place with quite different environment.
This brings difficulties in model parameterization in an un-gauged river basin.
9) WetSpa model assumes that the groundwater table is below the root zone, which
constrains the use of the model in wetland areas where groundwater table is close to
the land surface. Moreover, the model simulates groundwater flow on small
subcatchment scale. It estimates the groundwater flow and groundwater storage for
each small subcatchment at each time step, but cannot predict the spatial distribution
of groundwater table, as well as its variation during the simulation period.
2.
Future perspectives
There are many directions to improve the WetSpa model in further research. One of
the most important aspects is to complete a detailed quantitative sensitivity analysis
and uncertainty assessment of the model, in order to examine the relative contribution
of the model parameters, initial conditions, and input meteorological variables to the
model’s overall predictive uncertainty. In applications of this modelling system, there
will be cost restraints on the collection and preparation of necessary geophysical and
meteorological input data. It is essential to know which of the inputs are most
important and what spatial and temporal resolution are required to the generation of
accurate results. Another important area of future research is to study the spatial
characteristics of global model parameters used in the model, so as to create all model
parameters in a spatial way in relation with terrain features, and enable the model to
be used in un-gauged river basins without model optimization. Other possible future
researches on the WetSpa model can be as following:
1) Automated calibration of the most important spatial model parameters, which can
be implemented by coupling WetSpa model with PEST, a model-independent
nonlinear parameter estimator as described in chapter VII. The proposed scheme is to
multiply the spatial parameters by a factor and run the model as many times as it
needs to adjust selected parameters within their predetermined range until the
discrepancies between model outputs and a complementary set of flow observations is
reduced to a minimum in the weighted least squares sense.
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2) Development of a practical method to account for the joint effect of altitude, slope,
aspect, general circulation of the atmosphere, etc., on the spatial distribution of
precipitation, temperature and PET. This may highly increase the reliability of model
inputs and decrease the uncertainty of model outputs, especially for modelling in a
large mountainous catchment. The radar information may also be coupled in the
WetSpa model to estimate the spatial distribution of rainfall at each time step.
3) Incorporation of variable travel time into flow routing schemes, for which the
flow velocity is estimated as time variant variable depending upon the channel
geometry and runoff volumes. This may overcome the shortage that flow velocity is
assumed time invariant for a flood event in the current modelling approach.
4) Coupling an intelligent interflow routing scheme into the WetSpa model, for
which the interflow out of one cell is routed to the downhill neighbouring cells
depending on their elevation difference. The scheme of multiple flow path division
may give a more realistic prediction of soil wetness distribution and be used to predict
the saturated runoff source areas in regions with convergent topographies.
5) Improvement of the simple snowmelt model used in the WetSpa model taking
account the variability of degree-day constant, the effect of radiation on snowmelt,
snow drift and deposition in steep terrain, and so on. This will make the snowmelt
model more realistic enabling the simulation of snow cover and melting runoff more
accurately over extensive and heterogeneous landscapes.
6) Incorporating the influence of lake and reservoir operation in the WetSpa model
by combining efficient hydraulic models for engineering purpose. This will make the
modelling system more flexible for flow simulation of large river basins with lakes
and reservoirs involved.
7) Updating the current WetSpa into a real fully distributed model by combining
with a distributed groundwater model. Groundwater balance is then calculated on grid
cell basis allowing the estimation of groundwater table fluctuation and the simulation
of saturation overland flow once the water table reaches the ground surface.
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Summary and conclusions
8) Application of the WetSpa model to study the soil erosion and deposition patterns
allowing to keep a physically meaningful control on the effects of different land
management scenarios on landscape-scale processes, for which the spatial parameters
related to soil erosion and sedimentation will be generated.
9) Application of the WetSpa model to study the pollutant loading and transport in
the surface water and ground water system for the point and non-point source
contaminations, for which a range of chemical, biological and physical parameters
related to contaminant generation and transport will be generated.
In any of the above future perspectives, there will be a significant increase of model
parameters to be estimated and consequently more complex model identifications
have to be performed. This will make the model more and more complicated and
difficult to be accomplished by untrained users. However, parallel extensions can be
built according to the purpose of the project and focusing on specific directions.
Generally, this research has laid a foundation for a GIS-based distributed hydrological
modelling system for the prediction of flood and the simulation of water balance on
catchment scale. Although the simulation results from the model indicate that
additional works are necessary to improve model structure and model parameters, the
WetSpa model at its current state of development provides a substantial framework on
which further researches can be conducted.
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Appendix A
WetSpa Extension: A GIS-based hydrological model for flood
prediction and watershed management
Documentation and User Manual
Abstract
A GIS-based distributed watershed model, WetSpa Extension, has been under
development suitable for use of flood prediction and watershed management on
catchment scale. The model is physically based and simulates hydrological processes
of precipitation, snowmelt, interception, depression, surface runoff, infiltration,
evapotranspiration, percolation, interflow, groundwater flow, etc. continuously both
in time and space, for which the water and energy balance are maintained on each
raster cell. Surface runoff is produced using a modified coefficient method based on
the cell characteristics of slope, land use, and soil type, and allowed to vary with soil
moisture, rainfall intensity and storm duration. Interflow is computed based on the
Darcy’s law and the kinematic approximation as a function of the effective hydraulic
conductivity and the hydraulic gradient, while groundwater flow is estimated with a
linear reservoir method on a small subcatchment scale as a function of groundwater
storage and a recession coefficient. Special emphasis is given to the overland flow and
channel flow routing using the method of linear diffusive wave approximation, which
is capable to predict flow discharge at any converging point downstream by a unit
response function. The model accounts for spatially distributed hydrological and
geophysical characteristics of the catchment and therefore is suitable for studying the
impact of land use change on the hydrological behaviours of a river basin.
1.
Model description
Recent development of GIS and remote sensing technology makes it possible to
capture and manage a vast amount of spatially distributed hydrological parameters
and variables. Linking GIS and the distributed hydrological model is of rapidly
increasing importance in studying the impact of human activity on hydrological
Appendix A
behaviours in a river basin. Ideally, watershed models should capture the essence of
the physical controls of topography, soil and land use on runoff production as well as
the water and energy balance. Distributed parameter hydrological models are typically
structured in characterizing watershed conditions such as topography, soil type, land
use, drainage density, degree of soil saturation, and rainfall properties, for which it is
advantageous to use the data currently available in GIS format. This report describes
such a model, called WetSpa Extension.
1.1.
Model construction
1.1.1. Model objectives
WetSpa is a physically based and distributed hydrological model for predicting the
Water and Energy Transfer between Soil, Plants and Atmosphere on regional or basin
scale proposed by Wang et al. (1997) and Batelaan et al. (1996). The model
conceptualizes a basin hydrological system being composed of atmosphere, canopy,
root zone, transmission zone and saturation zone. The basin is divided into a number
of grid cells in order to deal with the heterogeneity. Each cell is further divided into a
bare soil and vegetated part, for which the water and energy balance are maintained.
Water movement in the soil is simplified as one-dimensional vertical flow, including
surface infiltration, percolation and capillary rise in the unsaturated zone and recharge
to groundwater. The model was designed to simulate the Hortonian overland flow and
the variable source area concept of runoff generation with time resolution of minutes.
Due to the complexity of the model structure and data limit, the model is difficult to
be used for an engineering purpose. Therefore, a WetSpa extension is developed with
a flexible data acquisition and higher computational efficiency. The main objectives
of the WetSpa Extension are:
1) To provide a comprehensive GIS-based tool for flood prediction and watershed
management on catchment scale, which is compatible with GIS technology and
remote sensing information.
2) To enable the use of the model for simulation of the spatial distribution of
hydrological processes, such as runoff, soil moisture, groundwater recharge, etc.
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3) To enable the use of the model for analysis of land use change and climate change
impacts on hydrological processes.
4) To provide for a distributed model that can operate on cell scale and a variable
time step, and a semi-distributed model on small subwatershed scale.
5) To provide a platform on which the future water quality and soil erosion models
can be developed at multiple scales.
1.1.2. Model structure
The model uses multiple layers to represent the water and energy balance for each
grid cell, taking into account the processes of precipitation, interception, snowmelt,
depression, infiltration, evapotranspiration, percolation, surface runoff, interflow and
groundwater flow. The simulated hydrological system consists of four control
volumes: the plant canopy, the soil surface, the root zone, and the saturated
groundwater aquifer. The precipitation that falls from the atmosphere before it reaches
the ground surface is abstracted by canopy interception storage. The remaining
rainfall reached to the ground is separated into two parts depending on the land cover,
soil type, slope, the magnitude of rainfall, and the antecedent moisture content of the
soil. The first component fills the depression storage at the initial stage and runs off
the land surface simultaneously, while the remaining part infiltrates into the soil. The
infiltrated part of the rainfall may stay as soil moisture in the root zone, move laterally
as interflow or percolate further as groundwater recharge depending on the moisture
content of the soil. Drainage water from a given cell flows laterally depending on the
amount of groundwater storage and the recession coefficient. The percolation out of
the soil layer is assumed to recharge the groundwater storage. Interflow from the root
zone is assumed to contribute overland flow and routed to the watershed outlet
together with surface runoff. The total runoff from each pixel cell constitutes the sum
of the surface runoff, the interflow and the groundwater flow. Evaporation takes place
from intercepted water, depressed water and the soil surface, while transpiration takes
place from the plant through root system in the soil layer, and a small part from the
groundwater storage. The water balance for the interception storage includes
precipitation, evaporation and through fall. The water balance for the depression
storage includes through fall, infiltration, evaporation and surface runoff. The water
balance for the soil column includes infiltration, evapotranspiration, percolation, and
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Appendix A
lateral subsurface runoff. The water balance for the groundwater storage includes
groundwater recharge, deep evapotranspiration, and lateral groundwater flow. Figure
A-1.1 shows schematically the model structure at a pixel cell level.
Evapotranspiration
Precipitation
Interception
CANOPY
Through fall
Depression
SOIL SURFACE
Surface runoff
Infiltration
SOIL
Interflow
Recharge
GROUNDWATER
D
I
S
C
H
A
R
G
E
Drainage
Figure A-1.1: Model structure of WetSpa Extension at a pixel cell level
The simple structure in Figure A-1.1 is used in the model because the emphasis here
is on developing and testing parameterizations for the root zone. Excess runoff,
infiltration, evapotranspiration, interflow and percolation estimates are point
calculations. Different slope, land use and soil properties in different grid cells of a
watershed result in different amounts of excess runoff when subjected to the same
amount of rainfall. The routing of runoff from different cells to the watershed outlet
depends on flow velocity and wave damping coefficient using the method of diffusive
wave approximation. Although the spatial variability of land use, soil and topographic
properties in a watershed are considered in this model, the groundwater response is
modelled on small subcatchment scale for the convenience of model parameterization
and model simulation. Two alternatives for determining groundwater flow are used in
the model, simulating groundwater flow with a simple linear reservoir method and
non-linear reservoir method. All model equations are specifically chosen to maintain a
physical basis and well supported by previous studies. The inputs to the model are
precipitation and potential evapotranspiration (PET). Temperature data are needed if
snow accumulation and melt occur during the simulation period. The digital maps of
topography, land use and soil type are used to derive all necessary spatial distributed
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model parameters. The main outputs of the model are river flow hydrographs and
spatially distributed hydrological characteristics, such as soil moisture, infiltration
rates, groundwater recharge, surface water retention or runoff, etc.
1.1.3. Model assumptions
1) Soil characteristics and landscape are isotropic and homogeneous for a single
raster cell.
2) Canopy cover and ground cover are homogeneous for a single raster cell.
3) Precipitation is spatially homogeneous within a raster cell.
4) The form of Hortonian overland flow is valid for most of the areas.
5) Evapotranspiration is neglected during a rainstorm and when the soil moisture is
lower than residual soil moisture.
6) Deep evapotranspiration takes place when soil is dry, and is restricted by the
amount of effective groundwater storage.
7) Soil moisture content is homogeneous in a single cell, while the groundwater
storage is uniformly distributed on small subcatchment scale at each time step.
8) Water flows along its pathway from one cell to another, and cannot be partitioned
to more than one adjacent raster cell.
9) The method of linear diffusive wave approximation is valid for routing of both
overland flow and channel flow.
10) Hydraulic radius is location dependent, varies with flood frequency, but remains
constant over a flood event.
11) Interflow occurs when soil moisture content is higher than field capacity and can
be estimated by Darcy’s law and kinematic approximation.
12) The water losses from overland and channel flow, as well as the water losses from
deep percolation are not important.
1.2.
Data preparation
The preparation of the database for WetSpa Extension to a specific watershed implies
the determination of the complete drainage structure of the watershed, the spatial
distribution of land use classes and soil types, as well as the collection of available
hydro-meteorological data related to the project.
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1.2.1. Digital data
The model uses geo-spatially referenced data as input for deriving model parameters,
which includes most data types supported by ArcView, such as coverage, shape file,
grid and ASCII file. Image can be used for reference within a view, but is not used
directly by the model. The digital maps of topography, land use and soil type are 3
base maps used in the model, while other digital data are optional depending upon the
data available and the purpose and accuracy requirement of the project.
1) Digital Elevation Model (DEM)
The raster-type DEM, generated from point or contour topographic map, is preferred
in order to be compatible with other remotely sensed data. The spatial and elevation
resolutions should be fine enough to capture the essential information allowing taking
care of the effects of spatial variability of the watershed characteristics on its
hydrological response. In practice, the chosen resolution must allow adequate
representation of the actual topography and accurate determination of the watershed
area, its river network, and its subwatersheds. In the absence of large water surfaces
(lakes, reservoirs, ponds, etc.) and large plains with little or no elevation variation,
processing of the DEM is relatively straightforward. After filtering of the initial data
to detect and remove erroneous extreme values, the slope, aspect, flow direction, flow
length and flow accumulation of each grid cell are determined. Over flat areas, no
slope and, hence, no direction can be computed. Also, the DEM may contain artificial
pits from which no water can flow out. These specific problems have to be reserved
by modifying elevations artificially to lead to flow directions as accurate as possible
on any of the cells. Next, the identification of river network is performed by assuming
that all cells draining more than a specified upstream area are part of that network.
More or less detailed river networks can be identified, depending on the selected
upstream threshold area. Finally, the stream links, stream orders and the
subwatersheds corresponding to these river reaches are identified.
2) Land use and soil type
Land use information is an important input to the WetSpa Extension, which is
normally obtained from high-resolution remotely sensed data for the same area as the
DEM, and with the same grid cell size. For hydrological simulation purpose, all land
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use classes initially determined are grouped together into 14 WetSpa classes
significantly distinguished from each other on the basis of their effect on hydrological
processes, namely crop, short grass, evergreen needle leaf tree, deciduous needle leaf
tree, deciduous broad leaf tree, evergreen broad leaf tree, tall grass, irrigated crop, bog
marsh, evergreen shrub, deciduous shrub, bare soil, impervious area and open water
surface. Each of these classes is characterized by quantitative attributes. The groups
may vary according to the algorithms used in the model. For instance, only 5 classes
are considered in defining potential runoff coefficient and depression storage capacity,
i.e. crop, grass, forest, bare soil and urban areas. For simulation purpose, the
percentage of bare soil and impervious areas are estimated for each grid cell based on
the high-resolution land use map.
Soil types of the catchment are obtained from the soil information furnished by soil
maps. The soil code system used in WetSpa Extension is based on the soil texture
triangle developed by the United States Department of Agriculture (USDA), which is
characterized by its percentage of clay, silt and sand, ranging from the fine textures
(clay), through the intermediate textures (loam), and the coarser textures (sand).
Therefore, the original soil coverage map has to be converted to a raster map with
WetSpa soil codes in the phase of data preparation. The grid must be adjusted to the
same grid structure as the DEM and limited to the same area by using the mask grid
of the catchment. The reclassification can be done within GIS framework, which
makes use of a reclassification table prepared in ArcInfo GIS or ArcView Spatial
Analyst. This work must be done with caution in order to make the conversion as
accurate as possible. The soil properties and hydraulic characteristics of those soil
types are considered constant in the present version of the model. Default values are
interpolated from literature as described in section A-3.1, but users can substitute any
other more appropriate values for them.
3) Optional digital data
Other optional digital data that can be used in the model include point coverage or
shape file of gauging station locations, line coverage or shape files of stream network
and major traffic lines, polygon coverage or shape files of boundary and sewer
systems, etc. These data are of great help in delineating watershed drainage path
network, estimating spatial rainfall distribution, as well as properly determining
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model routing parameters. If two or more rain gauges exist in or around the catchment
with measured data, the Thiessen polygon weighting method is then introduced to
calculate the rainfall distribution, for which the weighting factors are computed for
each grid cell and subwatershed. Otherwise, a uniform rainfall distribution is assumed
over the catchment. The internal streamflow gauges can be used in the watershed
discretization process, for which the watershed is split at those locations where gauges
are present. This makes it possible to compare measured and computed flow
hydrographs at a point or series points. The coverage of official river network and
catchment boundary is a very important geo-referenced data, which can be combined
within GIS in delineating watershed drainage network, particularly for meandering
rivers in flat areas. Usually, from the topographic information present in a DEM, it is
quite difficult to represent watershed boundary and meandering rivers in plain areas.
To account those cases, data coming from the hydrographical layer of digital maps
(boundary, rivers, lakes, ponds, etc.) are used in combination with the DEM to
identify drainage areas, find input and output cells for water bodies, and make any
necessary corrections to flow directions in order to have the river reaches flow where
they should and to be able to estimate the flow length closer to reality.
For hydrological modelling in a complex terrain, such as an urban or suburban
watershed, the sewer systems, communication lines, artificial channels, etc. are
important elements in drainage structure configuration, and govern flow direction
more strongly than the derived aspect at a local scale. Since most of these barriers are
not sufficient to be represented in a DEM, additional procedures in term of deriving
more realistic flow direction map are performed using GIS overlaying technique in
the model, where the general flow direction map is overlaid by the sewer flow
direction map, the communication line flow direction map and the river flow direction
map subsequently. This allows water draining from the sewer areas at its outlet and
water crossing communication lines at the concave points to join the river. The altered
flow direction map is then used for further drainage structure delineation.
1.2.2. Hydro-meteorological data
The basic input requirements for the WetSpa Extension consist of model parameters,
initial conditions, meteorological data and streamflow data for model calibration and
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validation. The basic meteorological data requirements are rainfall and PET.
Temperature data are optional used for simulation of snowmelt. In the case of
calculating PET by the Penman-Monteith equation, additional meteorological data are
required, including air temperature, radiation, relative humidity and wind speed. In
this section, the meteorological and hydrological data are described. The model
parameters and initial conditions are described in the subsequent sections.
1) Rainfall
Rainfall is the fundamental driving force and pulsar input behind most hydrological
processes. Rainfall-runoff models are particularly sensitive to the rainfall input and
any errors in estimates are amplified in streamflow simulations. The input rainfall
series must be in the same interval as the model running step. For instance, hourly
rainfall data are required for each raingauge when modelling in an hourly scale. In
many cases, rainfall data at certain stations are in a daily scale rather than an hourly
scale. These data can be used by disaggregation according to the temporal structure of
rainfall of the neighbouring hourly reference raingauges. The Thiessen polygon
method is then used to estimate areal rainfall during model simulation. Depending
upon the objective of the study and on the time scale of the catchment response, the
time resolution of rainfall input can be enlarged to a daily scale or reduced to a finer
resolution corresponding to the model time scale. The rainfall data are treated as
accumulated totals so that the rainfall associated with any particular time is the
rainfall volume since the end of last time step.
2) Potential evapotranspiration
WetSpa Extension requires PET data as one of the inputs with the same time interval
as rainfall series, which can be obtained from field measurement or estimated by
physical or empirical equations. Normally, daily values of PET are sufficient, for
which the value is either averaged to an hourly value or disaggregated with a simple
empirical equation as a function of hour as described in section A-2.7. If only one
measuring station is available, the PET data can be uniformly applied to the whole
study area for a small catchment. Otherwise, the value should be revised for different
virtual stations according to the local meteorological and geophysical conditions,
especially when modelling in mountainous areas. The areal PET is estimated using
the Thiessen polygon method. The evapotranspiration data are treated as accumulated
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Appendix A
totals so that the evapotranspiration associated with any particular time is the
evapotranspiration volume since the end of last time step.
3) Discharge
For the purpose of model calibration and evaluation, observed discharge data at the
basin outlet with the same time interval as the precipitation series are required for
visual comparison and statistical analysis. The discharge data at internal gauging sites
are optional for model verification. Data conversion to another time scale is necessary
according to the simulation time step. The discharge data at any particular time is the
average discharge since the end of last time step.
4) Optional meteorological data
Temperature data are required when snow accumulation and snowmelt occur in the
catchment. Normally, daily average temperature data are sufficient in simulating snow
processes. Anyhow, the temperature data should keep the same time interval as the
precipitation series. If the Penman-Monteith equation is chosen to calculate the PET,
when there is no measured data available in the study area, the data of air temperature,
short wave radiation, relative humidity, and wind speed are required in the model,
which can be obtained from the routine meteorological stations.
2.
Model formulation
WetSpa Extension is a distributed, continuous, physically based model describing the
processes of precipitation, runoff and evapotranspiration for both simple and complex
terrain. It is a distributed model because the watershed and channel network are
represented by a grid of mesh. Each cell is described by its unique parameters, initial
conditions, and precipitation inputs. It is continuous model because it has components
describing evapotranspiration and soil water movement between storms, and therefore
can maintain water and energy balance between storms. It is physically based because
the mathematical models used to describe the components are based on such physical
principles as conservation of mass and momentum. In this section, a brief description
about the model formulation involved in the processes of interception, snowmelt,
depression, infiltration, surface runoff, evapotranspiration, percolation, interflow and
groundwater flow is presented.
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2.1.
Precipitation
Rainfall is a fundamental component of any hydrological models. To obtain
information at a specific location in a catchment, either interpolation or extrapolation
of the existing data is required. The spatial distribution of rainfall is often estimated
by the elementary techniques from a set of fixed rainfall gauges, while the temporal
distribution is ignored by averaging the rainfall over a predetermined period. The
crudest method for estimating the precipitation over a region is to plot contours of
equal precipitation with the assistance of a structured grid. The average precipitation
is computed between successive isohyets. This method is difficult to realize for each
modelling time step with sparse precipitation data, although the task of plotting
isohyets is automated with the advance of GIS technology.
A common interpolation approach is the Thiessen polygons, which is also the method
used in the current version. In this approach, areas closest to a rainfall gauge adopt the
rainfall recorded at that gauge. This results in constant rainfall regions with
discontinuities between regions. In addition, there is no justification in assuming that
point rainfall measurements provide reliable estimates of precipitation in the
surrounding region. The inverse distance weighted method is an alternative approach,
for which the rainfall at any desired location is interpolated from the given data using
weights that are based on the distance from each rainfall gauge and the desired
location. This approach produces a smooth rainfall distribution along with the
undesirable troughs and peaks located at the rainfall gauges. However, interpolation is
difficult with the inverse distance weighted method for higher dimensional data sets.
A special case is the precipitation interpolation in high mountainous areas with few
point measurement. In order to account for the large variations in precipitation with
altitude, the reference series can be adjusted for each grid cell or subcatchment by the
method of lapse rate corrections in which the precipitation is assumed to vary linearly
with the elevation (Dingman et al., 1988):
Pi = Pref + Pref (H i − H ref )β
(2.1)
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where Pi is the precipitation at cell i (mm), Pref is the precipitation at the reference
precipitation station (mm), Hi and Href are the height at cell i and at the reference
station, and β is the precipitation lapse rate. Calibration is necessary in order to get a
proper precipitation lapse value. The last two methods are optional in addition to the
Thiessen polygon method.
2.2
Interception
Interception is that portion of the precipitation, which is stored or collected by vegetal
cover and subsequently evaporated. In studies of major storm events, the interception
loss is generally neglected. However, it can be a considerable influencing factor for
small or medium storms and water balance computations would be significantly in
error if evaporative losses of intercepted precipitation were not included.
