ECOMAG: Regional model of hydrological
cycle. Application to the NOPEX region
W AT
UN D
GRO
Z
ZZ ONE
ER
Yuri G. Motovilov, Lars Gottschalk, Kolbjørn Engeland, Alexander Belokurov
Institute Report Series No: 105 ISBN 82-91885-04-4 May 1999.
Department of Geophysics, University of Oslo P.O. Box 1022 Blindern 0315 OSLO, NORWAY
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Abstract
In connection to climate change studies a new hydrologic field has evolved - regional hydrological modelling or hydrologic macro modelling, which implies a repeated
application of a model everywhere within a region with a global set of parameters. An application of a physically based distributed model ECOMAG to river basins within
the NOPEX region with the use of global parameters is presented.
The model considers the main processes of the land surface hydrological cycle: infiltration, evapotranspiration, thermal and water regime of the soil, snowmelt,
formation of surface, subsurface and river runoff and groundwater. The spatial integration of small and meso-scale non-homogeneity of the land surface is a central
issue both for the definition of fundamental units of the model structure and for determination of representative values for model validation. ECOMAG is based on a
uniform hydrological (or landscape) unit representation of the river basin, which reflects topography, soil, vegetation and land use. As a first step the model was
calibrated using standard meteorological and hydrological data for seven years from a regular observation network for three basins. An additional adjustment of the
soil parameters was performed using soil moisture and groundwater level data from five small experimental basins. This step was followed by validation of the model
against runoff observation for 14 years from six other drainage basins, and synoptic runoff and evapotranspiration measurements performed during two concentrated
field efforts (CFEs) of the NOPEX project in 1994 and 1995. The results are promising and indicate directions for further research.
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CONTENTS
Abstract
1. Introduction
5
2. Scale issues
9
3. Hydrological model formulation
11
3.1 Introduction
11
3.2 General assumptions
15
3.3 Balance equations
17
3.4 Basic structure
21
3.4.1. Horizontal structure
21
3.4.2 Vertical structure
23
3.5 Process description
26
3.5.1 Surface water
26
3.5.2 Infiltration into soil
27
3.5.3 Surface retention
28
3.5.4 Soil horizons
29
3.5.5 Groundwater zone
32
3.5.6 Snow cower formation and snowmelting
32
3.5.7 Thermal conditions in snow and soil
34
3.5.8 Infiltration into frozen soil
35
3.5.9 River flow
36
3.6 Model calibration processing
37
3.6.1 Background information
37
3.6.2 Model parameters
37
3.6.3 Calibration procedure
39
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4. Data used
40
4.1 NOPEX region
40
4.2 Geographical data
41
4.3. River runoff
41
4.4. Meteorological data
43
4.5. Special NOPEX CFEs data
44
4.5.1. Synoptic runoff
44
4.5.2 Soil moisture and ground water
45
4.5.3. Evapotranspiration
46
4.6 Interpolation of meteorological data
47
4.6.1 Interpolation of precipitation by kriging.
5. Sensitivity analysis
47
49
5.1 River basin schematisation
49
5.2 Model realization
51
5.3 Model sensitivity
55
6. Model validation
59
6.1 Runoff at gauging stations
60
6.2 Synoptic runoff
67
6.3. Soil moisture and groundwater levels
68
6.4 Vertical flux exchange and water balance
71
7. Conclusions
77
8. Notations and dimensions
79
9. References
82
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Chapter 1 Introduction
1. Introduction
Hydrological models account for the storage and flow of water on the continents, including
exchanges of water and energy with the atmosphere and oceans. During the past three
decades, hydrologists have developed a large number of models ranging in sophistication
and complexity. Most of these models apply to geographical areas smaller than the area
represented by a typical GCM grid square, although some basin-scale hydrological models
have been applied to areas as large as 104 km2. “Macro-scale” hydrological models are
hydrological models that are compatible with the scale of a GCM grid square (e.g. 105 km2)
and can accept atmospheric model data as input.
Preparing macro-scale hydrological models is a major undertaking that will require the cooperative effort of hydrologists and other geo-scientists all over the world. The challenge is
to extend existing knowledge of hydrological processes, as they occur at a point location and
on the scale of small basins, to the macro-scale. Macro-scale hydrological models must be
able to exchange information with atmospheric models. Processes that occur at a sub-grid
scale must be accounted for internally in such hydrological models. Ultimately, it must be
possible to apply the model globally. There are no data to calibrate macro-scale hydrological
models in the same way that hydrologists usually calibrate catchment models. Therefore, the
required macro-scale models must account for the water balance of “ungauged areas”, and
model parameters must be estimated a priori using limited climate, soil and vegetation data.
Klemes (1985) noted the following requirements (among others) to hydrological models
designed to assess the sensitivity of water resources to climate processes:
i) they must be geographically transferable and this has to be validated in the real world;
ii) their structure must have a sound physical foundation and each of the structural components
must permit its separate validation.
Klemes (1986) presents a hierarchical scheme for systematic testing of the grounds for
credibility of a given hydrological model.
The models applied by hydrologists in climate change studies at present are poorly adapted
to the problem they are aimed to solve. The critical problem is that they are often lumped
(semi-distributed) with calibrated ‘effective’ parameters. This fact seriously hinders the
assessment of the scale (aggregation/disaggregation) that is the focal scientific problem. To
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Chapter 1 Introduction
better meet the new requirements to hydrological models, a new hydrologic research field
has evolved - regional hydrological modelling or hydrologic macro-modelling. This new
concept implies an application of a hydrological model over a large spatial domain (at least
105 km2) or, more precisely, a repeated application of a model everywhere within this
domain.
There are two approaches to the development of a macro-model (Arnell, 1993):
1. “Top-down” which treats each of the fundamental units as a single drainage basin, and
applies to each of them a lumped catchment model (the classical example is the Budyko
bucket model and its modifications, Korzun, 1978; more recent ones are provided by
Vorösmarty et. al. 1989; Vorösmarty and Moore, 1991; Dümenil and Todini, 1992; Sausen
et al., 1994).
2. “Bottom-up” which identifies representative hydrological areas and aggregates upwards to
the fundamental unit size ( see “scale issues” below)
For the latter approach, data for validation of the process description are essential. Of great
importance in this context is a series of recent and ongoing land surface experiments, where
hydrologists together with meteorologists, climatologists, plant physiologists, ecologists, soil
scientists, geohydrologists etc. study exchange processes between the land surface and the
atmosphere at a range of scales, from an individual soil column with vegetation to the globe
as a whole. The design and execution of these coordinated experiments constitute a landmark
in hydrology as the essence of physical science is experimentation (National Research
Council, 1991). Historically most hydrologic data have been collected to answer water
resources questions rather than scientific ones. The most critical barrier to future
development of theoretical hydrology is the availability of data for identifying and verifying
theories (Gottschalk and Askew, 1987). The recent and ongoing land surface experiments
provide such data.
Here data from the NOrthern hemisphere climate Processes land-surface EXperiment
(NOPEX) (Halldin et al., 1995, 1998) are utilised for calibration and validation of a
physically based distributed hydrological model ECOMAG (Motovilov, 1995). The NOPEX
study region is chosen to represent the boreal forests, common for northern landscapes which
plays an important role in global hydrological and biogeochemical cycles (Thomas and
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Chapter 1 Introduction
Rowntree, 1992). The NOPEX area is situated in southern Sweden, in the densest part of the
northern European boreal forest zone. The NOPEX region is also centrally situated in the
Baltic Sea drainage basin, which is the study region for the BALTEX project.
An extensive amount of meteorological and hydrological data collected during the NOPEX
concentrated field efforts (CFE) CFE1 (27 May to 23 June 1994) and CFE2 (18 April to 14
July 1995) have been utilised in the process of model calibration and validation. These data
include:
• Geographical data including a digital terrain model with a resolution of 50 m and land cover
data with 25 m resolution (both data sets from the National Land Survey of Sweden) and a
comprehensive digitised soil map with a resolution of 2 km (from Seibert, 1994).
• Regular mean daily discharge observation for the period 1981-1995 from the Swedish
Meteorological and Hydrological Institute (SMHI). The NOPEX area contains 11 standard
gauging stations in drainage basins covering the main part of the area.
• Daily observations from 25 precipitation stations, 7 temperature stations and 5 stations
measuring vapour pressure deficit for the period 1981-1995 belonging to SMHI's regular
climatic observation network. The temperature and vapour pressure deficit values were
interpolated to a regular 2 km grid by inverse distance weighting, and the precipitation values
were interpolated by kriging.
• Detailed hydrological studies were carried out in five experimental basins during the CFE1
and CFE2. These included measurements of discharge, groundwater levels and soil moisture,
as well as standard climatological variables. The sites for groundwater levels and soil
moisture measurements were chosen to represent different geomorphologic units (hollow,
slope, nose) within the experimental basins. The data set contains a total of about 2000
individual measurements of groundwater levels and about 16 000 measurements of soil
moisture content (the measurements were also performed outside CFE periods).
• Synoptic discharge measurements at 38 sites in the Fyrisån river basin on four occasions
during recession.
• Mast measurements of vertical fluxes from two forest sites, three agricultural and two lakes
sites.
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Chapter 1 Introduction
The validation of the ECOMAG model performed here is a test of its ability to live up to the
demands to a macro hydrological model. The work was carried out in the following steps:
• Calibration of the model against runoff for three basins with one global set of parameters.
• Adjustment of the soil parameters and validation of the model with the use of soil moisture
and groundwater level data from five small experimental subbasins.
• Validation against synoptic measurements of runoff.
• Validation against runoff in six other basins that has not been used for calibration.
• Validation against regional flux estimates (evapotranspiration) for the whole NOPEX region.
The task put forward is demanding and it can hardly be expected that a model will perform
well in relation to all the tests undertaken. The results of the validation may be useful to
elucidate critical issues and indicate possible improvements of
the model process
formulation and parameterisation.
The scale issue is essential for the definition of the spatial grid resolution of the model and
for comparing data measured at “points” with modelled data representing grid cells. This
topic is first discussed (Chapter 2) to give a background to both the model formulation and
validation procedure. Chapter 3 of the report presents the main features and equations of the
ECOMAG model. A brief description of the studied area and basic data sets are given in the
Chapter 4. Chapter 5 offers the results of sensitivity analysis of the model. Calibration and
validation results are presented in the Chapter 6. Finally, some conclusions based on the
gained experience are drawn in Chapter 7.
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Chapter 2 Scale issues
2. Scale issues
An ambition within the NOPEX project is to bring insight into the problem of scale
variability. For this purpose spatial digital geographic data for the NOPEX area (topography,
land cover, soil types and remotely sensed data) have been analysed with respect to
homogeneity, uniformity, correlation lengths and the effect of spatial aggregation (scaling)
on these properties (Sulebak, 1997). Soil moisture, groundwater and synoptic runoff
measurements were analysed with the aim of identifying spatial scales (patches,
representative areas) of relevance for aggregation approaches (Beldring et al., 1998).
In meteorology and also in subsurface hydrology there is a tradition of distinguishing
between spatial variability at different scales. In surface hydrology it is quite a recent way of
thinking. The concept of Representative Elementary Volume (REV), on which scale basic
theoretical equations are founded, is focal in this context. Wood et al. (1988, 1990) have
introduced the complementary concept of Representative Elementary Area (REA). At a
certain scale a landscape element (a drainage basin or a grid cell) might contain a sufficient
sample of the geomorphologic, soil and other relevant characteristics of the region. It is then
no longer necessary to take account of the pattern of these characteristics but only of their
distribution. The underlying variability may still be important in controlling both discharges
and evaporation fluxes, but the patterns are less important. The scale at which this happens
defines the REA. The REA concept is not a direct analogy with the REV in subsurface
hydrology as the REV denotes a scale at which average quantities of potential and moisture
content can be used in a continuum description of the fluxes. In the REA the distribution of
characteristics may still be important in determining the fluxes.
Figure 2.1 shows examples of plots used to identify the REA for terrain with till soils. A
preliminary conclusion is that for this type of terrain the main part of the spatial variability in
soil moisture and groundwater fluctuations is contained in the 2 km grid size used for
modelling (Beldring et al., 1998). Theoretical distribution functions that can take into
account this variability have been developed.
The possibility of identifying a REA is of vital importance for the process formulation in the
ECOMAG model as it indicates that within a grid cell of 2x2 km runoff is delivered directly
to the river network and that rivers provide the only exchange between grid cells in this type
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Chapter 2 Scale issues
of landscape. The exchange through groundwater flow is of a negligible order, as there are
no runoff formation factors acting at a between grid cell scale.
From the scale analysis it is obvious that measured soil moisture and groundwater level
values cannot be compared directly with the corresponding modelled ones. The latter values
do not reflect the full small-scale variability as illustrated by the left-hand side of the
diagrams in Fig. 2.1. Measured data must be averaged to the REA scale in order to match the
model output.
8. May 1996
8. May 1996
0
Groundwater table depth (m)
Volumetric soil moisture
0.6
0.5
0.4
0.3
0.2
0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1
10
100
1000
10000
100000
1
10
Square root of area (m)
19. June 1996
1000
10000
100000
10000
100000
19. June 1996
0
Groundwater table depth (m)
0.6
Volumetric soil moisture
100
Square root of area (m)
0.5
0.4
0.3
0.2
0.1
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
1
10
100
1000
10000
100000
1
10
100
1000
Square root of area (m)
Square root of area (m)
Figure 2.1 Spatial variations of soil moisture and groundwater levels as a function of scale of
aggregation (from Beldring et. al., 1998)
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Chapter 3 Hydrological model formulation
3. Hydrological model formulation
3.1 Introduction
Distributed hydrological models allow the determination of the water balance and its
variation across river basins. In connection to climate change studies, fully distributed
physically based hydrological models (e.g., SHE-model, Abbott et al., 1986; WPI-models,
Kuchment et al., 1983, 1986, 1990) might be more suitable than the others. Parameters of
such models have a physical interpretation and, in principle, they can be measured. Such
models are physically based in the sense that the main hydrological processes of water
movement are modelled by finite difference representation of the partial differential
equations of mass, momentum and energy conservation. Spatial distribution of catchment
parameters, rainfall input and hydrological response is achieved in a horizontal space by a
grid network and in the vertical space by a column of horizontal layers for each grid cell.
In two of the most widely used distributed hydrological models, namely in the Système
Hydrologique Europeén (SHE-model) and Water Problems Institute models (WPI-models)
each of the primary processes of the terrestrial hydrological cycle is modelled as follows:
l
interception (the Rutter accounting procedure);
l
evapotranspiration (the SVAT scheme);
l
overland and channel flow (SHE: simplification of the St Venant equations; WPI: one
or two-dimensional kinematic wave equations for overland flow and the St Venant or onedimensional kinematic wave equations for flow in the river channel system);
l
unsaturated flow in the thawed soil (the one-dimensional Richards equation);
l
unsaturated flow in the frozen soil (WPI: one-dimensional heat and moisture transfer
equations);
l
saturated zone flow (two-dimensional Boussinesq equations);
l
snow cover formation and snowmelt (heat and moisture transfer equations, energy
budget method).
It is seen clearly that both these models are very similar and often use the same equations for
the description of the primary processes. However, they differs what concerns the used finite
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Chapter 3 Hydrological model formulation
difference methods for solving of equations, types of boundary conditions, parameterisation
of subgrid effects, input data, software and user interface, etc.
There are a large number of parameters associated with the processes simulated in the
models, which have to be estimated. These parameters take different values in different
model grid cells. For example, in the application of the SHE model to the Wye catchment it
was necessary to specify approximately 2400 parameter values (Beven, 1989). Obviously, it
is not possible to estimate all the parameter values adequately or measure them in field. A
pragmatic approach to the identification of the parameter values can be adopted instead.
