Journal of Hydrology 369 (2009) 44–54
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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Development and testing of a new storm runoff routing approach based
on time variant spatially distributed travel time method
Jinkang Du a, Hua Xie a, Yujun Hu a, Youpeng Xu a, Chong-Yu Xu b,c,*
a
School of Geographic and Oceanographic Sciences, Nanjing University, Nanjing 210093, PR China
Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, N-0316 Oslo, Norway
c
Department of Earth Sciences, Uppsala University, Villavgen 16, 75236 Uppsala, Sweden
b
a r t i c l e
i n f o
Article history:
Received 4 January 2008
Received in revised form 24 July 2008
Accepted 9 February 2009
This manuscript was handled by K.
Georgakakos, Editor-in-Chief, with the
assistance of Christa D. Peters-Lidard,
Associate Editor
Keywords:
Storm runoff
Spatially distributed routing
Geographic information systems, China
s u m m a r y
In this study, a GIS based simple and easily performed runoff routing approach based on travel time was
developed to simulate storm runoff response process with consideration of spatial and temporal variability of runoff generation and flow routing through hillslope and river network. The watershed was discretized into grid cells, which were then classified into overland cells and channel cells through river network
delineation from the DEM by use of GIS. The overland flow travel time of each overland cell was estimated by combining a steady state kinematic wave approximation with Manning’s equation, the channel
flow travel time of each channel cell was estimated using Manning’s equation and the steady state continuity equation. The travel time from each grid cell to the watershed outlet is the sum of travel times of
cells along the flow path. The direct runoff flow was determined by the sum of the volumetric flow rates
from all contributing cells at each respective travel time for all time intervals. The approach was calibrated and verified to simulate eight storm runoff processes of Jiaokou Reservoir watershed, a sub-catchment of the Yongjiang River basin in southeast China using available topography, soil and land use data
for the catchment. An average efficiency of 0.88 was obtained for the verification storms. Sensitivity analysis was conducted to investigate the effect of the area threshold of delineating river networks and
parameter K relating channel velocity calculation on the predicted hydrograph at the basin outlet. The
effects of different levels of grid size on the results were also studied, which showed that good results
could be attained with a grid size of less than 200 m in this study.
Ó 2009 Elsevier B.V. All rights reserved.
Introduction
In flood prediction and estimation of catchment response to
rainfall input, runoff routing is vital. The unit hydrograph theory
has played a prominent role in runoff routing computation for several decades since its development. This system response theory
assumes that the basin response to rainfall input is linear and time
invariant. The discharge at the basin outlet is given by the convolution of excess rainfall and the instantaneous unit hydrograph
(IUH, Dooge, 1959). In engineering practice, the unit hydrograph
is often determined by numerical de-convolution techniques
(Chow et al., 1988) using observed stream flow and rainfall data.
Many efforts have been made in linking the basin hydrological response to basin geomorphological features. Rodriguez-Iturbe and
Valdes (1979) introduced the concept of geomorphologic instantaneous unit hydrograph (GIUH), which was later generalized by
Gupta et al. (1980) and Gupta and Waymire (1983). The concept
* Corresponding author. Address: Department of Geosciences, University of Oslo,
P.O. Box 1047 Blindern, N-0316 Oslo, Norway. Tel.: +47 22 855825; fax: +47 22
854215.
E-mail address: chongyu.xu@geo.uio.no (C.-Y. Xu).
0022-1694/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2009.02.033
relates the geomorphologic structure of a basin to the IUH obtained
from the surface-water travel time probability density function,
which is defined in terms of watershed’s geomorphologic properties (Horton’s empirical laws) and by the probability density functions for travel times through channels. Mesa and Mifflin (1986)
and Gupta et al. (1980) obtained their GIUH by means of the width
function and the inverse Gaussian probability density function
(PDF). Similar methodologies were presented by Naden (1992)
and Troch et al. (1994). Sivapalan et al. (1990) incorporated the effect of partial contributing areas in the basic formulation of GIUH.
Rodriguez-Iturbe and Gonzalez-Sanabria (1982) proposed a geomorphoclimatic theory of the instantaneous unit hydrograph as a
link between climate, geomorphologic structure and hydrologic response of a basin based on GIUH. The probability density functions
of the peak flow and time to peak of the IUH can be derived as
functions of the rainfall characteristics and the basin geomorphological parameters. The geomorphoclimatic or geomorphological
theories of the instantaneous unit hydrograph offer a simple method of deriving a watershed’s unit hydrograph without the need for
observed rainfall and runoff data.
In recent years, the use of the geographic information system
(GIS) to facilitate the estimation of runoff from watersheds has
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
gained increasing attention. Maidment (1993) presented a grid
based methodology for deriving a spatially distributed unit hydrograph, which assumes a time invariant flow velocity field. It uses
GIS to describe the connectivity of each grid cell and the watershed
flow network. The travel time from each cell to the watershed outlet is calculated by dividing each flow length by a constant velocity.
