ECOMAG: Regional model of hydrological cyclefolk.uio.no/kolbjoen/nygen/ECOMAG-REPORT.pdfECOMAG:...
Transcript of ECOMAG: Regional model of hydrological cyclefolk.uio.no/kolbjoen/nygen/ECOMAG-REPORT.pdfECOMAG:...
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ECOMAG: Regional model of hydrologicalECOMAG: Regional model of hydrologicalECOMAG: Regional model of hydrologicalECOMAG: Regional model of hydrological
cycle. Application to the NOPEX regioncycle. Application to the NOPEX regioncycle. Application to the NOPEX regioncycle. Application to the NOPEX region
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GROUNDWATER ZONE
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 repeatedapplication 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 centralissue 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 wascalibrated 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 modelagainst 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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CONTENTSAbstract1. Introduction 52. Scale issues 93. 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. 47
5. Sensitivity analysis 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 778. Notations and dimensions 799. References 82
Chapter 1 Introduction
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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 co-
operative 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
Chapter 1 Introduction
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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
Chapter 1 Introduction
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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.
Chapter 1 Introduction
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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.
Chapter 2 Scale issues
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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
Chapter 2 Scale issues
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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
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Figure 2.1 Spatial variations of soil moisture and groundwater levels as a function of scale of
aggregation (from Beldring et. al., 1998)
Chapter 3 Hydrological model formulation
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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:
� interception (the Rutter accounting procedure);
� evapotranspiration (the SVAT scheme);
� 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 one-
dimensional kinematic wave equations for flow in the river channel system);
� unsaturated flow in the thawed soil (the one-dimensional Richards equation);
� unsaturated flow in the frozen soil (WPI: one-dimensional heat and moisture transfer
equations);
� saturated zone flow (two-dimensional Boussinesq equations);
� 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
Chapter 3 Hydrological model formulation
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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:
� they give a better understanding of the hydrological processes in the catchment;
� 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;
� 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;
� 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
Chapter 3 Hydrological model formulation
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of parameters is required, making the modles similar to lumped conceptual models (Beven,
1989);
� 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
Chapter 3 Hydrological model formulation
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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
Chapter 3 Hydrological model formulation
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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):
Chapter 3 Hydrological model formulation
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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
Chapter 3 Hydrological model formulation
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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
∂∂
∂∂
∂∂
∂∂
Wt
vx
vy
vz
Sx 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.
Chapter 3 Hydrological model formulation
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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:
∂∂
∂∂
∂∂
Wt
dxdydzvx
vz
S dxdydzZBL
x zZBL
000 000��� ���= − − −�
��
��� (3.2)
�
( ) ( )Z
dWdt
Z v vL
v v ZSx x Lz z Z=
−+ − +, ,
, , .00 (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:
( )ZdWdt
Q QBL
V V ELZ=
−+ − −0
0 . (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.
Chapter 3 Hydrological model formulation
- 19 -
soil particles
wiltingpoint capillary porosity
Wpfield capacity
FC
C
total porosity
unit widthP = 1-M
B = 1
(matrix)
M
horizontalinflow, Q0
horizontaloutflow, QL
verticalinflow, V0
verticaloutflow, VZ
hLh0
L
Znon-capillary porosity
D = P-FC
trans
pira
tion,
E
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):
( )ZdWdt
V V Ecc c Z c= − −, , .0 (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 non-
capillary zone of the soil column pores space (D) is written as (index nc):
Chapter 3 Hydrological model formulation
- 20 -
( )ZdW
dtQ Q
BLV V Enc L
nc nc Z nc=−
+ − −00, , . (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
hZW
Dnc= . (3.7)
Inserting Wnc into equation (3.6) and assuming a linear profile of water depth in x-
direction results in:
( )D d h hdt
Q QBL
V V EL Lnc nc Z nc2
0 00
( )., ,
+=
−+ − − (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):
( ) ( )ZdWdt
D d h hdt
Q QBL
V V V V E Ec L Lc c Z nc nc Z c nc+
+=
−+ − + − − −
20 0
0 0( )
., , , , (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:
.)(
20
dthhdD
dtdWZ
dtdWZ Lc +
+= (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 B h B hdt
Q QL
B V V EL L Lm nc nc Z nc2
0 0 00
( ), ,
+=
−+ − − , (3.11)
( )[ ]B ZdWdt
D d B h B hdt
Q QL
B V V Emc L L L
m Z++
=−
+ − −2
0 0 00
( ), (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 x-
direction.
The water balance equations (3.5), (3.8), (3.9), (3.11) and (3.12) are used for simulating
Chapter 3 Hydrological model formulation
- 21 -
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
Chapter 3 Hydrological model formulation
- 22 -
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
river links of the first tributary are
numbered, and the procedure
continues downstream towards the
last tributary. The landscape elements
are asigned numbers following the
same system, beginning with the left
side. When a slope contains more
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.
ZZ
GROUNDWATER ZONE
Figure 3.2 Schematisation of a catchment in the
ECOMAG model.