Some parameters can be estimated a priori and other parameters are assumed to vary
dependent on spatial distribution of soil and vegetation types. The number of parameters
actually supplied to the model is therefore much smaller, but a calibration of some
parameters is needed. The pragmatic approach to the parameter estimation and its
calibration weakens its "physical base".
Fully distributed physically based hydrological models have the following advantages:
l
they give a better understanding of the hydrological processes in the catchment;
l
they can be used for estimation of influence of human activity on the hydrological
processes and for development of alternative strategies to reduce the negative human
impacts;
l
they can be used for simulation when observation records are very short.
The main difficulties with the use of such models are connected mostly to high demands to
input data and complexity of the model structure. Fully distributed physically based
hydrological models:
•
require detailed data and parameters related to the physical characteristics of the river
basin., require data and parameters related to the physical characteristics of the river basin,
which might not be available for the whole basin;
l
are very sensitive to the completeness and quality of the input data (parameters, initial
and boundary conditions in the catchment). Whenever the data are not complete calibration
- 12 -
Chapter 3 Hydrological model formulation
of parameters is required, making the modles similar to lumped conceptual models (Beven,
1989);
l
are very complicate in application to the real watersheds. The experience shows that
often the adjusting of the model to the real catchment is determined by not only qualification
of specialists, but their skill and hydrological intuition too.
A number of principal problems arise when such models are applied on a regional scale
(Vinogradov, 1988; Beven, 1997; Refsgaard, 1997). Strictly speaking, theoretical equations
in partial differences are based on the micro-scale conception of the “representative
elementary volume” (REV). When solving these equations by finite difference method, the
resolution of the spatial grid has to correspond to the typical scale of the process. For
example, if a typical size of water depth on the slope is mm or cm then an acceptable spatial
resolution of the grid network must be maximum one or two orders more. However, the
equations of overland flow are often solved with the grid net resolution of hundreds meters
and even several kilometres. In such cases, obviously, the simulated values of depth and flow
velocity on the slope are far from reality (Vinogradov, 1988).
Some of processes (i.e. preferential flow, depression storage, effects of small scale variability
of basin's characteristics) are lost with a coarse grid net. Additional equations are introduced
into for parameterisation of such processes on the sub-grid scale. These equations are either
empirical or are obtained from general subjective considerations.
The above named scale problems require further investigations. Without additional
substantiation an application of such models at the typical grid scale of large river basins or
GCMs may be dubious (Beven, 1997).
Difficulties with application of the fully distributed physically based models to real
watersheds lead to attempts to develop their simplified versions which are more suitable in
practice, but still preserve the main features of distributed physically based models. As a
rule, the principal equations in such models are obtained either by spatial integration of the
initial equations in partial differences or by assumptions allowing simplified analytical
solutions. Such models occupy an intermediate place between fully distributed physically
based models and lumped conceptual hydrological models (Knudsen et al., 1986;
Refsgaard, 1997). In this sense simplified physically based models can be regarded as an
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Chapter 3 Hydrological model formulation
example of introduction of a physically based distributed representation into a conceptual
distributed model. The issue of aggregation/disaggregation, compromise between limitations
of data availability and complexity of a model structure, and possibility of a priori estimates
of the model parameters are the main challenges for the regional physically based
hydrological models, e.g. TOPMODEL (Beven and Kirkby, 1979), WATBAL (Knudsen et
al., 1986), HYDROGRAPH (Vinogradov, et. al., 1988).
A number of physically based distributed models are in common use but none of them
explicitly contains components reflecting important characteristics of the boreal landscape
like mires, lakes and the close relationship between soil moisture and ground water in the till
soil. Preliminary runoff data analysis indicates that the frequency of lakes and mires in
upstream areas are the main factors explaining the spatial runoff variation (Erichsen et al.,
1995).
A distributed physically based model ECOMAG (Motovilov and Belokurov, 1997) used
here has been developed for boreal conditions. Primary the model was constructed for
decision of applied tasks of a regional ecological monitoring (ECOMAG - ECOlogical
Model for Applied Geophysics). The model consists of two main modules. The first one
provides a description of the hydrological processes in catchment while the second describes
pollution transformation and transport in a basin. The model, which is based on 15-year’s
experience of the fully distributed physically based hydrological models WPI (Kuchment et.
al., 1983, 1986, 1989; Motovilov, 1986, 1987, 1993) has already been applied and tested in
Russia.
In 1995 a hydrological module of the ECOMAG was improved and adopted for regional
simulations of the terrestrial water cycle in northern landscapes (Motovilov, 1995). The
basic assumption used in the model is that a river basin can be sub-divided into a
mosaic of irregular or regular landscape elements, each to be viewed as a hydrological
unit. The REA concept referred to above is of vital importance here as it constitutes the
minimum size for such an element.
The model describes the processes of infiltration, evapotranspiration, thermal and water
regimes of the soil, surface and subsurface flow, groundwater and river flow, snow
accumulation and snowmelt. In its original form a drainage basin is approximated by
- 14 -
Chapter 3 Hydrological model formulation
irregular triangular or trapezoidal elements, taking into consideration peculiarities of
topography and spatial distribution of the soil and land cover types in a GIS frame. The
second version of the model is now under development (Gottschalk et al., 1998b;
Motovilov et al., 1998) and the present report describes a step in this new direction. The
main change is the use of a regular grid network (2 km x 2 km) in order to (after further
development) allow direct coupling with a meso-scale meteorological model and the use
of radar-evaluated precipitation data (Crochet, 1999).
3.2 General assumptions
Processes in the soil and snow cover have an important role for the terrestrial water
cycle. In the distributed physically based models Richard’s equation is often used to
describe water movement in the unsaturated soil and snow. This approach needs
detailed spatially distributed information about relationships between capillary-sorption
potential, hydraulic conductivity and moisture. In principle, Richard's equation is based
on a micro-scale concept of the "representative elementary volume" (REV).
This
approach makes it difficult to account for the effects of soil non-homogeneity and
macro-porosity, important for generation of preferential flow in the boreal regions.
A more simplified approach based on the concept of so-called “water constants” may be
useful for the description of a water regime in the soil and snow-pack at the meso-scale.
According to this approach water is divided into several classes depending on the nature
of the soil-water or snow-water interactions. Water in the porous medium, for example,
could be classified into three kinds (Baver, 1965):
Hygroscopic water, which is adsorbed from water vapour of atmosphere as a result of
attractive forces in the surface of the solid particles.
Capillary water, which is held by surface tension forces as a continuous film around the
particles and in the capillary spaces.
Gravitational water, which is not held by the soil and drains under the influence of
gravity.
In the soil and snow hydrology there are several so-called soil-water and snow-water
constants that are used to express water interactions under the action of different forces.
According to Baver (1965) and Maidment (1993):
- 15 -
Chapter 3 Hydrological model formulation
Wilting point (WP) refers to the soil moisture content at which soil cannot supply water
at a sufficient rate to maintain turgor, and the plant permanently wilts. The tension of
the soil water at WP is about 15 atmospheres. Water in the soil is held as a thin film
around the particles. The movement of water within the soil takes place mainly in the
vapour phase since the capillary conductivity is assumed zero.
Field capacity (FC) of the soil is defined as the amount of water held by surface tension
on the soil particles after the excess gravitational water has drained. The mean tension
of the soil water at FC is about 0.3 atmosphere. The hydraulic conductivity at FC
approaches zero at least decreases by several orders relatively saturated hydraulic
conductivity. Water movement is very slow at moisture content below FC.
This
constant seems to be similar for water holding capacity (WHC) in the snow.
Saturated soil (snow) represents the amount of water that is necessary to fill the whole
pore space. The moisture content is equal the total porosity (P). The capillary tension is
nearly to zero. The hydraulic conductivity is equal the saturated one. The water moves
due to the gravitational force.
The soil and snow water constants might be considered as boundaries which separate
different parts of the water concerning to the ability to move and change. The soil loses
the water by rapid drainage due to gravitational force until the moisture content
decreases from saturated state to field capacity (gravitational water). For the snow, such
behaviour proceeds until the moisture of snow decreases to the snow water holding
capacity. The movement of water takes place trough large non-capillary pores that do
not hold water tightly by capillary forces. The non-capillary porosity (D) is equal the
difference between total porosity and soil field capacity (water holding capacity for the
snow).
Due to evapotranspiration the moisture content of the soil can decrease from the field
capacity until it reaches the wilting point. The difference between field capacity and
wilting point represents the amount of water available to plants. This is actual capillary
porosity (C). The movement of water in the capillary zone during rain less period is less
pronounced and is carried out mainly from the thin films around soil particles to the
nearest root tissue of plants. Essentially, such movement can be considered as that in
- 16 -
Chapter 3 Hydrological model formulation
micro-scale relatively large-scale horizontal and vertical movement of gravitational
water in the non-capillary pores. In the snow the water in capillary pores in a moisture
range from water holding capacity to zero can change due to evaporation or refreezing
of snowmelt water during the cold period.
The decrease in soil moisture below the wilting point may be caused by evaporation
from the surface during long dry periods. In nature, such conditions are observed very
seldom and then mainly in desert regions.
The process parametrisation applied here is based the concept of water constants. These
constants represent a separation of the water in the porous space into several classes
with different regimes of changes.
3.3 Balance equations
Let us look at a separate soil layer as an example of the general balance equations used
in ECOMAG. The water conservation equation for a three dimensional element can be
written in the form
∂ v ∂ v y ∂ vz
∂W
=− x −
−
− S,
∂t
∂x ∂ y ∂z
(3.1)
where
W is the volumetric content of water per unit of volume;
vx, vy and vz are the volume water fluxes in the directions x, y and z (rate of water flow
per unit of area);
S is the rate of intrinsic source, for example, transpiration (volume of water per unit
volume per unit time);
t is the time.
- 17 -
Chapter 3 Hydrological model formulation
Let us consider an isotropic soil sample in the shape of a rectangular parallelepiped of
the dimension L x B x Z. By not allowing flow along the y axis (two-dimensional flow)
and assuming that the mean rates of horizontal and vertical water are known functions
of time, an integration of equation (3.1) yields:
∂v
∂W
æ ∂v
ö
ò0 ò0 ò0 ∂ t dxdydz = ò0 ò0 ò0 çè − ∂ xx − ∂ zz − S ÷ø dxdydz
L B Z
L B Z
(3.2)
Þ
Z
(
)
dW Z v x , 0 − v x , L
=
+ v z , 0 − v z ,Z + ZS .
dt
L
(
)
(3.3)
Denote Qo=BZvx,o, QL=BZvx,L, E=ZS, V0=vz,0 and VZ=vz,Z. Here Q is the discharge
through the left (index 0) and right (index L) cross sections of the soil sample, V is the
flow rate through unit area of the soil sample in the top (index 0) and bottom (index Z),
and E is the transpiration rate from the soil column over unit area. Substituting these
variables in (3.3), yields the water balance equation for the whole soil sample:
Z
dW Q0 − QL
=
+ (V0 − VZ ) − E.
dt
BL
(3.4)
Figure 3 illustrates a soil sample schematically with its different parts of porous space.
The water balance for each of these parts is treated separately. Dependent on
meteorological conditions the water content in the soil can vary between the total
porosity (P) and the wilting point (WP). Below WP water is strongly influenced by
capillary-sorption forces and does not move.
- 18 -
Chapter 3 Hydrological model formulation
vertical
inflow, V0
soi
l
M
pa
(m rticle
atr
s
ix)
L
fie FC
ld
W
cap
wi p
aci
ltin
ty
g
po
int ca C
pil
lar
y
transpiration, E
Z
un B = 1
it w
idt
h
P
tot = 1
al p -M
oro
sity
po
ro
sity
no D =
n-c
api P-FC
lla
ry
po
ro
sity
horizontal
inflow, Q0
horizontal
outflow, QL
h0
hL
vertical
outflow, VZ
Figure 3.1 Structure of soil sample and soil water constants
Water is slowly mobile in the capillary porous space (C) with soil moisture content
ranging from the wilting point to the field capacity. Changes in soil moisture content are
caused mainly by vertical fluxes viz. precipitation and evaporation, and also as an
intrinsic source via transpiration. The horizontal movement in capillary pores may
therefore be neglected. The water balance equation for the capillary pores can in this
case be written in the form (index c):
Z
(
)
dWc
= Vc , 0 − V c , Z − E c .
dt
(3.5)
Changes in water content in non-capillary pores, ranging between saturated state
(porosity) and field capacity, are caused mainly by vertical water fluxes. Water is
drained rapidly into deeper soil horizons due to gravitational forces. If deeper horizons
are less permeable than the given horizon, water in the non-capillary zone can both
accumulate and move in the direction of prevailing slope along the relatively
impermeable surface between horizons. The water balance equation for the noncapillary zone of the soil column pores space (D) is written as (index nc):
- 19 -
Chapter 3 Hydrological model formulation
Z
dWnc Q0 − QL
=
+ Vnc , 0 − Vnc ,Z − Enc .
BL
dt
(
)
(3.6)
ZWnc is the layer of water calculated over a surface unit of the soil column. Since the
water moves horizontal only in a part of the soil volume, the non-capillary porosity (D),
the actual water layer in the non-capillary zone of a soil column is calculated as
h=
ZWnc
.
D
(3.7)
Inserting Wnc into equation (3.6) and assuming a linear profile of water depth in xdirection results in:
D d ( h0 + hL ) Q0 − QL
=
+ Vnc , 0 − Vnc ,Z − E nc .
2
BL
dt
(
)
(3.8)
The total changes in soil moisture in the capillary and non-capillary zones of a soil
sample is found by adding the equations (3.5) and (3.8):
Z
dWc D d ( h0 + hL ) Q0 − QL
+
=
+ Vc , 0 − Vc ,Z + Vnc , 0 − Vnc ,Z − Ec − Enc .
2
BL
dt
dt
(
) (
)
(3.9)
Taking into account the fact that V=Vc+Vnc and E=Ec+Enc, equations (3.4) with
consideration of equation (3.9) is now expressed as:
Z
dWc D d (h0 + hL )
dW
.
=Z
+
2
dt
dt
dt
(3.10)
The equations, analogous to (3.8) and (3.9), for a landscape element of a trapezoidal
form in the plane are written as:
[(
]
D d ( BL hL + B0 h0 ) Q0 − QL
=
+ Bm Vnc , 0 − Vnc ,Z − E nc ,
2
L
dt
Bm Z
)
(3.11)
dWc D d ( BL hL + B0 h0 ) Q0 − QL
+
=
+ Bm (V0 − VZ ) − E ,
dt
dt
L
2
[
]
(3.12)
where Bm=(BL+B0)/2 is the mean width of the trapezoidal element. In these equations it
is assumed that the cross section of the water flow (Bh) is a linear function of the xdirection.
The water balance equations (3.5), (3.8), (3.9), (3.11) and (3.12) are used for simulating
- 20 -
Chapter 3 Hydrological model formulation
the dynamics in soil moisture and groundwater levels in ECOMAG. The same equations
could be used for a description of the water changes in the snow regarding porosity as
the snow space free of ice particles. If D=1 (non-capillary pores occupy the whole space
of the volume) then these equations can be applied as water balance equations for
surface water.
3.4 Basic structure
The structure of the hydrological model is based on the following description of the
processes of the hydrological cycle: During a summer period rain water infiltrates
partially into the soil and penetrates into deeper soil layers. After the surface
depressions are filled, the excess water not absorbed by the soil, runs off on the sloping
land surface to the river network (surface flow). Part of the water infiltrated into the
soil, flows along a temporary, relatively impermeable, boundary close to the surface of
the slopes as shallow groundwater (subsurface) flow. When soil is saturated, a lateral
subsurface flow can be released as return surface flow. Another part of infiltrated water
is transported in the groundwater zone and forms the base flow. Water in the surface
depressions and soil horizons is depleted by evapotranspiration. The surface, subsurface
and groundwater flow form the lateral inflow into the river network.