1) Mass balance of the interception storage
Interception is a complicated process, which is affected by the storm characteristics,
the species of vegetation, percentage of canopy cover, growth stage, season, and wind
speed, etc. Interception loss is higher during the initial phase of a storm and
approaches zero thereafter. In WetSpa Extension, the rainfall rate is reduced until the
interception storage capacity is reached. If the total rainfall during the first time
increment is greater than the interception storage capacity, the rainfall rate is reduced
by the capacity. Otherwise, all rainfall is intercepted in the canopy, and the remainder
of interception is removed from the rainfall in the following time increments. The
equation can be expressed as:
⎧ I i , 0 − SI i (t − 1)
⎪
I i (t ) = ⎨
⎪ P (t )
⎩ i
for Pi (t ) f I i , 0 − SI i (t − 1)
(2.2)
for Pi (t ) ≤ I i , 0 − SI i (t − 1)
where Ii(t) is the interception loss at cell i over the time interval (mm), Ii,0 is the cell
interception storage capacity (mm), SIi(t-1) is the cell interception storage at time step
t-1 (mm), and Pi(t) is the cell precipitation amount (mm). The mass balance of
interception storage at a pixel cell is computed as:
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SI i (t ) = SI i (t − 1) + I i (t ) − EI i (t )
(2.3)
where SIi(t-1) and SIi(t) are cell interception storage at time step t-1 and t (mm), EIi(t)
is the cell evaporation from interception storage (mm). EIi(t) = 0 when interception
storage is zero, or during the storm event; EIi(t) = SIi(t-1) under the condition of Pi(t)
= 0 and EP > SIi(t-1) > 0, in which EP is the potential evaporation (mm); and EIi(t) =
EP for the rest conditions.
2) Seasonal variation of interception storage capacity
Interception storage capacity is a function of leaf area index and vegetal species.
Evidently, it varies with season in template regions. Typical values can be found in
the literature (Horton, 1919; Clark, 1940; Lull, 1964; Simons, 1981; Rowe, 1983).
Through physical analysis and interpolations, a lookup table of maximum and
minimum interception storage capacity corresponding to summer and winter extremes
for different vegetation types are established. Specifically, the interception storage
capacity of crop is set to 0.8 mm during growing season and null for the rest. For
wetting losses on impervious areas, the adsorption storage capacity is set to 0.5 mm
(Bauwens et al., 1996). Since the interception storage capacity varies continuously
with time, a simple sine-shaped variation curve is proposed for the convenience of
model programming. The empirical equation is similar as that of estimating daily
potential evaporation based on statistical analysis of long-term measurements (De
Smedt, D., 1997), and is written as:
⎡1 1
d − 87
⎛
I i , 0 = I i , min + (I i , max − I i , min )⎢ + sin ⎜ 2π
365
⎝
⎣2 2
⎞⎤
⎟⎥
⎠⎦
b
(2.4)
in which Ii,min is the minimum interception storage capacity at cell i (mm), Ii,max is the
maximum interception storage capacity (mm), and d is the day of the year. The
exponent b controls the shape of the variation curve, and can be adjusted according to
the local conditions. Hourly interception storage capacity is assumed to be constant
during a day in the model. Therefore, the interception storage capacity is only a
function of the date. Figure A-2.1 gives a graphical presentation for the annual
variation of grass interception storage capacity, for which the minimum and
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maximum interception capacity is 0.5 and 2.0 mm respectively, and the exponent b is
set to 1.35.
Interception storage
capacity (mm)
2.5
b = 1.35
2.0
1.5
1.0
0.5
0.0
1/1
1 1/2
1 1/3
3
1/4
4
1/5
5 1/6
6
1/7
7 1/8
8
1/9
1/11 12
1/12
9 1/10
10 11
Date (d/m)
Figure 2.1: Annual variation of grass interception storage capacity
By substituting Eq. (2.2) to Eq. (2.3), the interception loss and interception storage at
each time step can be estimated. No interception loss exists when the interception
storage capacity is achieved, and all precipitation reaches ground surface. The
intercepted water in canopy loses by evaporation and returns to the hydrological cycle
with potential evaporation rate modified by a correction factor. Although interception
losses may be highly significant in the annual water balance, it is relatively
unimportant for flood-producing storms.
2.3. Snowmelt
Snow accumulation and melt are important hydrological processes in river basins,
where the snow pack acts as storage in which precipitation is retained during the cold
season and subsequently released as melt water during the warmer season. The
snowmelt is incorporated within WetSpa Extension. This component is optional and
temperature data is required additionally if the sow routine is selected. The conceptual
temperature index or degree-day method (Martinec et al., 1983) is widely used in
snowmelt modelling, in which the full energy balance is replaced by a term linked to
air temperature. It is physically sound in the absence of short wave radiation, when
much of the energy supplied to the snow pack is atmospheric long wave radiation. Its
reliance on daily temperature and precipitation data make it useful for modelling snow
processes in regions with a lack of regular snow observations, or historical periods
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with limited data. In WetSpa Extension, an additional snowmelt caused by the
advective heat transferred to the snow pack by precipitation is also considered. The
total snowmelt is calculated as
M i = C snow (Ti − T0 ) + C rain Pi (Ti − T0 )
where Mi is the daily snowmelt at cell i (mm/day), Ti
(2.5)
is the cell daily mean
temperature (°C), T0 is a threshold temperature (usually 0°C), Csnow is the degree-day
or melt factor (mm/°C/day), and Crain is a degree-day coefficient regarding to the heat
contribution from rainfall (mm/mm/°C/day). Specifically, temperature, precipitation
and snow cover often vary significantly within a mountainous catchment, and in many
cases, the hydro-meteorological information from mountainous areas is quite sparse.
To account for the large variations in temperature with altitude, the reference series is
adjusted for each grid cell by the lapse rate correction
T i = T ref + (H i − H ref )β
(2.6)
where Tref is the temperature at the reference station (°C), Hi and Href are the height at
cell i and at the reference station, and β is the temperature lapse rate. The degree-day
coefficient implicitly represents all terms of the energy budget that account for the
mass balance of a snow pack, and is therefore highly variable over time (Singh et al.,
2000), and different between vegetation types (Kite & Kouwen, 1992). However, a
constant value is used in the current version for simplicity. This factor can be
determined by field experiments, or will have to be obtained by calibration otherwise.
Moreover, the degree-day method by definition is only valid for daily melt
simulations, whereas simulations for short time intervals require finer temporal
resolutions. In this case, a fully energy balance module is suggested, and it will be
incorporated in the future version.
2.4.
Excess rainfall and infiltration
Excess rainfall, or effective rainfall, is that part of rainfall in a given storm, which
falls at intensities exceeding the infiltration capacity of the land surface. It may stay
217
Appendix A
temporarily on the soil surface as depression, or become direct runoff or surface
runoff at the watershed outlet after flowing across the watershed surface under the
assumption of Hortonian overland flow. Direct runoff forms the rapidly varying
portions of watershed hydrographs and is a key component for estimating the
watershed response.
Infiltration is the downward flow of water into the soil defined as the quantity of
rainfall that does not contribute to surface runoff. Under normal conditions, the
infiltration rate is mainly a function of: (1) rainfall characteristics, (2) surface
conditions, (3) soil characteristics, (4) initial moisture content of the soil, etc. It is
desirable to relate loss rates to physical characteristics of the watershed in a
continuous simulation so that loss rates may be computed as a function of catchment
characteristics and soil moisture conditions during a model simulation. In WetSpa
Extension, a modified coefficient method for estimating surface runoff and infiltration
processes is used relating runoff and infiltration with topography, soil type, land use,
soil moisture, and rainfall intensity. The equations can be expressed as:
⎡θ (t ) ⎤
PE i (t ) = C i [Pi (t ) − I i ((t ) )] ⎢ i ⎥
⎣⎢ θ i , s ⎦⎥
a
Fi (t ) = Pi (t ) − I i (t ) − PE i (t )
(2.7)
(2.8)
in which PEi(t) is the rainfall excess on cell i over the time interval (mm), Fi(t) is the
cell infiltration (mm), Ii(t) is the interception loss (mm), θi(t) is the cell soil moisture
content at time t (m³/m³), θi,s is the soil porosity (m³/m³), α is an exponent related with
rainfall intensity (-), and Ci is the cell potential rainfall excess coefficient or potential
runoff coefficient (-). This parameter Ci has a rather stable regularity under ideal
conditions. Default rainfall excess coefficients for different slope, soil type and land
cover are taken the reference from the literature (Kirkby 1978, Chow et al. 1988,
Browne 1990, Mallants & Feyen 1990, and Fetter 1980).
Based on the physical analysis and linear interpolations of these values, a look up
table is then established, relating potential rainfall excess coefficient to the different
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combinations of slope, soil type and land use. The rainfall excess is closely related
with the relative soil moisture content. No rainfall excess when soil is dry, and actual
rainfall excess coefficient approaches to the potential value when soil moisture
content close to saturation, under which the infiltrated water is considered to be used
for percolation, evapotranspiration and lateral interflow. The exponent in the formula
is a variable reflecting the effect of rainfall intensity on the rainfall excess coefficient.
The value is higher for low rainfall intensities resulting less surface runoff, and
approaches to 1 for high rainfall intensities. The threshold value can be defined during
model calibration. If α = 1, a linear relationship is assumed between rainfall excess
and soil moisture. The effect of rainfall duration is also accounted by the soil moisture
content, in which more excess produces due to the increased soil moisture content.
Figure A-2.2 shows the relationship between actual rainfall excess coefficient, relative
soil moisture content and potential rainfall excess coefficient with an exponent of 2.0.
Rainfall excess
co efficient
1.0
CC i==0.2
0.2
0.8
CC i==0.5
0.5
0.6
CC i==0.8
0.8
0.4
a = 2.0
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Relative saturation
Figure A-2.2: Relationship between rainfall excess coefficient and soil moisture
2.5.
Depression and overland flow
Precipitation that reaches the ground may infiltrate, or get trapped into several small
depressions, which is retained in puddles, ditches, and on the ground surface. As soon
as rainfall intensity exceeds the local infiltration capacity, the rainfall excess begins to
fill depression. Water held in depression at the end of rain either evaporates or
contributes to soil moisture and subsurface flow by the following infiltration.
Depression storage may be of considerable magnitude and may play an important role
in hydrological analysis. Stock ponds, terraces, and contour farming etc. tend to
moderate flood by increasing depression storage. Depression losses usually occur
219
Appendix A
during the initial period of the storm and are negligible after a certain time. Factors
that affect depression storage include: (1) nature of terrain; (2) slope, the more slope
gradient, the less depression losses; (3) type of soil surface, the more sandy soil, the
more depression losses; (4) land use, the more woody land use, the more depression
losses; (5) antecedent rainfall, the more soil water content, the less depression storage;
and (6) time, for which depression losses decrease with time. Depression is
considered included in the potential rainfall excess coefficient in the WetSpa
Extension, in order to emphasize its effects on surface runoff production, particularly
for the rough surfaces and for small flood events. Therefore, default potential rainfall
excess coefficient should be determined cautiously from the literature values, taking
the influence of interception and depression into account.
2.5.1. Formulation of depression storage
Due to the extreme variability of affecting factors, it is very difficult to specify a
general relationship for depression losses. In WetSpa Extension, a simple empirical
equation suggested by Linsley (1982) is used to estimate depression storage:
⎛
⎛ PC i ⎞ ⎞
⎟⎟
SDi (t ) = SDi , 0 ⎜1 − exp⎜⎜ −
⎟⎟
⎜
SD
i ,0 ⎠ ⎠
⎝
⎝
(2.9)
in which SDi(t) is the cell depression storage at time t (mm), SDi,0 is the cell
depression storage capacity (mm), and PCi is the accumulative excess rainfall on the
soil surface (mm). The concept of Eq. (2.9) is that both overland flow and depression
storage occurs simultaneously, allowing some of the water delivering as overland
flow, even if excess rainfall is less than the depression storage capacity. A sketch of
SDi(t) as a function of PEi is shown in Figure A-2.3.
The increment of depression storage can be obtained by derivation of t for both side
of Eq. (2.9) as:
⎛ PC i ⎞
⎟
∆SDi (t ) = PE i (t ) exp⎜ −
⎜ SD ⎟
i,0 ⎠
⎝
220
(2.10)
WetSpa Extension: Documentation and User Manual
where ∆SDi(t) is the increment of depression storage at cell i over the time interval
(mm), and PEi(t) is the excess rainfall for the time increment (mm). Considering that
the rainfall is interrupted between storm events, the accumulative excess rainfall can
be estimated based on Eq. (2.9), which is the excess rainfall at present time step plus
an excess rainfall corresponding to the depression storage at last time step.
⎛ SDi (t − 1) ⎞
⎟
PC i = PE i (t ) − SDi , 0 ln⎜1 −
⎜
SDi , 0 ⎟⎠
⎝
(2.11)
Obviously, PCi equals PEi(t) when depression storage at last time step, SDt-1, is zero,
and becomes a very large value when SDi(t-1) approaches to SDi,0, leading to a very
small depression storage increment, ∆SDi,t, from Eq. (2.10). The capacity of
depression storage, SDi,0, is mainly affected by landform, soil type and vegetation.
Based upon the analysis and linear interpolation of the typical values collected in the
literature (ASCE, 1969; SINCE, 1972; Sheaffer, 1982), a lookup table for default
depression storage capacity is set up according to the categories of slope, land use and
Depression storage (mm)
soil type, which is similar as the lookup table of potential rainfall excess coefficient.
SDi,0 = 3.5 mm
DS0
3.0
2.0
1.0
0.0
0.0
3.0
6.0
9.0
12.0
15.0
Rainfall excess (mm)
Figure A- 2.3: Sketch of depression storage as a function of excess rainfall
2.5.2
Mass balance of depression storage
As discussed above, the depressed water on soil surface will be depleted by
evaporation directly or infiltrated into the soil after the rainstorm. The mass balance of
depression storage can be expressed as:
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Appendix A
SDi (t ) = SDi (t − 1) + ∆SDi (t ) − EDi (t ) − Fi (t )
(2.12)
where EDi(t) and Fi(t) are cell evaporation and infiltration from depression storage for
the time increment after the rainstorm (mm); EDi(t) = 0 when Pi(t) > 0 or DSi(t-1) = 0;
EDi(t) = EP – Ei(t), when Pi(t) = 0 and DSi(t-1) ≥ EP-EIi(t), in which EP and EIi(t) are
the potential evaporation and the evaporation from the cell interception storage (mm);
EDi(t) = DSi(t) when Pi(t) = 0 and 0 < SDi(t) < EP-Ei,(t). The infiltration from
depression storage after rainstorm can be estimated using Eq. (2.7) and Eq. (2.8) by
taking the depressed water as rainfall on the ground surface.
2.5.3. Formulation of overland flow
Recall that the excess rainfall is a sum of overland flow and the change of depression
storage, the amount of overland flow, RSt (m), can be written as:
RS
i
(t ) =
⎡
⎛
PE i
PE i (t )⎢1 − exp ⎜⎜ −
⎝ SD i , 0
⎣⎢
⎞⎤
⎟⎥
⎟
⎠ ⎦⎥
(2.13)
Eq. (2.13) assumes that both overland flow and depression storage occur
simultaneously as described in Figure A-2.4, for which the overland flow approaches
to zero when the accumulative excess rainfall is very small, and approaches to PEi(t)
when the depression storage closes to its capacity. This is different with the
assumption that overland flow begins only after the depression storage capacity is
reached as the dashed line shown in the figure.
RS i (t) / PEi (t)
1.0
0.5
SD0
SDi ,0 = 3.5 mm
0.0
0.0
3.0
6.0
9.0
12.0
PEi (mm)
Figure A-2.4: Graphical presentation of excess rainfall and overland flow
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2.6.
Water balance in the root zone
Soil moisture storage is the actual quantity of water held in the soil at any given
instant, usually applied to a soil layer of root depth. Based on the different soil water
content, the moisture storage can be divided into saturation capacity, field capacity,
plant wilting point, residual soil moisture, etc. WetSpa Extension calculates water
balance in the root zone for each grid cell. Soil water is fed by infiltration and
removed from the root zone by evapotranspiration, lateral interflow and percolation to
the groundwater storage, as described in Figure A-2.5.
F
ES
θ
RS
D
RI
RG
Figure A-2.5: Graphical presentation of soil water balance
The moisture storage in the root zone is expressed by a simple balance equation as:
Di [θ i (t ) − θ i (t − 1)]i = Fi (t ) − ESi (t ) − RGi (t ) − RI i (t )
(2.14)
in which θi(t) and θi(t-1) are cell soil moisture content at time step t and t-1 (m³/m³),
Di is the root depth (mm); Fi(t) is the infiltration through soil surface for the time
increment (mm), including the infiltration during the rainstorm and the infiltration
from depression storage after the rainstorm (mm), ESi(t) is the actual
evapotranspiration from the soil for the time increment (mm), RGi(t) is the percolation
out of root zone or groundwater recharge (mm), and RIi(t) is the interflow or lateral
shallow subsurface flow out of the cell for the time increment (mm). Apparently, soil
moisture content in the root zone is a crucial factor in the model, which affects the
hydrological processes of surface runoff, actual evapotranspiration, interflow and
percolation out of the root zone soil.
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Appendix A
2.7.
Evapotranspiration from soil
2.7.1. Potential evapotranspiration
PET is defined as the quantity of water vapour, which could be emitted by plant or
soil surface per unit area and unit time under the existing conditions without water
supply limit. The main influencing factors to the potential evaporation are: (1) solar
radiation, providing energy or heat; (2) wind speed, transporting the moisture away
from the surface, and (3) specific humidity gradient in the air above the water surface,
being the driving forces for diffusion of water vapour. When taking all of these
variables into account in a continuous simulation model, it would make the model
much too complex. In WetSpa Extension, three options are available to estimate PET.
1) Penman-monteith equation
The original Penman-Monteith method has been modified by many researchers and
extended to plant surfaces by introducing resistance factors. A newly result is the
FAO-56 Penman-Monteith equation derived from the original Penman-Monteith
equation and the equation of aerodynamic and surface resistances, which can be used
to estimate PET on an hourly or daily time basis (Allen, 2000):
EP =
37
u 2 (e s − e a )
T + 273.2
∆ + γ (1 + 0.34u 2 )
0.408∆(R n − G ) + γ
(2.15)
where EP is the reference or PET (m), Rn is the net radiation (MJ/m²), G is the soil
heat flux (MJ/m²), T is the air temperature (C), es is the saturation vapour pressure at
air temperature (kPa), ea is the vapour pressure of air (kPa), u2 is the wind speed at 2
m (m/s), ∆ is the slope of saturation vapour pressure curve at air temperature (kPa/C),
and γ is the psychomotor constant (kPa/C). Eq.(2.15) is an estimate of EP from a
hypothetical short grass with a height of 0.12 m, a surface resistance of 70 s/m, and an
albedo of 0.23. Supporting equations of Eq. (2.15) for calculating es, ea, ∆, γ and G
can be found from Allen (2000). Once the meteorological data of net radiation, air
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temperature, relative humidity, and wind speed is available, the PET rate EP can be
estimated using Eq. (2.15) in the WetSpa Extension.
2) Statistical method based on historical records
Even though the Penman-Monteith method is physically based and can give good
estimate to the PET, but it is always the fact that collecting all relevant meteorological
data is rather difficult for many study areas. In this case, a statistical method can be
applied if a long series of evaporation records are available inside the catchment or
outside the catchment with similar meteorological environment. De Smedt, D. (1997)
derived a simple empirical equation for estimating potential evaporation from free
water surface applied to the Belgian situation. Through statistically analysis of the
daily potential evaporation records over the period 1901-1993 at Ukkel
meteorological station, Belgium, a mathematical equation that fits the curve of the
average daily potential evaporation was obtained as:
⎡
⎛ d − 87 ⎞⎤
EPd = 0.27 + 1.37 ⎢1 + sin ⎜ 2π
⎟
365 ⎠⎥⎦
⎝
⎣
1.35
(2.16)
in which EPd is the daily potential evaporation (mm), d is the day of a year, starting
from 1 for the first of January and ending with 365 for the 31st of December, while
intercalate days are not considered. Figure A-2.6 gives a graphical comparison
between observed and simulated daily potential evaporation at Ukkel for the year
1997. The hourly distribution of potential evaporation for a certain day is estimated by
the empirical equation as:
EP =
EPd
24
⎡
⎛ h − 6 ⎞⎤
⎢1 + 0.9 sin⎜ 2π 24 ⎟⎥
⎠⎦
⎝
⎣
(2.17)
where EP is the hourly potential evaporation (mm), h is the hour of a day between 0
and 24. Eq. (2.17) assumes that the hourly potential evaporation is always higher or
equal to 0.1EPd/24 and therefore never reaches zero. The maximum potential
evaporation rate occurs at solar noon and equals 1.9EPd/24. Obviously, the integral of
225
Appendix A
the above equation over a day is exactly equal to EPd of that day. A simulated curve
of hourly EP is presented in Figure A-2.7 with EPd = 3 mm.
7.5
EPd (mm)
Observed
Simulated
5.0
2.5
0.0
1/2 3/3
1/3
1/1 31/1
1/4
2/4
1/5
3/5
1/6
2/6
1/7
3/7
1/8
2/8
1/9 2/10
1/10 2/11
1/11 2/12
1/12
2/9
Date (d/m)
Figure A-2.6: Observed and simulated daily EP at Ukkel for the year 1997
EPh (mm)
0.3
0.2
0.1
0.0
0
4
8
12
16
20
24
Time (h)
Figure A-2.7: Simulated hourly EP at Ukkel with EPd = 3mm
For a given study area with available historical evaporation records, the constant 0.27,
1.37 and 1.35 in Eq. (2.19) can be readjusted in order to get a better fit to the
measurement. Due to the lack of theoretical basement behind, errors may arise in
certain hours. But in general, this method can meet the requirement of large flood
prediction and other engineering purpose. The main advantage of this method is that
the potential evaporation rate is only a function of the time, and can be easily coupled
in the model programming.
3) Measurement using pans
Evaporation pans provide a measurement of the combined effect of temperature,
humidity, wind speed and sunshine on the PET. The potential evaporation can be
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estimated with the pan evaporation multiplied by a pan coefficient, and used directly
in the model for parameter calibration and model simulation.
2.7.2. Actual evapotranspiration
Without considering the evaporation from interception storage and depression storage,
actual evapotranspiration is defined as the sum of the quantities of water vapour
evaporated from the soil and the plants when the ground is at its actual moisture
content. Thus, if soil is fully saturated, then it is expected that the actual
evapotranspiration rate equals to the PET rate. However, if the soil or vegetation is
water stressed, the evapotranspiration will be less than potential evapotranspiration.
Influencing factors to the actual evapotranspiration include weather, vegetation and
soil condition, etc. Since the actual evapotranspiration is governed by the availability
of water, soil moisture content becomes a crucial factor, which is determined by water
recharge and the soil characteristics.
In the WetSpa Extension, evapotranspiration consists of four parts: (1) evaporation
from
interception
storage,
(2)
evaporation
from
depression
storage,
(3)
evapotranspiration from soil, and (4) evapotranspiration from groundwater storage. It
is assumed that water evaporates to the atmosphere in a cascade way, i.e. from
interception storage, depression storage, soil matrixes, and groundwater storage
consequently. The evaporation from interception storage and depression storage has
been described in section A-2.2 and A-2.5, and the groundwater contribution to the
evapotranspiration will be described in section A-2.9. The actual evapotranspiration
from soil and plant is calculated for each grid cell using the relationship developed by
Thornthwait and Mather (1955) as a function of PET, vegetation and its growing stage,
and moisture content of the cell:
⎧
⎡θ i (t ) − θ i , w ⎤
⎪[c v EP − EI i (t ) − ED i (t )] ⎢
⎥ for θ i , w ≤ θ i (t ) p θ i , f
ES i (t ) = ⎨
⎢⎣ θ i , f − θ i , w ⎥⎦
⎪
for θ i (t ) ≥ θ i , f
⎩c v EP − EI i (t ) − ED i (t )
(2.18)
where ESi(t) is the actual soil evapotranspiration for the time increment (mm), cv is a
vegetation coefficient determined by land use classes varying throughout the year, θi(t)
227
Appendix A
is the cell average soil moisture content at time t (m³/m³), θi,f is the soil moisture
content at field capacity (m³/m³), and θi,w is the soil moisture content at plant
permanent wilting point (m³/m³). It can be concluded from Eq. (2.18) that when the
sum of interception and depression storage is greater than the PET, all evaporation
comes from the interception and depression storage with a potential rate. When the
sum of interception and depression storage is less than the amount of PET, all the
remaining storage evaporates at this time step, and there is a part of
evapotranspiration from the soil layer depending on the soil moisture content. For the
simulation between storm events, actual evapotranspiration is mainly from the soil
and plant, which varies linearly between PET when soil moisture content is at or
above field capacity, and zero when soil moisture content is below the wilting point.
A graphical presentation of soil evapotranspiration is given in Figure A-2.8, in which
θi,s is the soil porosity (m³/m³). For the cell in urban areas, soil evapotranspiration is
reduced by the impervious areas, and is calculated by cell evapotranspiration times
ESi(t)/cvEP
the pervious percentage.
1
0
θi,w
θi,f
Moisture content
θi,s
Figure A-2.8: Graphical presentation of soil evapotranspiration
2.8.