Chapter 3 Hydrological model formulation
- 23 -
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.
Chapter 3 Hydrological model formulation
- 24 -
River flow
precipitation
surface water storage surface water outflow
subsurface outflow horizon A
subsurface outflow horizon B
groundwater outflow
ice particles
field capacityWP
E4
surface water inflow
subsurface inflow horizon A
subsurface inflow horizon B
groundwater inflow
porosity
s
lio
s
lio
i
m
rta
x
i
m
rta
x
groundwater zone
horizon B
h4
evap
otra
nspi
ratio
n
melt watersnow cover
horizon A
infiltrationre
turn
flow
penetrationpenetration
h3
Z4
h2
Z2
Z3
capillary zone
non
zonecapillary
infiltration
h1
h5
non
zonecapillary
capillary zone
E5
E1
E2
E3
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.
Chapter 3 Hydrological model formulation
- 25 -
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. Small-
scale 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).
Chapter 3 Hydrological model formulation
- 26 -
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:
12 1 0 1 0 0 1 1 0
ddt
B h B h R B Q Q LL L m L( ) ( ) /, , , ,+ = − − , (3.13)
Q i h B n1 11 2
15 3
1= / / / , (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
R V V V Vr P0 1 2= − + − , (3.15)
where
Chapter 3 Hydrological model formulation
- 27 -
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 K( ) exp( )= − −1 α (3.16)
where
K1=α , (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:
��
���
���
��−−=−+= �� K
VKdFFdFVVC
V
CV
F
CCF
C 11
012 exp1)ln(1
1
1
α, (3.18)
where
)exp()( KKF C α−= ,
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.
Chapter 3 Hydrological model formulation
- 28 -
FV1
V1
0
K
FC=1
K = -lnFC/α
C
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):
ϕ ϕϕ
( ) * exp ( ( ) ( ))t V t E t dte pott
= − − −�
��
�
��
��
��
�0
0
11
, (3.19)
where
Ve= V1-V2+Vr,
ϕ0 is the maximum value of the depression storage;
Epot 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:
Chapter 3 Hydrological model formulation
- 29 -
( )dt
tdVP
*ϕ= . (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):
F FC FCFCM
( ) ,= �
��
�
��
β
F FC FCFCM0 1( ) ,= − �
��
�
��
β
FC FCM2 1=
+β
β, (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 VW
FCMj c jj
j, = − �
��
���
�
�
��1
β
, (3.23)
and the one into non-capillary zone (index nc) by:
Chapter 3 Hydrological model formulation
- 30 -
V VW
FCMj nc jj
j, = �
��
���
β
, (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:
ZdWdt
V Ejj
j c 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
E for W WE
EW WP
WE WPfor W WEj
pot j j j
pot jj j
j jj j
=
>−−
�
���
�
��� ≤
�
�
,
,
,
, (3.26)
where
E E kpot j pot 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
Chapter 3 Hydrological model formulation
- 31 -
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 non-
capillary zone in the form:
D ddt
B h B h V V V B Q Q LjL j L j j nc j r j m j L j2 0 0 1 0( ) ( ) ( ) /, , , , , ,+ = − − − −+ , (3.27)
Q BiK hj x j 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 P FCj j 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:
VQ Q B L for Q Q
for Q Qj rj j m j j
j j,
,max ,max
,max
( ) / , ,, ,
=− >
≤���
��0 (3.29)
where jjxj ZBiKQ ,max, = .
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:
V V V Q Q BLr L2 2 3 2 0 2, ,max, ,max,( ) / .= − + − (3.30)
Chapter 3 Hydrological model formulation
- 32 -
3.5.5 Groundwater zone (index 4)
The groundwater flow is calculated using equation (3.11) and Darcy's formula in the
which yields:
D ddt
B h B h V V V E B Q Q LL L d r m L4
4 0 4 0 4 4 4 4 4 02( ) ( ) ( ) /, , , , ,+ = + − − − − , (3.31)
Q BiK hx4 4 4= , , (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):
Chapter 3 Hydrological model formulation
- 33 -
fTssw
i SSERIhdtd +−−=)( 5ρ
ρ, (3.33)
fLTr SVESRhWdtd −−−+= 155 )( , (3.34)
( )ssi
sT
n
sW TWIhv
IESR
dtdh
,,, 555 −�
�
���
� +−=
ρρρ , (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 k T TM at T TMT T= − − >*( ) ( ) 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 :
00)()(* 5 ><−−= WandTMTforTMTkS TF . (3.37)
Evaporation of solid (Es) and liquid (Ew) components of snow are estimated using data
on the deficit of air vapour pressure as:
Chapter 3 Hydrological model formulation
- 34 -
���
��� +
=
IWdk
E
i
w
es
ρρ 51
, (3.38)
IW
EEi
wsL ρ
ρ 5= . (3.39)
Using the approach by Yosida et al., (1955) the velocity of snow compaction, vs, can be
described as (Motovilov, 1993):
( )( )[ ] wwis
wics WIT
hWIkvρρρ
ρρ5
255
2108.0exp ++−+
= , (3.40)
where
TT at T
at Ts =<≥
���
, ,, ,
00 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:
���
≤>−
=,,0,,/)(
5
5551 WHCWat
WHCWatthWHCWV
δ(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):
Chapter 3 Hydrological model formulation
- 35 -
QdHdt
TH
TH Hf
f f
f
t g
g f= −
−λ λ0 , (3.42)
H H Tt
Qt t tf
= +�
���
�
���
2
0 5
2λδ
.