Subsequently, isochronal curves and the time–area diagram are
determined, and the unit hydrograph is obtained as the incremental areas of the time–area diagram. The spatially distributed hydrograph can in fact be classified as a type of geomorphoclimatic unit
hydrograph, since its derivation depends on watershed geomorphology, rainfall and hydraulics. Maidment et al. (1996) presented
a more elaborate flow model than that by Maidment (1993), which
accounts for both translation and storage effects in grid cells. In
their paper, the watershed response is calculated as the sum of
the responses of individual sub-watersheds, which is determined
as a combined process of channel flow followed by a linear reservoir routing. Muzik (1996a) and Ajward (1996) applied Maidment’s procedure to watersheds and obtained good results. Even
though the unit hydrograph is derived in a distributed way, its
use is still lumped.
In natural conditions, the precipitation, the generation of runoff,
and the flow of water over the watershed are spatially distributed
processes, which limit the use of the unit hydrograph model. In
trying to relax the unit hydrograph assumptions of uniform and
constant rainfall, considerable research about distributed IUH has
been conducted in recent years.
Olivera and Maidment (1999) proposed a method for routing
spatially distributed excess precipitation over a watershed. A routing response function is defined for each grid cell by the first passage–time response function, which is derived from the advection–
dispersion equation of flow routing. Water movement from cell to
cell can be convolved to yield a response function along a flow
path; 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.
Liu et al. (2003) presented a diffusive transport approach for
flow routing. 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 determined by the local slope, surface roughness and the hydraulic radius. The flow path response function at the catchment outlet 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 convolution of the flow response from all spatially distributed
precipitation excess.
De Smedt et al. (2000) proposed a flow routing method in which
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 points
depending upon slope, flow velocity and dissipation characteristics
along the flow lines. All the calculations are performed with standard GIS tools.
Even though the distributed IUH method could route the variant spatially distributed rainfall to the watershed outlet, such a
method is a lumped linear model of watershed response. Since
many watersheds may display a nonlinear behavior over a wider
range of net rainfall and discharge, to minimize errors resulting
from the assumption of linearity, Pilgrim and Cordery (1993) suggested that unit hydrographs should be derived from floods of
magnitudes as close as possible to those that will be calculated
using the derived unit hydrographs. Muzik (1996b) stated that a
45
family of unit hydrographs should be derived for a considered watershed, each unit hydrograph being applicable within a certain
range of excess rainfall.
Another category of runoff routing is the distributed hydraulic
method, where the watershed is discretized into a number of computational elements, and one or two dimensional approximation
(kinematic wave or diffusive wave) to the St. Venant equations is
used to estimate overland flow or channel flow for each element.
This method is often found in physically-based distributed hydrological models, such as the SHE model (Abbott et al., 1986a,b), the
IHDM model (Institute of Hydrology Distributed Model; e.g., Calver
and Wood, 1995), the CSIRO TOPOG model (e.g., Vertessy et al.,
1993), and HILLFLOW (Bronstert and Plate, 1997). The advantage
of such methods is the full consideration of rainfall and flow properties in time and space, while the disadvantages are the low computation efficiency, complicated computational techniques, and
large data and computer power demands (Beven, 2001). The application of these methods is therefore limited.
Melesse and Graham (2004) proposed a routing model based on
travel time. The overland flow travel time of each overland cell was
estimated by combining a steady state kinematic wave approximation with Manning’s equation; the channel flow travel time of each
channel cell was estimated using Manning’s equation and the steady state continuity equation; the travel time from each grid cell to
the watershed outlet is the sum of travel times of cells along a flow
path; and the direct runoff flow was determined by the sum of the
volumetric flow rates from all contributing cells at each respective
travel time. Unlike previous approaches (e.g., Maidment, 1993;
Muzik, 1995, 1996a,b; Ajward, 1996), this method can develop a
direct hydrograph for each spatially distributed rainfall event without relying on developing a spatially lumped unit hydrograph. The
disadvantage of this model is that the travel time field variation
during the storm is not considered, and it cannot be used for flood
forecasting since it can only be calculated after the whole storm
process has finished.
In this paper, a GIS based simple and easily performed routing
approach has been put forward to simulate the storm runoff process with consideration of spatial and temporal variability of runoff
generation and flow routing through hillslope and river network.