Percolation and interflow
Percolation or groundwater recharge refers to the natural process by which water is
added from soil water zone to the saturation zone of the aquifer. Groundwater
recharge is an important component in the root zone water balance, which connects
the soil water and the saturated groundwater. The main influencing factors to the
groundwater recharge are the hydraulic conductivity, root depth, and water content of
the soil. In WetSpa Extension, percolation out of root zone is assumed to pass directly
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to the groundwater reservoir, and estimated based on the Darcy’s law, being the
product of hydraulic conductivity and the gradient of hydraulic potential. When an
assumption is made that the pressure potential only varies slightly in the soil, its
gradient can be approximated to zero, and the percolation is controlled by gravity
alone (Famiglietti and Wood, 1994). Based on this assumption, the percolation
amount out of root zone is simply specified as the hydraulic conductivity
corresponding to the average effective saturation in the respective soil layer. The
Brooks and Corey relationship between hydraulic conductivity and effective
saturation is used to define percolation, which is simply (Brooks and Corey, 1966):
⎡θ (t ) − θ i , r ⎤
RGi (t ) = Ki [θ i (t )]∆t = Ki , s ⎢ i
⎥ ∆t
⎢⎣ θ i , s − θi , r ⎥⎦
A
(2.19)
where RGi(t) is the percolation out of root zone over the time interval (mm), Ki[θi(t)]
is the effective hydraulic conductivity corresponding to the average soil moisture
content at time t (mm/h), ∆t is the time interval (h), Ki,s is the cell saturation hydraulic
conductivity (mm/h), θi,s is the soil porosity (m³/m³), θi,r is the cell residual moisture
content (m³/m³), and A is the pore disconnectedness index, calculated by the equation
A = (2+3B)/B, in which B is the cell pore size distribution index.
1.0
K[θik(/k
(t)]/K
s i,s
Sand
Loam
Clay
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(st-sr)/(ss/sr)
[θi(t)-θ
i,r]/(θi,s-θi,r)
Figure A-2.9: Effective hydraulic conductivity as a function of moisture content
Figure A-2.9 gives a graphical presentation for the effective hydraulic conductivity as
a function of moisture content for three different soil types: sand, loam and clay. It
can be seen that the effective hydraulic conductivity varies with moisture content
229
Appendix A
exponentially, reaching a maximum, the saturated conductivity, when soil is
completely saturated, and zero when soil becomes dry.
Interflow, or shallow subsurface lateral flow, is also a key component in the soil water
balance. It is defined as the water which infiltrates the soil surface and moves laterally
through the upper soil layers until it enters a channel, which includes litter flow,
return flow, unsaturated through flow, saturated through flow and so on, but excludes
the saturated groundwater flow. Due to the delayed flow time, interflow usually
contributes to the falling limb of a flood hydrograph, but it may also be a part of peak
discharge at the basin outlet, particularly for the areas with steep slope and forest
cover in humid or temperate regions. Factors that influence the amount of interflow
include: (1) physical properties and depth of the soil, for which coarse texture leads to
more vertical flow, while fine texture or layered soil results in resistance to vertical
flow and interflow may some time occur quickly; (2) vegetation cover and land use,
which are directly related to the maintenance of infiltration capacity and the
conditioning effect of organic material on soil structure, bulk density and porosity; (3)
topography, for which the slope gradient is a major factor determining the amount and
the velocity of interflow; (4) soil moisture content, for which higher moisture content
tends to generate more interflow; and (5) lithology and climate of the study area. In
WetSpa Extension, interflow is assumed to occur after percolation and cease when
soil moisture is lower than field capacity. The quantity of interflow out of each cell is
calculated from Darcy's Law and the kinematic approximation, i.e. the hydraulic
gradient is equal to the land slope of the grid cell:
RI i (t ) = c s Di S i K [θ i (t )]∆t Wi
(2.20)
in which RIi(t) (mm) is the amount of interflow out of the cell over the time interval
∆t (h), Di is the root depth (m), Si is the cell slope (m/m), K[θI(t)] (mm/h) is the cell
effective hydraulic conductivity at moisture content θi(t) (m³/m³), Wi is the cell width
(m), and ci (-) is a scaling factor depending on land use, used to consider stream
density and the effects of organic matter and root system on horizontal hydraulic
conductivity in the top soil layer. Apparently, rapid interflow may generate in areas
with high moisture, steep slope and well vegetation, while little is produced for other
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areas with Eq. (2.20). For modelling simplification, interflow is assumed to join the
surface runoff at the nearest channels or gullies serving as a supplementary discharge
to the stream flow during and after storm event without further divisions among down
slope neighbours. Soil hydraulic characteristics, such as porosity, field capacity,
residual saturation, hydraulic conductivity, and so on, are collected from the literature,
and used as default values in the WetSpa Extension.
2.9.
Groundwater storage and baseflow
Groundwater storage is defined as the quantity of water in the zone of saturation
including that part of such stage when water is entering and leaving storage.
Groundwater storage capacity refers to the volume of saturated groundwater that can
be alternatively extracted and replaced in the deposit under natural conditions.
Normally, the groundwater discharge forms a base flow to the hydrograph at basin
outlet. Groundwater storage capacity is governed by the thickness and extent of the
aquifer and its porosity, while the movement of groundwater is governed by the
hydraulic gradient and the hydraulic conductivity of the aquifer.
For the purpose of streamflow prediction, an estimate must be made of flow from the
groundwater storage into the stream for each time step. Since little is known about the
bedrock, the simple concept of a linear reservoir is used to estimate groundwater
discharge on a small subcatchment scale, while a non-linear reservoir method is
optional in the model with storage exponent of 2 (Wittenberg and Sivapalan, 1999).
The groundwater outflow is added to any runoff generated to produce the total
streamflow at the subcatchment outlet. The general groundwater flow equation can be
expressed as:
QG s (t ) = c g [SG s (t ) 1000]
m
(2.21)
where QGs(t) is the average groundwater flow at the subcatchment outlet (m3/s), SGs(t)
is the groundwater storage of the subcatchment at time t (mm), m (-) is an exponent,
m = 1 for linear reservoir ,and m = 2 for non-linear reservoir, cg is a groundwater
recession coefficient taking the subcatchment area into account, has a dimension of
231
Appendix A
(m2/s) for linear reservoir and (m/s) for non-linear reservoir, which is dependent upon
area, shape, pore volume and transmissivity of the subcatchment, and can be
estimated from recession portions of streamflow hydrographs if measurement data at
the subcatchment outlet are available. For each subcatchment, the groundwater
balance can be expressed as:
Ns
SGs (t ) = SGs (t −1) +
∑[RG (t )A ]
i =1
i
As
i
− EGs (t ) −
QGs (t )∆t
1000As
(2.22)
where SGs(t) and SGs(t-1) are groundwater storage of the subcatchment at time step t
and t-1 (mm), Ns is the number of cells in the subwatershed, Ai is the cell area (m2),
As is the subcatchment area (m2), EGs(t) is the average evapotranspiration from
groundwater storage of the subcatchment (mm), and QGi(t) is the groundwater
discharge (m³/s).
The component of evapotranspiration from groundwater storage is considered in the
WetSpa Extension, which may be produced by deep root system or by capillary drive
in the areas with shallow groundwater table. It happens only when soil moisture is
less than field capacity from Eq. (2.18) and has a greater impact during the summer
than the winter, giving the effect of a steeper recession during dry period. A simple
linear equation is used in the model relating deep evapotranspiration with PET and
groundwater storage as:
EGi (t ) = cd [cv EP − EIi (t ) − EDi (t ) − ESi (t )]
(2.23)
where EGi(t) is average evapotranspiration from groundwater storage (mm), EP is
PET (mm), and cd (-) is a variable, calculated by SGi(t)/SGs,0, in which SGi(t) is the
groundwater storage of the subwatershed at time t (mm), and SGs,0 is the groundwater
storage capacity of the subwatershed (mm). Using the method of groundwater
reservoir, there are only two groundwater parameters, the groundwater recession
coefficient and the storage capacity, which can be determined by calibration against
baseflow separated from the observed hydrograph.
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2.10.
Overland flow and channel flow routing
2.10.1 Flow response at a cell level
The routing of overland flow and channel flow in WetSpa Extension is implemented
by the method of a linear diffusive wave approximation. This method is suitable for
simulating sheet flow and channel flow at a certain degree, and one of the important
advantages is that it can be solved analytically, avoiding numerical calculation and
identification of the exact boundary conditions. Assuming the cell as a reach with 1-D
unsteady flow and neglecting the inertial terms in the St. Venant momentum equation,
the flow process in the cell can be modelled by the diffusive wave equation as (Miller
and Cunge, 1975):
∂Q
∂Q
∂ 2Q
+ ci
− di
=0
∂t
∂x
∂x 2
(2.24)
where Q (m³/s) is the flow discharge at time t (s) and location x (m), ci is the
kinematic wave celerity at cell i (m/s), di is the dispersion coefficient at cell i (m²/s).
Considering a system bounded by a transmitting barrier upstream and an adsorbing
barrier downstream, the solution to Eq. (2.24) at the cell outlet, when the flow
velocity and diffusion coefficient are constant, can be obtained by the first passage
time density distribution of a Brownian motion and expressed as (Eagleson, 1970):
ui (t ) =
⎡ (c t − l )2 ⎤
exp⎢− i i ⎥
4d i t ⎦
2 πdit 3
⎣
li
(2.25)
where ui(t) is the cell impulse response function (1/s), and li is cell size (m). Two
parameters ci and di are needed to define the cell response function, which can be
estimated using the relation of Manning as (Henderson, 1966):
5
ci = vi
3
(2.26 )
233
Appendix A
di =
vi Ri
2S i
(2.27)
where Ri is the average hydraulic radius of cell i (m), Si is the cell slope (m/m), and vi
is the flow velocity of the cell i (m/s). The hydraulic radius is determined by a power
law relationship with an exceeding probability (Molnar and Ramirez, 1998), which
relates hydraulic radius to the controlling area and is seen as a representation of the
average behaviour of the cell and the channel geometry:
Ri = a p ( Ai ) p
b
(2.28)
where Ai is the drained area upstream of the cell (km²), which can be easily
determined by the flow accumulation routine in ArcView GIS, ap (-) is a network
constant and bp (-) a geometry scaling exponent, both depending on the discharge
frequency. The flow velocity is calculated by the Manning’s equation as:
2
vi =
1
1 3 2
Ri S i
ni
(2.29)
where ni is the Manning’s roughness coefficient (m-1/3s), which depends upon land use
categories and the channel characteristics. Default Manning’s roughness coefficients
can be collected from literature. The velocity calculated by Eq. (2.29) may be very
large or even zero due to variations in land surface slope. Therefore it is bounded
between predetermined limits vmin and vmax during model calculation. Flow velocity is
a time-dependent, discharge-related and location-related hydrological variable. But to
be applicable of the diffusive wave approximation method for hydrological analysis,
the flow must be only location-related. In reality, water depth usually increases as
water goes downstream. As water deepens, the effective resistance of the streambed
and banks on the flow diminishes because the hydraulic radius increases. To reflect
this property, the channel roughness coefficient is set between predetermined limits
nmax and nmin, depending upon the GIS derived stream orders in the WetSpa Extension.
Thus, with the supporting Equations (2.26) to (2.29), the cell impulse unit response
function ui(t) can be calculated for each grid cell over the entire watershed, which
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reflects the redistribution tendency in the flow element serving as a flow redistribution
function.
2.10.2. Flow response at a flow path level
Under the assumption of linear routing system, the flow response at the end of a flow
path, resulting from a unit impulse input to a single cell, can be calculated without the
interference of the inputs to the other cells. Determining the flow-path response
consists in routing the impulse through the corresponding sequence of cells down to
the system outlet. Along the flow-path, the impulse travels through many cells, each
of them having a different unit-impulse response function. In this routing process, the
output of any cell becomes the input to the receiving cell, and the original input
distribution is continuously modified by the flow dynamics in the cells, which are
described by their impulse response functions. The flow path response is found by
successively applying the convolution integral, giving:
N
Ui (t) = ∏u j (t )
(2.30)
j =1
where Ui(t) is flow path response function (1/s), the subscript i refers to the cell in
which the input occurs, j is the cell sequence number, and N is the total number of
cells along the flow path. The diffusion equation model satisfies Eq. (2.30) within the
cells, which means that it allows for longitudinal decomposability. Since the cell unit
impulse response functions are time-invariant, the result of the convolutions of Eq.
(2.30) is also time-invariant, and therefore, there is a linear relation between the flow
path response and the impulse input. Assuming that the flow path response Ui(t) is
also a first passage time distribution, De Smedt F. et al. (2000) and Liu et al. (2002,
2003) proposed an approximate numerical solution to Eq. (2.30), relating the
discharge at the end of a flow path to the available runoff at the start of the flow path:
U i (t ) =
1
2πσ i2 t 3
⎡ (t − t i ) 2 ⎤
exp ⎢−
⎥
2
t i3
⎣ 2σ i t / t i ⎦
(2.31)
235
Appendix A
where ti is the mean flow time from the input cell to the flow path end (s), and σi2 is
the variation of the flow time (s²). The parameters ti and σi2 are spatially distributed,
and can be obtained by convolution integral along the topographic determined flow
paths as a function of flow celerity and dispersion coefficient:
N ⎛
1
ti = ∑ ⎜
⎜
c
j =1 ⎝ j
⎞
⎟l j
⎟
⎠
⎛ 2d j
⎜ 3
j =1 ⎝ c j
N
σ i2 = ∑ ⎜
(2.32)
⎞
⎟l j
⎟
⎠
(2.33)
The summations presented in Eq. (2.32) and (2.33) can be calculated for each grid cell
as a weighted flow length to the water outlet or any downstream converging point
with the routine FLOWLENGTH involved in the standard GIS tools. Examples of
such flow path impulse response function are presented in Figure 2.10 for different
mean flow time and its variation. It is seen that the response function is asymmetric
with respect to time caused by the wave attenuation.
0.08
ti = 1800, σi2 = 9002
Series1
Ui (t) (1/s)
0.06
ti = 3600, σi2 = 18002
Series2
ti = 7200, σi2 = 27002
Series3
0.04
0.02
0
0
1800
3600
5400
7200
9000
10800
t (s)
Figure A-2.10: Flow path response functions with different ti and σi2
The flow response at the end of a flow path, to an arbitrary input at the start cell, can
be calculated by convolving the input runoff volume by the flow path unit impulse
response function. From a physical point of view, this is equivalent to decomposing
the input into infinite impulses and adding all the responses into a single response.
Thus, the outflow hydrograph to an arbitrary input can be determined as:
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Q i (t ) =
t −τ
∑ V (τ )U (t − τ )
τ
i
=0
i
(2.34)
where Qi(t) is the outflow at the end of a flow path produced by an arbitrary input in
cell i (m³/s); Ui(t-τ) is the flow path response function (1/s), being equivalent to the
instantaneous unit hydrograph (IUH) used in the conventional hydrology, and τ is the
time delay (s); Vi(τ) is the input runoff volume at cell i and at time τ (m³), including
surface runoff and interflow, as well as groundwater runoff if cell i is located at the
subcatchment outlet.
2.10.3. Flow response of the catchment
Considering the areal decomposability in a linear routing system, the catchment flow
response can be determined as the sum of its elements responses from all contributing
cells. Thus, the catchment flow response can be calculated as:
Q (t ) =
Nw
∑ Q (t )
i =1
i
(2.35)
where Q(t) is the total flow at the catchment outlet (m³/s), Nw is the number of cells
over the entire catchment. Hence, the flow routing consists of tracking runoff along its
topographic determined flow path, and evaluating groundwater flow out of the
subcatchment. The total discharge is the sum of the overland flow, interflow and
groundwater flow, and is obtained by convolution of the flow response from all grid
cells. The advantage of this approach is that it allows the spatially distributed runoff
and hydrological parameters of the terrain to be used as inputs to the model, and can
route runoff from a certain land use area to the catchment outlet or any downstream
converging point.
2.11.
Subwatershed integration
In case of watershed modelling on medium or large scale, model parameterisation and
computation on small grid size are tedious, costly and time consuming. On the other
237
Appendix A
hand, working with coarse spatial resolution may introduce errors by aggregation of
spatial input data and misrepresentation of the true watershed characteristics. To cope
with this problem, WetSpa Extension provides a simplified semi-distributed option
working on the scale of a small hydrological unit, so as to allow adequate simulation
and mapping of the areal distribution of the hydrological processes. These units
correspond to very small subcatchments, built up from high resolution DEM data,
rather than to large grid cells with approximately the same area as the subwatersheds.
This has the advantage of allowing for the internal drainage structure of the units,
which would be impossible by using large grid cells. Model parameters,
meteorological data input, and state variables for each simulation unit are obtained by
integration of the values from all cells of that subcatchment. Meanwhile, the water
and energy balance, as well as the process state variables, are computed on each unit
during model simulation at each time step.
The subwatershed parameters calculated by WetSpa Extension include area, slope,
potential rainfall excess coefficient, interception capacity, depression capacity, soil
physical properties, etc. Flow hydrographs are first calculated at the outlet of each
subcatchment using the subcatchment response function, and thereafter, the flow is
routed to the catchment outlet along the river channel by means of channel flow
response function. Considering the effect of cell characteristics on the subwatershed
IUH, the subcatchment response function is computed by integration of the flow path
response functions for all cells in the subcatchment weighted by their potential rainfall
excess coefficient. The equation can be written as:
Ns
Ns
i =1
i =1
U s (t ) = ∑ [CiU i (t )] ∑ Ci
(2.36)
where Us(t) is the response function or IUH of the subcatchment (1/s), Ci is the
potential rainfall excess coefficient at cell i (-), Ui(t) is the flow path response function
at the subcatchment outlet with runoff input at cell i (1/s), and Ns is the number of
cells in the subcatchment. The flow hydrograph at subcatchment outlet is obtained by
summation of its surface runoff, interflow and groundwater flow, and can be
expressed as:
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Q s (t ) =
t −τ
∑ V (τ )U (t − τ ) + QG (t )
s
τ =0
s
s
(2.37)
where Qs(t) is the flow hydrograph at the subcatchment outlet (m³/s), Vs(τ) is volume
of readily available runoff of the subcatchment including surface runoff and interflow
(m³), τ is the time delay (s), and QGs(t) is the groundwater flow at the subcatchment
outlet (m³/s). The total hydrograph at the watershed outlet is obtained by integration
of the flow hydrographs produced from each subwatershed, and can be expressed as:
Q (t ) =
Nr
∑ Q (τ )U (t − τ )∆ t
s =1
s
r
(2.38)
where Q(t) is the flow hydrograph at the catchment outlet (m³/s), Ur(t) is the channel
response function from the subcatchment outlet to the catchment outlet calculated by
Eq. (2.31) (1/s), ∆t is the time interval (s), and Nr is the number of subcatchment or
the number of stream links in the catchment. With the unit response functions defined
for each simulation unit and the corresponding river channel, water can be routed
accumulatively downstream up to the catchment outlet. However, the process of flow
routing within each subcatchment can be omitted in case of highly intensive
watershed discretization, since the water may flow out of the subwatershed within the
first time step. In practice, division of the watershed should be performed according to
the project purpose and the complexity of the terrain. A few simulations are necessary
to decide the watershed discretization to meet varies objectives of the project.
2.12.
Catchment water balance
Water balance for the entire catchment is used to keep track of water changes in the
hydrological system, and also a measure of model performance by comparing the
simulation results with the field observations. Among the constituents in the system,
soil water content is an important state variable that influence fluxes into and out of
the root zone (infiltration, evapotranspiration, percolation and interflow) and the
energy balance on the land surface. The stores of interception, depression, soil
moisture and groundwater are treated as separate control volume, but related
239
Appendix A
subsequently. Precipitation is the input to the system, while direct runoff, interflow,
groundwater flow, and evapotranspiration are losses from the hydrological system.
When modelling for a relatively long time period, changes in the storage of
interception, depression and channel can be neglected, and the general watershed
water balance can be expressed as:
P = RT + ET + ∆SS + ∆SG
(2.39)
where P is the total precipitation in the watershed over the simulation period (mm),
RT and ET are total runoff and total evapotranspiration (mm), ∆SS is the change in
soil moisture storage for the watershed between the start and the end of the simulation
period (mm), and ∆SG is the change in groundwater storage of the watershed (mm).
For a given simulation period T (s) and initial moisture and groundwater storage
condition, these components can be expressed as:
Nw
T
P = ∑ ∑ Pi (t ) N w
(2.40)
T Nw
T Nr
⎡ QG s (t ) ⎤
∆t ⎥ N r
RT = ∑ ∑ [RS i (t ) + RI i (t )] N w + ∑ ∑ ⎢
As
t = 0 i =1
t = 0 s =1 ⎣
⎦
(2.41)
t = 0 i =1
Nw
T
T
Nr
ET = ∑∑ [EI i (t ) + EDi (t ) + ES i (t )] N w + ∑∑ [EGi (t )] N r
t = 0 i =1
Nw
∆SS = ∑ Di [θ i (T ) − θ i (0)] N w
(2.42)
t =0 s =1
(2.43)
t =1
Nr
∆SG = ∑ [SG s (T ) − SG s (0)] N r
(2.44)
s =1
where θi(T) and θi(0) are cell soil moisture content at the end and the start of the
simulation period (m³/m³), SGs(T) and SGs(0) are subcatchment groundwater storage
at the end and the start of the simulation period (mm), and the others have been
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described in above sections. All of these components vary over time. A change in any
one component of the watershed water balance can result in changes in the other
components in the system. This is particularly useful for analysing the impact of land
use changes on the watershed hydrological processes. For instance, deforestation
results in more surface runoff and less infiltration, thus, decreasing the change in soil
moisture storage and groundwater storage for a storm event, and the
evapotranspiration is limited by the moisture content as well. When the model
performs on a very long time series, the changes in soil moisture and groundwater
storage will be less important, and the total precipitation is more or less equal to the
sum of the runoff and the evapotranspiration.
3.
Parameter identification and model evaluation
3.1.
Default model parameters
3.1.1. Default parameters characterizing soil texture classes
Soil textural classes are used to provide information concerning soil physical
properties, such as porosity, hydraulic conductivity, pore size distribution index, etc.
Although other descriptors such as horizon and structural size certainly influence the
hydraulic parameters of soils, Cosby et al. (1984) perform a two-way analysis of
variance of nine descriptors to conclude that soil texture alone can account for most of
the discernible patterns. Over the last two decades, a great deal of efforts has been
made to the estimation of soil hydraulic properties from the information on soil
textures in the literature (McCuen et al., 1981; Rawls et al., 1982; Cosby et al., 1984;
Rawls & Brakensiek, 1985; Carsel & Parrish, 1988). In WetSpa Extension, soil
textures are classified into 12 USDA (U.S. Department of Agriculture) classes
ranging from 1 to 12 based on the percentage of sand, silt and clay in the soil sample.
Fine textured soils have a high percentage of clay and are very sticky when wet and
hard when dry, while coarse textured soils have a high percentage of sand and are
loose and friable. A lookup table is then established as presented in Table A-3.1 to
estimate hydraulic properties as a function of soil texture classes using mean values
obtained from the literature.
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Appendix A
Table A-3.1: Default parameters characterizing soil textural classes
Texture classes
Sand
Loamy sand
Sandy loam
Silt loam
Silt
Loam
Sandy clay loam
Silt clay loam
Clay loam
Sandy clay
Silt clay
Clay
Hydraulic
conductiveity1 (mm/h)
208.80
61.20
25.92
13.32
6.84
5.58
4.32
2.30
1.51
1.19
0.90
0.60
Porosity1
(m³/m³)
0.437
0.437
0.453
0.501
0.482
0.463
0.398
0.471
0.464
0.430
0.479
0.475
Field
capacity1
(m³/m³)
0.062
0.105
0.190
0.284
0.258
0.232
0.244
0.342
0.310
0.321
0.371
0.378
Wilting
point1
(m³/m³)
0.024
0.047
0.085
0.135
0.126
0.116
0.136
0.210
0.187
0.221
0.251
0.251
1
Obtained by analysis of data presented in Rawls et al. (1982)
2
Obtained from Cosby et al. (1984)
Residual
moisture1
(m³/m³)
0.020
0.035
0.041
0.015
0.015
0.027
0.068
0.040
0.075
0.109
0.056
0.090
Pore size
distribution
index2 (-)
3.39
3.86
4.50
4.98
3.71
5.77
7.20
8.32
8.32
9.59
10.38
12.13
Soil texture is a key variable in the coupled relationship between climate, soil, and
vegetation. Under given climatic and vegetation conditions the above soil-texturedependent physical properties, through their influence on soil water movement and
the energy state of the water in the soil column, determine the soil wetness values
which in turn establish the water condition of the vegetation (Fernandez-Illescas et al.,
2001). One advantage in favour of using texture as the only distinguishing factor
among components is that this approach significantly simplifies model data
management. When only a single distinguishing factor is used, components with a
common texture can be lumped together and the spatial soils information passed from
the GIS to the hydrology model is set at 12 different specifications. Among the soil
properties listed in Table A-3.1, hydraulic conductivity has by far the largest
coefficient of variation based on the analysis of Carsel & Parrish (1988), and is more
sensitive than other soil related parameters. These parameters allow to be revised
during model calibration for refining better fit as described in Chapter A-4.