During cold periods of the year, the above scheme is supplemented by hydrothermal
processes - snow cover formation, snowmelt, freezing and thawing of the soil, and
infiltration of snowmelt water into the frozen soil.
3.4.1. Horizontal structure
In the ECOMAG model a catchment is subdivided into landscape elements on the basis of
topography, landuse and soil. GIS is used for spatial analysis of this information creating
files with coordinates and parameter classes of each landscape and river element. The
process of a catchment schematisation starts by dividing the river basin into subbasins
using the river network and topography. Water movement is assumed to take place in the
direction of the prevailing slope towards the river. The subbasins are divided into
prevailing slopes, and the river network into river links. Each river element has two
adjacent slopes. Landscape elements shown in Figure 3.2 are then determined for all the
slopes using landuse and slope. The landscape elements have the form of polygons with
- 21 -
Chapter 3 Hydrological model formulation
three or four corners. Coordinates of the polygon corners are registered, and their area,
length, width and slope are calculated. Each of the landcape elements is assigned a soil
and land use class. This set of parameters represents physical characteristics of each
landscape element. The river links are characterized by length, width, slope and Manning’s
roughness coefficient.
Another option is to construct the landscape elements as a regular gridnet. The
schematisation is then more objective, but the flexibility given by the varying size and
shape is lost.
Both the landscape elements and the river links form a tree-structure and are numbered
following a hierarchical system as
illustrated in Figure 3.3. Each river
link is given a number, starting at the
source of the main river with the
numbers increasing downstream. The
Z
ZZ ON E
river links of the first tributary are
ER
W AT
UN D
GRO
numbered,
and
the
procedure
continues downstream towards the
last tributary. The landscape elements
are asigned numbers following the
same system, beginning with the left
Figure 3.2 Schematisation of a catchment in the side. When a slope contains more
ECOMAG model.
than one landscape element, the
numbering starts at the top of the
slope. Such a structure allows easy calculation of both water movement between elements
and along the river network .
All this information in ASCII format is used as input files in ECOMAG.
- 22 -
Chapter 3 Hydrological model formulation
Figure 3.3 Numbering of landscape elements and river links in ECOMAG.
3.4.2 Vertical structure
In the ECOMAG model the vertical distribution is achived by dividing each landscape
element into several layers. Figure 3.4 shows five such layers: a snow cover layer for the
cold period, a surface layer and three soil layers (a top layer, horizon A, a transition layer,
horizon B, and a bottom layer called groundwater-zone). Usually horizon A is the soil
layer of high porosity and conductivity, while horizon B is a deeper layer of much lower
porosity and conductivity.
Simulation of hydrological processes for each landscape element is executed consistently
for each layer. In the warm period, rain precipitation is treated by surface layer processes.
In the cold season, the first group of processes is simulated for the snow cover layer and
thermal conditions of the soil (freezing and thawing of the soil, formation of snow cover
and snow melting).
The phase of precipitation is determined by the daily average air temperature and the
threshold temperature. The snowmelt rate is calculated using the degree-day method.
Evaporation of solid and liquid phases of snow is estimated using data on air
temperature and vapour pressure deficit.
- 23 -
Chapter 3 Hydrological model formulation
precipitation
E5
non
capillary
zone
capillary
zone
ice particles
snow cover
h5
melt water
E1
infiltration
subsurface inflow
horizon A
s
o
i
l
m
a
t
r
i
x
horizon A
non
capillary
zone
capillary
zone
penetration
evapotranspiration
E2
Z2
infiltration
surface water storage
E3
subsurface inflow
horizon B
Z3
s
o
i
l
WP
horizon B
porosity
h3
E4
groundwater
inflow
Z4
surface water outflow
h2
River flow
subsurface outflow
horizon A
field capacity
groundwater zone
h4
penetration
m
a
t
r
i
x
h1
return flow
surface water
inflow
subsurface outflow
horizon B
groundwater outflow
Figure 3.4 Vertical structure of ECOMAG for a landscape element
It is assumed that the vertical temperature profiles in the snow, as well as in the frozen
and thawed soil, differ only slightly from linear ones, and that the migration of moisture
to the freezing front is negligible. Under these conditions the soil-frost and soil-thawing
depth dynamics can be described by a system of ordinary differential equations
(Motovilov and Nazarov, 1991).
The rain or melted water, which reaches the surface, is treated by surface layer processes.
Some of the water infiltrates into the soil. It is assumed that surface water layer appears
when intensity of rain or melt water exceeds the infiltration rate into the soil. Infiltration of
rain and melt water into the frozen soil is simulated taking into account the influence of
ice content in the frozen soil on the soil hydraulic conductivity.
Part of the surface water is spent to fill a depression storage. The remaining part flows on
the surface, and reaches the next landscape element on the same slope or flows to the river
link element. Surface runoff on the slopes is described by a simplified version of the
kinematic wave equation, based on Rose's approximation (Rose et al., 1983). The
infiltrating water is treated in the next group of processes for soil horizon A.
- 24 -
Chapter 3 Hydrological model formulation
According to assumptions in sections 3.2 and 3.3, each soil horizon is divided in two zones
-viz capillary zone and non-capillary zone. Infiltrated water penetrates into the capillary
zone if the capillary soil moisture is less than field capacity, in the other case it drains into
the non-capillary zone.
From the capillary zone water can only disappear by evapotranspiration. A simple method
is used for simulation of the actual evapotranspiration (Thornthwaite-Budyko approach,
after Brutsaert, 1982, Feddes et al., 1974). Under the condition of high soil moisture
content the actual evapotranspiration equals the potential one, and it linearly decreases
to zero at soil moisture content equal to the wilting point.
From the non-capillary zone water penetrates into a deeper horizon or can partially
accumulate on a relatively impermeable boundary between soil horizons. In this latter
case water moves along the landscape element as subsurface flow, reaches the next
element on the same slope or flows into the river link. If the non-capillary zone is filled up,
the exceeding water is released as return flow on the surface. In the groundwater zone
some water can be exchanged with still deeper groundwater horizons. The subsurface and
groundwater flow is modelled as a Darcy flow.
Finally, the processes in the river network are simulated using kinematic wave equations.
The landscape information extracted from the GIS grasps only large-scale features. Smallscale fluctuations in landscape characteristics, however, are important for the runoff
formation processes. A common approach in lumped hydrological models is to resolve this
variability in terms of spatial distribution functions (Kuchment et al. 1986). A possible
simplification is to use the same distribution for all elements allowing the mean value to vary
between them.
The within element variability is taken into consideration in this manner in ECOMAG for
three parameters - the vertical saturated hydraulic conductivity of soils, surface depression
storage and soil field capacity. For the first two parameters an exponential function is applied
(Vinogradov, 1988, Popov 1979) and for the third - a parabolic function (Bergström, 1976;
Dümenil and Todini, 1992).
- 25 -
Chapter 3 Hydrological model formulation
3.5 Process description
Different water fluxes and intrinsic sources play different roles for the snow, surface and
soil layers. To account for the peculiarities of processes in different layers, a landscape
element can be divided into five blocks: (see Fig.3.4) a surface layer in the zone of
surface runoff formation, two soil layers (a top layer, horizon A, and a deeper soil layer,
horizon B), a layer in the groundwater zone and a snow cover layer for a cold period. A
trapezoidal form of the landscape element will be adopted here.
3.5.1 Surface water (index 1)
The flow of surface water along the slope of a landscape element is described by a
simplified version of a kinematic wave equation in the form of a mass conservation
equation (3.11), assuming D=1, and Manning’s formula:
1 d
( B h + B0 h1, 0 ) = R0 Bm − ( Q1, L − Q1, 0 ) / L ,
2 dt L 1, L
(3.13)
Q1 = i11/ 2 h15/ 3 B / n1 ,
(3.14)
where
Q1 is the horizontal flux (discharge) of surface water;
h1 is the depth of surface flow;
R0 is the rainfall excess, which forms the overland flow;
B and L are the width and length of a landscape element, respectively;
Bm=(B0+BL)*0.5 is the mean width of an element;
i is the slope of an element;
n is the Manning’s roughness coefficient;
Indices 0 and L denote the values on the upper and lower boundaries of a landscape
element in a plane.
The effective rainfall excess R0 is calculated as
R0 = V1 − V2 + Vr − VP ,
(3.15)
where
- 26 -
Chapter 3 Hydrological model formulation
V1 is the rain or snowmelt water flux on the surface;
V2 is the infiltration rate into the soil;
Vr is the rate of return inflow of subsurface water on the surface;
VP is the rate of water losses in the depression storage.
3.5.2 Infiltration into soil
It is assumed that the space distribution function (F) of the vertical saturated hydraulic
conductivity (K) for each landscape element can be approximated by an exponential
function:
F ( K ) = 1 − exp( −αK )
(3.16)
where
α=
1
,
K
(3.17)
K is the mean value of K over the area.
Assume that for each point of the element's area the following relations exist between
water flux on the surface (V1) and infiltration rate (V):
V=K,
for V1>K,
V= V1,
for V1<K.
Then the infiltration rate into the soil, V2, over a whole element’s area can be expressed
as:
FVC1
V2 = ò V1dF C +
0
1
ò
FVC1
−
1
é
ù
ln( F C )dF C = K ê1 − expæç − V1 ö÷ú ,
K
è
øû
α
ë
(3.18)
where
F C ( K ) = exp(−αK ) ,
FC(K) is the exceedance probability distribution.
Figure 3.5 illustrates this relationship. Vinogradov (1988) obtained the same formula for
calculation of infiltration into the soil using other assumptions.
- 27 -
Chapter 3 Hydrological model formulation
K
K = -lnFC/ α
V1
0
FCV1
FC=1
Figure 3.5 Saturated hydraulic conductivity distribution and infiltration for a landscape
element
3.5.3 Surface retention
To describe the dynamics of the water in the depression storage an approximation of the
surface depressions' distribution for a landscape element by an exponential function is
used (Popov, 1979):
ìï
é 1
ù üï
ϕ ( t ) = ϕ0 * í1 − exp ê− ò (Ve ( t ) − E pot ( t ))dt ú ý ,
ïî
ë ϕ0 t
û ïþ
(3.19)
where
Ve= V1-V2+Vr,
ϕ0 is the maximum value of the depression storage;
E pot is the rate of potential evaporation, which is calculated by the empirical Dalton's
formula.
Epot=ked,
(3.20)
where
d is the air vapour pressure deficit;
ke is the empirical coefficient.
Equation (3.19) is solved in two steps. First, the function ϕ*(t) is founded assuming
Epot(t)=0 and the rate of water losses in the surface depressions is calculated as:
- 28 -
Chapter 3 Hydrological model formulation
dϕ * (t )
VP =
.
dt
(3.21)
Then actual evaporation Epot(t) is taken in account for calculating ϕ(t).
3.5.4 Soil horizons (index j=2,3)
Two soil layers are considered: horizon A (index j=2) and horizon B (index j=3). Each
soil horizon is divided into two parts (Fig. 3.4): a capillary and non-capillary zone. It is
assumed that in each point the infiltrated water penetrates into the capillary zone if the
capillary soil moisture, W, is less than field capacity, FC, otherwise it drains into the
non-capillary zone:
Vj,c = Vj and Vj,nc= 0 for Wj < FCj,
Vj,c = 0 and Vj,nc=Vj for Wj = FCj.
The separation of the infiltrated water between these two zones over the area of a
landscape element is achieved using a spatial distribution function of field capacity
(Bergström, 1976):
β
β
æ FC ö
æ FC ö
F ( FC ) = ç
÷ , F0 ( FC ) = 1 − ç
÷ ,
è FCM ø
è FCM ø
FC2 = FCM
β
,
β +1
(3.22)
where
FCM is the maximum FC value for a landscape element;
FC2 is the mean FC value;
F and F0 are the spatial distribution function and the exceedance probability for FC;
β is the parameter of the distribution function.
The penetration into the capillary zone (index c) is then given by:
V j ,c
β
é æW j
ö ù
= V j ê1 − ç FCM ÷ ú ,
jø
û
ë è
(3.23)
and the one into non-capillary zone (index nc) by:
- 29 -
Chapter 3 Hydrological model formulation
β
V j ,nc
æW
ö
= V j ç j FCM ÷ ,
è
jø
(3.24)
where Wj is the volumetric soil moisture in the capillary zone of j-th soil layer.
Capillary zone
Soil moisture in the capillary zone is calculated using equation (3.5) as:
Zj
dW j
dt
= V j ,c − E j ,
(3.25)
where
Zj is the depth of soil layer j;
Ej is the evapotranspiration rate from soil layer j.
Thornthwaite-Budyko approach is used for estimation of the actual evapotranspiration.
Under the condition of high soil moisture content the actual evapotranspiration equals
the potential one, and then linearly decreases to zero as soil moisture content diminishes
to the wilting point (WP):
E pot , j ,
ì
ï
æ W j − WPj ö
Ej = í
çç
÷÷ ,
E
pot
j
,
ï
WE
WP
−
è
ø
j
j
î
for W j > WE j
for W j ≤ WE j
(3.26)
where
E pot , j = E pot k w, j , is the potential evapotranspiration from soil layer j;
WEj=(FCj+WPj)*0.5 is the critical moisture content for potential evapotranspiration;
kw,j is a weighting factor, distributing the potential evapotranspiration between soil
layers influenced by the distribution of the roots system.
Non-capillary zone
Water, that entered into the non-capillary zone, can penetrate into the deeper soil layer
with the rate Vj+1, which equals the vertical saturated hydraulic conductivity of soil
(Kj+1) in the layer j+1. If the penetration rate Vj,nc is higher than Kj+1, then the infiltrated
water can accumulate in the non-capillary zone and move in the direction of prevailing
- 30 -
Chapter 3 Hydrological model formulation
slope on the relatively impermeable boundary between layers j and j+1. During storm
precipitation the non-capillary zone of upper soil horizon A can be completely filled and
return surface flow occurs. The flow of subsurface water flow is supposed to be a Darcy
flow. Equation (3.11) can be used for the description of water balance in the noncapillary zone in the form:
Dj d
( B h + B0 h j , 0 ) = (V j ,nc − V j ,r − V j +1 ) Bm − ( Q j , L − Q j , 0 ) / L ,
2 dt L j , L
(3.27)
Q j = BiK x , j h j ,
(3.28)
where
Qj is the horizontal flux (discharge) of subsurface water in the soil horizon j;
hj is the water level in the non-capillary zone;
Kx, j is the soil saturated hydraulic conductivity in a horizontal direction (usually it is a
function of depth, hj);
D j = Pj − FC j is the non-capillary porosity.
Rj,r is the rate of return inflow of subsurface water to the upper layer and is calculated
as:
ïì( Q j − Q j ,max ) / Bm L,
V j ,r = í
ïî0,
for Q j > Q j ,max ,
for Q j ≤ Q j ,max ,
(3.29)
where Q j ,max = BiK x , j Z j .
When horizon A is considered, V2,r is the return surface flow. This flow is also formed if
the incoming surface flux V1 occurs on the saturated areas. In this case we have:
V2,r = V2 − V3 + ( Q2,max, 0 − Q2,max, L ) / BL.
(3.30)
- 31 -
Chapter 3 Hydrological model formulation
3.5.5 Groundwater zone (index 4)
The groundwater flow is calculated using equation (3.11) and Darcy's formula in the
which yields:
D4 d
( B h + B0 h4, 0 ) = (V4 + Vd − V4,r − E4 ) Bm − ( Q4,L − Q4, 0 ) / L ,
2 dt L 4, L
(3.31)
Q4 = BiK x , 4 h4 ,
(3.32)
where
Q4 is the horizontal inflow (index 0) and outflow (index L) of groundwater for a
landscape element;
h4 is the groundwater level;
Vd is the rate of water exchange between groundwater zone and deeper layers;
Kx,4 is the horizontal saturated hydraulic conductivity (usually a function of depth, h4);
D4=P4-FC4 is the non-capillary porosity in the groundwater zone;
E4=Epotkw 4 is the evapotranspiration from the groundwater zone;
kw,4 is the weighting factor for a groundwater zone, distributing the potential
evapotranspiration between soil layers.