The approach proposed here is based on the model developed by
Melesse and Graham (2004), and an improvement was made by
considering travel time field variation due to rainfall variation in
time. The model is based on raster data structures; grids are used
to describe spatially distributed terrain parameters (i.e., elevation,
land use, soil type, etc.), and hydrologic features of each grid (i.e.,
slope, flow direction, flow accumulation, flow length, stream network, etc.) can be determined using standard functions included
in GIS. The model is described and applied to simulate eight storm
runoff processes for Jiaokou Reservoir watershed, a sub-basin of
Yongjiang River in southeast China with available topography, soil
and land use data for the watershed. Finally sensitivity analysis
was conducted to study the effect of the area threshold of delineating river networks and parameter K relating channel velocity calculation on the predicted hydrograph at the basin outlet.
Study area and data
The study area, Jiaokou Reservoir watershed (259 km2) with
elevation ranges from 59 m to 976 m, is a sub-basin of Yongjiang
River basin located in Zhejiang province, southeastern part of China. The land use of the watershed consists of forest (78.3%), agriculture (14.5%), grassland (2.5%), water surface (2.7%), and
residential areas (1.9%). The dominant soil is poorly drained clay
with high runoff potential, falling into D hydrologic soil group
according to the SCS classification. The region has a typical
46
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
subtropical monsoon climate. The average annual temperature is
16.3 °C with the minimum and maximum temperatures of
11.1 °C and 39.5 °C occurring in January and July, respectively.
The mean annual precipitation is about 2000 mm with most of
the rainfall occurring between March and September.
There are three rain gauging stations and one river flow gauging
station. The watershed location, elevation, distribution of rainfall
and flow gauging stations, and streams are seen in Fig. 1.
The data collected for this study include land cover processed
from Landsat TM images, hydrologic soil group (HSG) from the soil
maps (Fig. 2), 50 m resolution DEMs produced from digital topographic map, GIS point coverage of rain gauge locations and river
flow gauge station site, and hourly rainfall and discharge data at
the Jiaokou Reservoir watershed.
A total of eight isolated storms with observed runoff responses
were selected to calibrate and verify the approach. The direct runoff hydrographs were obtained using a straight line base flow separation method, and the spatial distribution of rainfall for each
storm was calculated by constructing Thiessen polygons with three
rainfall gauges using ArcView. The summary of eight rainfall and
discharge events is given in Table 1.
The digitized contour maps (1:50,000 scale) are used to generate DEM by using the Kriging interpolation method; to avoid producing a large number of pixels for the catchment, 50 m was
selected as the size of each grid, even so, the total grid cells reach
103,600. The DEM was then used to derive hydrologic parameters
of the watershed, such as slope, flow direction, flow accumulation,
and stream network. A threshold number of cells (minimum support area) is selected when the delineated channel network was
coincided with the digitized river network from contour maps.
The spatial distribution of Manning’s coefficient was determined for each storm based on the values published in the litera-
ture for the appropriate land cover (Brater and King, 1976;
Montes, 1998). The land cover information of the area was derived
from Landsat TM image on 18 May 1987; the classification procedure was performed by using a Maximum–Likelihood–Classifier,
which results in four land use classes. Furthermore, from soil type
maps (1:300,000 scale), three hydrological soil types and their distributions were obtained.
Methodology
As discussed in the introduction section, the spatially distributed direct hydrograph travel time method (SDDH) developed by
Melesse and Graham (2004) takes the excess rainfall intensity as
a constant for calculating the travel time field for the whole rainfall
process, and does not take into account the temporal variation of
surface runoff leading to the change of travel time field. In the
present study, a new approach, named time variant SDDH method,
has been developed to route spatially–temporally distributed surface runoff to the watershed outlet.
The developed approach is a distributed runoff routing technique based on GIS, the flow path and network are needed for
the model which can be derived from the digital elevation model
(DEM). A single downstream cell, in the direction of the steepest
descent, can be defined for each DEM cell by the use of flow direction GIS function, so that a unique connection from each cell to the
watershed outlet can be determined. This process produces a cell
network presenting the paths of the watershed flow system. For
defining the hillslope and channel network, a threshold number
of cells (minimum support area) is set to delineate the channel network for the watershed. Any cell with a number of cells upstream
equal to or greater than the threshold value is considered to be a
Fig. 1. Location of the stations and the catchment in the map of PR China.
47
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
Fig. 2. Hydrologic soil group of the study area.
Table 1
Summary of rainfall and discharge events.
Storm no.
1
2
3
4
5
6
7
8
Storm date
August 23, 1979
August 30, 1981
September 9, 1987
July 29, 1988
August 30, 1990
August 28, 1992
September 13, 2000
June 23, 2001
a
Rainfalla
Direct runoff
Depth (mm)
Duration (h)
Average intensity (mm/h)
Peak (m3/s)
Time to peak (h)
377.7
458.6
304.1
222.7
386.0
504.4
262.8
153.6
60
96
73
19
43
89
53
85
6.3
4.8
4.2
11.7
9.0
5.7
5.0
1.8
828
1591
841
1483
1128
1481
693
249
42
45
49
15
33
80
30
29
Values represent weighed average from the three rain gauges.
channel cell; others are hillslope cells. The routing parameters of
each cell can be described from the flow path network, and the
key point of the approach is the travel time estimation.