3.1.2. Default parameters characterizing land use classes
Land use or land cover is an important boundary condition, which directly or
indirectly influence many hydrological processes. The most obvious influence of land
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use on the water balance of a catchment is on the evapotranspiration process.
Different land use types have different evapotranspiration rates, due to their different
vegetation cover, leaf area indices, root depths and albedo. During storms,
interception and depression rates are different for different land use types. Land use
also influences the infiltration and soil water redistribution process, because
especially the saturated hydraulic conductivity is influenced by plant roots and pores
resulting from soil fauna (Ragab & Cooper, 1993). An extreme example is the
influence of build up areas and roads on overland flow. Moreover, land use influences
surface roughness, which controls overland flow velocity and floodplain flow rates.
Therefore, the effect of land use should be taken into account as much as possible in
the simulation calculations.
Table A-3.2: Default parameters characterizing land use classes
Land use classes
Crop or mixed farming
Short grass
Evergreen needle leaf tree
Deciduous needle leaf tree
Deciduous broad leaf tree
Evergreen broad leaf tree
Tall grass
Irrigated crop
Bog or marsh
Evergreen shrub
Deciduous shrub
Bare soil
Impervious area
Open water
Vegetated
fraction1
(%)
85
80
80
80
80
90
80
80
80
80
80
5
0
0
Leaf area
index1
(-)
0.5 – 6.0
0.5 – 2.0
5.0 – 6.0
1.0 – 6.0
1.0 – 6.0
5.0 – 6.0
0.5 – 6.0
0.5 – 6.0
0.5 – 6.0
0.5 – 6.0
1.0 – 6.0
0.5 – 2.0
0.0 – 0.0
0.0 – 0.0
Root
depth1
(m)
1.0
1.0
1.5
1.5
2.0
1.5
1.0
1.0
1.0
1.0
1.0
1.0
0.0
0.0
Manning’s
coefficient2
(m-1/3s)
0.15
0.20
0.40
0.40
0.80
0.60
0.40
0.20
0.20
0.40
0.40
0.10
0.02
0.02-0.05
Interception
capacity3
(mm)
0.05 – 1.00
0.05 – 1.00
0.10 – 0.80
0.05 – 0.80
0.05 – 2.00
0.15 – 2.00
0.10 – 1.50
0.05 – 1.00
0.05 – 1.00
0.10 – 1.50
0.05 – 1.50
0.05 – 1.00
0.00 – 0.00
0.00 – 0.00
1
Obtained from Dickinson et al. (1993)
2
Obtained from Lull (1964), Zinke (1967) and Rowe (1983)
3
Obtained from Chow (1964), Haan (1982), Yen (1992) and Ferguson (1998)
Fourteen basic land use classes are specified in the WetSpa Extension, based on the
observed physical and biophysical cover of the land surface, as well as the function
and the actual purpose for which the land is currently being used. Such information is
obtained from ground surveys or remote sensing images. For each land use type,
243
Appendix A
several vegetation parameters are defined taking the reference of previous studies as
shown in Table A-3.2. In order to more correctly simulate the effect of vegetation on
interception and evapotranspiration, a range of leaf area index and interception
capacity is given in the table corresponding to the minimum and maximum values in a
year for each vegetation class. Calculation of the temporal variation is described in
Chapter A-2. Moreover, some of the parameters, such as root depth, roughness
coefficient, etc., should be determined as functions of both soil type and land use.
However, for the present implementation, these parameters remain a function of land
use type only.
Values of Manning’s roughness coefficient shown in Table A-3.2 are typical values
obtained from experiments reported in the literature. These values are generally
representatives of very small areas when correspondence exists between reality and
the mathematical model of one-dimensional flow over a plane. Therefore, if a larger
grid size, e.g. larger than 100 m, is used in the model, these values should be adjusted
downward to reflect the greater number of rills on long slopes (Wu et al., 1982;
Hairsine & Parlange, 1986; Vieux & Farajalla, 1994). In case the model is applied to a
medium or large watershed, the parameter of channel roughness coefficient, which is
governed mainly by bed material and channel cross section, will have a great
influence to the predicted hydrograph. In natural rivers without overbank flow, the
roughness coefficient is generally small for downstream channels due to their fine bed
materials, and is large for upstream channels in contrast. To account for these effects,
a linear relationship is assumed in the model relating Manning’s roughness coefficient
to the stream order described as:
⎛ O − Omin ⎞
⎟⎟(nr , max − nr , min )
nr = nr , max − ⎜⎜
⎝ Omax − Omin ⎠
(3.1)
where nr is the Manning’s coefficient (m-1/3s) for stream order O, Omax and Omin are
maximum and minimum stream order derived from ArcView GIS, and nr,max and
nr,min are maximum and minimum Manning’s coefficients corresponding to Omax and
Omin (m-1/3s). Clearly, the Manning’s coefficient has largest value for the channel with
minimum order and smallest value for the channel with maximum order with
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Equation 3.1. The value of nr,max and nr,min can be defined in the script according to
the channel characteristics.
3.1.3. Potential runoff coefficient
The runoff coefficient of a grid or catchment is the ratio of runoff volume to rainfall
volume. A simple and practical technique is developed in WetSpa Extension to
estimate the runoff coefficient under varying land use, soil type, slope, rainfall
intensity and antecedent soil moisture condition as described in Chapter A-2.
Undoubtedly, these variables act independently but also interact in their effects on the
runoff coefficient and soil infiltration. A table of potential runoff coefficient is built
for deferent land use, slope and soil type combinations and under the condition of
near saturated soil moisture as shown in Table A-3.3. Water lost from the soil surface
is considered to infiltrate into the soil used for further vertical percolation,
evapotranspiration and lateral interflow.
Table A-3.3: Potential runoff coefficient for different land use, soil type and slope
Sandy
Silty
Land Slope Sand Loamy Sandy Loam Silt Silt clay Clay clay Sandy Silty Clay
use (%)
sand loam
loam
loam loam loam clay clay
Forest <0.5
0.5-5
5-10
>10
Grass <0.5
0.5-5
5-10
>10
Crop <0.5
0.5-5
5-10
>10
Bare <0.5
soil 0.5-5
5-10
>10
IMP
0.03
0.07
0.13
0.25
0.13
0.17
0.23
0.35
0.23
0.27
0.33
0.45
0.33
0.37
0.43
0.55
1.00
0.07
0.11
0.17
0.29
0.17
0.21
0.27
0.39
0.27
0.31
0.37
0.49
0.37
0.41
0.47
0.59
1.00
0.10
0.14
0.20
0.32
0.20
0.24
0.30
0.42
0.30
0.34
0.40
0.52
0.40
0.44
0.50
0.62
1.00
0.13
0.17
0.23
0.35
0.23
0.27
0.33
0.45
0.33
0.37
0.43
0.55
0.43
0.47
0.53
0.65
1.00
0.17
0.21
0.27
0.39
0.27
0.31
0.37
0.49
0.37
0.41
0.47
0.59
0.47
0.51
0.57
0.69
1.00
0.20
0.24
0.30
0.42
0.30
0.34
0.40
0.52
0.40
0.44
0.50
0.62
0.50
0.54
0.60
0.72
1.00
0.23
0.27
0.33
0.45
0.33
0.37
0.43
0.55
0.43
0.47
0.53
0.65
0.53
0.57
0.63
0.75
1.00
0.27
0.31
0.37
0.49
0.37
0.41
0.47
0.59
0.47
0.51
0.57
0.69
0.57
0.61
0.67
0.79
1.00
0.30
0.34
0.40
0.52
0.40
0.44
0.50
0.62
0.50
0.54
0.60
0.72
0.60
0.64
0.70
0.82
1.00
0.33
0.37
0.43
0.55
0.43
0.47
0.53
0.65
0.53
0.57
0.63
0.75
0.63
0.67
0.73
0.85
1.00
0.37
0.41
0.47
0.59
0.47
0.51
0.57
0.69
0.57
0.61
0.67
0.79
0.67
0.71
0.77
0.89
1.00
0.40
0.44
0.50
0.62
0.50
0.54
0.60
0.72
0.60
0.64
0.70
0.82
0.70
0.74
0.80
0.92
1.00
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Appendix A
To simplify the table, the original land use classes are reclassified into 5 classes as
forest, grass, crop, bare soil and impervious area. The potential runoff coefficients for
impervious (including open water surface) areas are set to 1. In addition, surface slope
is discritized into 4 classes as shown in Table A-3.3. Values in the table are taken the
reference from literature (Kirkby 1978, Chow et al. 1988, Browne 1990, & Fetter
1980) and adjusted after Mallants and Feyen (1990). In order to estimate the potential
runoff coefficient on the basis of a continuous slope, a simple linear relationship
between potential runoff coefficient and slope is created, which can be described as:
C = C 0 + (1 − C 0 )
S
S + S0
(3.2)
where C is the potential runoff coefficient for a surface slope S (%), C0 is the potential
runoff coefficient for a near zero slope corresponding to the values listed on the first
row of each land use class in Table A-3.4, and S0 (%) is a slope constant for different
land use and soil type combinations, as listed in Table A-3.4, which is calibrated
using the data in Table 3.4. Figure A-3.1 gives a graphical presentation of the grid
potential runoff coefficient for a forest cover as a function of slope and different soil
types.
Table A-3.4: Slope constant S0 for determining potential runoff coefficient
Land
use
Sand Loamy Sandy Loam Silt Silt
loam
sand loam
Forest 0.680
Grass 0.580
Crop 0.500
Bare soil 0.420
0.650
0.551
0.471
0.393
0.620
0.522
0.442
0.365
0.590
0.493
0.413
0.338
0.560
0.464
0.384
0.311
0.530
0.435
0.355
0.284
Silty
Sandy
clay Clay clay Sandy Silty Clay
loam loam loam clay clay
0.500
0.405
0.325
0.256
0.470
0.376
0.296
0.229
0.440
0.347
0.267
0.202
0.410
0.318
0.238
0.175
0.380
0.289
0.209
0.147
0.350
0.260
0.180
0.120
The left figure of Figure A-3.1 shows the potential runoff coefficient for a slope
ranging from 0 to 20% and the supporting points, and the right one shows the
potential runoff coefficient for a slope ranging from 0 to 300%. Clearly, the potential
runoff coefficient approaches to C0 when slope is very small, and 1 when slope is
infinite. The figure also shows that the changing magnitude of potential runoff
coefficient is decreasing along with the increasing of surface slope. This conforms
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that the runoff volume for a certain amount of rainfall is less or even not affected by
slope beyond a critical slope (Sharma, 1986).
0.7
1.0
Potential runoff coefficient
Potential runoff coefficient
0.6
0.5
0.4
0.3
0.2
0.8
Sand
Loamy sand
Sandy loam
Silt loam
Silt
Loam
Sandy clay loa m
Silt clay loam
Clay loam
Sandy clay
Silt clay
Clay
0.6
0.4
0.2
0.1
0.0
0.0
0
5
10
15
20
Slope (%)
0
50
100
150
200
250
300
Slope (%)
Figure A-3.1: Potential runoff coefficient vs. slope for forest and different soil types
The influence of urban areas to the storm runoff is self-evident. Due to the grid size,
cells may not be 100% impervious in reality. In WetSpa Extension, the remaining
area is assumed to be pervious and covered by grass, and therefore, the potential
runoff coefficient for urban areas is calculated as:
C u = IMP + (1 − IMP ) C grass
(3.3)
where Cu and Cgrass are potential runoff coefficient for urban and grass grid, and IMP
is the proportion of impervious area. Table A-3.5 is developed to associate an
impervious cover percent with several of the specified land use categories. Impervious
percent for residential area, commercial and industrial is estimated based on the
information in Chow et al. (1988). Other estimates are considered reasonable guesses.
Zero impervious percent is assumed for land use categories not listed (i.e. agriculture,
grass land, and forest land).
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Appendix A
Table A-3.5: Impervious percentages associated with selected land use classes
No.
1
2
3
4
5
6
7
Land use description
Residential area
Commercial and industrial area
Mixed urban or built-up land
Transportation and communication utilities
Streams, Canals, lakes and reservoirs
Forest wetland
Bare exposed rock
Impervious percent (%)
30
70
50
100
100
100
100
In case the model is applied to a medium or large watershed, direct flow generated
from the flow surface becomes an essential part of the storm runoff. Due to the effect
of grid size, upstream channel cells may not be fully occupied by flow. Equation 3.4
is then used to calculate the potential runoff coefficient for these channel cells:
C r = RP + (1 − RP )C
(3.4)
where Cr is the potential runoff coefficient for a channel grid, C is the potential runoff
coefficient without considering the channel effect, and RP is the percentage of
channel area of the grid calculated by the estimated flow width divided by the grid
size. The flow width is determined by a power law relationship with an exceeding
probability (Molnar & Ramirez, 1998), which relates flow width to the controlling
area and is seen as a representation of the average behaviour of the cell and the
channel geometry:
Wi = aW ( Ai ) W
b
(3.5)
where Ai is the drained area upstream of the cell (km²), aW (-) is a network constant
and bW (-) a geometry scaling exponent both depending on the flood frequency.
Researches have shown that the runoff efficiency (volume of runoff per unit of area)
increases with the decreasing catchment area, i.e. the larger the catchment area the
smaller the runoff efficiency (Boers & Ben-Asher, 1982; Brown et al., 1999).
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Analogously, the potential runoff coefficient is affected by the grid size, in which
more surface runoff is produced when modelling with a small grid size, and vice
versa. This can be explained by that spatial variability in climatic inputs such as
rainfall and hydrometorological variables, in soil characteristics such as hydraulic
conductivity and porosity, in topography, and land use, increase with spatial scale
(Vijay & Woolhiser, 2002). For instance, the average saturated hydraulic conductivity
and the surface retention capacity are higher when modelling in a coarser resolution,
causing more infiltration and less surface runoff. These have been addressed in many
of the literatures (Loague, 1988; Mazion & Yen, 1994; Saghafian et al., 1995).
Therefore, the grid size should be chosen properly in order to adequately represent the
spatial heterogeneity of a watershed, and the values of potential runoff coefficient are
allowed to readjust during calibration.
3.1.4. Depression storage capacity
Depression storage capacity is a value that is land use dependent and represents the
total amount of water that can be stored in small surface depressions. Moreover, the
soil type and the slope steepness also affect the depression storage capacity for
ponding water and thereby the conditions for surface runoff. Generally rougher
surfaces store more surface water than smoother surfaces and steeper slopes store less
surface water than gentle slopes (Moore and Larson, 1979; Ullah and Dickinson,
1979a, b; Onstad, 1984). After the depression storage amount is met, runoff within a
cell begins. A table of depression storage capacity, as shown in Table A-3.6, is built
in WetSpa Extension for different land use, soil type and slope combinations, based
on the analysis of data in ASCE (1969), SINCE (1972), Sheaffer et al., (1982), and
Geiger et al. (1987). The depression storage capacity for impervious areas is considered
as wetting loss, and set to 0.5 mm (Fronteau & Bauwens, 1995).
In order to obtain a depression storage capacity as a function of a continuous slope
used in the WetSpa Extension, a simple regression equation as in Hansen et al. (1999)
is applied, in which the depression storage capacity is controlled by land use and soil
type, and decreases with slope exponentially:
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Appendix A
Sd = Sd0 exp(−bS )
(3.5)
where Sd is the depression storage capacity (mm), S is the slope (%), Sd0 is the
depression storage capacity for a near zero slope and different soil types (mm)
corresponding to the values listed on the first row of each land use class in Table A3.6, and b = -9.5, calibrated using the data in Table A-3.6.
Table A-3.6: Depression storage capacity for different land use, soil type and slope
Land Slope
use (%)
Forest <0.5
0.5-5
5-10
>10
Grass <0,5
0.5-5
5-10
>10
Crop <0.5
0.5-5
5-10
>10
Bare <0.5
soil 0.5-5
5-10
>10
IMP
Sand Loamy Sandy Loam
sand loam
8.00 7.50 7.00 6.50
6.31 5.91 5.52 5.13
3.92 3.68 3.43 3.19
1.92 1.80 1.68 1.56
5.00 4.73 4.45 4.18
3.94 3.73 3.51 3.30
2.45 2.32 2.18 2.05
1.20 1.14 1.07 1.01
3.00 2.86 2.73 2.59
2.37 2.26 2.15 2.04
1.47 1.40 1.34 1.27
0.72 0.69 0.66 0.62
1.50 1.45 1.41 1.36
1.12 1.09 1.05 1.02
0.74 0.72 0.70 0.67
0.36 0.35 0.34 0.33
0.50 0.50 0.50 0.50
Silt
loam
6.00
4.73
2.94
1.44
3.91
3.08
1.92
0.94
2.45
1.94
1.20
0.59
1.32
0.99
0.65
0.32
0.50
Silt
5.50
4.34
2.70
1.32
3.64
2.87
1.78
0.87
2.32
1.83
1.14
0.56
1.27
0.95
0.63
0.31
0.50
Sandy
clay
loam
5.00
3.94
2.45
1.20
3.36
2.65
1.65
0.81
2.18
1.72
1.07
0.52
1.23
0.92
0.61
0.30
0.50
Clay
loam
4.50
3.55
2.21
1.08
3.09
2.44
1.52
0.74
2.05
1.61
1.00
0.49
1.18
0.88
0.58
0.28
0.50
Silty
clay
loam
4.00
3.15
1.96
0.96
2.82
2.22
1.38
0.68
1.91
1.51
0.94
0.46
1.14
0.85
0.56
0.27
0.50
Sandy
clay
3.50
2.76
1.72
0.84
2.55
2.01
1.25
0.61
1.77
1.40
0.87
0.43
1.09
0.81
0.54
0.26
0.50
Silty
clay
3.00
2.37
1.47
0.72
2.27
1.79
1.11
0.55
1.64
1.29
0.80
0.39
1.05
0.78
0.52
0.25
0.50
Clay
2.50
1.97
1.23
0.60
2.00
1.58
0.98
0.48
1.50
1.18
0.74
0.36
1.00
0.75
0.49
0.24
0.50
Figure A-3.2 shows the depression storage capacity for a grass cover as a function of
slope and different soil types. The left figure of Figure A-3.2 shows the depression
storage capacity for a slope ranging from 0 to 20% and the supporting points, and the
right one shows the depression storage capacity for a slope ranging from 0 to 100%.
Clearly, the depression storage capacity approaches to Sd0 for a very small slope, and
0 for a steep slope. This conforms that the depression storage may have a significant
effect for gentle slope, but is not important for a steep slope in controlling overland
flow generation (Hansen et al., 1999).
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5.0
Depression storage capacity (mm)
Depression storage c apacity (mm)
5.0
4.0
3.0
2.0
1.0
0.0
Sand
Loamy sand
Sandy loam
Silt loam
Silt
Loam
Sandy clay loam
Silt clay loam
Clay loam
Sandy clay
Silt clay
Clay
4.0
3.0
2.0
1.0
0.0
0
5
10
15
20
0
Slope (%)
20
40
60
80
100
Slope (%)
Figure A-3.2: Depression storage capacities vs. slope for grass and different soil types
The computation of depression storage capacity for urban areas is the same like the
process in calculating potential runoff coefficient, which is the weighted mean of the
depression storage capacity for impervious area and grassland. The equation can be
expressed as:
Sdu = 0.5IMP + (1 − IMP) Sd grass
(3.6)
where Sdu and Sdgrass are the depression storage capacity for an urban and grass grid
respectively (mm). As there is no depression loss on water surface, the depression
storage capacity for a channel cell can be calculated as:
Sd r = (1 − RP ) Sd
(3.7)
where Sdr (mm)is the depression storage capacity for a channel grid, and Sd (mm) is
the depression storage capacity without considering the channel effect. The values of
depression storage capacity are also affected by the grid size as discussed in section
A-3.1.3. Therefore, cautions should be made with regards to use these values for a
large grid. These parameters are allowed to modify during the GIS preprocessing in
order to get a better fit.
251
Appendix A
3.2.
Global parameters
For simplifying the process of parameter calibration, 12 global parameters are used in
the WetSpa Extension, i.e. the correction factor of PET, interflow scaling factor,
groundwater recession coefficient, initial soil moisture, initial groundwater storage,
base temperature for snowmelt, temperature degree-day coefficient, rainfall degreeday coefficient, surface runoff exponent, and the rainfall intensity corresponding
surface runoff exponent of 1. These parameters have physical interpretations and are
important in controlling runoff production and hydrographs at basin outlet, but
difficult to assign properly on a grid scale. Therefore, calibration of these global
parameters against observed runoff data is preferable in addition to the adjustment of
distributed model parameters.
1) Correction factor for PET
The PET data used in the model are obtained from pan measurement or calculated by
Pemman-Monteith or other equations using available weather data. These reference
evapotranspiration rates refer to water surface or a grass cover in large fields. Actual
reference or PET rates, however, may depend on local factors that are not addressed
by these methods. For instance, the land use, elevation, as well as the micrometeorological conditions for the grid to be simulated may be different from those
prevailing at the site of the meteorological station whose data are being used. To
account for these effects, a correction factor is required in the computed PET. The
correction factor is normally close to 1, and can be calibrated by the model through a
long-term water balance simulation. Specifically, when modelling in a mountainous
catchment, the evapotranspiration stations are usually very sparse and are located in
the river valley. To account for the effect of elevation, the correction factor for PET
may be much lower in this case.
2) Scaling factor for interflow computation
Interflow or subsurface runoff is an essential runoff component for the humid
temperate region especially for the areas with sloping landscapes and well-vegetated
cover. In WetSpa Extension, interflow is assumed to occur when soil moisture
exceeds the field capacity and there is sufficient hydraulic gradient to move the water.
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Darcy’s law is then used for the simulation of interflow. Dingman (1994) pointed out
that soil water preferentially flows laterally given greater lateral hydraulic
conductivity than vertical due to the anisotropy of water content dependent hydraulic
conductivity. Even though a uniform soil matrix is considered in the model, but in fact,
the porosity and permeability of soil tend to decrease with depth given the weight of
overlying soil and the translocation of material in percolating water to lateral
subsurface flow. Moreover, soil water passing quickly to a stream through root canals,
animal tunnels, or pipes produced by subsurface erosion may become a critical
component of peak flow. To account for theses effects, a scaling factor for lateral
hydraulic conductivity in computing interflow is used in the model. This scaling
factor is generally greater than 1, and can be calibrated by comparing the recession
part of computed flood hydrographs with the observed hydrographs.
3) Groundwater recession coefficient
Groundwater flows are estimated on subcatchment scale in WetSpa Extension as
described in Chapter A-2. The groundwater recession coefficient reflects the storage
characteristics of the subwatershed and, therefore, is the same for all hydrographs at a
given location. In accordance with Equation (2.21), the groundwater recession
coefficient will remain constant if storage and discharge volumes are divided by area
and expressed as depth in mm (Wittenberg, 1999). This is under the condition that
groundwater flow for each subcatchment has the same recession constant, and total
groundwater at the outlet of the river is only a time-shifted superposition of partial
groundwater flow from each subcatchment.
In real river basins, baseflow recession coefficient for each subcatchment may not be
the same, and may have a considerable deviation from the theoretical constant. A
great portion of the deviation is associated with variability of subcatchment
characteristics. Others may be attributed to aquifer heterogeneity and divergence from
the Dupuit-Forchheimer assumption of essentially horizontal groundwater flow. For
model simplification, a general value of groundwater flow recession coefficient is
determined at the basin outlet in the input file. A linear correction is then performed
for each subcatchment based on its drainage area and the average slope, for which
253
Appendix A
higher values are assigned for the subcatchments with large drainage area and steep
slope, and lower values for the subcatchments with small area and gentle slope. The
shape and stream density of the subcatchment is not accounted for in the current
version. The equation can be expressed as:
c g ,s = c g
Ss
Ws
S
(3.8)
where cg,s and cg (m2/s) are groundwater recession coefficient of the subcatchment and
the entire basin, Ss and S are average slope of the subcatchment and the entire basin,
and Ws is the areal weight of the subcatchment. cg can be derived by the analysis of
flow records as described in Martin (1973) and Wittenberg (1999). Calibration of this
parameter is necessary by comparing the computed and observed low flow
hydrographs.