, (3.43)
Q L W Wf w f j u= −ρ ( ) , (3.44)
50 hH
HTT
ffs
fs
λλλ
+= , (3.45)
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):
V K VKf f
f2 2
1
21, ,
,exp= − −�
��
���
�
�
�� , (3.46)
K KP I WP
P WPk If i2 2
2 2 2
2 2
4
221, / ( )=
− −−
�
��
�
�� + , (3.47)
Chapter 3 Hydrological model formulation
- 36 -
I W W H Hw
ij u f t2 = −
ρρ
η( ) ( , ) , (3.48)
η( , )( ) / , ,( ) / , ,, ( ) ,
H HH H Z at H ZZ H Z at H Z and H Z
at H Z and H Z or Hf t
f t f
t f t
f t f
=− <
− ≥ <≥ ≥ =
��
��
2 2
2 2 2 2
2 20 0 (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;
I2 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:
( ) RLlatRLLR LQQQhBhBdtd /)(
21
,60,60,60,,6, −+=+ , (3.50)
RRR nBhiQ /35
62
16 = , (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;
Chapter 3 Hydrological model formulation
- 37 -
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
Q Qlat j nj
==� , ,
1
4
(3.53)
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
Chapter 3 Hydrological model formulation
- 38 -
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
models contain parameters and
coefficients that have a direct physical
interpretation and, in principle, can be
measured in the field.Example of such
parameters in the ECOMAG model are
the soil water constants (Tab. 3.1). The
initial values of these parameters for the
different soil types can be determined
on the basis of regional information
about the hydrological properties of the
soil and supplemented by data from
literature sources (Nyberg, 1995, Stähli
et al., 1996).
For other parameters, experimental
results allow to establish empirical
relations (heat conductivity of both soil
and snow, unfrozen water content in
frozen soil, snow water holding
capacity) or indicate reasonable well-
defined limits for parameter values
(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.
Table 3.1 Model parameters
Parameters of soil classesVolume density
Porosity
Field capacity
Wilting point
Vertical saturated hydraulic conductivity
Horizontal saturated hydraulic conductivity
Heat conductivity for thawed and frozen
Unfrozen water in frozen soill
Thickness of soil horizon
Parameter of distribution of field capacity
Parameters of land use classesMaximal retention storage
Manning’s roughness coefficient for slope
Degree-day factor
Parameters for whole catchmentPrameter of potential evaporation
Critical temperature snow/rain
Density of new snow
Snow water holding capacity
Parameter of snow compaction
Depth of unchanged ground temperature
Manning’s roughness coefficient for river
Chapter 3 Hydrological model formulation
- 39 -
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:
( ) ( )( )2
22
2
�
��−
−−−=
QQQQR
od
cd
od
od (3.54)
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).
Chapter 4 Data used
- 40 -
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
fluctuates between 600 and 800 mm. Monthly
values has a minimum in August and a
maximum in February. 20 to 30 per cent of
the total annual precipitation falls as snow. A
snow cover exists from the middle of
November and has a duration of 100 to 110
days on the average, but normally it is not
continuos throughout the winter. The mean
annual temperature for 1961-1990 at the
station Uppsala is +6oC. The daily average
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
10°E 20°E0°
NorwaSweden
70°N
30°E
Finland
NOPEX area
Denmark
UppsalaOslo
65°N
60°N
55°N
Figure 4.1 Localization of the NOPEX area
Chapter 4 Data used
- 41 -
(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
Chapter 4 Data used
- 42 -
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 River Coordinates X Y
Stationnumber
Area(km2)
Altitude(m.a.s.l.)min max