Overland flow travel time estimation
Overland flow travel time in a grid cell can be estimated by
combining the kinematic wave approximation with Manning’s
equation (Singh and Aravamuthan, 1996).
For overland flow, the continuity equation and momentum
equation can be written as:
@h @q
þ
¼ ie
@t @l
Momentum equation : Sf ¼ S0
Continuity equation :
ð1Þ
ð2Þ
where h is the depth of water on the surface (m); q is the unitwidth discharge (m2/s); ie is the vertical net incoming flux (m/s);
l is the length of the slope (m), if the cell has horizontal or vertical flow directions, l is equal to grid size; if the cell has diagonal
pffiffiffi
flow directions, l is equal to the grid size multiplied by 2; t is
the time (s); Sf is the friction slope; and So is the slope of the
surface.
The surface flow rate is calculated by Manning’s equation
(Chow et al., 1988):
V ¼ S1=2
f h
2=3
=n
ð3Þ
where n is Manning’s roughness coefficient of the surface.
For steady state overland flow, q can be written as:
q ¼ ie l
ð4Þ
For overland flow, q can also be written as:
q ¼ hV
ð5Þ
48
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
From Eqs. (4) and (5), h can be obtained
h ¼ ie l=V
ð6Þ
Substituting Eq. (6) into Eq. (3), and solving for V
V¼
3=10 2=5 2=5
S0 l ie n3=5
1=4 3=4
V ¼ KS3=8
n
o Q
ð7Þ
The travel time, to, for each overland cell is computed from the cell
velocity and the travel distance of the cell as
t o ¼ l=V
ð8Þ
Channel flow travel time estimation
The calculation of travel time for channel cell to the watershed
outlet requires computation of flow velocity. Channel flow velocity,
V, is computed using Manning’s equation and the continuity equation for a wide channel following the procedure described below
(Muzik, 1996a,b; Melesse, 2002):
For channel flow with no lateral inflow, the continuity equation
is given by
@Q @A
þ
¼0
@l
@t
ð9Þ
where A is flow section area of channel (m2); l is flow length (m); Q
is the cumulative discharge (m3/s) through the cell that is determined by summing up the upstream flow contributions and the
contribution from precipitation excess for that cell.
If the flow is steady, @A
¼ 0, thus @Q
¼ 0 indicating Q is constant
@t
@l
In this case the continuity equation reduces to
Q ¼ VA ¼ VBh
ð10Þ
h ¼ Q=VB
ð11Þ
where B is the channel effective width (m).
Channel flow velocity V is calculated by Manning’s equation
(Chow et al., 1988) as
2=3
V ¼ S1=2
=n
f R
ð12Þ
where R is the hydraulic radius (area of flow section divided by the
wetted perimeter), n is Manning’s roughness coefficient, and Sf is
the friction slope.
Using Manning equation for a wide channel (R = h), and combining the kinematic wave approximation Sf = S0 yields
V ¼ V 2=3 B2=3 Q 2=3 S1=2
o =n
ð14Þ
where S0 is the slope of the cell that can be obtained from DEM. Eq.
(14) is the travel velocity method used by Muzik (1996a,b); Melesse
(2002) and Melesse and Graham (2004).
Due to the difficulty in obtaining the river width, the Manning
equation (12) was approximated as (Kouwen et al., 1993; Arora
et al., 2001):
1=3
V ¼ S1=2
=n
f A
ð15Þ
where A is the channel cross-sectional area. Replacing Sf by So, the
formula for the outflow Q is obtained as:
4=3
Q ¼ S1=2
=n
o A
tc ¼ l=V
ð16Þ
ð17Þ
Replacing A in Eq. (15) with Eq. (17) yields
V¼
1=4 3=4
S3=8
n
o Q
ð20Þ
where l is travel distance (if the cell has horizontal or vertical flow
directions, l is equal to grid size; if the cell has
pffiffiffidiagonal flow directions, l is equal to grid size multiplied by 2); V is the channel
velocity estimated by Eq. (19).
Cumulative travel time and runoff estimation
P
In the SDDH method, the cumulative travel time
ti of surface
runoff for each grid cell to the watershed outlet is computed by
summing up travel times along the respective flow paths from each
cell following the flow direction. Once the cumulative travel time
of each cell to the outlet is computed, the volumetric flow rate contributed by that cell (excess rainfall intensity of each cell multiplied by the cell area) at that time is noted. The direct runoff is
determined by the sum of the volumetric flow rate at each respective travel time from all contributing cells. This method takes travel time of surface runoff for each grid cell invariant for a storm
event and ignores the variation of travel time due to the variation
of surface runoff in time.