4) Initial soil moisture
Soil moisture content is a key element in the model controlling the hydrological
processes of surface runoff production, evapotranspiration, percolation and interflow.
A proper initial soil moisture condition may provide a much more realistic starting
point for predictions. However, for a long-term flow simulation in a watershed, the
initial soil moisture condition is less important, as it affects the hydrological processes
only in the initial part of the simulation. An assumption of uniform initial moisture
distribution can be made in this case with modelling purpose of flood prediction under
present condition. A ratio against field capacity is then defined in the input parameter
file for setting up the initial soil moisture conditions. This value can be adjusted
during calibration by analysis of water balance output and comparison between the
computed and observed hydrographs for the initial phase.
If the model is used for short-term flow simulation or event-based flood prediction,
the antecedent moisture condition becomes one of the most important factors in runoff
production as well as its distribution. The concept of topographic wetness index (TWI)
adapted from Moore et al. (1993) can be introduced in the model to evaluate
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WetSpa Extension: Documentation and User Manual
antecedent moisture condition of a watershed with TWI = ln(A/S), where ln(.) is the
natural logarithm, A is the upslope drainage area (m2), and S is the local slope (-). The
TWI distribution can be easily obtained from a high resolution DEM. Those cells with
high TWI values have larger upslope contributing areas or smaller cell slopes or a
combination of the two properties that lead to accumulation of soil moisture. While an
assumption is made for maximum and minimum moisture content within the
watershed, the antecedent moisture distribution can be obtained by simply relating
moisture content to the TWI values. Cells with very high TWI values may consider to
be saturated with runoff coefficient of one. These cells are normally distributed along
the main river or in the depression areas in a watershed.
5) Initial groundwater storage
In WetSpa Extension, groundwater balance is maintained on subcatchment scale and
for the active groundwater storage, which is that part of storage in perched or shallow
aquifers that contribute to the surface stream flow. Water percolating from the root
zone storage may flow to active groundwater storage or may be lost by deep
percolation. Active groundwater eventually reappears as baseflow, but deep
percolation is considered lost from the simulated system. A value of initial
groundwater storage in depth (mm) is set up in the input parameter file for all
subcatchment. This value can be adjusted during calibration by comparing the
computed and observed low flows for the initial phase.
6) Base temperature for snowmelt
The precipitation is assumed to fall as snow if the temperature is below the base
temperature. Snowmelt starts when the temperature is above the base temperature.
The base temperature is typically a value near 0°C, particularly for short computation
period using average temperature as input. The user may specify this value during
model calibration.
7) Temperature degree-day coefficient
The range of the temperature degree-day coefficient is typically 1.8 – 3.7 mm/°C/day
for rain-free conditions (Anderson, 1973; Male and Gray, 1981). This value can be
255
Appendix A
determined by comparison between computed and observed spring flood hydrographs
during calibration. In general, the temperature degree-day coefficient is varied both in
time and space. For instance, the albedo is very high for new, cold snow falling in the
beginning of the accumulation season and decreases with the age of the snow, which
results in an increase of the degree-day coefficient. Moreover, the temperature degreeday coefficient is also land use dependent, for which forest cover leads to a smaller
value, while bare soil leads to a higher value. For simplicity purpose, these
influencing factors are not accounted for in the current model, and recommended to
be coupled in the future version.
8) Rainfall degree-day coefficient
The rainfall degree-day coefficient determines the rate of snow melting caused by
condensation of humid air on the snow surface and the advective heat transferred to
the snow pack by precipitation, and is used for calculation of an additional snowmelt
due to rainfall. The value of rainfall degree-day coefficient is generally very small,
typically around 0.01 (mm/mm/°C/day), and can be determined during model
calibration. If zero value is given, the effect of rainfall on snowmelt is not considered.
9) Surface runoff exponent for a near zero rainfall intensity
Rainfall intensity has a big influence in controlling the proportion of surface runoff
and infiltration. As pointed by Dunne (1991), infiltration rate increases with rainfall
intensity for two reasons: (1) Higher rainfall intensity tends to exceed the saturated
hydraulic conductivity of larger proportions of the soil surface, and thereby to raise
the spatially averaged hydraulic conductivity, and (2) Higher rainfall intensity gives
more surface runoff rate and the inundated flow depth. To account for this effect on
the production of surface runoff, an empirical exponent is introduced in the model as
described in Eq. (2.7). The concept is that the proportion of surface runoff is very
small, or even nil, under the condition of very small rainfall intensity, and the
proportion increases along with the increase of rainfall intensity up to a stage for
which a potential runoff coefficient is achieved. In WetSpa Extension, this exponent
is assumed to be a variable starting from a higher value for a near zero rainfall
intensity, and changing linearly up to 1 along with the rainfall intensity, when the
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predetermined maximum rainfall intensity is reached. This value is generally less than
3 according to the previous applications. If an exponent value 1 is given, the actual
runoff coefficient is then a linear function of the relative soil moisture content, and the
effect of rainfall intensity on the runoff coefficient is not taken into account.
10) Rainfall intensity corresponding to a surface runoff exponent of 1
This parameter corresponds to a threshold rainfall intensity in unit of mm/h or mm/d
depending upon the temporal resolution of the model simulation, over which the
surface runoff exponent equals 1, and the actual runoff coefficient becomes a linear
function of the relative soil moisture content. Calibration of this parameter can be
performed by comparison of the observed and computed surface runoff volume and
the peak discharge for high floods. This parameter is in fact spatially distributed,
depending upon the cell characteristics, such as soil type, land use, and slope, etc. A
constant value is assumed in the current model for simplification.
3.3. Model evaluation
In order to evaluate how well WetSpa Extension reproduces an observed hydrograph,
a series of statistics are used. In addition to the evaluation based on a visual
comparison and an evaluation of peak flow rate and time to the peak, the bias, model
confidence, and the model efficiency are also taken into account. These statistical
measures provide quantitative estimates for the goodness of fit between observed and
predicted values, and are used as indicators of the extent at which model predictions
match observation. Based on the results of these tests, model predictive capabilities
are assessed. The goodness of fit in the peak discharge and time to the peak can be
evaluated by their relative and absolute errors respectively, while other evaluation
criteria are described as following:
1) Model bias
Model bias can be expressed as the relative mean difference between predicted and
observed stream flows for a sufficiently large simulation sample, reflecting the ability
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Appendix A
of reproducing water balance, and perhaps the most important criterion for comparing
whether a model is working well in practice. The criterion is given by the equation
N
CR1 =
∑ (Qs
i =1
i
− Qoi )
(3.9)
N
∑ Qo
i =1
i
where CR1 is the model bias, Qsi and Qoi are the simulated and observed stream
flows at time step i (m3/s), and N is the number of time steps over the simulation
period. Model bias measures the systematic under or over prediction for a set of
predictions. A lower CR1 value indicates a better fit, and the value 0.0 represents the
perfect simulation of observed flow volume.
2) Model confidence
Model confidence is one of the important criteria in assessment of continuous model
simulation, and can be expressed by its determination coefficient, which is calculated
as the portion of the sum of the squares of the deviations of the simulated and
observed discharges from the average observed discharge.
∑ (Qs
CR 2 =
i =1
∑ (Qo
i
)
− Qo
)
(3.10)
2
N
i =1
− Qo
2
N
i
where CR2 is the model determination coefficient,
Qo
is the mean observed stream
flow over the simulation period. CR2 represents the proportion of the variance in the
observed discharges that are explained by the simulated discharges. It varies between
0 and 1, with a value close to 1 indicating a high level of model confidence.
3) Nash-Sutcliffe efficiency
The Nash-Sutcliffe coefficient (Nash and Sutcliffe, 1970) describes how well the
stream flows are simulated by the model. As pointed out by Kachroo and Natale
(1992), this efficiency criterion is commonly used for model evaluation, because it
involves standardization of the residual variance, and its expected value does not
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change with the length of the record or the scale of runoff. The equation can be
described as
N
CR 3 = 1 −
∑ (Qs
i
− Qo i )
∑ (Qo
)
i =1
(3.11)
2
N
i =1
2
i
− Qo
where CR3 is the Nash-Sutcliffe efficiency used for evaluating the ability of
reproducing the time evolution of stream flows. The CR3 value can range from a
negative value to 1, with 1 indicating a perfect fit between the simulated and observed
hydrographs. CR3 below zero indicates that average measured stream flow would
have been as good a predictor as the modelled stream flow. A perfect model
prediction has CR3 score equal to 1.
4) Logarithmic version of Nash-Sutcliffe efficiency for low flow evaluation
A logarithmic transformed Nash-Sutcliffe criterion is presented in Equation 3.11,
which gives emphasize for evaluating the quality of low flow simulations (Smakhtin
et al., 1998).
N
CR 4 = 1 −
∑ [ln (Qs
i =1
N
2
∑ [ln (Qo
i =1
+ ε ) − ln (Qo i + ε )]
i
i
(
+ ε ) − ln Qo + ε
)]
(3.12)
2
where CR4 is a logarithmic Nash-Sutcliffe efficiency for evaluating the ability of
reproducing the time evolution of low flows, and ε is an arbitrary chosen small value
introduced to avoid problems with nil observed or simulated discharges. The value of
ε should be sufficiently low, and those observed discharges lower than ε value are
negligible. Otherwise the CR3 criterion would present a bias. Similar as CR3, a
perfect value of CR4 is 1.
5) Adapted version of Nash-Sutcliffe efficiency for high flow evaluation
An adapted version of the Nash-Sutcliffe criterion is proposed as in Equation 3.12. It
is in fact a combination between the calibration criteria used by Guex (2001) for the
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Appendix A
hydrological study on the Alzette river basin and the HEC-1 objective function
(USACE, 1998).
∑ (Qo
)
N
CR 5 = 1 −
i =1
N
∑ (Qo
i =1
+ Qo (Qs i − Qo i )
i
i
)(
+ Qo Qo i − Qo
2
)
(3.13)
2
where CR5 is an adapted version of Nash-Sutcliffe criterion for evaluating the ability
of reproducing the time evolution of high flows. As can be seen in the formula, more
weight is given on high discharges than low ones. A perfect value of CR5 is 1.
4. Model operation
4.1. Program installation
Installation of WetSpa requires a Windows 98/ME/2000/XP or Windows NT 4.0
operating system. Also required are licensed versions of ESRI’s ArcView 3.2 GIS
Application and Spatial Analyst v2.0 Extension. In addition, the software of Visual
FORTRAN 6.1 or other FORTRAN compilers are required if the user wants to edit
and modify the program source code. The minimum drive space required is 100MB.
Additional space may be necessary depending on the spatial and temporal scale of the
project. By simple copy and paste operation, the model can be installed and run on
any computer drives and under any existing directories. Specific folders are
referenced from that drive location throughout the modelling process. Figure A-4.1
gives a schematic view of the model’s project folders.
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Project
Document
ArcView
Model
DEM
Ascii
Input
Soil type
Data
Output
Land use
Help
PEST
Coverage
Script
Program
Table
Source
Temp
Project.apr
Figure A-4.1: Schematic view of the model’s project folders
Where Project is the general folder of the modelling project, and the others are:
1) Document: for storing model documents
2) ArcView: for storing ArcView GIS components
3) Ascii: for storing spatial parameter maps in ASCII format
4) Data: for storing spatial data of base maps
5) Help: for storing model help files
6) Script: for storing ArcView Avenue scripts
7) Table: for storing model lookup tables.
8) Temp: project working directory for storing intermediate and temporary files
9) Project.apr: ArcView project of the model
10) DEM: digital elevation model
11) Soil type: digital soil type map in grid format
12) Land use: digital land use map in grid format
13) Coverage: for storing coverage data including stations, streams, boundaries, etc.
14) Model: for storing model inputs, outputs and programs
15) Input: for storing model input files
16) Output: for storing model output files
17) PEST: for storing programs of automatic parameter estimation
18) Program: for storing model executive programs
19) Source: for storing program source codes
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Appendix A
4.2. Program description
4.2.1. Avenue scripts and their tasks
1) conductivity: creates a grid of saturated hydraulic conductivity
2) delta_h: calculates standard deviation of flow time from cells to the basin outlet
3) delta_s: calculates standard deviation of flow time from cells to the main river
4) depression: calculates depression storage capacity for each cell
5) fieldcapacity: creates a moisture grid at soil field capacity
6) fillsink: fill sinks to remove small imperfections from DEM
7) flowacc: creates an accumulated flow grid at each cell
8) flowdir: creates a flow direction grid from each cell to its steepest downslope
neighbour
9) flowlen: calculates a downstream distance grid along its flow path
10) interception: calculates minimum and maximum interception storage capacity
11) lai: creates a grid of leaf area index
12) manning: calculates Manning’s roughness coefficient for each cell
13) mask: creates a mask grid of the watershed
14) moisture: creates an initial soil moisture grid based on the topographic index
15) poreindex: creates a grid of soil pore size distribution index
16) porosity: creates a moisture grid at soil porosity
17) radius: calculates hydraulic radius for each cell according to flood frequency
18) residual: creates a moisture grid at residual soil moisture content
19) rootdepth: creates a grid of root depth
20) runoffco: creates a grid of potential runoff coefficient
21) slope: creates a slope grid for both land surface and river channel
22) curvature: creates a curvature grid and its root mean square profile curvature
23) streamlink: assigns unique values to sections of stream network
24) streamnet: creates a grid of stream network
25) streamorder: assigns a numeric order to branches of a river network
26) streamtoline: converts stream grid to a line coverage
27) t0_h: calculates flow time from each cell to the basin outlet
28) t0_s: calculates flow time from each cell to the main river
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29) thiessen: creates a grid of Thiessen polygons
30) velocity: creates a velocity grid for both overland flow and channel flow
31) v_fraction: creates a grid of maximum fractional vegetation cover
32) watershed: determines subwatersheds based on stream links
33) wiltingpoint: creates a moisture grid at permanent wilting point
4.2.2. Lookup tables
1) depression.dbf: default values of depression storage capacity for different land use,
soil texture, and near zero slopes
2) landuse_reclass.dbf: land use reclassification table for deriving potential runoff
coefficient and depression storage capacity of the 5 main land use classes
3) landuse_remap.dbf: default model parameters based on land use classes, including
root depth, Manning’s roughness coefficient, interception capacity, vegetated
fraction and leaf area index
4) radius: default parameters governing average hydraulic radius for a certain flood
frequency
5) runoff_coefficient.dbf: default potential runoff coefficient for different land use,
soil texture, and near zero slopes
6) soil_remap: default parameters based on soil texture categories, including
hydraulic conductivity, porosity, field capacity, wilting point, residual moisture,
pore size distribution index, etc.
4.2.3. FORTRAN programs and their tasks
1) mean: calculates mean parameters of each subcatchment
2) iuh: calculates the unit response function of each cell to the catchment and
subcatchment outlet, the unit hydrograph of each subcatchment to the catchment
and subcatchment outlet, and the unit hydrographs of main rivers.
3) model1: semi-distributed model on subcatchment scale
4) model2: fully distributed model on cell scale
5) water_balance: calculates water balance on grid scale without flow routing
6) evaluation: statistics of simulation results and model evaluation
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Appendix A
4.2.4. PEST files and their tasks
1) input: PEST input template file
2) qtotal: PEST output instruction file
3) wetspa: PEST control file
4) pest: PEST executable file
5) pest_wetsap: PEST MS-DOS batch file
4.3. GIS pre-processing
The purpose of GIS pre-processing is to create all necessary spatial parameter maps
used in the WetSpa Extension. Open a new ArcView project ‘project’ (or other name)
under the subdirectory \project\arcview. Set the project’s working directory to
\project\arcview\temp, in which the intermediate and temporary GIS files are stored
and all other input and output files are transferred from or to their subdirectory
referencing to this path. Before performing GIS pre-processing, be sure that the
ArcView Extensions: Spatial Analyst, GeoProcessing, WetSpa and Create Thiessen
Polygons, are added to the ArcView project. Next, Load grid themes of elevation,
landuse and soiltype from the subdirectory \project\arcview\data to the View
‘Topography’, ‘Landuse’ and ‘Soiltype’ separately. Set the theme names as
‘Elevation’, ‘Landuse’ and ‘Soil’. Note that the extent of these three base maps must
be the same in order to perform the model simulation properly.
4.3.1. Surface grid preparation
Surface parameter grids based on a DEM are prepared in the view Topography of the
ArcView project. The preparation of a proper DEM employs many geo-processing
schemes, and can be implemented independently from the project using more
powerful GIS software, such as ArcInfo etc. From the available DEM, its
hydrological potential is calculated in ArcView by performing the following
functions: filling sinks, determining flow direction and flow accumulation, assigning
stream network, stream link and stream order, calculating slope and hydraulic radius,
and delineating subcatchments, etc. Figure A-4.2 gives a screenshort of the surface
grid menu.
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Figure A-4.2: Screenshort of surface menu
1) Fill Sinks
A sink is a cell or set of spatially connected cells whose flow direction cannot be
assigned one of the eight valid values in a flow direction Grid. This can occur when
all neighbouring cells are higher than the processing cell. In ArcView GIS, sinks are
considered to have undefined flow directions and are assigned a value that is the sum
of their possible directions. To create an accurate representation of flow direction and
therefore accumulated flow, it is required to use a data set that is free of sinks. The fill
sinks request in the surface menu takes a grid theme ‘Elevation’ and fills all sinks and
areas of internal drainage contained within it. The process of filling sinks can create
new sinks, so a looping process is used until all sinks are filled (ESRI, 1999). The
output theme is named as ‘Filled Elevation’ displayed in the same view, and the
corresponding
ASCII
file
‘elevation.asc’
is
saved
in
the
subdirectory
/project/arcview/ascii used for estimation of altitude-distributed temperature.
2) Mask
A mask grid defines the study region in the grid domain, which can be used to extract
catchment boundary, determine the extent of other grids, etc. The request takes the
grid theme ‘Filled Elevation’ and assigns a unique value 1 for the cells within the
study catchment with output theme ‘Mask’ displayed in the same view.
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Appendix A
3) Flow direction
The flow direction request calculates the direction of flow out of each cell into one of
its eight neighbours. The direction of flow is determined by finding the direction of
steepest descent from each cell. If a cell is lower than its 8 neighbours that cell is
given the value of its lowest neighbour and flow is defined towards this cell. If the
descent to all adjacent cells is the same, the neighbourhood is enlarged until the
steepest descent is found (ESRI, 1999). The request takes the grid theme ‘Filled
Elevation’ and calculates flow direction for each cell with output theme ‘Flow
Direction’ displayed in the same view.
4) Flow accumulation
The flow accumulation request creates a grid of accumulated flow to each cell by
accumulating the weight for all cells that flow into each downslope cell. The
accumulated flow is based upon the number of cells flowing into each cell in the
output grid. Output cells with a high flow accumulation are areas of concentrated
flow, and therefore can be used to identify stream channels. Output cells with a flow
accumulation of zero are local topographic highs and can be used to identify ridges.
The request takes the grid theme ‘Flow Direction’ and calculates flow accumulation
for each cell with output ‘Flow Accumulation’ displayed in the same view.
5) Stream network
The results of the flow accumulation are used to create a vector stream network by
applying a threshold value to subset cells with a high-accumulated flow. All cells
that have more than a user-defined number of cells flowing into them are assigned a
value of one; all other cells are assigned no data. The resulting stream network can
be used as a predicted hydrography (ESRI, 1999). The stream network request takes
the grid theme ‘Flow Accumulation’ and delineates a stream network grid ‘Stream
Network’ displayed in the same view.
6) Stream link
Links are the sections of a stream channel connecting two successive junctions, a
junction and the outlet, or a junction and the drainage divide (ESRI, 1999). The
stream link request takes the grid themes ‘Flow Direction’ and ‘Stream Network’, and
assigns unique values to sections of a stream network between intersections. The
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output theme is named as ‘Stream Link’ displayed in the same view, which can be
used as the source grid to create drainage basins that correspond the branches of a
stream network. Meanwhile, the output grid data is written to an ASCII file ‘link.asc’
used to calculate IUH of stream channels.
7) Stream order
The stream order request takes the grid themes ‘Flow Direction’ and ‘Stream
Network’, and assigns a numeric order to segments of the stream network. The
Shreve method is used in the model, in which all links with no tributaries are assigned
an order of 1 and the orders are additive downslope. When two links intersect, their
magnitudes are added and assigned to the downslope link. The output theme is named
as ‘Stream Order’ displayed in the same view, and used as a source grid in assigning
Manning’s n for stream channels.
8) Slope
The process of slope derivation calculates the rate of maximum change for locations
on the elevation grid theme and creates a new grid theme ‘Slope’ as output. Each cell
in the output theme contains a continuous slope value represented as a percentage.
Considering that the stream network is in a vector style, and its slope is determined
by the elevation difference and distance between the up and down cells along the
streamline, the channel slope is calculated separately from the general slope using
DEM and the stream network information. This avoids the disturbance in channel
slopes for a river, especially for stream channels with asymmetric side slopes of the
riverbank. The final slope grid is then obtained using the general slope grid overlaid
by the grid of channel slope. An ASCII file ‘slope.asc’ is saved in the subdirectory
/project/arcview/ascii for use in calculating interflow from each cell.
9) Hydraulic radius
The hydraulic radius request takes the grid theme ‘Flow accumulation, and calculates
hydraulic radius for each grid cell. The hydraulic radius is determined by a power law
relationship with an exceeding probability, which relates hydraulic radius to the
controlling area and is seen as a representation of the average behaviour of the cell
and the channel geometry. Generally, a flood frequency with 2-year return period is
chosen for normal floods. The two controlling parameters can be adjusted in the
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Appendix A
lookup table ‘radius.dbf’ to meet the specific characteristics of catchment. The output
grid theme is named as ‘Radius (m)’, and is used for calculation of flow velocity.
10) Watershed
The watershed request takes the grid themes ‘Flow Direction’ and ‘Stream Link’, and
determines the subcatchment for each stream link. The output grid theme is named as
‘Watershed’ displayed in the same view, and is saved as an ASCII file for semidistributed modelling and the simulation of groundwater balance. If the subcatchment
does not delineate as expected, delete the grid themes ‘Stream Network’, ‘Stream
Link’ and ‘Watershed’ by invoking the delete theme command in the edit dropdown
menu, and rebuild the three grid themes by setting a new threshold value. Often it is
necessary to closely zoom into the area of interest to ensure the outlet point’s location
is positioned correctly.
4.3.2. Soil based grid preparation
To calculate the soil hydraulic properties, activate the view ‘Soiltype’, select the
‘Parameter’ dropdown menu, and the commands related to soil types are highlighted
(Figure A-4.3), including ‘Conductivity’, ‘Porosity’, ‘Field capacity’, ‘Residual
moisture’, ‘Pore distribution index’, and ‘wilting point’, etc. The commands
‘Maximum saturation’, ‘Arithmetic mean of G’ and ‘Geometric mean of G’ are
designed for future model improvement, where G is the capillary drive (mm). By
clicking each of the command, the grid files are created to redefine and display the
soil units with respect to their hydrological properties, and the corresponding ASCII
files are saved in the subdirectory /project/arcview/ascii.
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Figure A-4.3: Screenshort of parameter menu
Another activated function under the dropdown menu is the ‘Initial moisture’. This
function creates an initial relative saturation grid of the soil using the method of the
Topographical Wetness Index. A minimum ratio reflecting the moisture condition of
the driest cells is asked in a pop up window, which can be selected from the provided
list. The output theme is named as ‘Initial Moisture’ displayed in the same view, and
the ASCII file ‘moisture.asc’ is saved in the subdirectory /project/arcview/ascii. Note
that this operation is optional and designed for event based flood modelling, for which
the initial soil moisture condition is rather important.
4.3.3. Land use based grid preparation
To calculate the land use dependent model parameters, activate the view ‘Landuse’,
select the ‘Parameter’ dropdown menu, and the commands related to land use grid are
highlighted, including ‘Root depth’, ‘Vegetated fraction’, ‘Interception capacity’,
‘Manning’s coefficient’, and ‘Leaf area index’. There are two interception capacity
themes created by the command ‘Interception capacity’, e.g. maximum and minimum
interception capacity, corresponding to the summer and winter situation. The
command ‘Manning’s coefficient’ creates a map of Manning’s roughness coefficient
for both hillslope and river channels. Therefore, the theme ‘Stream order’ needs to be
269
Appendix A
created firstly in the view ‘Topography’. A selection list is shown in the window
asking for a Manning’s n interpolation method for the stream channels.
1) Interpolation among different stream orders, for which the channel Manning’s n is
defined based on the stream orders with lower values downstream and higher
value upstream. A maximum and a minimum Manning’s n value are asked to
determine corresponding to the lowest and highest stream order.