During a cold period of the year ECOMAG considers the processes of snow cover
formation and snowmelt, freezing and thawing of the soil, infiltration of snowmelt
water into the frozen soil.
3.5.6 Snow cower formation and snowmelt (index 5)
The snow cover varies in time due to precipitation, evaporation, snow compaction, melting
and freezing of meltwater in the snow. In the ECOMAG model the phase composition of
precipitation (R), i.e. snow or rain, is determined by the daily average air temperature
(T) as : T < Tcr - snow (Rs), T ≥ Tcr - rain (Rr).
The following system of equations describes snow cover formation and snowmelting
(Motovilov, 1986, 1993):
- 32 -
Chapter 3 Hydrological model formulation
ρi d
( Ih5 ) = Rs − E s − S T + S f ,
ρ w dt
(3.33)
d
(W5 h5 ) = Rr + S T − E L − V1 − S f ,
dt
(3.34)
éR
dh5
S + Es ù
= ρW ê s − T
ú − v s (h5 , I ,W5 , Ts ) ,
dt
ρi I û
ë ρn
(3.35)
where
h5 is the snow depth;
I is the volumetric content of ice per unit volume of snow;
W5 is the volumetric content of liquid water per unit volume of snow;
V1 is the meltwater yield from snow (flux of snowmelt water on the surface);
Ts is the temperature of the snow surface;
ρi is the ice density;
ρw is the water density;
ρn is the density of new snow.
The snowmelt rate, ST, is calculated using the degree-day method:
S T = kT * (T − TM )
at (T − TM ) > 0 ,
(3.36)
where
TM is the threshold temperature for snowmelt;
kT is the degree day factor.
A similar procedure is used to describe the freezing rate of meltwater in snow, Sf :
S F = kT * (T − TM )
for (T − TM ) < 0 and W5 > 0 .
(3.37)
Evaporation of solid (Es) and liquid (Ew) components of snow are estimated using data
on the deficit of air vapour pressure as:
- 33 -
Chapter 3 Hydrological model formulation
Es =
æ1 +
ç
è
EL = Es
ke d
ρ wW5
ö
ρ i I ÷ø
,
(3.38)
ρ wW5
.
ρi I
(3.39)
Using the approach by Yosida et al., (1955) the velocity of snow compaction, vs, can be
described as (Motovilov, 1993):
k c ( ρ i I + ρ wW5 )h52
vs =
,
exp[− 0.08Ts + 21( ρ i I + ρ wW5 )]ρ w
(3.40)
where
ìT ,
Ts = í
î0,
at T < 0,
at T ≥ 0,
kc is the parameter of snow compaction.
The rate of water yield from the snow, which reaches the soil surface, V1, is calculated by
the following equation:
ì(W5 − WHC )h5 / δt ,
V1 = í
î0,
at W5 > WHC ,
at W5 ≤ WHC ,
(3.41)
where
WHC is the water holding capacity of the snow;
δt is the calculation time step.
When there is no snow cover, V1 equals to the rate of rain precipitation, Rr.
3.5.7 Thermal conditions in snow and soil
The vertical temperature profiles in snow, frozen and unfrozen soil are supposed to be
approximately linear, and the transport of moisture to the freezing-front can be neglected.
Under these conditions the soil frost depth, Hf, and the soil thawing depth, Ht, are
described by the following equations (Vehviläinen and Motovilov, 1989; Motovilov and
Nazarov, 1991):
- 34 -
Chapter 3 Hydrological model formulation
Qf
dH f
dt
=
λ f T0
λt Tg
−
,
Hf
Hg − H f
æ
δt ö
÷
H t = çç H t2 + 2λt T
Q f ÷ø
è
(3.42)
0.5
,
(3.43)
Q f = ρw L f (W j − Wu ) ,
(3.44)
λs H f
,
λ s H f + λ f h5
(3.45)
T0 = T
where
Wj is the volumetric water content in horizon j of the soil;
Wu is the volumetric unfrozen water content in the soil;
Tg is the soil temperature at the depth Hg, where it remains practically unchanged during
the winter season;
T0 is the temperature snow-soil interface;
Lf is the latent heat of the ice fusion;
λt is the heat conductivity of the unfrozen soil;
λf is the heat conductivity of the frozen soil;
λs is the heat conductivity of the snow.
3.5.8 Infiltration into frozen soil
Frozen soil has reduced hydraulic conductivity due to the ice present in the pores.
Infiltration of rain and meltwater into the frozen soil is described as (Motovilov and
Nazarov, 1991):
é
æ−V
öù
V2, f = K 2, f ê1 − expç 1 K ÷ ú ,
è
2, f ø û
ë
(3.46)
4
K 2, f
é P − I 2 − WP2 ù
2
= K2 ê 2
ú / (1 + k i I 2 ) ,
P
−
WP
2
2
ë
û
(3.47)
- 35 -
Chapter 3 Hydrological model formulation
I2 =
ρw
(W j − Wu )η( H f , H t ) ,
ρi
(3.48)
ì( H f − H t ) / Z2 , at H f < Z2 ,
ï
η( H f , H t ) = í( Z2 − H t ) / Z2 , at H f ≥ Z2 and H t < Z2 ,
ï
at ( H f ≥ Z2 and H t ≥ Z2 ) or H f = 0,
î0,
(3.49)
where
K2 is the vertical saturated hydraulic conductivity of unfrozen soil in horizon A;
K2,f is the vertical saturated hydraulic conductivity of the frozen soil;
I 2 is the fraction of ice content in the soil;
P2 is the porosity;
WP2 is the wilting point;
Z2 is the thickness of horizon A;
ki is the empirical constant.
3.5.9 River flow (index 6)
River flow is described by a simplified version of the kinematic wave equation in the
form of mass conservation equation (3.11), assuming D=1, and Manning’s formula as:
1 d
(BR,L h6,L + BR,0 h6,0 ) = (Qlat + Q6,0 − Q6,L ) / LR ,
2 dt
1
5
Q6 = i R 2 h6 3 BR / n R ,
(3.50)
(3.51)
where
Q6 is the river discharge;
H6 is the depth of river flow;
LR is the length of a river link;
BR is the width of a river link;
iR is the slope of a river link;
- 36 -
Chapter 3 Hydrological model formulation
nR is the Manning’s roughness of the river bed.
Indices 0 and L denote the variables at the inlet and outlet of a river link.
Qlat is the lateral inflow into a river link from ajacent landscape-elements. Qlat is
calculated as
4
Qlat = å Q j ,n ,
(3.53)
j =1
where index n denotes the lateral inflow into the river link from ajacent landscape
elements.
3.6 Model calibration processing
3.6.1 Background information
The following data are required for simulations of processes of the hydrological cycle:
precipitation, temperature and air humidity records with a daily resolution. Observations of
river runoff, snow cover, soil moisture, groundwater levels, soil temperature, soil frost
depth, evapotranspiration etc. can be used for calibration of parameters and validation of
the model.
Discretization of a river basin into landscape elements is carried out using thematic maps in a
GIS frame. Digital terrain data, physiographic, soil and land use maps are required. After
discretization into landscape element each of these is assigned a set of parameters, reflecting
its form (area, length, width and elevation gradient), soil and land use classes. Information
about soil and land use properties is needed to choose the model parameters.
3.6.2 Model parameters
Soil properties control the main processes of the terrestrial water cycle: infiltration,
evaporation, water exchange between soil horizons, lateral groundwater flow etc. Table 3.1
shows the model parameters related to the soil characteristics. Land use properties
influence mainly surface processes like surface flow, water retention in relief depressions
and snowmelt. Soil parameters like soil volume density, vertical saturated hydraulic
conductivity, thickness of the top soil horizon, which usually are measured at agricultural
- 37 -
Chapter 3 Hydrological model formulation
fields, may be different for other land cover classes (for example, for forested area). This
is achieved in the model with references to coefficients of corresponding values from a
certain soil class. Table 3.1 presents also parameters valid for the catchment as a whole.
Many equations of physically based
Table 3.1 Model parameters
models
Parameters of soil classes
contain
parameters
and
coefficients that have a direct physical
Volume density
interpretation and, in principle, can be
Porosity
Field capacity
measured in the field.Example of such
Wilting point
parameters in the ECOMAG model are
Vertical saturated hydraulic conductivity
the soil water constants (Tab. 3.1). The
Horizontal saturated hydraulic conductivity
initial values of these parameters for the
Heat conductivity for thawed and frozen
different soil types can be determined
Unfrozen water in frozen soill
on the basis of regional information
Thickness of soil horizon
Parameter of distribution of field capacity
about the hydrological properties of the
Parameters of land use classes
soil and supplemented by data from
Maximal retention storage
literature sources (Nyberg, 1995, Stähli
Manning’s roughness coefficient for slope
et al., 1996).
Degree-day factor
For other parameters, experimental
Parameters for whole catchment
Prameter of potential evaporation
results allow to establish empirical
Critical temperature snow/rain
relations (heat conductivity of both soil
Density of new snow
and snow, unfrozen water content in
Snow water holding capacity
frozen
Parameter of snow compaction
soil,
snow
water
holding
capacity) or indicate reasonable well-
Depth of unchanged ground temperature
defined limits for parameter values
Manning’s roughness coefficient for river
(degree-day
factor
and
critical
temperature for snowmelt, parameter of
snow compaction). In still other cases, the limits are not so well defined (for example,
horizontal hydraulic conductivity for calculation of shallow groundwater flow) and the
parameter values must be determined by calibration. The fact that not all parameters
can be well defined originates from scale issues simplifications and non-adequacies in
the model description.
- 38 -
Chapter 3 Hydrological model formulation
3.6.3 Calibration procedure
The various groups of model parameters may be calibrated in separate steps using only
data about the dynamics of evapotranspiration, soil moisture, groundwater, snow cover,
frozen soil and river runoff, respectively. Parameter values can be adjusted by means of
a visual comparison of the simulated and observed values or a numerical performance
criterion. Here the Nash-Sutcliffe efficiency measure R2 (Nash and Sutcliffe, 1970) is
used:
R
2
å (Q
=
o
d
) − å (Q
å (Q − Q )
−Q
2
o
d
o
d
− Qdc
)
2
(3.54)
2
where
d is the day number;
Q is the observed mean value;
Q0d is the observed value;
Qcd is the calculated value.
An automatic calibration is performed using the Rosenbrock's optimization procedure
(Rosenbrock, 1960).
- 39 -
Chapter 4 Data used
4. Data used
4.1. NOPEX region
The model development is centred around data from the NOPEX experiment (Halldin et. al.,
1995 , 1998) performed north of the city of Uppsala in southern Sweden (Fig. 4.1.).
The annual precipitation in the NOPEX area
0° 10°E 20°E 30°E
fluctuates between 600 and 800 mm. Monthly
70°N
values has a minimum in August and a
maximum in February. 20 to 30 per cent of
65°N
the total annual precipitation falls as snow. A
snow cover exists from the middle of
Sweden Finland 60°N
Norwa
Oslo
November and has a duration of 100 to 110
Uppsala
Denmark
days on the average, but normally it is not
55°N
continuos throughout the winter. The mean
annual temperature for 1961-1990 at the
NOPEX area
station Uppsala is +6oC. The daily average
Figure 4.1 Localization of the NOPEX area
has a
maximum in July (+17oC) and a
minimum in February (-5oC). The vegetation
period lasts about 180 days (Seibert, 1994).
The NOPEX region is an area of small differences in elevation. The landscape was
formed during the Quaternary period. In the research area, the glacier left behind unsorted
deposits in ground moraines. The area is crossed by some in N-S oriented eskers reaching
a height of 20-50 m over the surrounding terrain. The eskers provide important
groundwater resources. Also outcrops of bedrock rise over the plain.
Till is the most common soil type in the area, particularly in the north. The thickness of the
till is decreasing from the western part with depths of 10 to 20 meters, to the eastern parts
with depths of 3 to 4 meters. The fine grained clay soils, together with areas of sandy and
silty materials, dominate in the south. The glacial clay reaches a depth of 15-100 meters. A
part of the area is covered by peatland having the largest extend in the northern part.
The NOPEX area has a heterogeneous surface cover, represented by coniferous and
mixed forest (57%), open land, mainly agricultural (35.8 %), mires (2.6 %), lakes
- 40 -
Chapter 4 Data used
(2.6%) and urbanized areas (2.0%) (evaluated from digital maps of the National Land
Survey of Sweden). The portion of forest increases from south towards north. Most of the
forest is coniferous.
4.2 Geographical data
Geographical data used includs a digital elevation model (DEM) with a resolution of 50
m and land cover data with 25 m resolution (both data sets from the National Land
Survey of Sweden), and comprehensive digitized soil map with a resolution of 2 km
(from Seibert, 1994).
The slope was calculated as the average slope within each grid cell of resolution 2x2 km
on the basis of the DEM. The land cover map included five classes (open land, forest,
lakes, swamp and urban areas). This information was aggregated to a grid net of 2x2 km
(Fig 4.2). The soil map included five classes: peat, clay, sand, till and shallow bedrock
and lakes (Fig. 4.2.).
Figure 4.2 Distribution of soil and land cover classes in the NOPEX area (2X2 km grid)
4.3. River runoff
The regular discharge observation network run by the Swedish Meteorological and
Hydrological Institute (SMHI) within the NOPEX area contains 11 standard gauging stations
in drainage basins covering the major part of the area. Daily values for the period 1981-1995
- 41 -
Chapter 4 Data used
from 10 of the stations were used. Table 4.1 and Figure 4.3 offer some information about
the basins.
Table 4.1 Runoff station used in ECOMAG
Station
Gränvad
Härnevi
Lurbo
Ransta
Sävja
Sörsätra
Stabby
Tärnsjö
Ulva
Kvarndam
Vattholma
River
168.0
305.0
124.0
198.0
727.0
612.0
6.6
14.0
950.0
Altitude
(m.a.s.l.)
min
15
15
15
15
5
35
18
55
5
max
75
105
75
105
75
145
55
105
95
284.0
25
65
Coordinates
X
Y
Station
number
Area
(km2)
Lillån
Örsundaån
Hågaån
Sävaån
Sävjaån
Sagån
Stabbybäcken
Stalbobäkken
Fyrisån
661637
662438
663271
662754
663592
662278
663200
666859
664509
155504
157112
160107
158926
160652
155498
159982
156333
159902
61-2217
61-2248
61-2245
61-2247
61-2243
61-2220
61-1742
54-2299
61-2246
Vattholmaån
665713
160736
61-244
Figure 4.3 The ten gauged river basins and five experimental basins in the NOPEX area
- 42 -
Chapter 4 Data used
4.4. Meteorological data
Daily values from 25 precipitation stations, 7 temperature stations, 5 stations for vapour
pressure deficit and 1 snow depth station for the period 1981-1995 from the climatic
network run by SMHI were used (see information in Tab. 4.2 and Fig. 4.4.).
Table 4.2 Climate stations used in ECOMAG
Station name
Station nr. Station name
Arlanda
9739
Österby
Drälinge
9759
Sala*
Enköping
9738
Skjorby
Fagerstad
10500
Skultuna
Films Kyrkby**
10714
Sundby
Folkärna**
10610
Tärnsjö
Gysinge
10617
Ultuna*
Hallstaberg
9639
Uppsala**
Harbo
10708
Uppsala flygplats**s
Hyvlinge
9745
Västerås Hasslö**
Köping
9631
Vattholma
Lisjö
9642
Vittinge
Nybyholm
9731
* The station is also measuring temperature
** The station is also measuring temperature and air humidity
s
The station is also measuring snow depth
- 43 -
Station nr.