In our method, named time variant SDDH, the variation of surface
runoff and rainfall is considered by dividing the rainfall process into
several time intervals, and for each time interval the excess rainfall
intensity of each cell was calculated, the travel time, and cumulative
travel time for each cell were calculated according to Eqs. (8) and
(20). Therefore, the cumulative travel time for each cell at each time
step may be different due to variant surface runoff. Once the cumuP
lative travel time
t i of each cell to the outlet at time interval t is
computed, the volumetric flow rate at time step t (excess rainfall
intensity of each cell at that time interval multiplied by the cell area)
P
t i þ ðt 1ÞDt. The
is noted by arriving time ta computed as t a ¼
direct runoff at each respective arriving time is determined by the
sum of the volumetric flow rates with the same arriving time for
all time intervals from all contributing cells.
Runoff generation
To test the developed time variant SDDH approach, the Soil
Conservation Service (SCS) curve number (CN) method (as cited
by Chow et al. (1988)) was used to calculate runoff products. Dingman (2001) stated that the SCS–CN method will continue to be
used since (a) it is computationally simple, (b) it uses readily available watershed information, (c) it appears to give reasonable results under many conditions, and (d) there are a few other
practicable methodologies for obtaining a priori estimates of runoff
that are known to be better. In our approach, the curve number
method in its differential form (Mancini and Rosso, 1989) is used
to compute spatially distributed excess rainfall.
In the differential form of the SCS-CN method, the excess rainfall depth Qt (mm) of each element cell at the time step t is computed as
Qt ¼
Solving Eq. (16) for A yields
A ¼ S3=8
Q 3=4 n3=4
o
ð19Þ
The travel time, tc, for each channel cell is computed from the cell
velocity and the travel distance of the cell as
ð13Þ
Solving for V yields
V ¼ S3=10
Q 2=5 B2=5 n2=5
o
To account for the estimation error for n and So, parameter K is
added to Eq. (18), which will be determined by calibration. So Eq.
(18) can be written as
If ðPt > 0:2SÞ
ð21Þ
where Pt (mm) is the cumulative depth of precipitation at time step
t, computed as
Pt ¼
ð18Þ
ðPt 0:2SÞ2
ðpt þ 0:8SÞ
t
X
j¼1
pj Dt
ð22Þ
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
where pj is the rainfall intensity at the time step j (mm/s), Dt is time
step length (s), S is the maximum soil potential retentions (mm), gi 254 where CN (1–100) is runoff curve number,
ven by S ¼ 25400
CN
which is determined from hydrologic soil group (HSG), land use,
hydrologic conditions as well as antecedent soil moisture condition
(AMC) (Mishra and Singh, 1999). CNs for each storm were determined from both land cover and HSGs based on the CN tables of
the US Department of Agriculture, Soil Conservation Service (Chow
et al., 1988). The soil antecedent moisture condition can be classified into three levels according proceeding 5 days accumulated
rainfall: AMC-I for dry, AMC- II for normal, and AMC-I for wet conditions. Fig. 3 shows one of the CNs with AMC-II. When Pt 6 0.2S, the
rainfall is completely absorbed by soils, no overland flow generates
and the runoff depth is zero.
The surface runoff rate it (mm/s) from each grid cell at the time
step t is
it ¼ ðQ t Q t1 Þ=Dt
ð23Þ
49
where Oi is the observed system response at discrete times i, Zi is
the predicted system response at discrete times i, and O is the mean
of the observed values over all times. Obviously, a bigger EF value
means a better efficiency of the model performance, and if the VCI
is close to 1, the simulation quality is higher.
Results and discussion
AMC determination
AMC is an important factor in determining surface runoff in the
SCS-CN method, because of the lack of data in preceding rainfall
storms, VCI was employed here to determine the AMC levels, i.e.,
one of the three AMC levels (AMC-I, AMC-II and AMC-III) was selected if it made VCI close to 1. For the eight storms, the most suitable antecedent soil moisture condition was selected (Table 2). It is
seen from Table 2 that AMC has a significant effect on runoff
volume.
Model evaluation criteria
Model calibration
The model efficiency coefficient (EF), volume conservation index (VCI), absolute error of the time to peak (DN) and relative error
of peak flow rate (dPmax) were used in this study to evaluate the
performance of the approach. EF and VCI were calculated from
Eqs. (24) and (25), respectively.