2) Remain the default constant as in the lookup table, for which a constant
Manning’s n is defined for the river channels using the value assigned in the
lookup table.
3) Change to another constant, for which a modified constant Manning’s n is defined
for the river channels.
The command ‘Leaf area index’ is designed for future model improvement. By
clicking each of the commands, the grid files are created to redefine and display the
land use units with respect to their hydrological properties based on the predefined
lookup table, and the corresponding ASCII parameter files are saved in the
subdirectory /project/arcview/ascii.
4.3.4. Potential runoff coefficient and depression storage capacity
Next, the parameter maps of potential runoff coefficient and depression storage
capacity are generated in the view ‘Runoff coefficient & depression’. Since both
parameter maps are functions of slope, soil type and land use, these three base maps
need to be created firstly in their views. The program can load these three grid themes
directly from their views, and the parameter grids are created and displayed in a
separate view ‘Runoff coefficient & depression’ in order to give a clear view of them.
By activating the view ‘Runoff coefficient & depression’, selecting the ‘Parameter’
dropdown menu, the commands ‘Runoff coefficient’ and ‘Depression capacity’ will
be highlighted. An impervious percentage for urban cells is asked when calculating
the grid of potential runoff coefficient. A default value 30% is given for a grid with
cell size 100×100 m. By clicking each of the commands, the resulting grid files are
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created and displayed in the view, and the corresponding ASCII parameter files are
saved in the subdirectory /project/arcview/ascii.
4.3.5. Flow routing parameters
The flow routing parameter grids are calculated in the view ‘Routing Parameter’,
including flow velocity, mean flow times to the basin outlet and to the main river
from each cell, and the standard deviations of the flow times. These parameter maps
are used for calculating flow response functions from each cell to the basin outlet as
well as to the main river. By activating the view ‘Routing Parameter’ and selecting
the ‘Parameter’ dropdown menu, the commands ‘Velocity’, ‘T0_h’, ‘Delta_h’, ‘T0_s’
and ‘Delta_s’ will be highlighted. By clicking each of the commands, the resulting
grid files are created and displayed in the view, and the corresponding ASCII
parameter files are saved in the subdirectory /project/arcview/ascii.
1) Run the script ‘Velocity’ from the menu ‘Parameter’. This function creates a flow
velocity grid based on the Manning’s n, hydraulic radius and slope grid. A popup
window shows and asks you if a flow velocity limit is necessary. The flow
velocity is set to the upper limit when the calculated velocity is higher than the
upper limit and to the lower limit vice versa. The upper and lower limits 3.0 m/s
and 0.005 m/s are given by default.
2) Run the script ‘T0_h’ from the menu ‘Parameter’. This function creates a flow
travel time grid in hours from each cell to the catchment outlet using the weighted
FLOWLENGTH routine. The ASCII file ‘t0_h.asc’ is saved in the subdirectory
/project/arcview/ascii.
3) Run the script ‘Delta_h’ from the menu ‘Parameter’. This function creates a
standard deviation grid of flow times in hours from each cell to the catchment
outlet using the weighted FLOWLENGTH routine. The ASCII file ‘delta_h.asc’ is
saved in the subdirectory /project/arcview/ascii.
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Appendix A
4) Run the script ‘T0_s’ from the menu ‘Parameter’. This function creates a flow
travel time grid in hours from each cell to its subcatchment outlet. The ASCII file
‘t0_s.asc’ is saved in the subdirectory /project/arcview/ascii.
5) Run the script ‘Delta_s’ from the menu ‘Parameter’. This function creates a
standard deviation grid of flow times in hours from each cell to its subcatchment
outlet.
The
ASCII
file
‘delta_s.asc’
is
saved
in
the
subdirectory
/project/arcview/ascii.
4.3.6. Thiessen polygon
Rainfall and PET data used in WetSpa Extension are tabular data gathered from point
measuring stations inside or surrounding the catchment. In order to obtain a more
accurate estimate of rainfall and PET values for a grid or a working unit, the Thiessen
Polygon extension in ArcView is executed together with the themes of weather
stations and the catchment boundary. This involves creating a Thiessen polygon
theme in ArcView for all stations, then identifying each grid with the covering station
identity number. The steps for creation of Thiessen polygon of rainfall data as well as
its grid and ASCII file are:
1) To begin this process, three themes, rainfall stations, catchment boundary and a
mask grid, need to be loaded into the View ‘Thiessen Polygon’, from which all
others themes can be created. The rainfall station theme is obtained from a point
shape file named as ‘stations’, which contains the fields of latitude, longitude,
station name and station ID. The boundary shape file is obtained by conversion of
a mask grid map to a polygon shape file.
2) Activate the theme ‘Stations’ by clicking on the name in the View’s theme list.
Then, run the avenue script by clicking the command ‘Thiessen polygon’ in the
dropdown menu ‘Surface’. Select ‘ID’ when prompted to "Select point field for
polygon link ID", and select ‘Boundary’ when prompted to ‘Select polygon theme
for boundary’. Define the name of the output file as ‘thiessen.shp’ in the
subdirectory /project/arcview/data. The Thiessen polygon coverage theme is then
displayed in the view after the execution.
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3) If it is wanted to convert the Thiessen polygon from coverage to grid, click ‘Yes’
when asked ‘Covert the Thiessen.shp to grid Thiessen?’. Define the grid name as
‘thiessen’ in the subdirectory /project/arcview/data. Set the output grid cell size,
number of rows and number of columns the same as the mask map, and pick the
field ‘ID’ for cell values. A gird named ‘Thiessen’ will be displayed in the view,
after clicking ‘Yes’ when promoted to ‘Add grid as theme to the view’.
4) Click ‘Yes’ when promoted to ‘Save the Thiessen polygon grid as Ascii file’, the
ASCII file ‘Thiessen_p.asc’ is stored in the subdirectory /project/arcview/ascii.
Following the same procedures, the Thiessen polygon grid for PET and temperature
can be created using the point theme of PET and temperature stations instead of
rainfall stations. The corresponding ASCII fill is named as ‘Thiessen_e.asc’ and
‘Thiessen_t.asc’ stored in the subdirectory /project/arcview/ascii. Note that there must
be at least 2 stations in the point theme for performing the ‘Thiessen polygon’
command. If only one station exists, the Thiessen polygon grid is just the same as the
musk grid with cell values of station ID number.
4.3.7. Drainage systems for a complex terrain
In case the WetSpa Extension is used for modelling a complex terrain, e.g. an urban
or suburban watershed, on a small catchment scale, the sewer systems,
communication lines, and artificial canals, lakes, reservoirs, etc., are important
elements in drainage structure configuration, and govern flow direction more strongly
than the derived aspect at local scale. Surface flow on these areas should thus be
described with more detailed methodology, which allows a correct physical
representation of the flow regime. Since most of these barriers are not sufficient to be
represented in a DEM, additional procedures in term of deriving more realistic flow
direction map are performed using GIS overlaying technique in the model. The
procedures are:
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1) Compute a general flow direction grid using the elevation grid alone without
considering the effect of artificial areas, from which a stream network grid is
generated.
2) Compute flow direction maps independently for sewer areas, main communication
lines, artificial canals, and the stream network derived from the general flow
direction grid, etc., based on the DEM and the available line and polygon themes.
3) Overlay the general flow direction map by the flow direction maps of sewer areas,
communication lines, artificial canals, and the stream network subsequently,
which allowing water to drain from the sewer areas at their outlets and water to
cross communication lines and canals at their concave points to join the river.
4) The drainage paths delineated from the DEM are compared with existing
hardcopy maps. Make any necessary corrections to the generated flow direction
map in order to have the river reaches flow where they should and to be able to
estimate a flow length closer to reality, particularly for the areas close to the
catchment boundary, lakes, reservoirs and the meandering channel reaches.
As an option, the above procedures can be integrated by modifying the elevation grid
using ArcView GIS tools, in which the elevation of sewer areas, communication lines,
and stream networks are lowered subsequently, e.g. 0.2, 0.4, 0.6 m. Similar flow
direction grid can be obtained based on the modified elevation grid, but cautions
should be made when performs this method to an even more complex terrain. The
derived flow direction map is then used for further drainage structure delineation. The
above procedures can be omitted, if the effects of human infrastructures are not
remarkable to the flow regime in the catchment.
4.4. Creation of input files
4.4.1. Input files of time series
WetSpa Extension reads input data from four input files. The names of these files are
fixed during data preparation, namely p.txt, pet.txt, t.txt and q.txt. All files are in a
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text format and stored in the subdirectory /project/model/input. All data are of
unformatted statements, so that the exact position of each entry is not crucial.
However, there must be at least one space or a comma between entries and data must
be entered for each item.
1) Precipitation series
The input precipitation series are in the format of year, month, day, hour, and
followed by the precipitation values in mm at each gauging station. The first row of
the file is year, month, day and hour, followed by the elevations of each precipitation
station (m) for use in potential topographic precipitation interpolation. The
precipitation series must be in an ascending order corresponding to the ID number in
the precipitation Thiessen polygons. If the model runs on a daily scale, set the hour
value zero. Table A-4.1 gives a sample file of precipitation series on hourly scale.
Table A-4.1: Sample file of precipitation series p.txt
year
1998
1998
1998
1998
1998
1998
1998
1998
Month
10
10
10
10
10
10
10
10
day
23
23
23
23
23
23
23
23
hour
16
17
18
19
20
21
22
23
904
1.406
2.018
0.966
1.054
0.352
9.656
0.264
0.528
570
1.4
2.01
0.963
1.05
0.35
9.618
0.263
0.525
473
1.38
1.98
0.95
1.03
0.34
9.48
0.26
0.52
312
1.36
1.92
0.93
1.01
0.33
9.51
0.25
0.51
2) Potential evapotranspiration series
The file pet.txt contains PET data in mm for all evaporation stations used in the model
simulation. This input file is omitted if other PET calculation method is selected
instead of using measured data. The format of pet.txt file is the same as the
precipitation series. The first row of the file is year, month, day and hour, followed by
the elevations of each evaporation station (m) for use in potential topographic
evapotranspiration interpolation. The data series must be in an ascending order
corresponding to the ID number in the evapotranspiration Thiessen polygons. If the
model runs on a daily scale, put a zero value in the hour’s column. Table A-4.2 gives
a sample file of PET series on hourly scale.
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Table A-4.2: Sample file of PET series pet.txt
Year
1998
1998
1998
1998
1998
1998
1998
1998
Month
10
10
10
10
10
10
10
10
Day
23
23
23
23
23
23
23
23
hour
16
17
18
19
20
21
22
23
901
0.05
0.048
0.048
0.05
0.05
0.05
0.04
0.04
380
0.05
0.047
0.047
0.05
0.05
0.05
0.038
0.038
270
0.048
0.043
0.043
0.048
0.048
0.048
0.036
0.036
3) Temperature series
Temperature data is optional, used only when snow accumulation and snowmelt occur
in the study catchment. The first row of the file is year, month, day and hour, followed
by the elevations of each temperature station (m). The format of the rest of the file is
the same as that in the precipitation series with temperature unit of °C. If the model
runs on a daily scale, set the hour value zero as shown in Table A-4.3. Note that the
temperature stations should be listed in a continuously ascending order and
corresponding to the station numbers in the temperature Thiessen polygons.
Table A-4.3: Sample file of temperature series t.txt
Year
1991
1991
1991
1991
1991
1991
1991
1991
1991
month
1
1
1
1
1
1
1
1
1
Day
10
11
12
13
14
15
16
17
18
hour
0
0
0
0
0
0
0
0
0
295
2.5
4.7
3.5
2
-3.5
-4
-3.4
-5.3
-1.8
141
4
5.9
4.8
4.2
-1.7
-2.7
-3.6
-5.1
-3.1
702
4.4
2
2.9
-0.3
-6.2
-7.6
-7.5
-6.7
-3.8
4) Discharge series
The observed discharge series are optional, used only for graphical comparison of the
model outputs and statistical analysis for model evaluation. The format of the
discharge file is the same as the precipitation file with values in m3/s. Set the hour
value zero if the model runs on a daily scale. Table A-4.4 gives a sample file of
discharge series on hourly scale.
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Table A-4.4: Sample file of discharge series q.txt
Year
1998
1998
1998
1998
1998
1998
1998
1998
month
10
10
10
10
10
10
10
10
Day
23
23
23
23
23
23
23
23
hour
16
17
18
19
20
21
22
23
q1
1.664
1.664
1.664
1.719
1.794
2.255
2.558
3.026
q2
1.784
1.829
1.93
2.031
2.069
2.713
3.092
3.905
q3
0.946
1.015
1.056
1.132
1.225
1.529
2.481
4.39
4.4.2. Global parameters and spatial output specifications
1) Global model parameters
Before running WetSpa model, several global model parameters must be prepared,
which are applied to each grid cell or each subcatchment. The file is named as
input.txt and stored in the subdirectory /project/model/input. Table A-4.5 illustrates a
template of global parameters in the input file input.txt.
Table A-4.5: Template of global model parameters
dt (h)
24
Ci
Cg K_ss
2.0 0.01 0.95
K_ep G0
G_max T0 K_snow K_rain K_run P_max
1.00 250.0 300.0 0.0 2.0
0.00 2.5
50.0
Where dt is the time step of the model (h), for which the value in the second row of
the table can be any hours, e.g. 1 for hourly scale and 24 for daily scale. Ci is an
interflow scaling factor reflecting the effect of organic material and root systems in
the topsoil layer on horizontal hydraulic conductivity. Cg is a groundwater flow
recession coefficient reflecting the groundwater recession regime for entire catchment.
K_ss is a soil moisture ration relative to the field capacity for setting up the initial soil
moisture content. This gives a uniform distribution of initial relative moisture
condition and can be used for model simulation with a long time series. For
performing an event based flood simulation, the initial moisture grid by the method of
TWI can be applied. To do so, a negative value of K_ss should be given in the file, for
instance, -1.0. K_ep is a correction factor for PET. G0 is the initial groundwater
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storage in depth (mm). G_max is the maximum groundwater storage in depth (mm).
T0 is a base temperature (°C) for estimating snowmelt, in which the precipitation
shifts from rain to snow at T0. K_snow is a temperature degree-day coefficient
(mm/°C/day) for calculating snowmelt. K_rain is a rainfall degree-day coefficient
(mm/mm/°C/day) determining the rate of snowmelt caused by rainfall. Note that if
there is no snow accumulation occurred in the study catchment, the parameters T0,
K_snow and K_rain are set to negative values, e.g. –1.0, and the temperature input
dataset ‘t.txt’ is not necessary. K_run is an exponent reflecting the effect of rainfall
intensity on the actual surface runoff coefficient when the rainfall intensity is very
small. P_max is a threshold of rainfall intensity in mm/day or mm/hour depending on
the modelling time step, over which the value of K_run is set to 1.
2) Location and time specifications for spatial output
In order to obtain flow hydrographs at some specified subcatchment outlets, as well as
the spatial distribution of hydrological processes, such as surface runoff, interflow,
groundwater recharge, soil moisture and actual evapotranspiration, for a certain period,
a station and time list must be prepared before running the model. The list is attached
in the same file input.txt stored in the subdirectory /project/model/input, following the
part of global model parameters. Table A-4.6 shows a template of spatial output
specifications.
Table A-4.6: Template of spatial output specifications
Q_sub 6
3 5 8 12 25
Surface runoff
1
1997 8 9 0
Interflow
1
1997 1 1 0
Groundwater-recharge
1
1997 1 1 0
Soil moisture
1
1997 8 9 0
Evapotranspiration
0
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36
1997
8
10
0
1997
12 31
0
1997
12 31
0
1997
8
0
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a) Flow hydrograph at subcatchment outlet
The number of the interested subcatchments is given after the mark ‘q_sub’, and the
sequence number of each subcatchment is listed in the following line. This option is
useful for simulating flow hydrographs simultaneously both at catchment outlet and at
some gauging stations inside the catchment. The identification of specified
subcatchments can be realized by modifying the stream link theme by using ArcView
edit tools and making the discretization of the catchment.
b) Spatial distribution of surface runoff
This option gives a series of accumulative surface runoff distribution files after
running the fully distributed model. The number of expected spatial outputs is given
under the mark ‘Surface runoff’, and the wanted time periods are listed in the
following lines. The input time period is in the format of start year, month, day, hour,
and end year, month, day, hour as shown in the Table. If the model runs on a daily
scale, set the hour value to be zero. If no spatial outputs are wanted, put zero value
under the mark ‘Surface runoff’.
c) Spatial distribution of interflow
This option gives a series of accumulative interflow distribution files after running the
fully distributed model. The format of the input values is the same as for the surface
runoff list.
d) Spatial distribution of groundwater recharge
This option gives a series of accumulative groundwater recharge distribution files
after running the fully distributed model. The format of the input values is the same as
for the surface runoff list.
e) Spatial distribution of relative soil saturation
This option gives a series of soil moisture distribution files after running the fully
distributed model. The format of the input values is the same as the surface runoff list.
f) Spatial distribution of actual evapotranspiration
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This option gives a series of accumulative actual evapotranspiration distribution files
after running the fully distributed model. The format of the input values is the same as
for the surface runoff list.
4.5.
Model calibration and verification
4.5.1. Calibration and verification processes
The purpose of calibration is to derive characteristics, equation constants, weighting
factors, and other parameters that serve to define the model for a particular watershed.
In distributed and continuous simulation, the calibration process is more rigorous and
complex than that in model calibration for lumped model and discrete storm analysis,
in that more parameters are involved in a distributed continuous model, a much
greater amount of hydro-meteorological data is employed, and the fitting of the model
requires a greater number of hydrological factors and more rigorous statistical
procedures. To overcome these problems, calibration of WetSpa is not carried out for
all model parameters, but for the most important parameters only, for instance, the
channel roughness coefficient, plant coefficient, interflow scaling factor, and
groundwater flow recession coefficient. Other parameters, such as hydraulic
conductivity, root depth, interception and depression storage capacity, and so on, are
set to values interpolated from the literature representing average conditions, and not
calibrated but fixed to the selected values.
Once the preparation of input data and model parameters are accomplished, the user
can start to run the model for parameter calibration and model prediction. Programs
can be run within the Arcview project interface, or directly executed in the
subdirectory /project/model/program. Since the running of fully distributed model
costs large memory space and computing time depending upon the catchment area,
grid size, the length of time series and interval, it is preferable to run the semidistributed model firstly, adjust roughly the global and distributed model parameters,
and then go to the fully distributed model, in order to save computing time for model
calibration. The following is an outline of the steps for model calibration within
ArcView interface.
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1) Calculating mean parameters for each subcatchment
From the menu ‘Model’ of the ArcView project or any view of the project, run the
program ‘Mean’. This program computes mean model parameters of each
subcatchment for use in the semi-distributed modelling and adjusting global model
parameters preliminarily during model calibration. This operation can also be
implemented independently by clicking the program ‘mean’ in the subdirectory
/project/model/program. The output file ‘mean.txt’ is saved in the subdirectory
/project/model/output.
2) Calculating unit hydrographs
Run program ‘IUH’ from the dropdown menu. This program calculates unit response
function from each grid cell to the main rivers and basin outlet for use in fully
distributed model, from each subcatchment to the main rivers and basin outlet for use
in semi-distributed model, the unit response function for main rivers for use in both
distributed and semi-distributed models, and unit response function for the entire
catchment used for general parameter analysis. This operation can also be
implemented independently by clicking the program ‘IUH’ in the subdirectory
/project/model/program. The output text files ‘uh_cell_h.txt’, ‘uh_cell_s.txt’,
‘uh_sub_h.txt’, ‘uh_sub_s.txt’, ‘uh_river.txt’ and ‘uh_watershed.txt’ are in the same
format and saved in the subdirectory /project/model/output.
3) Modelling with a semi-distributed approach
From the menu ‘Model’ of the ArcView project or any view of the project, run the
program ‘Model1’. Two options are available in the program: Predict outflow at
catchment outlet and predict outflow both at catchment outlet and subcatchment
outlets. Both options simulate flow hydrograph and water balance on a subcatchment
scale, with output files q_tot.txt and balance.txt saved in the subdirectory
/project/model/output. Additionally, option two routs water firstly to the
subcatchment outlet, and then to the catchment outlet using channel response
functions. Therefore, the produced hydrographs at the catchment outlet may be
slightly different from the result of option one due to truncation errors in computing
IUH. It also gives another output file q_sub.txt, which are the predicted discharges at
selected subcatchment outlet saved in the subdirectory /project/model/output. Since
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both options give the same output file name q_tot.txt and balance.txt, the modeller
needs to rename the file name if it is expected to keep the previous modelling results.
4) Model evaluation
Run program ‘Model Evaluation’ from the dropdown menu. This program gives a
detailed description the observed data, simulation results, as well as the assessment of
the current model parameters. The output file ‘evaluation.txt’ is saved in the
subdirectory /project/model/output.
5) Calibration of global parameters
Based on the evaluation results and the visual comparison between observed and
calculated hydrographs, adjust global parameters in the input file ‘input.txt’, repeat
step 3 and 4, until a good match is reached. Another way of model calibration is to
use the automated calibration scheme by setting properly the up and down limits of
the parameter values in the PEST control file. However, manual parameter adjustment
is still needed to avoid the ill-pose problems. If obvious errors exist and can not be
overcome by adjusting global parameters, users may return to the GIS pre-processing
phase, adjust values in the lookup table and recalculate the spatial parameter grids so
as to make the input parameters more reliable.
6) Modelling with a fully distributed approach
Keep the input files as in Model1, run program ‘Model2’ from the dropdown menu
‘Model’. This program simulates hydrological processes on cell scale, and predicts
hydrograph at basin outlet, water balance on catchment scale, as well as spatial
distribution of surface runoff, interflow, groundwater recharge, soil moisture and
actual evapotranspiration at selected time periods. Output files ‘q_tot.txt’, ‘q_sub.txt’,
‘balance.txt’ and other spatial distribution outputs are saved in the subdirectory
‘/project/model/output’.
a) The output files ‘q_tot.txt’, ‘q_sub.txt’ and ‘balance.txt’ are in the same format as
the outputs of Model1. If users want to keep the flow and water balance results of
Model1, those files must be renamed to avoid being replaced.
b) The output spatial runoff distribution files are named in the order listed in the
‘input.txt’, for instance, ‘runoff1.asc’, ‘runoff2.asc’, etc. Other spatial outputs are
given similarly, such as ‘interflow1.asc’, ‘recharge1.asc’, ‘moisture1.asc’,
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‘evaporation1.asc’, and so on. All these output files are saved in the subdirectory
/project/model/output.
c) The computation time becomes much longer if too many spatial outputs are asked
in the input file while running the fully distributed model. Therefore, it is
suggested to generate less spatial outputs during model calibration. All expected
spatial outputs can be given at the final run after model calibration, or using the
program ‘Water balance’ as described below.
d) Run program ‘Model Evaluation’ again to see the performance of the fully
distributed model. Users are allowed to readjust global and spatial distributed
input parameters in order to make a better match between calculated and observed
hydrographs.
7) Simulation of water balance without flow routing
This program is designed to compute water balance for each grid cell within the
simulation period. Since the program does not cover the parts of flow routing, it can
run more quickly and gives exactly the same water balance and spatial distribution
outputs as Model2.
a) Keep the input files as in Model1 or Model2, run program ‘Water balance’ from
the dropdown menu ‘Model’.
b) The output file ‘balance.txt’ and other spatial output file are saved in the
c) The output file ‘balance.txt’ and other spatial output file are saved in the
subdirectory ‘project/model/output’. The previous output files need to be renamed
if the user wants to keep them.
d) The spatial input parameters can be reviewed based on the analysis of these spatial
outputs, and some of the input parameter maps may need to be recalculated
accordingly.
8) Model verification
Model verification is being used to validate the calibrated model parameters by
running the model for an independent period of record and comparing the results with
observed data after calibration of the model is complete. This procedure will help to
ensure that the calibration is not unique and limited to the data set employed for
calibration.
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4.5.2. Manual parameter adjustment
In WetSpa Extension, manual calibration runs are made with trial simulation. Model
output is compared with observed stream flow both at the catchment outlet and the
internal discharge monitoring stations, and evaluated by the 5 assessment criteria
described in section A-3.3. Based upon those comparisons and evaluations, parameter
adjustments are made to improve the performance of the model. The initial choice of
model parameters is not a critical concern since adjustments will be made during
calibration. However, those parameters that have physical relevance should be
determined to reduce the possibilities for future adjustment during model calibration.