9740
9655
9733
9644
9641
10612
9749
9751/2
9753
9635
10701
9754
Chapter 4 Data used
NOPEX area
Climate stations run by SMHI
Gysinge
Films Kyrkby
6680000
Folkärna
Tärnsjö
Harbo
6660000
Vattholma
Drälinge
Fagersta
Lisjö
6620000
6600000
1500000
Köping
1520000
Uppsala flygplats
Uppsala
Ultuna
Vittinge
Sala
6640000
Hyvlinge
Skultuna
Sundby
Hallstaberg
Österby
Enköping
Västerås-Haslö
Nybyholm Skjorby
1540000
1560000
1580000
1600000
Arlanda
1620000
Coordinates in Rikets Nät (RT 90)
10000
0
10000
20000
SMHI climate station
30000
METERS
Figure 4.4 Climate stations used in ECOMAG
4.5. Special NOPEX CFEs data
An extensive amount of hydrological data collected during the NOPEX concentrated
field efforts (CFE): CFE1 (27 May to 23 June 1994) and CFE2 (18 April to 14 July
1995) has been utilized in the process of model calibration and validation. The data were
taken from the SINOP database in the NOPEX project (Halldin and Lundin, 1994).
4.5.1. Synoptic runoff
Synoptic discharge measurements at 38 sites in the Fyrisån river basin were performed on
four occasions during recession (7-9 June 1994, 21-23 April 1995, 3-5- May 1995 and 2627 July 1995), and data from 12 of the sites were used (Tab. 4.3.). The measurements
followed the procedures described by Krasovskaia (1988).
- 44 -
Chapter 4 Data used
Table 4.3 Synoptic runoff measurements used in ECOMAG
St. number
3
4
7
9
12
14
15
16
17
41
39
19
River
Tegelsmoån
Toboån
Vendelån
Sävastabäcken
Vendelån
Vendelån
Tassbäcken
Velångsbäcken
Björklingeån
Fyrisån
Vattholmån
Björklingeån
X-coordinate
16605
16027
16017
16024
16066
15998
15986
15925
15925
15990
16074
15967
Y-coordinate
66865
66840
66654
66625
66563
66693
66712
66583
66583
66451
66571
66573
The discharge was calculated by the velocity-area-method. The velocity was measured
with a current meter at the depths of 0.2 and 0.8 times the total depth at several vertical
transects along a river cross section, on the average during 60 seconds. At every site two
estimations of runoff were done, and if the difference between the two estimations was
bigger than 5%, new measurements were done.
The observations in each campaign were performed during 2-3 days, and therefore the data
are not strictly speaking synoptic. However, since the measurements were performed
during recession period, this does not introduce a serious error.
4.5.2 Soil moisture and ground water
The sites for groundwater level and soil moisture measurements were chosen to represent
different geomorphologic units (hollow, slope and nose) within five small experimental
basins (see Fig. 4.3), These basins represent different soil and land use types. This data set
contains about 2000 individual measurements of groundwater levels and about 16000
measurements of soil moisture content (the measurements were also performed outside CFE
periods).
Soil moisture
Soil moisture content was measured in five small experimental basins: Marsta,
Damsarhällarna, Buddby, Östfora and Tärnsjö within the NOPEX area during CFE1 and
CFE2. Table 4.4 shows locations of observation points in each campaign for different
basins and the table indicates their soil and land cover type.
- 45 -
Chapter 4 Data used
Table 4.4 Number of observation points of soil moisture and groundwater level within
experimental drainage basins
Basin
Buddby
Dansarhellarna
Östfora
Östfora
Marsta
Tärnsjö
Number
points
Soil
moisture
151
75
50
25
50
of
observation
Soil type
Land use
till
till
till/sand
peat
clay
sand
forest
forest
forest
mire
open area
forest
Groundwater
16
16
19
15
-
The measurements were performed in June 1994 and April to October 1995. Only the data
from 1995 were used for simulations, since the record for 1994 was too short, and the soil
moisture content was almost constant throughout that period.
The measurements were carried out by the TDR-method. The method is described by
Tallaksen and Erichsen (1995).
The soil moisture was measured in the top 15 cm of the soil. Within each experimental
basin the locations of grid nets, each of 5x5 measuring points separated by two meters,
were carefully chosen to represent different geomorphologic units to get values
representative of the whole basin, comparable to simulated values in computational
elements.
Ground water
Groundwater level was measured manually in tubes in three experimental basins, as
indicated in Table 4.4. The measurements are performed in lines following a slope to
represent different geomorphologic units. However, due to difficulties in installing tubes in
till soils many of the tubes goes empty during dry conditions, especially those in the top of
the slopes.
4.5.3. Evapotranspiration
Two forest sites (Norunda and Siggefora) and three agricultural sites (Tisby, Marsta and
Lövsta) were equipped with eddy correlation instruments for flux measurements of latent
and sensible heat fluxes with a temporal resolution in the rate of 10 Hz. At two lakes micro-
- 46 -
Chapter 4 Data used
meteorological studies were performed (Tourula et. al., 1997). Heat energy exchange over
the lakes was measured by the eddy correlation techniques.
Data from local flux measurements at these sites distributed over the NOPEX region were
used to estimate weighted average regional fluxes using land cover data to obtain the weight
factors for spatial averaging (Gottschalk et al., 1998a).
4.6 Interpolation of meteorological data
The temperature and vapour pressure deficit observed at the stations were interpolated into
grid cells by inverse distance weighting.
4.6.1. Kriging interpolation of precipitation
The precipitation from 25 stations (see Tab. 4.2 and Fig. 4.4) were interpolated by kriging.
It is shown that a precipitation-field RA(X,t) can be modelled by two components, the
changing phenomenon RI(X,t) and the inner variability F(x,t). RI(X,t) is a binary function
identifying areas of precipitation and no precipitation. F(x,t) corresponds to precipitation
height. Two semivariograms must be estimated, one for binary precipitation and one for
precipitation height. First, the binary precipitation is interpolated. The interpolated value
will receive a value between 0 and 1, and for the interpolated RI(X,t) greater than 0.5 there
is precipitation and for the interpolated RI(X,t) less than 0.5 there is no precipitation. Then
the precipitation height is interpolated to the points of precipitation (Barancourt et al.,
1992). The semivarogram is chosen to be constant in time.
The identification of the semiovarigrams was done by Wai Kwok Wong from the
Department of Geophysics University of Oslo. Daily precipitation for the years 1961-1995
were used. For binary precipitation an exponential semivariogram with parameters: range
50 km, sill, 0.094 and nugget 0.0 was fitted. The semivariogram is shown in Fig. 4.5. For
interpolation of precipitation height an exponential semivariogram with parameters: range
70 km, sill 4.7 mm2 and nugget 0.0 mm2 was fitted (Fig. 4.6).
- 47 -
Chapter 4 Data used
Empirical and theoretical semivariogram for binary
precipitation. Exponential model, nugget = 0.0, sill = 4.7
and range = 50 km
0.14
Semivariance
0.12
0.1
0.08
Empirical
0.06
Theoretical
0.04
0.02
0
0
20
40
60
80
100
120
140
Distance (km)
Figure 4.5 Semivariogram for binary precipitation
Empirical and theoretical semivariogram for precipitation
height. Eksponetial model, nugget = 0.0 mm2, sill = 4.7 mm2
8 and range = 70 km
Semivariance (mm2)
7
6
5
4
Empircal
3
Theoretical
2
1
0
0
20
40
60
80
100
Distance (km)
Figure 4.6 Semivariogram for precipitation height
- 48 -
120
140
Chapter 5 Sensitivity analysis
5. Sensitivity analysis
The ECOMAG model was applied for simulating hydrological cycle processes at the
Fyrisån river basin in the biggest one in the NOPEX area in order to study
l
adequacy of the model structure and its possibilities to reflect the main features of
hydrological processes in a boreal environment,
l
role and importance of the model parameters in the common model structure,
l
sensitivity of the model to changes in the model parameters.
The trapezoidal version of the ECOMAG model was used for these tasks.
5.1 River basin schematisation
The Fyrisån cathment was divided into computational elements according to the procedures
described in section 3.4. Figures 5.1-5.3 shows the digitised map used. Figure 5.4 offers the
obtained landscapelements and river links, ordered hierarchically within the model. In this
application a simplified procedure of homogeneous meteorological zones was used for
interpolation of meteorological data into grid cells. Figure 5.5 shows spatial distribution of
the main parameters' classes.
Elevations:
m a.s.
m a.s.
m a.s.
m a.s.
m.a.s.
Rivers and lakes
Figure 5.1 Relief (a) and river network (b) for the Fyrisån catchment
- 49 -
Chapter 5 Sensitivity analysis
Forest
Open land
Rivers and lakes
Figure 5.2 Land cover map for the Fyrisån catchment
Sand
Till
Clay
Peat
Figure 5.3 Soil map for the Fyrisån catchment
- 50 -
Chapter 5 Sensitivity analysis
25
1
3
2
4
23
24
5
6
7
28
29
15
19
18
16 17
8
27
Vattholma
26
20
21
Ulva Kvarndamn
9
10
22
11
12
13
14
Figure 5.4 Element numbers for landscape and river elements in the Fyrisån catchment
Class assignation for landscape elements
Soil and groundwater zone classes Vegetation and landuse classes
Peat
Clay
Sand
Till
Slope (length/length)*100
Precipitation zones
Forest
Open land
Figure 5.5 Soil and land cover classes, slope and precipitation zones in the Fyrisån
catchment
5.2 Model run
Runoff data at Ulva Kvarndam during 15 years were used for the model calibration and
validation. The model runs started 1 August each year. The data for years 1981/82,
1985/86, 1987/88, 1990/91, 1992/93 and 1994/95 were used for calibration. These years
were chosen to reflect a big variation in the climatic conditions. The remaining data
were used for validation. Modeled snow depth for one element was calibrated and
- 51 -
Chapter 5 Sensitivity analysis
validated against snow depth measured at Uppsala flygplats. In addition, soil moisture
and groundwater measurements were used for adjustment of the soil water parameters.
The calibration was performed both by visual criterions, to fit the observed and
simulated curves, and using the Rosenbrock's optimization procedure of the NashSutcliffe criterion (3.54).
Totally 14 parameters were calibrated or adjusted, four parameters for snow depth, 3
for soil water measurements and seven parameters for river runoff data. Table 5.1 offers
values of the Nash-Sutcliffe criteria for the calibration years, and Figure 5.6 shows
results of the runoff simulations for these years. Table 5.2 and Figure 5.7 show results of
the model validation against runoff data for the years not included into calibration.
Year
R2
1981/82
0.87
1984/85
0.88
1987/88
0.88
1990/91
0.72
1992/93
0.85
1994/95
0.81
Average
0.84
Table 5.1 Nash-Sutcliffe criterion for calibrated years
Year
R2
1982/83
0.84
1983/84
0.77
1985/86
0.94
1986/87
0.90
1988/89
0.80
1989/90
0.95
1991/92
0.85
1993/94
0.78
Average
0.85
Table 5.2 Nash-Sutcliffe criterion for validated years
- 52 -
Chapter 5 Sensitivity analysis
Results for years used for calibration of ECOMAG
The time series start 01. August each year
T e m p . (oC )
P re c ip .( m m /d a y )
19 81/82
R u no ff ( m 3 /s )
T e m p . (oC )
P re c ip .( m m /d a y )
1984/85
R uno ff (m 3/s )
80
80
60
60
60
60
40
40
20
50
20
50
0
0
-2 0
-2 0
40
-4 0
40
-4 0
-6 0
-6 0
-8 0
30
-8 0
30
-1 0 0
-1 0 0
-1 2 0
20
-1 2 0
20
-1 4 0
-1 4 0
-1 6 0
-1 6 0
10
-1 8 0
10
-1 8 0
-2 0 0
0
-2 2 0
1
31
61
91
121
151
181
211
241
271
301
-2 0 0
0
D a y
361
T e m p . (oC )
P r e c ip .( m m / d a y )
1987/88
R u no f f ( m 3 /s )
331
1
31
61
91
12 1
1 51
1 81
2 11
24 1
2 71
30 1
-2 2 0
36 1 D a y s
T e m p . (oC )
P re c ip .( m m /d a y )
199 0/91
R u no f f ( m 3/s )
33 1
80
60
60
80
60
60
40
20
50
40
20
50
0
0
-2 0
40
-4 0
-2 0
40
-4 0
-6 0
-8 0
30
-6 0
-8 0
30
-1 0 0
-1 2 0
20
-1 0 0
-1 2 0
20
-1 4 0
-1 4 0
-1 6 0
10
-1 8 0
-1 6 0
10
-1 8 0
-2 0 0
0
1
31
61
91
121
151
181
211
241
271
301
-2 2 0
361 D a ys
T e m p . (oC )
P re c ip .( m m /d a y )
1992/93
R u no ff (m 3 /s )
331
-2 0 0
0
-2 2 0
1
31
61
91
121
151
181
211
241
271
301
80
60
60
50
60
40
20
50
0
0
-20
40
-40
-2 0
40
-4 0
-60
-80
30
-6 0
-8 0
30
-10 0
-12 0
20
-1 0 0
-1 2 0
20
-14 0
-1 4 0
-16 0
10
-18 0
-1 6 0
10
-1 8 0
-20 0
0
1
31
61
91
121
151
181
Observed runoff
211
2 41
271
301
331
-22 0
361 D a y s
D a ys
80
60
40
20
361
T e m p . (oC )
P re c ip .( m m /d a y )
1994/95
R u no f f (m 3 /s )
331
-2 0 0
0
1
Simulated runoff
31
61
91
121
151
181
Precipitation
211
241
271
301
331
-2 2 0
361 D a ys
Temperature
Figure 5.6 Observed and simulated runoff at Ulva Kvarndam, Fyrisån, for calibrated years
- 53 -
Chapter 5 Sensitivity analysis
Results for years used for validation of ECOMAG
The time series starts 01. August each year
T e m p . (oC )
P re c ip .( m m /d a y )
1 982/83
R u no ff (m 3 /s )
T e m p . (oC )
P re c ip .( m m /d a y )
1983/84
R u no f f (m 3 /s )
80
80
60
60
60
60
40
40
20
50
20
50
0
0
-2 0
40
-4 0
-20
40
-40
-6 0
-8 0
30
-60
-80
30
-10 0
-1 0 0
-1 2 0
20
-12 0
20
-14 0
-1 4 0
-1 6 0
10
-1 8 0
-16 0
10
-18 0
-2 0 0
0
-2 2 0
1
31
61
91
121
151
181
211
241
271
301
-20 0
361 D a y s
T e m p . (oC )
P re c ip .( m m /d a y )
1 98 5/86
R uno ff (m 3 /s )
331
0
1
31
61
91
121
151
181
211
241
2 71
301
80
80
60
60
60
60
40
40
20
50
20
50
0
0
-2 0
-2 0
40
-4 0
40
-4 0
-6 0
-6 0
-8 0
30
-8 0
30
-1 00
-1 00
-1 20
20
-1 20
20
-1 40
-1 40
-1 60
-1 60
10
-1 80
10
-1 80
-2 00
-2 00
0
1
31
61
91
121
151
181
211
241
271
301
-2 20
361 D a y s
T e m p . (oC )
P re c ip . ( m m /d a y )
198 8/89
R uno ff (m 3 /s )
3 31
0
1
31
61
91
121
151
181
211
241
271
301
60
80
60
60
40
40
20
50
20
50
0
0
-2 0
-2 0
40
-4 0
40
-4 0
-6 0
-6 0
-8 0
30
-8 0
30
-1 00
-1 20
20
-1 00
-1 20
20
-1 40
-1 40
-1 60
-1 60
10
-1 80
10
-1 80
-2 00
0
-2 20
1
31
61
91
121
151
181
211
241
2 71
301
-2 00
0
361 D a y s
T e m p . (oC )
P re c ip .( m m /d a y )
1991/92
R uno f f ( m 3 /s )
331
1
31
61
91
121
151
181
2 11
241
271
301
60
80
60
60
40
40
20
50
0
20
50
0
-2 0
40
-4 0
-2 0
40
-4 0
-6 0
-8 0
30
-6 0
-8 0
30
-1 00
-1 20
20
-1 0 0
-1 2 0
20
-1 40
-1 4 0
-1 60
10
-1 80
-1 6 0
10
-1 8 0
-2 00
0
-2 20
1
31
61
91
121
151
181
Observed runoff
211
241
271
301
331
-2 20
361 D a y s
T e m p . (oC )
P r e c i p .( m m / d a y )
1993 /94
R u no f f ( m 3 /s )
331
80
60
-2 20
361 D a y s
T e m p . (oC )
re c ip .( m m /d a y )
1989/90
R uno f f ( m 3 /s )
331
80
60
-22 0
361 D a y s
T e m p . ( oC )
P re c ip .( m m /d a y )
1 98 6/87
R u no f f ( m 3 /s )
331
-2 0 0
0
361 D a y s
1
Simulated runoff
31
61
91
121
151
181
Precipitation
211
2 41
271
3 01
331
-2 2 0
3 61 D a y s
Temperature
Figure 5.7 Observed and simulated runoff at Ulva Kvarndam, Fyrisån, for validated years
The presented simulation results shows the ECOMAG model gives in general a good
- 54 -
Chapter 5 Sensitivity analysis
agreement between the observed and simulated discharges. This justifies use
investigation of the river basin hydrological cycle processes in the NOPEX area.