Storm 1 with a single peak was selected for model calibration. A
preliminary sensitivity analysis of parameters showed that the
channel threshold and parameter K have a great influence on the
simulation accuracy, and they need to be calibrated. Five levels
of channel threshold (1, 5, 10, 50 and 100 cells), and six values of
K (1, 5, 7.5, 10, 20 and 30) were set to simulate the storm, and
the results (parts of them are listed in Table 3) indicated that when
channel threshold was equal to 10, a minimum relative peak ratio
could be obtained, and when channel threshold was equal to 1, a
maximum efficiency could be obtained, making this multiobjective
PN
ðOi Z i Þ2
EF ¼ 1 Pi¼1
N
2
i¼1 ðOi OÞ
,
N
N
X
X
Zi
Oi
VCI ¼
i¼1
i¼1
ð24Þ
ð25Þ
Fig. 3. Distribution of curve numbers.
50
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
Table 2
Volume conversation indexes under different antecedent soil moisture conditions.
Table 4
Simulation results for seven storms.
No.
Flood date
VCI
Storm no.
Peak (m3/s)
Time to peak (h)
dPmax
|DN| (h)
EF
VCI
AMC-I
AMC-II
AMC-III
1
2
3
4
5
6
7
8
August 23, 1979
August 30, 1981
September 9, 1987
July 29, 1988
August 30, 1990
August 28, 1992
September 13, 2000
June 23, 2001
0.79
0.75
0.80
0.71
0.77
0.85
0.63
0.65
1.11
0.92
1.15
1.10
1.06
1.08
0.86
1.15
1.29
1.04
1.37
1.46
1.24
1.22
1.04
1.56
2
3
4
5
6
7
8
1289
782
1602
1161
1555
658
384
43
49
14
27
80
28
28
0.25
0.09
0.03
0.02
0.04
0.07
0.26
1
0
1
6
0
1
1
0.93
0.97
0.93
0.93
0.96
0.97
0.48
1.04
1.15
1.10
1.05
1.08
1.04
1.14
Selected AMC level
II
III
II
II
II
II
III
II
times and higher peak flows when A keeps unchanged (Fig. 6a
and b). (3) Both Figs. 5c and 6c showed when either channel
threshold A or parameter K takes values smaller than or equal to
3, the model efficiency value became either low or unstable. Furthermore, as the channel threshold increases, the K value that corresponding to the highest efficiency also increases (Fig. 5c); the
efficiency increases steeply with the increase of K value from 1
to 3, and decreases smoothly with the increase of K value after
the highest efficiency value has been reached except with A = 1
(Fig. 6c). (4) In general, the model efficiency, peak flow, and time
to peak are more sensitive when A = 1 and 3 and/or K = 1 and 3
than other A and K values (Figs. 5 and 6). (5) The threshold values
A and parameter K had little effect on VCI (Figure is not shown), because they have no effect on the calculation of rainfall excess.
problem have no optimal solution, but Poreto solutions. Considering all the evaluation criteria, i.e., relative peak ratio, time to peak
error, efficiency, and time to peak, a compromised solution is obtained with the K = 7.5, and channel threshold = 5 as the values
of calibrated parameters.
Model verification
Simulations for other seven storms were performed with this
approach using the parameter values calibrated by storm 1. Table
4 summarizes the results of model simulation and error statistics.
It is seen that six out of seven storms have efficiencies greater than
0.90, five out of seven storms have a relative error of peak flow rate
less than 10%, and only one storm has time to peak error with 6
hours.
Observed and predicted hydrographs for all seven storms are
shown in Fig. 4. The model predicted runoffs for storms 2, 3, 4, 5,
6, and 7 very well. The peak flow rate, time to peak and total runoff
volume were all simulated with good accuracy, and a few subpeaks of these storms were also reproduced. Storm 8 with double
peaks was not simulated well. In general, the simulation results
showed that the observed and predicted hydrographs agreed well
and the error statistics are acceptable for practical purposes.
Comparison with SDDH simulation
For comparative purposes, the SDDH method was also used to
simulate the eight storms, the best results were found when channel threshold was 1 cell and K = 5. The results of the two methods
were shown in Table 5. It can be seen that, in the test catchment,
the modified SDDH method improved the results of the SDDH
method in more cases than not meaning that it is of importance
to consider the temporal variation of travel time field during rainfall in flow simulation. It is anticipated that the improvement
would be larger for large catchments.
Sensitivity analysis
Effects of grid size on simulation
Sensitivity analysis was conducted to assess the change in four
criteria for changes in model parameters. In our study, sensitivity
analysis was carried out for the threshold value for stream network
delineation (i.e., classification of overland versus channel cells) and
parameter K.