Gränvad Lillån 661637 155504 61-2217 168.0 15 75Härnevi Örsundaån 662438 157112 61-2248 305.0 15 105Lurbo Hågaån 663271 160107 61-2245 124.0 15 75Ransta Sävaån 662754 158926 61-2247 198.0 15 105Sävja Sävjaån 663592 160652 61-2243 727.0 5 75Sörsätra Sagån 662278 155498 61-2220 612.0 35 145Stabby Stabbybäcken 663200 159982 61-1742 6.6 18 55Tärnsjö Stalbobäkken 666859 156333 54-2299 14.0 55 105UlvaKvarndam
Fyrisån 664509 159902 61-2246 950.0 5 95
Vattholma Vattholmaån 665713 160736 61-244 284.0 25 65
Figure 4.3 The ten gauged river basins and five experimental basins in the NOPEX area
Chapter 4 Data used
- 43 -
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 Station nr.Arlanda 9739 Österby 9740Drälinge 9759 Sala* 9655Enköping 9738 Skjorby 9733Fagerstad 10500 Skultuna 9644Films Kyrkby** 10714 Sundby 9641Folkärna** 10610 Tärnsjö 10612Gysinge 10617 Ultuna* 9749Hallstaberg 9639 Uppsala** 9751/2Harbo 10708 Uppsala flygplats**s 9753Hyvlinge 9745 Västerås Hasslö** 9635Köping 9631 Vattholma 10701Lisjö 9642 Vittinge 9754Nybyholm 9731* The station is also measuring temperature** The station is also measuring temperature and air humiditys The station is also measuring snow depth
Chapter 4 Data used
- 44 -
NOPEX areaClimate stations run by SMHI
6680000
6660000
6640000
6620000
66000001500000 1520000 1540000 1560000 1580000 1600000 1620000
Gysinge
FolkärnaTärnsjö
Fagersta
Harbo
Films Kyrkby
Vattholma
Uppsala flygplats
Ultuna
Drälinge
Uppsala
ArlandaÖsterby
Skjorby
Vittinge
Hyvlinge
Enköping
Nybyholm
Sala
Lisjö
Köping
Västerås-Haslö
HallstabergSundby
Skultuna
10000 20000 3000010000 0
METERS
SMHI climate station
Coordinates in Rikets Nät (RT 90)
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 26-
27 July 1995), and data from 12 of the sites were used (Tab. 4.3.). The measurements
followed the procedures described by Krasovskaia (1988).
Chapter 4 Data used
- 45 -
Table 4.3 Synoptic runoff measurements used in ECOMAG
St. number River X-coordinate Y-coordinate3 Tegelsmoån 16605 668654 Toboån 16027 668407 Vendelån 16017 666549 Sävastabäcken 16024 6662512 Vendelån 16066 6656314 Vendelån 15998 6669315 Tassbäcken 15986 6671216 Velångsbäcken 15925 6658317 Björklingeån 15925 6658341 Fyrisån 15990 6645139 Vattholmån 16074 6657119 Björklingeån 15967 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.
Chapter 4 Data used
- 46 -
Table 4.4 Number of observation points of soil moisture and groundwater level within
experimental drainage basins
Basin Number of observationpoints
Soil type Land use
Soilmoisture
Groundwater
Buddby 151 16 till forestDansarhellarna 75 16 till forestÖstfora 50 19 till/sand forestÖstfora - 15 peat mireMarsta 25 - clay open areaTärnsjö 50 - sand forest
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-
Chapter 4 Data used
- 47 -
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).
Chapter 4 Data used
- 48 -
Empirical and theoretical semivariogram for binary precipitation. Exponential model, nugget = 0.0, sill = 4.7 and range = 50 km
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 20 40 60 80 100 120 140
Distance (km)
Sem
ivar
ianc
e
EmpiricalTheoretical
Figure 4.5 Semivariogram for binary precipitation
Empirical and theoretical semivariogram for precipitation height. Eksponetial model, nugget = 0.0 mm2, sill = 4.7 mm2
and range = 70 km
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100 120 140Distance (km)
Sem
ivar
ianc
e (m
m2 )
EmpircalTheoretical
Figure 4.6 Semivariogram for precipitation height
Chapter 5 Sensitivity analysis
- 49 -
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
� adequacy of the model structure and its possibilities to reflect the main features of
hydrological processes in a boreal environment,
� role and importance of the model parameters in the common model structure,
� 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.
m a.s.m a.s.m a.s.m a.s.m.a.s.