5.3 Model sensitivity
The model sensitivity has been tested by estimating the changes in simulated
hydrological cycle characteristics induced by the changes in of the model parameters.
Numerical experiments show that a number of parameters are of primer importance for
satisfactory results of runoff simulations. The processes surface and subsurface flow
formation are defined by three parameters to a large extent horizontal hydraulic
conductivity in horizon A, vertical hydraulic conductivity in horizon B and parameter of
potential evaporation. Combination of these parameter values governs the amount of
water that penetrates into deeper soil layers, evaporates, and flows as subsurface runoff.
The thickness of soil horizon A controls the response of the catchment. The thinner
horizon A is made, the sharper is the runoff response to precipitation. The simulated
dynamics of soil moisture in horizon A show also a faster response on changes in
evapotranspiration and precipitation when the thickness of the horizon A decreases. The
thickness of horizon A also controls the volume of the quick return surface flow during
storm rainfall.
Using data from literature as a first approximation for the soil water constants allows to
get dynamics of soil moisture close to the observed. As a rule, there is only a difference
in the mean values of simulated and observed soil moisture content. This difference can
be easily assessed by tuning both the wilting point and field capacity constants.
Horizontal hydraulic conductivity in a groundwater zone controls the formation of base
groundwater flow during recession periods.
One of the important parameters is also the maximal retention storage, used in the
Popov's formula. Increasing this parameter, might help to lower down too high
estimated flood peaks.
Snow cover parameters were calibrated using data of snow cover depth at Uppsala
flygplats (Fig. 5.8). Snow depth was measured in a point, and these values were compared
to the snow depth simulated for a landscape element with an area of several square
- 55 -
Chapter 5 Sensitivity analysis
kilometers. Comparison with snow water equivalent data, measured by coursing, would be
more adequate in this case as the snow depth in point values do not reflect micro-scale
variability of snow cover. However, there is no such information for the NOPEX area.
That is why the calibration results are of a limited value.
The following snow parameters have been calibrated: critical temperature snow/rain,
density of new snow, parameter of snow compaction and degree-day factor. The critical
temperature snow/rain controls the processes of snow accumulation, while the degreeday factor defines the intensity of snow melting. When snow cover data are not at hand,
these parameters may be estimated on the basis of river runoff information with
sufficient accuracy.
The density of new snow and the parameter of snow compaction are important only for
simulation of the snow cover depth. However, indirectly they control the processes of
soil freezing as well. Soil frost is common during spring runoff formation in many
boreal regions, e.g. for the central part of Russia. However, in the Nordic countries it is
often of a minor importance for spring runoff formation (Bergstrom, 1976, Vehvilainen,
Motovilov, 1989). The main reasons for that are the large content of both sand and stone
components in the till soil, its high hydraulic conductivity, as a rule, small frost depth. A
weak sensitivity of the model to the frost conditions in the NOPEX area allows to assign
the values of both snow and soil frost parameters taken from literature.
- 56 -
Chapter 5 Sensitivity analysis
Observed and simulated snow depth
The time series starts 01. August each year
S n o w d e p th ( c m )
S n o w d e p th ( c m )
1981/82
70
70
60
60
50
50
40
40
30
30
20
1 9 8 2 /8 3
20
10
10
D a ys
0
1
31
61
91
121
151
181
S no w d e p th ( c m )
211
241
271
301
331
D a ys
0
361
1
31
61
91
121
151
S n o w d e p th ( c m )
1 98 3/8 4
70
70
60
60
50
50
40
40
30
30
181
211
241
271
301
331
361
241
271
301
331
361
241
271
301
331
361
241
271
301
33 1
361
241
2 71
301
331
3 61
241
271
301
331
361
241
271
301
331
361
1984/85
20
20
10
10
D a ys
0
1
31
61
91
121
151
181
S n o w d e p th ( c m )
2 11
2 41
2 71
301
331
D a ys
0
1
361
31
61
91
121
151
S n o w d e p th ( c m )
1985/86
70
70
60
60
50
50
40
40
30
30
20
181
211
1 9 8 6 /8 7
20
10
10
D a ys
0
1
31
61
91
1 21
151
S n o w d e p th ( c m )
181
211
2 41
271
301
3 31
D a ys
0
3 61
1
31
61
91
121
151
S n o w d e p th ( c m )
1987/88
70
70
60
60
50
50
40
40
30
30
20
181
211
1988/89
20
10
10
D a ys
0
1
31
61
91
121
151
S n o w de pth ( c m )
181
211
241
271
301
331
D a ys
0
361
1
31
61
91
12 1
151
S n o w d e p th ( c m )
19 89/9 0
70
70
60
60
50
50
40
40
30
30
20
181
21 1
1 9 9 0 /9 1
20
10
10
D a ys
0
1
31
61
91
121
151
S no w d e pth (c m )
1 81
211
241
2 71
301
3 31
D a ys
0
3 61
1
31
61
91
1 21
151
S n o w d e p th ( c m )
1991/92
70
70
60
60
50
50
40
40
30
30
20
181
2 11
1992/93
20
10
D a ys
0
10
D a ys
0
1
31
61
91
121
151
S n o w d e p th ( c m )
18 1
211
24 1
271
301
331
361
1
31
61
91
121
151
S n o w d e p th (c m )
1 9 9 3 /9 4
70
70
60
60
50
50
40
40
30
30
181
211
1994/95
20
20
10
10
D a ys
0
1
31
61
91
121
151
181
2 11
2 41
Observed snow depth
271
301
3 31
3 61
D a ys
0
1
31
61
91
121
151
181
211
Simulated snow depth
Figure 5.8 Observed snow depth at Uppsala flygplats and simulated by ECOMAG snow depth in
landscape element 58
Numerical experiments have also shown that the model is not much sensitive to changes in
vertical hydraulic conductivity of horizon A. This parameter defines the process of the
- 57 -
Chapter 5 Sensitivity analysis
surface runoff formation. Evidently, such phenomenon has of a secondary significance in the
NOPEX area mainly covered by forest and soils of high hydraulic conductivity.
The surface roughness has no importance since the temporal resolution is as coarse as 24 h.
For simulating runoff at this time scale, the effective rainfall is much more important than
surface water transformation.
Sensitivity analysis performed for the Fyrisån river basin indicates possibilities both for
improving and simplification of the model structure for better adapt it to conditions of the
NOPEX area. For example numerical experiments have shown that the model is not very
sensitive to the majority of parameters for horizon B. This soil horizon has function of
transition layer between top soil horizon and groundwater zone. Such soil layer is important
when groundwater is deep and there is a week connection between surface water and
groundwater zone. In the NOPEX experimental watersheds a typical depth of the
groundwater level is about 1 - 2 m, which facilitates interaction between surface and ground
water. In this case, it is possible to exclude soil horizon B from the model structure
essentially decreasing the amount of model parameters with the stability of the model
increasing. This has been done when simulating hydrological cycle chracteristics for the
whole NOPEX area.
- 58 -
Chapter 6 Model validation
6. Model validation
The ECOMAG model has been applied for simulation of hydrological cycle processes for
the whole NOPEX area. A validation of the model has been performed aimed at testing its
ability to satisfy to the demands for a macro hydrological model. One of the main objectives
of this exercise was to find a global parameters set that could be used everywhere within the
NOPEX region.
The model was first calibrated against runoff for three basins with one global set of
parameters, then the soil parameters were adjusted against soil moisture and groundwater
level data from five small experimental subbasins. After that the model was validated
against:
•
runoff in six other basins that were not used for calibration,
•
synoptic measurements of runoff.
•
regional flux estimates (evapotranspiration) for the whole NOPEX region.
The spatial distribution was obtained by dividing of an area into a square grid network with
the resolution 2x2 km, a size that was defined in the scale study (see Chapter 2). Each cell
has been considered as a representative elementary area (REA) or landscape unit (element).
In the results of the sensitivity analysis (Chapter 5), each landscape element was divided
vertically in four layers: snow cover layer, surface layer and two soil layers (horizon A and
groundwater zone).
Calibration followed the procedure described in Chapter 3.6 and data described in Chapter 4
were used for calibration of parameters and model validation.
Calibration was done in three steps. First, the model parameters, related to the soil and
land cover classes, were calibrated against discharge data. This calibration was done
simultaneously for three basins with different conditions of runoff formation to find a
global parameter set for the whole NOPEX area. The calibration was performed using
the Rosenbrock's optimisation procedure. The optimisation criterion was calculated as
the mean value of R2 for these river basins during the optimisation period. In the second
step the soil water parameters for different soil types were adjusted using soil moisture
and groundwater level data for five experimental river basins in the NOPEX area for
- 59 -
Chapter 6 Model validation
1995 including CFE period. These basins were considered as the REA units
representing different landscapes. The adjustment was carried out by a visual
comparison of simulated and observed dynamics of soil moisture and groundwater
levels. In a third step, the remaining model parameters were calibrated again against
runoff in the same way as in the first step.
6.1 Runoff at gauging stations
Calibration of the model parameters against runoff was carried out in three river basins,
different in size and conditions for runoff formation: Fyrisån (at Ulva Kvarn) with an
area of 950 km2; Lillån (at Gränvad) with an area of 168 km2 and Stabbybäcken (at
Stabby) with an area of 6.2 km2. Seven years of observation were used for the
calibration: 1986-1993. This period was the most "difficult" one in the available sample
for modeling, with continued years with low annual flow and unstable winters. The
remaining seven years were used for the validation. Satisfactory agreement between the
observed and simulated runoff has been obtained (see Fig. 6.1 and Tab. 6.1).
Numerical experiments have shown that the calibration results might be improved
slightly if the parameters of the model were calibrated separately for each basin. The
parameter values were naturally different for different basins in this case. However, a
good agreement between the observed and simulated values with the use of separately
calibrated parameters does not guarantee that they can be assigned a physical meaning
or that they can be transfered to other basins. A good model performance can be
obtained for many different combinations of optimised parameters (Beven and Binley,
1992). It was easy to check that the parameters obtained for one basin did not provide a
good performance of the model when applied to another one.
When a global set of parameters is required for a number of basins with different
conditions of flow formation, the possibility of finding the “correct” values physically
reasonable is greater. This conclusion can be drawn studying the values of R2 offered
by Table 6.2 for the simulation with the global parameters. Fig. 6.2a and 6.2b show
examples of simulations for all nine basins for two years: one with a good agreement
between the observed and simulated runoff (1984-85), and with a poor agreement
(1994-95).