Sensitivity analysis was performed for combinations of the two
parameters, i.e., channel threshold A and parameter K. The results
for twenty five parameter combinations, i.e., five channel threshold
values (1, 3, 5, 7, and 10 cells) and five K values (1, 3, 5, 7.5, and 10)
are shown in Figs. 5 and 6. It is indicated that (1) larger channel
threshold A values (more overland cells and shorter channel distance) when K keeps unchanged resulted in slower travel times
that delayed the time to peak and also lower peak discharge compared to the observed data (Fig. 5a and b). (2) Larger K values increased the channel flow velocity resulting in shorter travel
Changes in spatial resolution of the model will lead to different
values of the GIS derived slope, flow direction, and spatial distribution of flow paths, which, in turn, affect the model simulation. In
this paper, three types of DEMs with grid sizes of 100 m, 200 m,
and 300 m were used to simulate the eight storm runoffs. With
each type of DEMs the best channel threshold and parameter K
were selected, and the results were shown in Table 6.
It can be seen that, low-resolution of DEMs with a grid size of
100 m leads to a little change in efficiency, relative peak ratio
and time to peak, which may be caused by several reasons. On
one hand, lower resolution leads to a decrease of derived slope
resulting in longer travel times and lower peak flows; on the other
hand, lower resolution also leads to a decrease of flow path resulting in shorter travel times and high peak flows, and these two
Table 3
The statistic results of runoff simulation for storm no.1 at different values of K and channel threshold with Grid size = 50 m.
k
1
5
7.5
10
Channel threshold = 1
Channel threshold = 5
Channel threshold = 10
dPmax
DN
EF
VCI
dPmax
dN
EF
VCI
dPmax
DN
EF
VCI
0.05
0.41
0.39
0.44
9
0
1
1
0.07
0.92
0.93
0.92
1.11
1.11
1.11
1.11
0.09
0.16
0.15
0.17
9
0
0
1
0.09
0.85
0.89
0.91
1.11
1.11
1.11
1.11
0.14
0.03
0.03
0.03
12
1
0
1
0.19
0.77
0.83
0.85
1.10
1.10
1.10
1.10
51
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
2000
1000
storm No.1
3 -1
3 -1
Discharge(m s )
Discharge(m s )
storm No.2
1600
800
600
400
1200
800
400
200
0
0
0
20
40
60
0
20
40
Time (h)
60
1600
1000
storm No.3
storm No.4
3 -1
3 -1
Discharge(m s )
800
Discharge(m s )
80
Time (h)
600
400
1200
800
400
200
0
0
0
20
40
0
60
10
20
1200
storm No.6
1200
3 -1
Discharge(m s )
3 -1
40
1600
storm No.5
1000
Discharge(m s )
30
Time (h)
Time (h)
800
600
400
800
400
200
0
0
0
10
20
30
40
0
20
40
Time (h)
60
800
storm No.8
600
3 -1
Discharge(m s )
Discharge(m s )
100
400
storm No.7
3 -1
80
Time (h)
400
200
0
300
200
100
0
0
20
40
60
Time (h)
0
20
40
60
80
100
Time (h)
Fig. 4. Comparison of the observed (solid line) and simulated (dashed line) discharges for the eight storms.
effects compensate for each other resulting in a small change in
travel time and peak flow. Another effect of lower resolution of
DEM is the change in optimal channel threshold values, pertaining
relatively the channel length. Just as pointed out by Horritt and
Bates (2001), predictions with a low-resolution may also give an
essentially correct result in many cases.
The effect of accumulated runoff excess on lower grid cells is
very small; as can be seen from Table 6 that the VCI (which can
show accumulated runoff excess) have a small decreasing change
with increasing grid size.
However, this study also showed that when grid size is equal to
200m and 300m the results were poor, meaning that good results
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
a
0.4
k=1
k=3
k=5
k=7.5
k=10
relative peak flow error
0.3
0.2
0.1
0
-0.1
-0.2
a
0.4
relative peak flow error
52
0.3
-0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.4
1
3
5
7
channel threshold A
time to peak error
3
10
b
12
time to peak error
1
b
A=1
A=3
A=5
A=7
A=10
8
k=1
k=3
k=5
k=7.5
k=10
10
12
8
4
A=1
A=3
A=5
A=7
A=10
4
0
-4
1
3
-4
1
3
5
7
10
channel threshold A
c
5
parameter K
7.5
10
1
0.8
k=1
k=3
k=5
k=7.5
k=10
0.6
0.4
efficiency
1
0.8
efficiency
7.5
16
0
c
5
parameter K
0.6
0.4
A=1
A=3
A=5
0.2
A=7
A=10
0
0.2
1
0
1
3
5
7
10
channel threshold A
Fig. 5. Sensitivity analysis results – change of model performs with the channel
threshold A.
could be attained with a grid size of less than 200 m in the study
case.