Model parameters that are typically encountered in a continuous simulation of
WetSpa Extension are listed in Table A-4.6, in which the parameters that can be
determined by independent analysis are indicated. For other parameters that need to
be empirically determined, the initial value might be determined based upon known
values in previous simulation studies, characteristic values of similar catchment, or
default values collected from the literature. A desirable part of the calibration process
is to make an independent estimate of the basin’s water balance. This calculation
would yield the whole, annual or perhaps monthly estimates of basin precipitation,
evapotranspiration, runoff, soil moisture and groundwater storage that can be helpful
in calibrating the model parameters. Adjustments are made firstly to those parameters,
which have the greatest impact on the model output, then proceeding to variables with
lesser sensitivity. The process may be expressed as five basic steps with each having
several trials.
1) Achieve fit of runoff volumes throughout the simulation period. This process
preliminary involves adjustment of precipitation weighting factors, potential
runoff coefficient, evapotranspiration factors, as well as interflow and
groundwater flow production factors. Calibration fit is usually judged by
comparing monthly, annual and the total runoff volumes.
2) Achieve fit of peak discharge and the time to peak. This step involves working
with runoff distribution and routing factors, particularly for the components in
controlling high flow hydrographs, such as hydraulic radius, channel roughness
coefficient, etc.
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3) Achieve fit of hydrograph shape. This step mainly involves adjustment of model
parameters in controlling low flow hydrographs, such as the interflow and
groundwater flow factors, as well as evapotranspiration factors during dry period.
4) Achieve fit of snow melting floods if snow accumulation and snowmelt occurs in
the study catchment. This step involves adjustment of model parameters in
controlling snowmelt processes, including base temperature, temperature degreeday coefficient, rainfall degree-day coefficient, and temperature lapse rate.
5) Refine hydrograph fit. This final step involves working with different initial
conditions and other distributed runoff production and flow routing parameters to
refine a better hydrograph shape.
4.5.3. Parameter sensitivity
Parameter sensitivity comprises the determination of changes in the individual
parameters, in order to get an insight into the required precision of the model
parameters relative to the precision of the model output. Table A-4.7 describes the
order of parameter priority in more detail and gives a relative sensitivity of the
variables, which are used in the WetSpa Extension. The ‘Relative sensitivity’ in Table
A-4.7 indicates the degree to which parameter affects model output. ‘Major effects’
indicates which aspect of the output is primarily affected. ‘Calibration priority’
suggests the order in which parameters are typically adjusted. And ‘Independent
evaluation’ indicates those parameters that are typically determined independent of
the calibration process, because they are more physically based. All parameters in
WetSpa Extension represent a physical process. It is essential that parameter values
remain physically reasonable throughout the calibration process to keep the fit from
being a local optimization that will not work when extrapolated to new data.
Therefore, a verification step is desirable to ensure that the fit is a general solution,
not one unique only to the calibration data used.
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Table A-4.7: Parameter sensitivity for manual calibration
Relative
Major
Calibration Independent
Parameter
sensitivity
Effects
priority
evaluation
Precipitation/Evapotranspiration
Station weight
High
Runoff volume
1
√
Correction factor
High
Runoff volume
1
Vegetation fraction
High
Runoff volume
2
Vertical precipitation gradient Medium Runoff volume
2
√
Vertical PET gradient
Medium Runoff volume
2
√
Maximum groundwater storage Medium Low flow shape
2
Snowmelt
Base temperature
High
Snowmelt
1
√
Temperature degree-day factor High
Snowmelt
1
√
Rainfall degree-day factor
High
Snowmelt
2
√
Temperature lapse rate
High
Snowmelt
2
√
Runoff distribution
Potential runoff coefficient
High
Volume, high flow
1
Surface runoff exponent
High
Volume, peak flow
1
Threshold rainfall intensity
High
Volume, peak flow
1
Impervious fraction
High
Volume, high flow
1
√
Interception capacity
Medium Runoff volume
2
√
Depression capacity
Medium Runoff volume
2
√
Flow routing
Surface roughness coefficient Medium High flow shape
2
√
Channel roughness coefficient High
High flow shape
2
√
Hydraulic radius
High
High flow shape
2
Threshold of minimum slope Medium High flow shape
3
Threshold of stream network Medium High flow shape
3
Volume, flow
Interflow scaling factor
High
1
shape
Baseflow recession coefficient High
Low flow shape
1
Number of subcatchments
Medium Low flow shape
3
Soil properties
Hydraulic conductivity
Medium Runoff volume
3
√
Porosity
Low
Runoff volume
3
√
Field capacity
Low
Runoff volume
3
√
Wilting point
Low
Runoff volume
3
√
Residual moisture content
Low
Runoff volume
3
√
Pore size distribution index
Low
Runoff volume
3
√
Root depth
Medium Runoff volume
3
√
Initial conditions
Soil moisture
Low
Flow shape
3
√
Groundwater storage
Low
Flow shape
3
√
Interception storage
Low
Flow shape
3
√
Depression storage
Low
Flow shape
3
√
Initial baseflow
Low
Flow shape
3
√
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4.6. Model output
4.6.1. Intermediate output
WetSpa Extension produces the mean parameters for each subcatchment and the unit
response functions for each grid cell, subcatchment and the main river channels
separately, in order to avoid repeatable computations during model calibration. These
intermediate outputs are further used as inputs in the distributed and semi-distributed
models. Since WetSpa Extension simulates hydrological processes continuously, it
uses and creates an immense amount of data, particularly if a long period of record is
involved. Judging the fit of the final stream flow output along is difficult for model
calibration. Reviewing these intermediate outputs therefore provides a possibility for
efficiently parameter adjustments.
1) Mean parameters of each subcatchment
Taking the Bissen subcatchment in the Alzette river basin, the Grand-duchy of
Luxembourg, as a testing area, a sample intermediate output file mean.txt is shown in
Table A-4.8.
Table A-4.8: Sample output file of mean.txt
No
1
2
3
4
5
6
7
8
9
10
C
0.41
0.40
0.37
0.45
0.36
0.40
0.33
0.44
0.40
0.42
S
9.42
11.9
13.3
9.64
8.16
12.6
7.88
8.98
7.85
8.15
Kc
10.9
11.9
12.1
17.6
25.7
9.2
21.4
8.6
26.2
13.4
PS
0.49
0.48
0.47
0.49
0.48
0.48
0.47
0.49
0.48
0.49
FC
0.29
0.28
0.25
0.29
0.26
0.29
0.26
0.31
0.26
0.3
PI
11.1
11.0
11.0
10.4
9.7
11.2
9.8
11.3
9.7
10.8
WP
0.12
0.12
0.11
0.12
0.11
0.12
0.12
0.13
0.11
0.12
RM
0.05
0.05
0.07
0.04
0.05
0.05
0.07
0.04
0.05
0.04
IX
1.14
1.18
1.25
0.99
1.12
1.21
1.26
1.06
1.05
1.04
IN
0.48
0.48
0.49
0.46
0.48
0.48
0.48
0.48
0.46
0.47
DP
1.85
1.71
1.87
1.56
2.31
1.72
2.8
1.58
2.33
1.83
RD
1
1
1
1
1
1
1
1
1
1
TP
3
4
4
3
2
4
1
4
2
4
TE
3
3
3
3
2
3
1
3
2
3
TT
3
3
3
3
2
3
1
3
2
3
IMP
0
0.01
0.02
0
0
0.01
0
0
0
0
A
11.3
25.6
20.9
8.28
14.3
24.4
5.31
13
2.03
6.95
Where No is the number of the subcatchment, C is the potential runoff coefficient (-),
S is the mean subcatchment slope (%), Kc is the mean hydraulic conductivity (mm/h),
PS is the mean soil porosity (m³/m³), FC is the mean field capacity (m³/m³), PI is the
mean pore size distribution index (-), WP is the mean wilting point (m³/m³), RM is the
287
Appendix A
mean residual soil moisture (m³/m³), IX is the maximum interception capacity (mm),
IN is the minimum interception capacity (mm), DP is the mean depression storage
capacity (mm), RD is the mean root depth (m), TP is the Thiessen polygon number
for precipitation (-), TE is the Thiessen polygon number for PET (-),TT is the
Thiessen polygon number for temperature (-), IMP is the percentage of urban areas
(%), and A is the subcatchment area (km²).
2) Instantaneous unit hydrographs
The files of instantaneous unit hydrograph (IUH) or the unit impulse response
function include uh_cell_h.txt for routing water from cell to the basin outlet,
uh_cell_s.txt for routing water from cell to the main river, uh_sub_h.txt for routing
water from subcatchment to the basin outlet, uh_sub_s.txt for routing water from
subcatchment to its outlet, uh_river.txt for routing water from subcatchment outlet to
basin outlet, and uh_watershed txt which is the IUH for the entire catchment. All
IUH files are in the same format. The total rows in the file uh_cell_h.txt and
uh_cell_s.txt are the count of effective cells over the catchment. The total rows in
uh_sub_h.txt, uh_sub_s.txt and uh_river.txt are equal to the number of subcatchments.
And there is only one row in the file uh_watershed.txt. An example of the file
uh_cell_h.txt is shown in Table A-4.9, where the first column is the start non-zero
time step of the IUH, the second column is the end non-zero time step, and the values
from the third column till the end are IUH non-zero values at each time step.
Table A-4.9: Parts of output file uh_cell_h.txt
1
1
3
1
1
3
0
1
0
1
288
21
22
35
20
13
36
6
26
10
15
0.027
0.018
0.007
0.109
0.478
0.005
0.882
0.001
0.004
0.389
0.147
0.112
0.022
0.214
0.218
0.018
0.075
0.043
0.596
0.228
0.180
0.155
0.040
0.184
0.116
0.035
0.022
0.100
0.192
0.135
0.158
0.150
0.057
0.137
0.068
0.052
0.010
0.126
0.089
0.083
0.125
0.128
0.069
0.098
0.042
0.065
0.005
0.126
0.048
0.053
0.094
0.103
0.077
0.070
0.027
0.074
0.003
0.113
0.029
0.035
0.070
0.080
0.080
0.050
0.018
0.077
0.002
0.097
0.018
0.024
0.052
0.062
0.078
0.036
0.012
0.077
0.038
0.047
0.074
0.027
0.008
0.074
0.028
0.036
0.069
0.020
0.006
0.069
0.021
0.027
0.062
0.014
0.004
0.063
0.016
0.021
0.055
0.011
0.002
0.057
……
……
……
……
……
……
0.080 0.065 0.052 0.042 0.033 ……
0.012 0.008 0.004 0.001
0.017 0.012 0.008 0.006 0.004 ……
WetSpa Extension: Documentation and User Manual
4.6.2. Final output
WetSpa Extension produces a variety of output files, depending on the selected
options during the simulation run. The basic output files are the time series including
predicted hydrographs at the catchment outlet or the selected subcatchment outlets,
and water balance for the entire catchment over the simulation period. Other output
files contain information about the spatial distributions of simulated hydrological
processes at a predetermined time period. The program writes output into ASCII files,
for which the file names are fixed in the program, or identified in the input file. All
output files are stored in the subdirectory /project/model/output.
1) Discharge at the catchment outlet
A sample output file q_tot.txt for the Bissen catchment is shown in Table A-4.10,
where the first 4 columns are year, month, day and hour. If the model runs on a daily
scale, the values in the Hour’s column are zero. P is the hourly rainfall (mm), Qs is the
calculated surface runoff (m3/s), Qi is the calculated interflow (m3/s), Qg is the
calculated groundwater flow (m3/s), and Q is the total runoff at the catchment outlet
calculated by the summation of surface runoff, interflow and groundwater flow (m3/s).
This file is the most useful output providing the simulated rainfall and runoff plot, in
which the time increment for the output hydrograph is equal to the parameter dt given
in the input file.
Table A-4.10: Sample output file of q_tot.txt
year
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
month
10
10
10
10
10
10
10
10
10
10
day
23
23
23
23
23
23
23
23
24
24
Hour
16
17
18
19
20
21
22
23
0
1
P
1.38
1.99
0.95
1.03
0.34
9.51
0.26
0.52
0
0.43
Qs
0.274
0.569
1.535
2.262
3.033
3.497
9.084
11.122
12.723
13.545
Qi
0.539
0.542
0.544
0.549
0.554
0.560
0.567
0.585
0.606
0.628
Qg
0.947
0.948
0.949
0.950
0.951
0.952
0.952
0.953
0.953
0.953
Q
1.760
2.059
3.029
3.761
4.538
5.009
10.603
12.659
14.282
15.126
2) Discharge at the selected subcatchment outlet
289
Appendix A
Table A-4.11 gives an example of output file q_sub.txt for the Bissen catchment,
where the first 4 columns are year, month, day and hour, and the next 4 columns are
calculated discharges at the outlet of subcatchment 1, 5, 10, and 11. This file gives
simulated discharge data at a user selected location, which is useful for plotting
hydrographs at an interested site, or comparing with observed hydrographs if an
internal flow gauge exists at that site.
Table A-4.11: Sample output file of q_sub.txt
year
1998
1998
1998
1998
1998
1998
1998
1998
1998
1998
month
10
10
10
10
10
10
10
10
10
10
day
23
23
23
23
23
23
23
23
24
24
Hour
16
17
18
19
20
21
22
23
0
1
1
0.645
0.834
1.245
1.214
1.210
1.046
3.808
2.637
1.983
1.436
5
0.809
0.927
1.204
1.227
1.247
1.156
2.853
2.324
1.937
1.579
10
0.410
0.506
0.713
0.681
0.678
0.596
2.027
1.332
1.012
0.782
11
0.516
0.684
0.960
0.785
0.769
0.633
2.975
1.093
0.772
0.615
3) Water balance for the entire catchment
Both the semi-distributed and the fully distributed model produce a water balance
time series. A sample output file balance.txt for the Bissen catchment is show in Table
A-4.12, where T is the time step (-), P is the average hourly rainfall (mm), I is the
average interception losses (mm), Sm is the average soil moisture in the root zone
(mm), F is the average infiltration losses (mm), Et is the average actual
evapotranspiration losses (mm), Perc is the average percolation out of root zone
(mm), Rs is the average surface runoff (mm), Ri is the average interflow (mm), Rg is
the average groundwater flow (mm), R is the total runoff (mm), and GT is the average
active groundwater storage at this time step (mm). This file provides information on
the simulated water balance for the entire catchment at each time step, which can be
used for model calibration and evaluation.
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Table A-4.12: Sample output file of balance.txt
T
1
2
3
4
5
6
7
8
9
10
P
1.384
1.986
0.952
1.034
0.342
9.506
0.261
0.521
0
0.431
I
0.594
0
0.049
0.049
0.049
0.049
0.049
0.039
0
0.074
Sm
282.46
283.99
284.66
285.40
285.60
292.90
293.02
293.35
293.73
293.97
F
0.616
1.546
0.703
0.766
0.228
7.324
0.163
0.371
0.42
0.275
Et
0.048
0.049
0.049
0.049
0.049
0.049
0.039
0.039
0.039
0.029
Perc
0.017
0.018
0.019
0.02
0.02
0.02
0.028
0.028
0.028
0.029
Rs
0.121
0.331
0.131
0.14
0.036
2.006
0.024
0.057
0
0.051
Ri
0.007
0.007
0.007
0.008
0.008
0.008
0.011
0.011
0.011
0.011
Rg
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
R
0.14
0.349
0.15
0.16
0.056
2.026
0.047
0.08
0.023
0.074
GT
150.17
150.17
150.18
150.19
150.20
150.21
150.22
150.24
150.25
150.27
4) Spatial output
Table A-4.13 shows a part of the output file runoff.asc, which is the spatial
distribution of surface runoff over the catchment for the time interval 14-15, Oct. 18,
1998, where ncols is the number of columns, nrows is the number of rows, xllcorner
is corner coordinate in x direction (m), yllcorner is corner coordinate in y direction
(m), cellsize is the cell size (m), and nodata_value is the no data value. This file
contains information on simulated surface runoff on each grid cell, and can be
imported to ArcView for further analysis. Other spatial distribution files, e.g.
interflow, groundwater recharge, soil moisture, and actual evapotranspiration, are in
the same format as for the surface runoff. The output file names are defined in the
program in an ascending order, e.g. runoff1.asc, runoff2.asc, etc.
Table A-4.13: Parts of the output file runoff.asc
ncols
nrows
xllcorner
yllconer
cellsize
nodata_value
-1.000 -1.000
-1.000 -1.000
-1.000 -1.000
-1.000 -1.000
-1.000 -1.000
-1.000 -1.000
-1.000 -1.000
539
356
45240
84580
50
-1.000
-1.000
-1.000
-1.000
-1.000
-1.000
-1.000
2.463
-1.000
-1.000
-1.000
-1.000
-1.000
2.463
4.364
-1.000
-1.000
-1.000
-1.000
2.463
0.994
1.342
-1.000
-1.000
-1.000
2.152
2.463
1.342
1.342
-1.000
-1.000
2.152
2.463
2.863
1.342
2.261
2.463
2.463
2.463
2.863
2.863
2.261
2.261
2.463
2.463
2.863
2.863
2.863
2.261
2.261
……
……
……
……
……
……
……
291
Appendix A
5) Evaluation results
Table A-4.14 gives a sample evaluation output evaluation.txt for the Bissen catchment
after running the fully distributed model for an hourly time series in the year 1997.
Table A-4.14: Model evaluation result evaluation .txt
Area of the catchment (km2)
288.8
Period of simulation
1/1/1999:0 - 31/12/1999:23
Measured precipitation, evaporation and discharge
P
Em
Qm
Qm
unit
(mm) (mm) (mm) (m3/s)
sum
1041
630
416 33360
% of P
60.5
30.0
mean
0.12
0.07
0.05 3.81
max
9.1
0.72
0.77 61.7
Calculated water balance for the simulation period
P
I
DS
F
E
Perc
Rs
Ri
Rg
R
DG
unit
(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)
sum
1041
137
37.1
752
512
269
148 103 252 503 -15.2
% of P
13.2
3.56 72.2 49.2 25.8 14.2 9.90 24.2 48.3 -1.46
mean
0.119 0.016 271 0.086 0.058 0.031 0.017 0.012 0.029 0.057 132
max
9.39
1.12
352
7.23 0.713 0.289 1.69 0.120 0.066 1.78 207
Model evaluation
CR1 CR2 CR3 CR4 CR5
0.048 0.825 0.792 0.807 0.832
Where P, Em and Qm are observed precipitation (mm), PET (mm) and discharge
(mm) (m3/s) respectively, while the period of missing discharge data is not taken into
account. I is the interception losses (mm), DS is the soil moisture difference between
the start and the end time step (mm), F is the infiltration losses (mm), Et is the actual
evapotranspiration (mm), Perc is the percolation out of root zone (mm), Rs is the
surface runoff (mm), Ri is the interflow (mm), Rg is the groundwater flow (mm), R is
the total runoff (mm), and DG is difference in groundwater storage between the start
and the end time step (mm). CR1 is model bias. CR2 is model determination
coefficient. CR3, CR4 and CR5 are Nash-Sutcliffe model efficiencies as described in
section A-3.3. The evaluation results also contain the information on the catchment
area, the period of model simulation, as well as the periods of missing discharge data
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if they exist. Specifically, the change in soil moisture and groundwater storage over
the simulation period is given in the evaluation output file, in order to make water
balance compatible with other items, but its mean and maximum values are estimated
state variables.
4.6.3. Post processing of model outputs
In the current WetSpa Extension, no special effort has been paid in developing
programs for the post processing of model output. However, the visual comparison
between calculated and observed hydrographs can be carried out using Excel or other
available software by loading the data from their text files. Moreover, the simulated
hydrological processes for the entire catchment, such as precipitation, runoff,
evapotranspiration, soil moisture, etc., can be viewed by plotting the data from the
water balance output file. These graphs are helpful in adjusting model parameters
more accurately and improving the model to have a better performance. Finally, the
spatial output data including surface runoff, interflow, groundwater recharge, etc., can
be imported to the ArcView project. Using the GIS tools, e.g. reclass, zoom, etc., a
clear view can be obtained at the points of special interest. This information is not
only a plot of spatial distribution of hydrological processes, but also a valuable
feedback in refining model parameters.
5.
Case study: Bissen catchment, Luxembourg
5.1.
Description of the study area
The Bissen catchment is located in the Attert River basin covering an area of 294 km2
in the Grand-duchy of Luxembourg (Figure A-5.1). The Attert River is a main
tributary of the Alzette River, where high-magnitude floods occurred frequently and
have caused important damages since the early 1990’s. The study catchment is
homogeneous from a lithological point of view with essentially marls (El Idrissi et al.,
2000). Using hourly rainfall-runoff series, the main goals are to apply the WetSpa
Extension in predicting of flood hydrographs at basin outlet, estimating the spatial
distribution and variability of the hydrological processes, and testing the sensitivity of
model parameters with respect to catchment characteristics.
293
Appendix A
#
#
BELGIUM
#
Town
River
Clervaux
Alzette basin
GERMANY
Wiltz
Grand-Duchy of Luxembourg
Bissen catchment
#
Ell
#
rt
Atte#Bissen
#
Mersch
Echternach
N
W
Alzette
#
Ettelbruck
S
#
Luxembourg-city
#
#
E
Remich
0
10
20 km
Esch/Alzette
FRANCE
Figure A-5.1: Location of the Bissen catchment
The climate of the region has a northern humid oceanic regime without extremes.
Rainfall is the main source of runoff. The average annual precipitation varies between
800 mm to 1000 mm, which is characterized by distinctive winter and summer
seasons. December is the wettest month of the year with average monthly
precipitation of 84mm and April is the driest month of the year with average
precipitation of 58 mm. The monthly PET values in the basin vary from 13.5 mm in
winter to 81.8 mm in mid summer. High runoff occurs in winter and low runoff in
summer due to the higher evapotranspiration. Winter storms are strongly influenced
by the westerly atmospheric fluxes that bring humid air masses from the Atlantic
Ocean (Pfister et al., 2000), and floods happen frequently because of saturated soils
and low evapotranspiration. Statistical analysis of the observed data from the
Luxembourg airport from 1947-1999 shows a uni-modal distribution of temperature
with January being the coldest month of the year with an average temperature of
0.7°C and July is the warmest month of the year with average temperature of 17°3C.
The study area has a hilly topography, with elevation ranging from 220.6 to 545.0 m
and average basin slope of 8.8% (Figure A-5.2). The land-use of the area, as shown in
Figure A-5.3, is composed of agricultural land (23.7%), grassland (36.8%), forest
(34.5%), urban areas (4.8%) and other land-use types (0.2%). Loam, silt loam, sandy
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clay loam and loamy sand are main soil types covering 52.0%, 16.0%, 12.5% and
11.6% respectively as shown in Figure A-5.4.
N
Elevation (m)
220 - 247
247 - 274
274 - 301
301 - 328
328 - 355
355 - 382
382 - 409
409 - 436
436 - 463
463 - 490
490 - 517
517 - 545
W
E
S
0
2.5
5.0 km
Figure A-5.2: Topography map of Bissen
N
Landuse
Crop
Short grass
Bog marsh
Deceduous shrub
Bare soil
Urban area
Open water
W
E
S
0
2.5
5.0 km
Figure A-5.3: Land use map of Bissen
Bissen
#
Reichlange # Platen
#
#
#
#Ell
Niederpallen Useldange
Soil type
Sand
Loamy sand
Silt loam
Silt
Loam
Sandy clay loam
Silt clay loam
N
W
N
E
S
0
2.5
5.0 km
Figure A-5.4: Soil type map of Bissen
#
Hydrologic station
River network
Theissen polygon
Catchment boundary
W
E
S
0
2.5
5.0 km
Figure A-5.5: River network and
Thiessen polygons of Bissen
5.2.
Data availability
1) Topographic data
The topographic data is obtained from the numerical elevation data sets of the public
ACT (Administration du Cadastre et de la Topographie, Luxembourg). A DEM with
50×50 m grid size for the Bissen catchment is built using 2-meter resolution elevation
contour map (Figure A-5.1). To check the validity of the data set, flow directions are
295
Appendix A
estimated from the elevation data set and the rivers were generated. Then this is
overlain with the actual river network. From this comparison as shown in Figure A5.5, it is seen that the data set has sufficient accuracy to carry out model simulation.
2) Land use data
The land use information is taken from CORINE (Co-ordination of Information on
the Environment) provided by the Luxembourgian Ministry of Environment, and the
cadastral BD-L-TC (La Base de Donnée Topo/Cartographique du Luxembourg) data.
Both data sets are based on remote sensing information. These vector data sets are
converted firstly to 50×50 m grid according to WetSpa land use classification, as
shown in Figure A-5.3, and then reclassified to 6 basic land use classes (forest, grass,
crop, bare soil, urban and open water) for deriving model parameters of potential
runoff coefficient and depression storage capacity.