Elevations:
Rivers and lakes
Figure 5.1 Relief (a) and river network (b) for the Fyrisån catchment
Chapter 5 Sensitivity analysis
- 50 -
Forest
Open land
Rivers and lakes
Figure 5.2 Land cover map for the Fyrisån catchment
SandTillClayPeat
Figure 5.3 Soil map for the Fyrisån catchment
Chapter 5 Sensitivity analysis
- 51 -
12 3
25
4
56
23
24
7
8
910
26
27
2211
1213
14
21
20
2928
1918
171615
Ulva Kvarndamn
Vattholma
Figure 5.4 Element numbers for landscape and river elements in the Fyrisån catchment
Soil and groundwater zone classes Vegetation and landuse classes Slope (length/length)*100 Precipitation zones
ForestOpen land
SandTill
Peat
Clay
Class assignation for landscape elements
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
Chapter 5 Sensitivity analysis
- 52 -
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 Nash-
Sutcliffe 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 0.871984/85 0.881987/88 0.881990/91 0.721992/93 0.851994/95 0.81Average 0.84
Table 5.1 Nash-Sutcliffe criterion for calibrated years
Year R2
1982/83 0.841983/84 0.771985/86 0.941986/87 0.901988/89 0.801989/90 0.951991/92 0.851993/94 0.78Average 0.85
Table 5.2 Nash-Sutcliffe criterion for validated years
Chapter 5 Sensitivity analysis
- 53 -
Results for years used for calibration of ECOMAGThe time series start 01. August each year
Observed runoff Simulated runoff Precipitation Temperature
1981/82
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y
R uno ff ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y ) 1984/85
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff (m 3/s )
-2 2 0
-2 0 0
-1 8 0
-1 6 0
-1 4 0
-1 2 0
-1 0 0
-8 0
-6 0
-4 0
-2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1987/88
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y ) 1990/91
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1992/93
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y ) 1994/95
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
Figure 5.6 Observed and simulated runoff at Ulva Kvarndam, Fyrisån, for calibrated years
Chapter 5 Sensitivity analysis
- 54 -
Results for years used for validation of ECOMAGThe time series starts 01. August each year
Observed runoff Simulated runoff Precipitation Temperature
1982/83
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y ) 1983/84
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1986/87
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1988/89
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y ) 1989/90
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) r e c i p . ( m m / d a y )
1991/92
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1985/86
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno ff (m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
1993/94
0
1 0
2 0
3 0
4 0
5 0
6 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1 D a y s
R uno f f ( m 3/s )
- 2 2 0
- 2 0 0
- 1 8 0
- 1 6 0
- 1 4 0
- 1 2 0
- 1 0 0
- 8 0
- 6 0
- 4 0
- 2 0
0
2 0
4 0
6 0
8 0
T e m p . ( o C ) P r e c i p . ( m m / d a y )
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
Chapter 5 Sensitivity analysis
- 55 -
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
Chapter 5 Sensitivity analysis
- 56 -
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 degree-
day 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.
Chapter 5 Sensitivity analysis
- 57 -
Observed and simulated snow depthThe time series starts 01. August each year
Observed snow depth Simulated snow depth
1 9 8 1 / 8 2
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 4 /8 5
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p th ( c m )
1 98 7 / 88
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
19 9 0 /9 1
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p th ( c m )
1 9 9 2 / 9 3
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 9 4 / 9 5
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 2 / 8 3
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 3 / 8 4
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 5 / 8 6
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 8 / 8 9
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 6 / 8 7
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 8 9 / 9 0
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 9 1 / 9 2
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p t h ( c m )
1 9 9 3 /9 4
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
1 3 1 6 1 9 1 1 2 1 1 5 1 1 8 1 2 1 1 2 4 1 2 7 1 3 0 1 3 3 1 3 6 1
D a y s
S n o w d e p th ( c m )
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
Chapter 5 Sensitivity analysis
- 58 -
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.
Chapter 6 Model validation
- 59 -
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
Chapter 6 Model validation
- 60 -
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).
Chapter 6 Model validation
- 61 -
Fyrisån Lillån Stabbybäcken
Year 1981/82
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1981/82
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1981/82
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1982/83
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1982/83
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1982/83
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1983/84
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1983/84
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1983/84
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1984/85
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1984/85
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1984/85
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1985/86
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1985/86
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1985/86
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1986/87
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1986/87
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1986/87
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1987/88
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1987/88
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1987/88
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Qobserved Qsimulated
Chapter 6 Model validation
- 62 -
Fyrisån Lillån Stabbybäcken
Year 1988/89
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1988/89
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1988/89
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1989/90
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1989/90
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1989/90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1990/91
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1990/91
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1991/92
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1991/92
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1991/92
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1992/93
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1992/93
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1992/93
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1993/94
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1993/94
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1993/94
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1994/95
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1994/95
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Year 1994/95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Year 1990/91
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Qobserved Qs imulated
Figure 6.1 Observed and simulated runoff for riverbasins used for calibration
Chapter 6 Model validation
- 63 -
Fyrisån year 1984/85
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Sävjaån year 1984/85
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Sävaån year 1984/85
0
5
10
15
20
25
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)Hågaån year 1984/85
0
2
4
6
8
10
12
14
16
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Örsundaån year 1984/85
0
5
10
15
20
25
30
35
40
45
50
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)Lillån ear 1984/85
0
5
10
15
20
25
30
35
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Sagån year 1984/85
0
10
20
30
40
50
60
70
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Stalbobäcken year 1984/85
0
0.2
0.4
0.6
0.8
1
1.2
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Stabbybäcken year 1984/85
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Sum of all river basins year 1984/85
0
50
100
150
200
250
300
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Qs imulatedQobs erved
a) 1984/85
Chapter 6 Model validation
- 64 -
Sagån Year 1981/82
0
10
20
30
40
50
60
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)Fyrisån year 1994/95
0
5
10
15
20
25
30
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Lillån year 1994/95
0
2
4
6
8
10
12
14
16
18
20
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Örsundaån year 1994/95
0
2
4
6
8
10
12
14
16
18
20
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Sävjaån year 1994/95
0
5
10
15
20
25
30
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Stalbobäcken year 1994/95
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
Stabbybäcken year 1994/95
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Sum of all river basins year 1994/95
0
20
40
60
80
100
120
140
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m 3/s)
Hågaån year 1994/95
0
1
2
3
4
5
6
7
8
9
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s) Sävaån year 1994/95
0
2
4
6
8
10
12
1 6 1 1 2 1 1 8 1 2 4 1 3 0 1 3 6 1Days
Q (m3/s)
QsimulatedQobserved
b) 1994/95
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).