Conclusions
This study has developed a new approach to simulate storm
runoff with consideration of spatial and temporal variability of
runoff generation and routing. The runoff production was estimated using the SCS-CN method, and runoff routing at each time
step was performed by the use of a time variant SDDH. The approach was applied to the Jiaokou watershed in southeast China
and produced acceptable results. When reliable spatially distributed geographic and climatic data are available, the time variant
SDDH approach is preferable to the SDDH approach and time–area
method, since it can directly use time variant spatially distributed
excess rainfall. The SDDH method uses the average excess rainfall
intensity of a flood event to estimate travel time, ignoring the
changes of travel time due to variant surface runoff caused by
3
5
parameter K
7.5
10
Fig. 6. Sensitivity analysis results – change of model performs with the parameter K
values.
changing excess rainfall. However, in reality the average excess
rainfall intensity will never be known before the whole storm process has finished, and such a method can only be used for storm
runoff simulation rather than forecasting. The time–area method
(Maidment, 1993; Muzik, 1996a; Maidment et al., 1996) is a unit
hydrograph approach, which requires spatially constant excess
rainfall, ignoring the spatial variation of precipitation. Moreover,
the unit hydrograph derived is also invariant for a storm event
and ignores changes of travel time.
The approach developed in this study has a simple structure
and can easily be performed in a GIS environment. It uses only
DEMs, land cover, soil type, and rainfall data which are becoming
more and more available. Most parameters needed for this approach can be derived from these data, and only channel threshold
and parameter K need to be determined by calibration. With only
two parameters needed to be calibrated, and taking spatial and
temporal variations of rainfall into account for runoff production
and runoff routing, the method has promising application potential
in storm runoff simulation.
It should be noted that in this approach, although the calculation of overland and channel travel time uses the physically-based
53
J. Du et al. / Journal of Hydrology 369 (2009) 44–54
Table 5
The comparison of two methods.
Storm no.
SDDH
1
2
3
4
5
6
7
8
Method in this paper
Improved
dPmax
DN
EF
VCI
dPmax
DN
EF
VCI
dPmax
DN
EF
VCI
0.25
0.20
0.07
0.09
0.01
0.09
0
0.28
1
1
1
0
4
3
1
52
0.90
0.95
0.96
0.86
0.88
0.91
0.94
0.59
1.11
1.04
1.15
1.10
1.09
1.08
1.04
1.15
0.15
0.25
0.09
0.03
0.02
0.04
0.07
0.26
0
1
0
1
6
0
1
1
0.89
0.93
0.97
0.93
0.93
0.96
0.97
0.48
1.11
1.04
1.14
1.10
1.04
1.08
1.03
1.14
0.10
0.05
0.02
0.06
0.01
0.05
0.07
0.02
1
0
1
1
2
3
0
51
0.01
0.02
0.01
0.07
0.05
0.05
0.03
0.11
0
0
0.01
0
0.05
0
0.01
0.01
Table 6
The statistic results of storm runoff simulation with different Grid size.
Storm no.
1
2
3
4
5
6
7
8
Average
Grid size = 50 m, channel
threshold = 5, K = 7.5
Grid size = 100 m, channel
threshold = 1, K = 7.5
Grid Size = 200 m, channel
threshold = 1, K = 15
Grid Size = 300 m, channel
threshold = 1, K = 15
dPmax
DN
EF
VCI
dPmax
DN
EF
VCI
dPmax
DN
EF
VCI
dPmax
DN
EF
VCI
0.15
0.25
0.09
0.03
0.02
0.04
0.07
0.26
0
0
1
0
1
6
0
1
1
1
0.89
0.93
0.97
0.93
0.93
0.96
0.97
0.48
0.88
1.11
1.04
1.14
1.10
1.04
1.08
1.03
1.14
1.09
0.13
0.22
0.05
0.14
0
0.01
0.03
0.54
0.07
0
1
0
1
6
0
1
1
1.25
0.93
0.92
0.97
0.89
0.88
0.97
0.94
0.18
0.84
1.04
0.98
1.07
1.03
1.01
1.03
1.00
1.05
1.03
0.05
0.43
0.32
0.25
0.19
0.19
0.17
0.37
0.14
1
6
1
1
1
0
4
1
0.63
0.72
0.76
0.84
0.70
0.82
0.80
0.86
0.03
0.69
1.03
0.97
1.06
1.02
0.90
1.02
0.98
1.04
1.00
0.25
0.60
0.47
0.36
0.44
0.30
0.48
0.11
0.35
1
1
0
1
6
0
2
47
4.5
0.48
0.56
0.63
0.58
0.54
0.68
0.58
0.14
0.52
1.02
0.96
1.06
0.99
0.66
1.01
0.94
1.00
0.96
methods, as Melesse and Graham (2004) pointed out that calibration of parameter K and cell threshold casts some doubt on the
physical basis for these parameters. Nevertheless, it is suggested
that these parameters shall be calibrated and verified when applying the method to other watersheds.
Acknowledgments
The study is financially supported by the National Natural Science Foundation of China (Nos. 40171015 and 40371020). The
authors would like to thank the reviewers for their valuable comments and suggestions which significantly improved the quality of
the paper.
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