- 60 -
Chapter 6 Model validation
Year 1981/82
Q (m3/s)
Stabbybäcken
Lillån
Fyrisån
35
50
30
Year 1981/82
Q (m3/s)
Year 1981/82
Q (m3/s)
60
0.9
0.8
0.7
25
40
0.6
20
0.5
30
0.4
15
0.3
20
10
10
5
0
0
Days
1
61
1 21
1 81
241
301
361
0.1
Days
1
Year 1982/83
Q (m3/s)
0.2
61
1 21
241
301
Days
1
61
1 21
1 81
241
301
361
301
361
Year 1982/83
Q (m3/s)
0.9
35
0.8
30
50
0
361
Year 1982/83
Q (m3/s)
60
1 81
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
0.2
10
5
0
Days
1
61
1 21
1 81
241
301
361
Days
1
Year 1983/84
Q (m3/s)
0.1
0
61
1 21
35
50
30
241
301
0
Days
1
361
Year 1983/84
Q (m3/s)
60
1 81
61
121
181
241
Year 1983/84
Q (m3/s)
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
10
5
0
0
Days
1
61
121
1 81
241
301
0.1
Days
1
361
Year 1984/85
Q (m3/s)
0.2
61
1 21
1 81
241
301
Year 1984/85
Q (m3/s)
0
61
121
35
0.9
50
30
0.8
181
241
301
361
301
361
301
361
301
361
301
361
Year 1984/85
Q (m3/s)
60
0.7
25
40
Days
1
361
0.6
20
0.5
30
20
10
15
0.4
10
0.3
0.2
5
0
Days
1
61
1 21
1 81
241
301
Days
1
361
Year 1985/86
Q (m3/s)
0.1
0
61
1 21
35
50
30
241
301
0
361
Days
1
61
121
1 81
241
Year 1985/86
Q (m3/s)
Year 1985/86
Q (m3/s)
60
1 81
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
10
0.2
5
0
Days
1
61
1 21
1 81
241
301
361
Days
1
Year 1986/87
Q (m3/s)
0.1
0
61
1 21
35
50
30
241
301
0
Days
1
361
Year 1986/87
Q (m3/s)
60
1 81
61
121
1 81
241
Year 1986/87
Q (m3/s)
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
10
0.2
5
0
Days
1
61
121
1 81
241
301
361
Days
1
61
1 21
60
35
50
30
1 81
241
301
61
121
1 81
241
Year 1987/88
Q (m3/s)
0.9
0.8
0.7
0.6
20
0.5
15
0.4
30
20
Days
1
25
40
0
361
Year 1987/88
Q (m3/s)
Year 1987/88
Q (m3/s)
0.1
0
0.3
10
0.2
10
5
0
Days
1
61
1 21
1 81
241
301
361
Qobs erved
0.1
0
Days
1
61
1 21
1 81
241
301
361
Q s imulated
- 61 -
0
Days
1
61
1 21
181
241
Chapter 6 Model validation
Year 1988/89
Q (m3/s)
Stabbybäcken
Lillån
Fyrisån
35
50
30
Year 1988/89
Q (m3/s)
Year 1988/89
Q (m3/s)
60
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
10
0.2
5
0
Days
1
61
121
181
241
301
Days
361
1
Year 1989/90
Q (m3/s)
0.1
0
61
1 21
1 81
241
301
61
1 21
35
0.9
50
30
0.8
1 81
241
301
361
301
361
301
361
301
361
301
361
301
361
301
361
Year 1989/90
Q (m3/s)
60
0.7
25
40
Days
1
Year 1989/90
Q (m3/s)
0
361
0.6
20
0.5
15
0.4
30
20
0.3
10
0.2
10
5
0
Days
1
61
1 21
1 81
241
301
Days
361
1
Year 1990/91
Q (m3/s)
0.1
0
61
1 21
181
241
301
35
0.9
50
30
0.8
121
1 81
241
Year 1990/91
0.7
25
0.6
20
0.5
15
0.4
30
20
61
Q (m3/s)
60
40
Days
1
Year 1990/91
Q (m3/s)
0
361
0.3
10
0.2
10
5
0
0
Days
1
61
1 21
1 81
241
301
Year 1991/92
Q (m3/s)
0.1
Days
1
361
61
1 21
35
50
30
241
301
0
361
Days
1
Year 1991/92
Q (m3/s)
60
1 81
61
1 21
1 81
241
Year 1991/92
Q (m3/s)
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
0.3
20
10
10
5
0
0
Days
1
61
1 21
1 81
241
301
361
0.1
Days
1
Year 1992/93
Q (m3/s)
0.2
61
121
181
241
301
Year 1992/93
Q (m3/s)
0
35
0.9
50
30
0.8
25
0.5
15
0.4
0
0
Days
1
61
121
181
241
301
Year 1993/94
Q (m3/s)
0.1
Days
61
1 21
35
50
30
1 81
241
301
0
Days
1
361
Year 1993/94
Q (m3/s)
60
Year 1992/93
0.2
1
361
241
0.3
10
5
1 81
0.6
20
10
1 21
0.7
30
20
61
Q (m3/s)
60
40
Days
1
361
61
1 21
1 81
241
Year 1993/94
Q (m3/s)
0.9
0.8
0.7
25
40
0.6
20
0.5
15
0.4
30
20
0.3
10
10
5
0
0
Days
1
61
1 21
1 81
241
301
0.1
Days
1
361
Year 1994/95
Q (m3/s)
0.2
61
121
35
50
30
241
301
61
1 21
1 81
241
Days
Year 1994/95
Q (m3/s)
0.8
0.7
0.6
20
0.5
15
0.4
30
20
1
0.9
25
40
0
361
Year 1994/95
Q (m3/s)
60
1 81
0.3
10
0.2
10
5
0
Days
1
61
1 21
181
241
301
361
Qobs erved
0.1
0
Days
1
61
121
1 81
241
301
361
0
Days
1
61
1 21
1 81
241
Q s imulated
Figure 6.1 Observed and simulated runoff for riverbasins used for calibration
- 62 -
Chapter 6 Model validation
a) 1984/85
Fyrisån year 1984/85
Q (m3/s)
Sagån year 1984/85
Q (m3/s)
60
70
50
60
50
40
40
30
30
20
20
10
10
0
Days
1
61
1 21
1 81
241
301
Days
1
61
1 21
1 81
241
301
361
Örsundaån year 1984/85
Q (m3/s)
Lillån ear 1984/85
Q (m3/s)
0
361
50
35
45
30
40
25
35
30
20
25
15
20
10
15
10
5
5
0
Days
1
61
1 21
181
241
301
Days
1
61
1 21
181
241
301
361
301
361
Sävaån year 1984/85
Q (m3/s)
Hågaån year 1984/85
Q (m3/s)
0
361
25
16
14
20
12
10
15
8
10
6
4
5
2
0
Days
1
61
121
1 81
241
301
Sävjaån year 1984/85
Q (m3/s)
0
Days
1
361
61
121
241
Stalbobäcken year 1984/85
Q (m3/s)
60
1 81
1.2
50
1
40
0.8
30
0.6
20
0.4
10
0.2
0
Days
1
61
1 21
181
241
301
Days
1
Stabbybäcken year 1984/85
Q (m3/s)
0
361
61
Q (m3/s)
0.9
1 21
1 81
241
301
361
Sum of all river basins year 1984/85
300
0.8
250
0.7
0.6
200
0.5
150
0.4
0.3
100
0.2
50
0.1
0
0
Days
1
61
121
181
Q obs erved
241
301
361
Days
1
61
Q s imulated
- 63 -
1 21
181
241
301
361
Chapter 6 Model validation
b) 1994/95
Fyrisån year 1994/95
Q (m3 /s)
Q (m 3/s)
30
60
25
50
20
40
15
30
10
20
5
Sagån Year 1981/82
10
0
Day s
1
61
1 21
1 81
241
301
Day s
1
Lillån year 1994/95
Q (m3/s)
0
361
61
20
18
16
18
14
14
12
12
10
8
10
6
6
4
2
4
1 81
241
301
361
Örsundaån year 1994/95
Q (m 3/s)
20
1 21
16
8
2
0
Days
1
61
1 21
1 81
241
301
Day s
1
61
1 21
1 81
241
301
361
Sävaån year 1994/95
Q (m 3/s)
Hågaån year 1994/95
Q (m3/s)
0
361
12
9
8
10
7
8
6
5
6
4
4
3
2
2
1
0
Days
1
61
1 21
1 81
241
301
Days
1
61
1 21
1 81
241
301
361
Stalbobäcken year 1994/95
Q (m3/s)
Sävjaån year 1994/95
Q (m 3/s)
0
361
0.4
30
0.35
25
0.3
20
0.25
0.2
15
0.15
10
0.1
5
0.05
0
0
Days
1
61
1 21
1 81
241
301
Q (m 3/s)
Stabbybäcken year 1994/95
Q (m 3/s)
Days
1
361
0.45
140
0.4
120
0.35
61
1 21
1 81
241
301
361
Sum of all river basins year 1994/95
100
0.3
0.25
80
0.2
60
0.15
40
0.1
20
0.05
0
Days
1
61
1 21
1 81
Q obs erved
241
301
0
Days
1
361
61
1 21
1 81
241
301
361
Q s imulated
Figure 6.2 Observed and simulated runoff at six basins not used for calibration of
regional parameters and three basins used for calibration. 1984/85 (a) and 1994-95 (b).
- 64 -
Chapter 6 Model validation
Table 6.1 Model performance (R2) for the gauged river basins in the NOPEX area
Basin
Year
1981/82
Fyr
Sag
Lil
Örs
Håg
Sva
Svj
Stl
Stb
Total
0.73
0.76
0.60
0.64
0.72
0.72
0.83
0.88
0.64
0.75
0.76
0.83
0.65
0.73
0.14
0.29
0.58
0.72
0.79
0.81
1982/83
0.81
0.84
0.56
0.60
0.62
0.70
0.52
0.73
0.43
0.83
0.62
0.80
0.53
0.61
0.70
0.72
0.59
0.60
0.76
0.80
1983/84
0.72
0.78
0.57
0.61
0.65
0.81
0.64
0.72
0.56
0.82
0.69
0.75
0.50
0.63
0.84
0.83
0.61
0.66
0.74
0.78
1984/85
0.78
0.84
0.83
0.86
0.75
0.90
0.84
0.94
0.77
0.96
0.90
0.96
0.82
0.93
0.75
0.88
0.68
0.93
0.90
0.95
1985/86
0.83
0.88
0.50
0.28
0.69
0.74
0.80
0.81
0.76
0.81
0.82
0.91
0.86
0.90
0.30
0.20
0.57
0.81
0.88
0.90
1986/87
0.88
0.94
0.48
0.46
0.57
0.71
0.69
0.72
0.53
0.71
0.73
0.84
0.69
0.77
0.45
0.54
0.54
0.75
0.77
0.79
1987/88
0.86
0.91
0.48
0.51
0.72
0.85
0.76
0.85
0.56
0.66
0.75
0.80
0.66
0.77
0.75
0.83
0.57
0.77
0.77
0.83
1988/89
0.70
0.84
0.25
0.33
0.32
0.46
0.22
0.60
0.26
0.64
0.27
0.64
0.19
0.58
0.62
0.76
0.26
0.44
0.48
0.68
1989/90
0.91
0.93
0.69
0.76
0.66
0.77
0.77
0.85
0.70
0.92
0.80
0.89
0.83
0.88
0.85
0.90
0.75
0.91
0.86
0.90
1990/91
0.77
0.92
0.35
0.19
0.62
0.84
0.62
0.74
0.53
0.62
0.71
0.78
0.60
0.65
0.60
0.68
0.71
0.85
0.72
0.75
1991/92
0.80
0.87
-
0.60
0.77
0.52
0.70
0.19
0.44
0.57
0.80
0.63
0.77
0.57
0.58
0.44
0.70
0.81
0.91
1992/93
0.90
0.94
-
0.74
0.78
0.71
0.73
0.64
0.78
0.65
0.72
0.78
0.85
0.73
0.79
0.76
0.85
0.84
0.87
1993/94
0.70
0.87
-
0.40
0.76
0.39
0.71
0.59
0.74
0.55
0.75
0.61
0.80
0.46
0.50
0.54
0.75
0.67
0.88
1994/95
0.72
0.78
-
0.61
0.78
0.53
0.91
0.24
0.70
0.69
0.91
0.69
0.84
0.67
0.66
0.65
0.95
0.80
0.92
1981-91
0.81
0.87
0.69
0.81
0.75
0.83
0.63
0.81
0.77
0.86
0.71
0.80
0.57
0.67
0.61
0.78
0.81
0.85
1981-95
0.81
0.87
0.67
0.80
0.71
0.83
0.60
0.80
0.76
0.85
0.71
0.81
0.59
0.68
0.62
0.79
0.82
0.88
0.57
0.60
-
Numenator - R2 daily values
Denumenator - R2 monthly values
0.00 - data included in calibration.
0.00 - validation.
According to common practice (e.g. Popov, 1979) simulation results are considered to
be good for values of R2 ≥0.75, and satisfactory R2 values between 0.75 and 0.36.
According to this gradation good simulation results, based on daily observations, were
- 65 -
Chapter 6 Model validation
obtained for Fyrisån, Sävaån and for the total gauged area of all the basins. For the rest
of the basins the agreement was satisfactory. The values of R2 obtained as the average of
monthly values were good for all the basins with the exception of Sagån and
Stalbobäcken, where they were satisfactory. However, the gradation referred to is, as a
rule, applied for individually calibrated basins, while in this study a global set of
parameters for the whole NOPEX area was used. For this latter case there is yet no
common practice concerning the reasonable accuracy demands.
Comparing the diagrams in Figs. 6.1 and 6.2 it can be noted that the simulated curves
are as a rule sharper than the observed ones. This can be explained by the fact that at
this stage the actual amount of water delivered to the river net from REA elements is
calculated and the flow transformation in the channel is not yet considered. For small
and medium-sized basins with a lag time of less than the one day, this does not make
any significant difference. A consideration of the transformation in the channel would
smooth the hydrographs and possibly increase the R2 for daily values in the larger
basins. It should also be noted, that for the purpose of coupling of hydrological and
meteorological models, the instantaneous values of the hydrological cycle
characteristics are required and, in particular, the amount of water delivered to the river
net. The agreement between the simulated and observed discharge at the outlet sites of
river basins including channel transformation is of a secondary importance in this case.
The R2 efficiency criterion reflects the agreement between observed and calculated
hydrographs, i.e. the dynamics of the discharge and not necessarily the agreement
between the observed and calculated flow volumes. Table 6.2 shows the results of a
comparison of the simulated water balance characteristics with the estimated values by
Seibert (1994) on the basis of observed data. It is seen that the precipitation values used
in simulations and those defined by Seibert are different. This discrepancy is explained
by the difference in the method of calculation of areally averaged precipitation for the
basins.
Seibert obtained the mean values of precipitation for the river basins by
multiplying the values of precipitation at each gauging station by individual correction
factors for wind and moistening and the precipitation values for each basin were
obtained by weighted averages of the observations at the nearest stations. Here a single
correction factor of 1.2 was used for all the stations with precipitation less than 40
- 66 -
Chapter 6 Model validation
mm/day and for those with higher daily precipitation a correction factor of 1.0 was
used. Calculation of areally averaged precipitation for the basins was done by means of
interpolation of the observations to 2 km grid cells with the use of kriging.
Table 6.2 Annual water balance of the gauged river basins in the NOPEX area (1981-1991)
according to Seibert (1994): observed precipitation (P*), observed runoff (Q*) and
evapotranspiration as resudial term (E*); and according to ECOMAG modelling: observed
precipitation (P), calculated evapotranspiration (E) and calculated runoff (Q). ∆Q = Qmodel Qobserved
Basin
Fyrisån
Sagån
Lillån
Örsundaån
Hågaån
Sävaån
Sävjaån
Stalbobäcken
Stabbybäcken
Station
Ulva Kvarn
Sörsätra
Gränvad
Härnevi
Lurbo
Ransta
Sävja
Tärnsjö
Stabby
P*
(mm)
755
729
726
738
750
734
732
733
639
E*
(mm)
534
384
481
448
436
456
488
462
458
Q*
(mm)
222
346
245
290
313
278
245
272
235
P
(mm)
731
720
709
715
716
715
719
728
709
E
(mm)
502
484
461
468
450
464
464
472
463
(mm)
(mm)
∆Q
|∆
∆Q/Q*|
229
237
249
248
265
251
254
257
246
7
-109
4
-42
-48
-27
9
-15
11
3
31
2
14
15
10
4
6
5
Q
(%)
It is seen in Tab. 6.2 that the simulated values were unsatisfactory for Sagån. No
obvious reasons for such a discrepancy were found as runoff formation conditions in
Sagån are similar to those in other river basins in the NOPEX area, in particular Fyrisån,
for which the agreement was good. At the same time, the difference between the
measured average annual values for Fyrisån and Sagån is 150 mm for evaporation and 124 mm for runoff. One of the possible reasons for the discrepancy may be the poor
quality of the observed data, caused by inaccuracies in the rating curve. In any case, the
observed data for Sagån need a thorough further analysis.
6.2 Synoptic runoff
An idea about the spatial variability of river runoff can be obtained through synoptic
runoff measurements (Krasovskaia, 1988). Four runoff surveys were performed at 38
sites during flow recession in the: two for wet conditions and two for dry conditions. It
was possible to identify 12 of these sites along the river network used in the model (Fig.
6.3a). Fig 6.3b shows a comparison of the simulated and measured river runoff for these
12 sites on four measurement occasions. In general the agreement is good especially
bearing in mind that the synoptic data have not at all been involved in the calibration.
- 67 -
Chapter 6 Model validation
The range of variation and the variance are similar for both data sets. A more detailed
analysis reveals certain discrepancies, which hardly can be fully explained. They might
have been caused by inaccuracy in determination of the areas of small tributaries and
the spatial interpolation of meteorological characteristics, especially rainfall. Besides,
the synoptic runoff measurements, describing instantaneous discharge values, were
carried out within a period of two or three days. The simulated discharges, on the other
hand, give the average for a certain day, which might also cause discrepancies.
Comparison of measured and simulated discharges
100
Observed discharges (m^3/s)
Basin Fyrisån
Synoptic measurements
10
1
0.1
Simulated discharges (m^3/s)
0.01
0.01
0.1
1
10
100
Observed discharges (m^3/s)
30
25
20
15
10
5
Simulated discharges (m^3/s)
0
0
5
10
15
20
25
30
Figure 6.3 Validation of the model performance; a) synoptic runoff observations at 12 sites in the
Fyrisån river and b) comparison with those modelled from four different campaigns
6.3. Soil moisture content and groundwater levels
Soil moisture content and groundwater levels were observed in a number of small
experimental basins within the NOPEX area during CFE1 and CFE2 (the measurements
were performed also outside CFEs periods). The observation points were chosen to represent
different geomorphologic units (hollow, slope and nose), soil types (till, clay, sand) and land
use (open area, forest, mire) found in the area. Simultaneous campaign measurements were
performed in these experimental basins. The data obtained within each such basin were
- 68 -
Chapter 6 Model validation
averaged and taken as a characteristic of an assumed REA. These data were used for the
adjustment of soil water parameters at the stage of model calibration. Table 4.4 offers
information about the number of observation points in each basin including their soil and
land surface cover type.
The modelled and averaged observed soil moisture content are in good agreement (Fig. 6.4).
It can be noted, that soil moisture measurements were carried out in the top soil layer, 15-20
cm thick on the average, while soil moisture content has been modelled for an averaged 4060 cm thick soil layer (horizon A). This difference make observed soil moisture content
much more sensitive to external factors (rain, evaporation) than the more integrated
modelled results, resulting discrepancies between the simulated and observed values.