Chapter 6 Model validation
- 65 -
Table 6.1 Model performance (R2) for the gauged river basins in the NOPEX area
Basin Fyr Sag Lil Örs Håg Sva Svj Stl Stb TotalYear1981/82 0.73
0.760.600.64
0.720.72
0.830.88
0.640.75
0.760.83
0.650.73
0.140.29
0.580.72
0.790.81
1982/83 0.810.84
0.560.60
0.620.70
0.520.73
0.430.83
0.620.80
0.530.61
0.700.72
0.590.60
0.760.80
1983/84 0.720.78
0.570.61
0.650.81
0.640.72
0.560.82
0.690.75
0.500.63
0.840.83
0.610.66
0.740.78
1984/85 0.780.84
0.830.86
0.750.90
0.840.94
0.770.96
0.900.96
0.820.93
0.750.88
0.680.93
0.900.95
1985/86 0.830.88
0.500.28
0.690.74
0.800.81
0.760.81
0.820.91
0.860.90
0.300.20
0.570.81
0.880.90
1986/87 0.880.94
0.480.46
0.570.71
0.690.72
0.530.71
0.730.84
0.690.77
0.450.54
0.540.75
0.770.79
1987/88 0.860.91
0.480.51
0.720.85
0.760.85
0.560.66
0.750.80
0.660.77
0.750.83
0.570.77
0.770.83
1988/89 0.700.84
0.250.33
0.320.46
0.220.60
0.260.64
0.270.64
0.190.58
0.620.76
0.260.44
0.480.68
1989/90 0.910.93
0.690.76
0.660.77
0.770.85
0.700.92
0.800.89
0.830.88
0.850.90
0.750.91
0.860.90
1990/91 0.770.92
0.350.19
0.620.84
0.620.74
0.530.62
0.710.78
0.600.65
0.600.68
0.710.85
0.720.75
1991/92 0.800.87 -
0.600.77
0.520.70
0.190.44
0.570.80
0.630.77
0.570.58
0.440.70
0.810.91
1992/93 0.900.94 -
0.740.78
0.710.73
0.640.78
0.650.72
0.780.85
0.730.79
0.760.85
0.840.87
1993/94 0.700.87 -
0.400.76
0.390.71
0.590.74
0.550.75
0.610.80
0.460.50
0.540.75
0.670.88
1994/95 0.720.78 -
0.610.78
0.530.91
0.240.70
0.690.91
0.690.84
0.670.66
0.650.95
0.800.92
1981-91 0.810.87
0.570.60
0.690.81
0.750.83
0.630.81
0.770.86
0.710.80
0.570.67
0.610.78
0.810.85
1981-95 0.810.87 -
0.670.80
0.710.83
0.600.80
0.760.85
0.710.81
0.590.68
0.620.79
0.820.88
Numenator - R2 daily valuesDenumenator - 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
Chapter 6 Model validation
- 66 -
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
Chapter 6 Model validation
- 67 -
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 Station P*
(mm)E*
(mm)Q*
(mm)P(mm)
E(mm)
Q(mm)
∆∆∆∆Q(mm)
|∆∆∆∆Q/Q*|(%)
Fyrisån Ulva Kvarn 755 534 222 731 502 229 7 3Sagån Sörsätra 729 384 346 720 484 237 -109 31Lillån Gränvad 726 481 245 709 461 249 4 2Örsundaån Härnevi 738 448 290 715 468 248 -42 14Hågaån Lurbo 750 436 313 716 450 265 -48 15Sävaån Ransta 734 456 278 715 464 251 -27 10Sävjaån Sävja 732 488 245 719 464 254 9 4Stalbobäcken Tärnsjö 733 462 272 728 472 257 -15 6Stabbybäcken Stabby 639 458 235 709 463 246 11 5
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.
Chapter 6 Model validation
- 68 -
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
Basin FyrisånSynoptic measurements
0
5
10
15
20
25
30
0 5 10 15 20 25 30
Simulated discharges (m^3/s)Obs
erve
d di
scha
rges
(m^3
/s)
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Simulated discharges (m^3/s)Obs
erve
d di
scha
rges
(m^3
/s)
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
Chapter 6 Model validation
- 69 -
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 40-
60 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.
Chapter 6 Model validation
- 70 -
Ground water level, Dansarhällarna
Soil moisture, Buddby
Ground water level, Buddby
Soil moisture, Östfora
Soil moisture, Marsta
Ground water level, Östfora
Soil moisture, Tärnsjö
Soil moisture, Dansarhällarna
Figure 6.4 Observed and modelled soil moisture content groundwater levels, each cross
represents a spatial average, compare Table 4.4.