3) Imperviousness and soil data
For model simulation, the previous and impervious areas in each grid are required.
For a grid size of 50 m, the impervious and pervious area ratio for different land use
categories was established as described in Chapter A-3. Impervious fraction is set to
70% for commercial and industrial area, 30% for residential areas, 100% for water
bodies and 0% for other land use categories. Information of soil types is obtained
from the digital 1:100,000 Soil Map of the European Communities. The map is
reclassified to 12 USDA soil texture classes based on their textural properties, and
concerted to 50 m grid to match with the base topographic data.
4) Rainfall data
6 rainfall stations are available in the Bissen catchment as shown in Figure A-5.5.
Among them, the Reichlange, located near the catchment centre, is a station recording
rainfall at an hourly time step, while others are daily recording raingauges. To obtain
an hourly rainfall series at each raingauge used in the WetSpa Extension, the hourly
rainfall measured at Reichlange is taken as a reference, and multiplied by the ratio
between the daily rainfall observed at the raingauge and the reference station:
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⎛P ⎞
Phour,i = ⎜ day,i ⎟Phour,r
⎜P ⎟
⎝ day,r ⎠
(5.1)
where Phour,i and Phour,r are hourly rainfall at gauging site i and the reference station
(mm), and Pday,i and Pday,r are daily rainfall at gauging site i and the reference station
(mm). Based on the raingauge network and the catchment boundary, the Thiessen
polygon map is created as shown in Figure A-5.5 using ArcView Thiessen Polygon
Extension. A unique hourly rainfall structure is then applied for each polygon, i.e. the
rainfall series for each grid is set equal to the rainfall series of the nearest raingauge.
4) Potential evapotranspiration
PET is estimated using the Penman-Monteith formula, as described in Chapter A-2,
with daily meteorological data measured at Luxembourg airport located about 20 km
south of the catchment. The same meteorological data series (net radiation, air
temperature, relative humidity, and wind speed) are then uniformly applied on the
whole study area. The average daily PET series for the Bissen catchment is achieved
by applying weighting factor for the daily PET series obtained for the land uses as
used in Drogue (2002):
EPd = %URB. EPurb,d + %AGR. EPagr,d + %GRA. EPgra,d + %FOR. EPfor,d
(5.2)
where EPd is the daily PET for the catchment, %URB, %AGR, %GRA and %FOR
are weighting factors (area of land use type / area of catchment) for urban areas,
cropland, grassland and forest as listed in Table A-5.2, and EPurb,d, EPagr,d, EPgra,d, and
EPfor,d are daily PET series for each type of land use observed in the catchment. The
PET from open water surface is neglected due do its very small percentage in the
catchment. The values of canopy resistance, albedo and vegetation height considered
in the PET calculation for the different land uses are given in Table A-5.1. For
cropland, distinction is made between summer and winter where the land use is
defined as a bare soil. The parameter values listed in Table A-5.1 are in accordance
with the values used in scientific publications (Szeicz and Long, 1959; Perrier, 1982;
Shuttelworth, 1989; Dickinson et al., 1993). Average values are used except for the
canopy resistance, which are chosen in the range of the common values.
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Table A-5.1: Default parameter values in the PET formula for different land uses
Land use
Grassland
Cropland (summer)
Cropland (winter, = bare soil)
Forest (mainly deciduous)
Impervious area
Canopy resistance
(100
/ )
70
100
150
-
Albedo (-)
0.20
0.20
0.20
0.15
-
Vegetation height
( )
0.12
1.00
0.12
15.0
-
The hourly PET series are finally computed from the daily data in proportion to the
hourly temperature distribution (Guex, 2001).
⎛T ⎞
EPh,i = EPd ⎜⎜ h,i ⎟⎟
⎝ Td ⎠
(5.3)
where EPh,i is the hourly PET value at hour i (mm), Th,i is the hourly temperature at
hour i (oC), and Td is the cumulative hourly temperature within a day (oC). In
computation of hourly PET with Equation 5.3, the hourly temperature is set to zero if
the actual temperature is lower than zero, and the hourly PET is considered to be zero
if Td is less than or equal to zero.
5) Discharge data
Six stream gauges, namely Ell, Reichlange, Useldange, Bissen, Niederpallen and
Platen, as shown in Figure A-5.5, exist in the study area recording water levels at a
15-minute time step. The stream gauge Niederpallen and Platen are located at the
outlet of two tributaries, while other 4 are located along the main channel with Bissen
at the outlet of the catchment. Hourly discharge data are obtained through available
rating curves at each gauging site. For Reichlange though, the rating curve has a low
reliability, the discharge data could be used for validation purpose on peak flows. A
total of 52 months of hourly rainfall, discharge and PET data from December 1996 to
March 2001 are available for model calibration, except for Ell and Useldange (29
months from November 1998 to March 2001). The average hourly flow at Bissen
during the monitoring period was 4.38 m³/s, with flows ranging from 0.86 to 86.3
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m³/s, and the measured maximum hourly rainfall intensity was 21.5 mm/h occurred
on July 7, 2000. Table A-5.2 presents the available data, geographical features, as
well as the land use composition of each subcatchment. All hydrometeorological data
sets used in this study come from the hydoclimatological database built-up and
validated by the CRP-GL (Centre de Recherche Public - Gabriel Lippmann of
Luxembourg).
Table A-5.2: Data available and characteristics of the Bissen catchment
Station
River
Area (km2)
Perimeter (km)
Average slope (%)
Raingauge type
Start of data series
End of data series
Max. flow (m3/s)
Urban (%)
Crop (%)
Grass (%)
Forest (%)
Water surface (%)
Rest (%)
5.3.
Ell
Reichlange Useldange Bissen Niederpalle Platen
Attert
Attert
Attert
Attert
Pall
Roubbach
107
166
255
294
34.6
47.1
49.9
64.4
75.3
82.1
32.6
33.0
9.4
9.2
8.9
8.8
6.1
11.1
Daily
Hourly
Daily
Daily
Daily
Daily
22/10/98 01/12/96 02/10/98 01/12/96 01/12/96 01/12/96
01/04/01 01/04/01 01/04/01 01/04/01 01/04/01 01/04/01
25.0
13.4
51.7
86.3
22.6
11.2
3.5
4.0
4.1
4.8
3.9
4.8
20.9
23.3
24.7
23.7
19.1
32.4
33.7
37.6
37.2
36.8
51.6
25.8
41.8
34.9
33.9
34.5
25.0
36.7
0.0
0.1
0.1
0.1
0.2
0.2
0.0
0.0
0.0
0.1
0.0
0.0
Basin delineation and parameter determination
The pre-processing starts with a creation of a depression-less DEM ensuring that
positive drainage will occur. Next, flow direction and flow accumulation grids are
calculated based on the flow path of steepest decent. The stream network is extracted
from the master DEM using a threshold cells value of 100, which ensures that a
channel is detected when the drainage area is greater than 0.25 km2. A grid of stream
order used for assigning channel Manning’s n is then derived from the stream network
grid by the Shreve method. A slope grid is derived from the DEM and the delineated
stream network, calculating slopes from each cell to its neighbours as percent rise for
both land surface and stream channels. A threshold of minimum slope 0.01% is
selected in order to deal with the problem of zero slopes in specific areas. The grid of
hydraulic radius (Figure A-5.6) is calculated using the power law relationship
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Appendix A
described in section A-2.10.1 with a network constant a = 0.07 and a geometry scaling
exponent b = 0.47, corresponding a flood frequency of 2-year return period. Finally, a
map of subcatchment is extracted from the master DEM with a cells threshold value
of 1000. 61 subcatchments are distinguished corresponding to an average
subcatchment area of 4.73 km2 with minimum subcatchment area of 0.043 km2 and
maximum subcatchment area of 14.5 km2. The resulting minimum subcatchment area
is much smaller than the threshold value 0.75 km2 due to the remainder of the
extraction. These subcatchments serve as working units in the semi-distributed model,
and are also used for simulating groundwater balance in the full-distributed model.
Hydraulic radius (m)
0.005 - 0.01
0.01 - 0.05
0.05 - 0.1
0.1 - 0.2
0.2 - 0.3
0.3 - 0.5
0.5 - 1
1 - 1.2
N
W
E
S
0
2.5
5.0 km
Runoff Coefficient
0.05 - 0.15
0.15 - 0.25
0.25 - 0.35
0.35 - 0.45
0.45 - 0.55
0.55 - 0.65
0.65 - 0.75
0.75 - 1
N
W
E
S
0
2.5
5.0 km
Figure A-5.6: Hydraulic radius of Bissen Figure A-5.7: Runoff coefficient of Bissen
The physical parameters created by ArcView based on the soil type map include the
saturated hydraulic conductivity, soil porosity, field capacity, plant wilting point,
residual moisture content, and the soil pore size distribution index. The land use based
parameters used in the model include root depth, interception capacity, and the
Manning’s coefficient. The Manning’s coefficients for river channels are interpolated
based on the GIS derived stream orders, with 0.03 m-1/3s for the highest order and
0.05 m-1/3s for the lowest order. The parameter maps of potential runoff coefficient
(Figure A-5.7) and depression storage capacity are created based on the combination
of the three base maps. The impervious percentage for urban cells is set to be 70%,
while the rest are assumed being covered by grass. The flow routing parameters
include flow velocity, average travel time and its standard deviation from cells to the
catchment outlet and to the subcatchment outlet. Figure A-5.8 and A-5.9 shows the
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calculated mean travel time and its standard deviation from cells to the basin outlet for
the Bissen catchment.
Standard deviation (h)
0-2
2-3
3-4
4-5
5-6
6-8
8 - 10
10 - 12
N
W
E
S
0
2.5
5.0 km
Travel time (h)
0-1
1-3
3-6
6 - 10
10 - 15
15 - 21
21 - 28
28 - 39
N
W
E
S
0
2.5
5.0 km
Figure A-5.8: Mean travel time to the basin
Figure A-5.9: Standard deviation of
Outlet of Bissen
flow time to the basin outlet
Finally, the Thiessen polygons for precipitation and PET (Figure A-5.5) are created
using the Thiessen polygon extension. Due to the fact that snow accumulation has a
very minor effect on the runoff process in this catchment, the snowmelt flow is not
accounted during the flow simulation. Therefore the preparation of temperature
Thiessen polygon and temperature data series is not necessary in this case study. At
this moment, all spatial parameters used in the model simulation are developed. A
visual inspection is performed to ensure that the general characteristic of the
parameter maps, such as the range, extreme values, etc., are logical and in the right
order.
5.4.
Model calibration and validation
Model calibration for the study catchment was performed for the time period of Dec.
1996 to Dec. 1999, while the period of Jan. 2000 to Apr. 2001 was used for model
validation. Both the visual and statistical comparisons for the observed and simulated
flow hydrographs at Bissen station were performed for the calibration and validation
periods. Comparisons at other three gauging stations inside the catchment were also
implemented as a kind of model validation. The comparisons of simulated and
observed values included runoff volumes, hourly time series of flow, and the time to
301
Appendix A
the peak for each individual flood. In addition to the above comparisons, the water
balance components (measured and simulated) were reviewed. This effort involved
displaying model results for the whole simulation period for the water balance
components of
precipitation, infiltration, total runoff, overland flow, interflow,
baseflow, PET, actual Evapotranspiration, interception, groundwater recharge, as well
as the differences in soil moisture and groundwater storage between the start and end
hour. Although observed values were not available for each of the water balance
components listed above, the average annual values and its spatial distribution were
checked for consistency with expected values for the region to ensure that overall
water balance reflected local conditions, as impacted by the catchment hydrological
and geographical characteristics. Calibration of the WetSpa Extension was a cyclical
process of making parameter changes, running the model, producing the comparisons
of simulated and observed values, and interpreting the results.
The calibration process was performed mainly for the global parameters including
interflow scaling factor, baseflow recession coefficient, evapotranspiration coefficient,
initial soil moisture and groundwater storage, as well as the surface runoff exponent
as listed in the input file. Other spatially distributed model parameters were assumed
to be reasonable and remained the values as they are. Calibration of the
evapotranspiration coefficient could be performed independently by comparing the
calculated and observed flow volume for a long time series. The interflow scaling
factor was calibrated by matching the computed discharge with the observed
discharge for the recession part of the flood hydrograph. Groundwater flow recession
coefficient could be obtained by the analysis of recession curves at discharge gauging
stations. Refinement of this baseflow recession coefficient was necessary to get a
better fit for the low flows. The initial soil moisture and initial groundwater storage
were adjusted based on the comparison between the calculated and observed
hydrographs for the initial period. And the runoff exponent and the rainfall intensity
threshold were adjusted based on the agreement between calculated and observed
flows for the small storms with lower rainfall intensity. Since these global model
parameters are physically based, the interval of their variation can be predetermined
based on the specific characteristics of the study catchment. For instance, the
interflow scaling factor is generally within the range of 1 to 10, and the
evapotranspiration coefficient should be close to 1. After the adjustment of the input
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global model parameters and running the model, the post-processing capabilities of
WetSpa Extension (listings, plots, statistics, etc.) were used extensively to evaluate
the calibration/verification effort. Figure A-5.10 shows a typical calibration result for
a flood series occurred in December 1997, corresponding to input global model
parameters of Ci = 7.5, Cg = 9.0 m2/s, K_ss = 1.03, K_ep = 1.02, G0 = 280 mm,
G_max = 300 mm, K_rain = 2.0 and P_max = 5.0 mm/h, where the meanings of
above denotations can be found in section A-3.2.
120
0
Observed Q
80
Calculated Q
10
Baseflow Qi+Qg
40
0
3/12/97
20
Preciîtation (mm/h)
Discharge (m 3/s)
Precipitation
30
7/12/97
11/12/97
15/12/97
Time (d/m/y)
19/12/97
Figure A-5.10: Observed and calculated flow at Bissen for the floods in Dec. 1999
It can be found from Figure A-5.10 that the calculated hydrograph is generally in a
good agreement compared with the observed hydrograph. A big storm occurred on the
fourth of December, 1997, but did not produce too much runoff due to the lower
antecedent soil moisture. Most of the rainfall were therefore infiltrated and used to
saturate the soil. Thereafter, another three big storms occurred successively on
December 5, 8 and 12, which yielded pick discharges of 44.0, 86.3 and 66.8 m3/s
respectively. The calculated pick discharges are 51.1, 73.1 and 58.1 m3/s
corresponding to relative errors of 16.1%, -15.3% and -13.0% respectively. The
simulated baseflow contribution was not remarkable for the first two floods, but
abundant for the third and fourth flood. This can be explained that the soil moisture
and the effective groundwater storage were low at beginning, and not sufficient to
generate abundant interflow and groundwater flow for the first two floods. Due to the
occurrence of following storms, soils were getting saturated and the surplus soil water
percolated to the groundwater storage, leading to a higher baseflow for the third and
fourth floods and also the following flow period.
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Appendix A
Table A-5.3: Statistics and model performance for the calibration/validation period
Station
Period
Ell
22/10/98-29/01/01
Useldange 02/10/98-31/10/00
12/01/96-31/12/98
Bissen
01/01/99-12/05/00
Total
rainfall
(m)
2.707
2.818
2.779
1.726
Total
runoff
(m)
1.511
1.455
1.202
0.798
Flow Mean
coef. flow CR1 CR2 CR3 CR4 CR5
(%) (m³/s)
55.8 2.25 0.035 0.765 0.772 0.653 0.786
51.6 4.68 0.012 0.815 0.798 0.715 0.824
43.3 3.66 -0.014 0.813 0.735 0.682 0.805
46.2 5.47 -0.025 0.762 0.614 0.667 0.753
Table A-5.3 presents the statistics of observed rainfall, runoff, the flow coefficient
(ratio of the outflow water volume at the measuring station to the volume of water
precipitated over the drainage area) and the mean flow discharge during the statistical
period, as well as the model performance for the calibration/validation period at
station Ell, Useldange and Bissen on hourly scale. The model performance is found to
be satisfactory as illustrated in the table. Model bias for the simulation period is
within the range of -0.025 to 0.035. Model determination coefficient is within the
range of 0.765 to 0.815. The flow efficiency coefficient is within the range of 0.614 to
0.798, while the efficiency coefficient ranges from 0.653 to 0.715 for low-flow, and
0.753 to 0.824 for high-flow. These evaluation results indicate that the model has a
high confidence and can give a fair representation of both low-flow and high-flow
hydrographs for the study catchment.
A graphical comparison between calculated and measured hourly flows at Bissen for
the validation year 1999 is presented in Figure A-5.11. With the simulated initial
hydrological condition at the end of the year 1998, the simulation results for the year
1999 were in fairly good agreement with the measured discharges. Similar simulation
results can be obtained for other hydrological years. Figure A-5.12 shows the plots of
18 observed peak discharges at Bissen against their calculated peak discharges
selected from the whole simulation period for Qpeak > 30 m3/s. The correlation
coefficient is 0.96, which proves that the flow peak discharges are well reproduced.
The errors of the time to the peak for the 18 floods were also examined, in which 12
of them are within the interval of -3 to 3 hours, and the rest are outside this range. The
maximum error is 10 hours for the flood on April 1996, as the precipitation lasted for
3 days with lower rainfall intensity, and long peak flow duration was observed.
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Figure A-5.11: Observed and calculated hourly flow at Bissen for the year 1999
3
Calculated peak (m /s)
100
80
60
40
20
20
40
60
80
100
3
Observed peak (m /s)
Figure A-5.12: Peak Qm Vs Peak Qc selected from the whole simulation period
Figure A-5.13 represents the observed and calculated hourly flow frequency curve for
the whole simulation period. The flow frequency curve demonstrates consistent
patterns between calibration and validation time periods, and in general showed good
agreement. However, there are some obvious deviations for small floods, especially
for the flow within the discharge interval of 2 to 6 m3/s, where the calculated flows
are over estimated. These deviations may be attributed to the uncertainties inherent in
modelling complex processes such as flood frequency related hydraulic radius,
interflow factors, etc.
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Appendix A
Figure A-5.13: Observed and calculated hourly flow frequency curves at Bissen
5.5.
Discussion
The hydrological modelling effort for the comprehensive study of the Bissen
catchment is an attempt to apply hydrological modelling from GIS data sets. The
modelling approach was developed efficiently and with consistent methodologies.
The ability to define spatially distributed model parameters interactively based on
topography, land use and soil maps using ArcView GIS allowed users to work quickly,
and the ability to compare the intermediate results with existing maps increased the
confidence in the validity of the model components. From the viewing and
manipulation of the geographical data, to the development of the physical parameters,
and to the post processing of the simulation results, it is clear that WetSpa Extension
has its ability to calculate basin characteristics directly from terrain models allowed
user to complete the comprehensive study in a timely manner.
Based on the hourly hydrograph comparisons at Bissen and other internal stations, it
can be concluded that the modelling results have a good to very good agreement with
observed hydrographs. Table A-5.4 tabulates the measured and calculated water
balance for each modelling component over the whole simulation period for the
Bissen catchment. The estimated volume of interception, surface runoff and
infiltration are 583.9, 688.2 and 3219 mm representing 13.0%, 15.3% and 71.5% of
the total precipitation. It can also be calculated from the table that 31.5% of the
infiltrated water is percolated out of the root zone, 19.4% of which becomes lateral
interflow, 46.3% of which is evapotranspirated into the atmosphere from the root zone
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(total evapotranspiration – interception – transpiration from the groundwater storage).
The transpiration from groundwater storage can be estimated from the percolation
amount subtracted by the groundwater volume, which is 249.1 mm in total
representing 10.7% of the total evapotranspiration. The rest are remained in the soil
moisture and groundwater storage. The estimated surface runoff, interflow and
groundwater flow are 688.2, 623.0 and 763.9 mm representing 33.2%, 30.0% and
36.8% respectively of the total runoff. Interflow is an important flow component in
this study due to the steep slope and well vegetation over the catchment.
Table A-5.4: Water balance estimation at Bissen for the whole simulation period
Component
Precipitation
Interception
Infiltration
Evapotranspiration
Percolation
Surface runoff
Interflow
Groundwater flow
Total runoff
SM difference
GWS difference
Measured
(mm)
4505
2467
2000
Calculated
(mm)
4505
583.9
3219
2323
1013
688.2
623.0
763.9
2075
47.11
45.68
Percentage
(%)
100
13.0
71.5
51.6
22.5
15.3
13.8
17.0
46.1
1.05
1.01
Mean
(mm/h)
0.119
0.015
0.085
0.061
0.027
0.018
0.016
0.020
0.055
287.2 (mm)
176.3 (mm)
Max
(mm/h)
21.49
1.121
15.84
0.732
0.303
5.243
0.183
0.037
5.259
372.8 (mm)
325.7 (mm)
SM: soil moisture, GWS: groundwater storage.
Despite the good performance of the model predictions, the model requires the user to
provide the necessary elevation, soil and land use data sources that are specific to the
study area. The DEM is the starting point for several processes in producing the
predicted hydrographs. Moreover, a successful hydrological model requires
information regarding the infiltration potential of the surface where the runoff occurs.
The preferred data consists of digital maps containing area soils and land use
information with associated potential runoff coefficient and depression storage
capacity corresponding to each grid cell with different slope, soil and land use
combinations. The functionality of WetSpa Extension was designed to accommodate
both overland flow and channel flow. The routing process is accomplished by the
method of linear diffusive approximation without considering the specific channel
characteristics for different cross sections, for instance, the channel loss properties,
307
Appendix A
channel width, compound channel roughness, etc.
A linear interpolation of
Manning’s n was then performed according to the stream orders by setting constant
roughness values for the highest and lowest stream order. For the very flat areas
(ponds, small lakes, and other zero slope cells), a minimum slope threshold was given,
0.01% for this case study, in order to keep the water moving in a right order on those
areas. All these treatments will greatly facilitate the task of data collection and
simplify the scheme of model calculation, but may bring errors and uncertainties to
the final simulation results.
6.
Concluding remarks
A GIS-based hydrological model, WetSpa Extension, in its fully and semi-distributed
version compatible with remote sensing and GIS has been described in this user
manual. The model runs on a microcomputer with a user-friendly interface, and can
be applied to a wide range of watersheds for simulating the hydrological behaviour
and especially runoff with due account for available topography, soil type, and land
use data. The approach consists of the development of a spatially distributed
modelling framework that accounts for spatial variability in terrain features to
facilitate flood management and the physically realistic spatial integration of the
complete water balance at a range of spatial and temporal scales. The model is
implemented entirely within ArcView using Avenue scripts along with its Spatial
Analyst and a hydrological extension integrated within a GIS environment.
Encouraging results have been achieved as illustrated in the case study.
The spatial characteristics of input meteorological variables, i.e. temperature,
precipitation and PET, are captured by means of Thiessen polygons, on which linear
topographic corrections are implemented within each polygon to account for the
altitude variation of these meteorological variables if necessay. The generation of
surface runoff depends upon rainfall intensity and soil moisture status and is
calculated as the net precipitation times a runoff coefficient, which depends upon
slope, land use and soil type. Snowmelt is estimated from typical temperature
variations and a degree-day type of snowmelt model. The runoff is subsequently
routed through the basin along flow paths determined from the high resolution DEM
using a diffusive wave transfer model that leads to response functions between any
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start and end point, depending upon slope, flow velocity and dissipation
characteristics along the flow lines. Interflow and percolation is controlled by soil
characteristics and modelled by Darcy’s law and kinematic approximation. The
groundwater flow and its storage are conceptualized as a linear reservoir on small
subcatchment scale with recession constant determined at reference gauging stations,
and estimated for each subcatchment in relation with its drainage area and average
slope.
The spatial variability of model parameters used in river basin simulations is known
to affect simulated results. Like other distributed models, WetSpa allows for
variability of model parameters in space over a catchment by incorporating
information from the spatial variability of soils, land use, and topography, which
gives a more accurate representation of natural hydrological processes. However, a
high degree of uncertainty exists for many model input parameters including the
potential runoff coefficient, soil hydraulic conductivity, roughness coefficient,
hydraulic radius, as well as the threshold values for determining stream network,
minimum slope and the percentage of impervious areas within an urban cell, etc.
Moreover, some global parameters, such as interflow scaling factor, plant coefficient,
degree-day coefficient, etc., are used in the model due to their complexity of
optimization and for the simplification of model calibration. The large number of
uncertainties associated with the input meteorological variables and the model
parameters may make the calibration and validation of the model a time intensive
undertaking. To deal with this problem, priorities are given to the model parameters
with high sensitivity during model calibration as described in chapter A-4. Further
refinement of other model parameters is recommended in order to improve the model
reliability. Additionally, pre-adjustment of model parameters to the channel geometry,
boundary conditions, and system connectivity are necessary to achieve the quality of
the final model simulation results.
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Appendix A
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