The simulated groundwater levels are also in a good agreement with the averaged
values of the groundwater level measurements (Fig. 6.4). The agreement is, however,
not as good as for the soil moisture content. This is mainly explained by the fact that the
groundwater observation tubes did not represent the variability in a REA well enough,
partly due to technical problems of installation of groundwater tubes in till soil. In
particular, groundwater tubes in nose positions went dry during longer periods without
rain. This leads to a systematical underestimating of the average groundwater depth.
The modelled groundwater depth is accordingly deeper than the observed averages for
till soils during dry conditions.
- 69 -
Chapter 6 Model validation
Soil moisture, Östfora
Soil moisture, Dansarhällarna
Ground water level, Östfora
Ground water level, Dansarhällarna
Soil moisture, Marsta
Soil moisture, Buddby
Ground water level, Buddby
Soil moisture, Tärnsjö
Figure 6.4 Observed and modelled soil moisture content groundwater levels, each cross
represents a spatial average, compare Table 4.4.
- 70 -
Chapter 6 Model validation
6.4 Vertical flux exchange and water balance
NOPEX concentrated field efforts during May - June 1994 and April - July 1995 provide
high quality data sets for estimation of vertical fluxes, especially evapotranspiration (latent
heat flux). Measurements were performed at a range of scales, in time and space, on the
ground and from airborne and space platforms. In many contexts these different flux
estimates are not directly comparable due to differences in temporal and spatial scales. Local
measurements from masts allow calculation of “point” estimates of heat fluxes from lakes
and land surfaces (forest, mires, agricultural land) using eddy correlation, profile and sap
flow methods. During events with airborne and radio-sounding measurements, estimates of
the fluxes are also available along flight transects. Regional flux estimates of sensible and
latent heat for the whole and/or parts of the area are available from meso-scale climate
modelling. A systematic evaluation and critical comparison of the different estimates
including those of the ECOMAG model have been performed (Gottschalk et al., 1998a).
The analysis of data within the NOPEX project is in an early stage and the
methodological problem of comparison of different flux estimates has been stressed in
this comparison.
Table 6.3 shows components of the water balance estimated with ECOMAG for the
whole NOPEX area during CFE1 and CFE2. The calculations show that during CFE1
the modelled evaporation was 10 mm higher than the observed precipitation and the
runoff was as low as 6 mm. During the longer CFE2 period the evaporation and runoff
parts of the water balance were 156 mm higher than the precipitation. This difference
between precipitation on one hand and evaporation and runoff on the other during both
CFE periods is balanced by a decrease is the soil moisture and groundwater supply,
accumulated before during snowmelt and rain in winter and spring.
Table 6.3 Water balance of the NOPEX area during CFE1 and CFE2 according to ECOMAG.
Period
Precipitation
(mm)
Evaporation
(mm)
Runoff
(mm)
∆W
(mm)
CFE1 27 May - 23 June 1994
64
74
6
-16
CFE2 18 April - 14 July 1995
215
289
82
-156
∆W - Water supply changes in soil and groundwater zone.
- 71 -
Chapter 6 Model validation
Fig. 6.5a and 6.5b illustrate the patterns of the main hydrologic components for CFE1
and CFE2 periods, respectively. The components show relatively large variation across
space. Precipitation has the smoothest variation, which is mainly explained by the
interpolation method (kriging). An evaluation of precipitation from weather radar data
gives a more patchy result (Crochet, 1997). It is seen that during both periods the lowest
precipitation amount is found in the south-western part of the NOPEX area, while the
highest values are observed in the northern part for CFE1 and north-eastern part for
CFE2.
As far as evaporation is concerned, the highest values during both periods were
observed in the north-eastern part covered by forest on primarily till soils, while the
lowest evaporation values are found in the south-eastern part of the NOPEX area with
mainly clay soils and shallow bedrock. In a more detailed resolution a decrease in
evaporation values in the areas with sandy soils is observed, while the evaporation
values increase over lakes and mires. The current version of the ECOMAG model does
not consider the role of different vegetation characteristics for evapotranspiration. There
are still obstacles, mainly related to scale issues, to overcome, in order to correctly compare
flux estimates with model calculations for individual “points”, patches and fundamental units
(REA). Preliminary comparisons with mainly mast measurements give good agreement for
individual patches on a daily base, although some discrepancies are noted. The variability
across space shown by the model remains to be supported by independent measurements.
Runoff patterns during CFE1 and CFE2 are non-homogeneous due to the non-linearity
of the runoff formation process involving precipitation, soil and land cover patterns,
slopes etc. In general, the highest specific runoff values are found in areas with shallow
bedrock and sandy soil. These soils have low water storage capacity in the unsaturated
zone and, as a rule, moderate evaporation, active recharge of groundwater and high base
flow and occur in association with eskers and in areas with steep slopes. Low runoff
values during the relatively short periods of CFE1 and CFE2 are found in areas with
peat and mires, though in the context of a longer time period (e.g. a year) the simulation
shows that mires act as runoff regulators. Low runoff was also found in flat areas. Table
6.4 shows the values of the simulated and measured river runoff in the gauged basins of
the NOPEX area for the CFE1 and CFE2. It is seen, that in general, the results are in a
- 72 -
Chapter 6 Model validation
good agreement for the runoff and also for the maximum daily discharges.
Table 6.4 Observed (Qo) and simulated (Qs) runoff characteristics of the gauged NOPEX
area during periods CFE1 and CFE2
CFE1, 27 May - 23 June 1994
CFE2, 18 April - 14 July 1995
Basin
Qo
Qs
Qomax
Qsmax
Fyrisån
(mm)
4
(mm)
6
(m3/s)
3.0
(m3/s)
3.0
Qo
(mm)
100
Sagån
-
6
-
Qs
(mm)
105
2.0
112
95
Qomax
(m3/s)
29
31
32
Lillån
3
6
0.2
0.5
94
103
Örsundaån
3
5
0.7
0.8
75
90
Hågaån
4
3
0.4
0.3
94
89
Sävaån
5
5
0.5
0.5
99
89
10
11
Sävjaån
5
6
1.8
2.3
98
92
24
28
Stalbobäcken
9
10
0.09
0.07
90
104
0.4
0.4
Stabbybäcken
2
3
0.01
0.01
73
83
0.5
0.3
9.4
97
97
Total gauged area
-
6
-
9.6
Qsmax
(m3/s)
29
12
5.9
101
11
20
9.2
138
Soil moisture distribution patterns are in general more directly related to the soil type. Higher
soil moisture content is found in areas with peat and clay soils, while soil moisture content is
low in areas with sandy soil and shallow bedrock.
- 73 -
Chapter 6 Model validation
a)
- 74 -
Chapter 6 Model validation
b)
Figure 6.5 Calculated water balance elements of the whole NOPEX area for a) CFE1 (27
May - 23 June 1994) and b) CFE2 (18 April - 14 July 1995)
The main comparison is performed for regional flux estimates for the whole NOPEX area
(Gottschalk et al., 1998a). The comparisons have been made for individual days when all
different estimates were available as well as for the whole of CFE1 and CFE2 when only
- 75 -
Chapter 6 Model validation
mast measurements and estimates from the meso-scale meteorological model and the
ECOMAG model were available. The agreement is acceptable taking into consideration the
uncertainty of the different estimates, but the problem needs further investigations. The
regional estimate of evapotranspiration by a weighted average of mast measurements for
CFE1 is 67 mm and CFE2 - 335 mm. The corresponding estimates by the ECOMAG model
are 74 mm and 289 mm, respectively (see Tab. 6.3). There was also relatively good
correlation between 24h values of evapotranspiration estimated by the ECOMAG model and
values estimated from mast measurements, with R2= 0.672 (Fig. 6.6).
Mast whole region (mm/day)
5
4
3
2
1
0
0
1
2
3
ECOMAG-model (mm/day)
4
5
Figure 6.6 Regional latent heat flux values estimated by mast measurements for the land cover
data of the whole region and estimates by the ECOMAG model.
- 76 -
Chapter 7 Conclusions
7. Conclusions
The conclusions referred to in the following are replica of those of Motovilov et al., (1998).
A physically-based distributed hydrological model ECOMAG has been applied to nine river
basins within the NOPEX area with the purpose of validating its ability for regional
modelling i.e. a repeated use of the model everywhere within a region with a global set of
parameters. The NOPEX concentrated field efforts during 1994 (CFE1) and 1995 (CFE2) as
well as the continuous climate monitoring (CCM) and runoff monitoring provide high
quality data sets for such a validation.
Most parameters of the ECOMAG model have a physical interpretation, for example soil
water parameters, which can, in principle, be measured. Others can be given reasonable
values from experience, for example the degree-day factor. However, calibration of some
model parameters is required to achieve an acceptable model performance. The question put
forward here is whether a calibration of a global set of parameters on a few basins in a region
provides an acceptable performance for basins not used in the calibration and for variables
not included in the calibration procedure. An immediate answer to this question from the
present study is yes, although with some reservations.
The global parameters were determined from a joint calibration against runoff data for seven
years from three drainage basins with an additional adjustment of soil parameters against soil
moisture and groundwater level data from five small experimental subbasins in 1994-1995
including CFE periods. The model with these parameters was then validated against runoff
data for 14 years from six other basins and the remaining seven years for the three basins
used for calibration, and against synoptic runoff measurements on four occasions in the
largest drainage basin Fyrisån during CFE1 and CFE2. Finally, regional estimates of daily
evapotranspiration were compared with estimates from flux measurements, to give an
independent assessment of the water balance.
The performance of simulated runoff was evaluated by the Nash-Sutcliffe efficiency
measure. For the larger basins and for the NOPEX area as a whole the results were classed as
good and for other basins as satisfactory. A striking result is the variation in the performance
criteria between different years, which partly might be explained by shifts between stable
and unstable climatic conditions. Some discrepancies in the model performance are
- 77 -
Chapter 7 Conclusions
suspected to be caused by poor quality of runoff data. However, the overall result must be
considered to be good as the simulations were performed without calibration.
The ability of the ECOMAG model to simulate the variation of average soil moisture for a
grid net of the resolution 2km x 2km as shown by this study is also good. The performance
has been evaluated by manual inspection of averaged observed values for grid cells with
those simulated. The performance is equally good for till, clay and sandy soils. Averaged
observed and simulated groundwater level data have been compared in the same manner,
with slightly worse results than in case of the soil moisture. A problem here has been to
obtain representative average groundwater level values for grids, because of the difficulties
with installing tubes at sufficient depth in till soils.
A more problematic question is the comparison of synoptic runoff observations with those
simulated. This focuses attention on the model’s ability to reproduce the spatial variation of
runoff. The total variability across space, as assessed by the 12 synoptic points, has a similar
pattern for observed and simulated values but the individual deviations between them are
difficult to explain at present. It has therefore not been possible to really validate the process
description and parameterisation of drainage from individual grid cells. The simulated water
balance components for grid cells show relatively high spatial variability and it has not been
possible to confirm this variability from independent observations. This problem needs to be
studied further.
Simulated water balance elements were integrated to the whole NOPEX area and
independent estimates from vertical flux measurements of regional evapotranspiration
have been used for validation. The noted discrepancies are within the uncertainties of
the estimated values. A further step here would be to develop a data assimilation scheme
for the regional model taking advantage of all separate data sources, not only those
traditionally used in modelling efforts by hydrologists.
- 78 -
Notation and dimensions
8. Notation and dimensions
Abbreviations
ASCII
BALTEX
CFE
DEM
ECOMAG
GCM
GIS
NOPEX
REA
REV
SHE
SINOP
SMHI
SVAT
TOPMODEL
WATBAL
WPI
American Standard Code for Information Interchange
The Baltic Sea Experiment
Concentrated Field Efforts
Digital Elevation Model
ECOlogical Model for Applied Geophysics
Global Circulation Model
Geographical Information System
NOrthem hemisphere climate Processes land-surface Experiment
Representative Elementary Area
Representative Elementary Volume
Systieme Hydrologigue European
System of Information in NOPex
Swedish Meteorological and Hydrological Institute
Soil-Vegetation-ATmosphere scheme
TOPography based hydrological MODEL¨
WATer BALance hydrological model
Water Problems Institute
Notations and dimensions
Symbol
Description
x,y,z
t
Lf
ρi
ρw
i
B
L
Z
d
R
Rr
Rs
T
H
E
Epot
I
Q
V
W
Units
Main constants and variables
Co-ordinates
Time
Latent heat of ice fusion
Density of ice
Density of water
Geometrical characteristics
Slope
Width
Length
Thickness
Meteorological characteristics
Deficit of air vapour pressure
Rate of precipitation
Rate of rain precipitation
Rate of snow precipitation
Air temperature
Main hydrological variables
Depth of water (snow) layer
Actual evapotranspiration
Potential evaporation
Volumetric content of ice per unit of volume
Horizontal water flux (discharge)
Vertical water flux
Volumetric content of water per unit of volume
- 79 -
m
day, s
179.0 kkal kg-1
917 kg m-3
1000 kg m-3
m m-1
m
m
m
mb
m day-1
m day-1
m day-1
o
C
m
m day-1
m day-1
m3 m-3
m3s-3 , m3 day-1
m day-1
m3 m3
Notation and dimensions
Symbol
kT
kc
vs
ST
Sf
Tcr
TM
T0
WHC
ρn
λs
ke
n
R0
ϕo
ϕ
FC
FCM
WP
P
C
D
WE
ρ
K
KX
lt
Hf
Ht
Kf
Wu
λf
Hg
Tg
Vd
Description
Units
Snow cover
Degree day factor
Parameter of snow compaction
Velocity of snow compaction
Rate of snowmelting
Rate of frost of meltwater in snow
Threshold air temperature for precipitation
Threshold air temperature for snowmelting
Temperature on the soil-snow surface
Water holding capacity
Density of new snow
Heat conductivity of snow
Surface
Potential evaporation parameter
Manning roughness coefficient
Effective rainfall excess
Maximal depression storage
Actual depression storage
Soil
Constants
Field capacity
Maximum value of FC
Wilting point
Total porosity
=FC-WP capillary porosity
=P-FC non-capillary porosity
=(FC-WP)/2 critical moisture for E
Volumetric density of dry soil
Unfrozen soil
Vertical saturated hydraulic conductivity
Horizontal saturated hydraulic conductivity
Heat conductivity w m-1day
Frozen soil
Frost depth
Thaw depth
Vertical saturated hydraulic conductivity
Volumetric content of unfrozen water
Heat conductivity
Ground water
Depth of groundwater level
Temperature of groundwater
Rate of water exchange between upper groundwater
zone and dipper layers
- 80 -
m day-1 oC-1
m2 kg-1 day-1
m day-1
m day-1
m day-1
o
C
o
C
o
C
m3 m-3
kg m3
w m-1day
m day-1 mb-1
day m-0.33
m
m
m
m3 m-3
m3 m-3
m3 m-3
m3 m-3
m3 m-3
m3 m-3
m3 m-3
kg m-3
m day-1
m day-1
m
m
m day-1
M3 M-3
w m-1day
m
C
m day-1
o
Notation and dimensions
Probability characteristics
Symbol
Description
F
Distribution function
F0
Probability of exceedanee distribution function
2
R
Nash-Sutcliffe coefficient
Parameters of probability distribution functions
α,β
Indices
C
Characteristics for capillary zone
l
Characteristics for liquid phase of water
m
Mean value
nc
Characteristics for non-capillary zone
s
Characteristics for solid phase of water (ice)
L
Characteristics for lower boundary of element on plane
0
Characteristics for upper boundary of element on plane
1
Characteristics for surface storage
2
Characteristics for horizon A of soil
3
Characteristics for horizon B of soil
4
Characteristics for groundwater zone
5
Characteristics for snow cover
6
Characteristics for river network
- 81 -
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