Chapter 6 Model validation
- 71 -
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 -16CFE2 18 April - 14 July 1995 215 289 82 -156
∆W - Water supply changes in soil and groundwater zone.
Chapter 6 Model validation
- 72 -
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
Chapter 6 Model validation
- 73 -
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 1995Basin Qo
(mm)Qs
(mm)Qomax(m3/s)
Qsmax(m3/s)
Qo
(mm)Qs
(mm)Qomax(m3/s)
Qsmax(m3/s)
Fyrisån 4 6 3.0 3.0 100 105 29 29
Sagån - 6 - 2.0 112 95 31 32
Lillån 3 6 0.2 0.5 94 103 9.6 11
Örsundaån 3 5 0.7 0.8 75 90 12 20
Hågaån 4 3 0.4 0.3 94 89 5.9 9.2
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
Total gauged area - 6 - 9.4 97 97 101 138
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.
Chapter 6 Model validation
- 74 -
a)
Chapter 6 Model validation
- 75 -
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
Chapter 6 Model validation
- 76 -
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).
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.
0
1
2
3
4
5
0 1 2 3 4 5ECOMAG-model (mm/day)
Mas
t who
le re
gion
(mm
/day
)
Chapter 7 Conclusions
- 77 -
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
Chapter 7 Conclusions
- 78 -
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.
Notation and dimensions
- 79 -
8. Notation and dimensions
AbbreviationsASCII American Standard Code for Information InterchangeBALTEX The Baltic Sea ExperimentCFE Concentrated Field EffortsDEM Digital Elevation ModelECOMAG ECOlogical Model for Applied GeophysicsGCM Global Circulation ModelGIS Geographical Information SystemNOPEX NOrthem hemisphere climate Processes land-surface ExperimentREA Representative Elementary AreaREV Representative Elementary VolumeSHE Systieme Hydrologigue EuropeanSINOP System of Information in NOPexSMHI Swedish Meteorological and Hydrological InstituteSVAT Soil-Vegetation-ATmosphere schemeTOPMODEL TOPography based hydrological MODEL¨WATBAL WATer BALance hydrological modelWPI Water Problems Institute
Notations and dimensionsSymbol Description Units
Main constants and variablesx,y,z Co-ordinates mt Time day, sLf Latent heat of ice fusion 179.0 kkal kg-1
ρi Density of ice 917 kg m-3
ρw Density of water 1000 kg m-3
Geometrical characteristicsi Slope m m-1
B Width mL Length mZ Thickness m
Meteorological characteristicsd Deficit of air vapour pressure mbR Rate of precipitation m day-1
Rr Rate of rain precipitation m day-1
Rs Rate of snow precipitation m day-1
T Air temperature oCMain hydrological variables
H Depth of water (snow) layer mE Actual evapotranspiration m day-1
Epot Potential evaporation m day-1
I Volumetric content of ice per unit of volume m3 m-3
Q Horizontal water flux (discharge) m3s-3 , m3 day-1
V Vertical water flux m day-1
W Volumetric content of water per unit of volume m3 m3
Notation and dimensions
- 80 -
Symbol Description UnitsSnow cover
kT Degree day factor m day-1 oC-1kc Parameter of snow compaction m2 kg-1 day-1
vs Velocity of snow compaction m day-1
ST Rate of snowmelting m day-1
Sf Rate of frost of meltwater in snow m day-1
Tcr Threshold air temperature for precipitation oCTM Threshold air temperature for snowmelting oCT0 Temperature on the soil-snow surface oCWHC Water holding capacity m3 m-3
ρn Density of new snow kg m3
λs Heat conductivity of snow w m-1daySurface
ke Potential evaporation parameter m day-1 mb-1
n Manning roughness coefficient day m-0.33
R0 Effective rainfall excess mϕo Maximal depression storage mϕ Actual depression storage m
SoilConstants
FC Field capacity m3 m-3
FCM Maximum value of FC m3 m-3
WP Wilting point m3 m-3
P Total porosity m3 m-3
C =FC-WP capillary porosity m3 m-3
D =P-FC non-capillary porosity m3 m-3
WE =(FC-WP)/2 critical moisture for E m3 m-3
ρ Volumetric density of dry soil kg m-3
Unfrozen soilK Vertical saturated hydraulic conductivity m day-1
KX Horizontal saturated hydraulic conductivity m day-1
lt Heat conductivity w m-1dayFrozen soil
Hf Frost depth mHt Thaw depth mKf Vertical saturated hydraulic conductivity m day-1
Wu Volumetric content of unfrozen water M3 M-3λf Heat conductivity w m-1day
Ground waterHg Depth of groundwater level mTg Temperature of groundwater oCVd Rate of water exchange between upper groundwater
zone and dipper layersm day-1
Notation and dimensions
- 81 -
Probability characteristicsSymbol DescriptionF Distribution functionF0 Probability of exceedanee distribution functionR2 Nash-Sutcliffe coefficientα,β Parameters of probability distribution functions
IndicesC Characteristics for capillary zonel Characteristics for liquid phase of waterm Mean valuenc Characteristics for non-capillary zones Characteristics for solid phase of water (ice)L Characteristics for lower boundary of element on plane0 Characteristics for upper boundary of element on plane1 Characteristics for surface storage2 Characteristics for horizon A of soil3 Characteristics for horizon B of soil4 Characteristics for groundwater zone5 Characteristics for snow cover6 Characteristics for river network
References
- 82 -
9. References
Abbott, M.B., J.C.Bathurst, J.A.Cunge, P.E.O’Conell and J.Rasmussen (1986) An
introduction to the European Hydrological System, “SHE”. Journal of Hydrology
87(1/2):45-77.
Arnell N.W. (1993) Data requirements for macroscale modelling of the hydrosphere. In:
Macroscale Modelling of the Hydrosphere (Proc. Of the Yokohama Symp., July 1993),
IAHS Publ., 214:139-149.
Barancourt, C., J.D.Creutin and J.Rivoirard (1992) A method for delineating and
estimating rainfall fields. Water Resources Research 28(4): 1133-1144
Baver, L.D. (1965) Soil physics. Wiley, New York
Beldring, S., L.Gottschalk, J.Seibert and L.M.Tallaksen (1998) Distribution of soil moisture
and groundwater levels in the patch and catchment scale. Accepted for publication in the
NOPEX special issue of Journal of Agricultural and Forest Meteorological Research
Bergström, S. (1976) Development and application of a conceptual runoff model for
Scandinavian catchments. Swedish Meteorological and Hydrological Institute RHO
Report 7, Norrköping.
Beven K.J. (1989). Changing ideas in hydrology - the case of physically based models.
Journal of Hydrology, 105: 157-172
Beven, K.J. and A.Binley (1992) The future of distributed models - model calibration
and uncertainty predictions. Hydrological processes, 6: 279-298
Beven, K.J., and M.J.Kirkby (1979) A physically based, variable contributing are model
of basin hydrology. Hydrological Sciences Journal 24(1):43-69.
References
- 83 -
Beven K.J. (1997) Process heterogeneity and scale in modelling soil moisture fluxes. NATO
ASI Series 1: Global Environmental Change, 46:191-214.
Brutsaert W. (1982) Evaporation into atmosphere. D.Reidel Pub. Co., Dordrecht, Holland.
Chenevey, R. (1995) Hydrological modelling and erosion potential. A GIS and remote
sensing approach. Royal Institute of Technology, Bull. No. TRITA-VBI-166,
Stockholm, Sweden.
Crochet P. (1997) Radar assessment of rainfall for the NOPEX area. Department of
Geophysics, University of Oslo Section 3.1, Precise from Philip
Dümenil, L., and E.Todini (1992) A rainfall-runoff scheme for use in the Hamburg
climate model. In: J.P.O'Kane (ed.) Advances in Theoretical Hydrology. A tribute to
James Dooge, Elsevier, Amsterdam: 129-158.
Erichsen, B., S. Beldring and A. Rohde (1995) Mesoscale runoff variability in the NOPEX
area (Abstract). Annales Geophysicae, Part II, Supplement II to Volume 13.
Feddes, R.A., E.Bresler and S.P.Neuman (1974) Field test of modified numerical model
for water uptake by root systems . Water Resources Research 10(6): 1166-1206.
Gottschalk, L. and A.Askew (1987) Hydrology and data acquisition. In: Hydrology
2000, IAHS Publ., 171:79-90
Gottschalk, L., E.Batchvarova, S.E.Gryning, A.Lindroth, D.Melas, Yu.Motovilov,
M.Frech, M.Heikinheimo, P.Samuelsson, A.Grelle and T.Persson (1998,a) Scale
aggregation - comparison of flux estimates from NOPEX. Submitted to the NOPEX
special issue of Journal of Agricultural and Forest Meteorological Research.
References
- 84 -
Gottschalk, L., S.E.Gryning, Yu.G.Motovilov and S.Beldring (1998,b) NOPEX
modelling activities: Towards a coupled hydrological and meteorological mesoscale
model. Fifth Meeting of the BALTEX SSG, Riga, Latvia April 1997. International
BALTEX Sectreteriat Publication No 10: A33-A42.
Halldin, S., and L-C.Lundin, (1994) SINOP-system for information in NOPEX. NOPEX
Technical Report No. l, Institute of Earth Sciences, Uppsala University.
Halldin,S., L.Gottschalk, A.A.Van de Griend, S-E.Gryning, M.Heikinheimo, U.Högstrom,
A.Jochum and L-C. Lundin (1995) Science plan for NOPEX. NOPEX Technical report No.
12, Institute of Earth Sciences, Uppsala University.
Halldin,S., L.Gottschalk, A.A.Van de Griend, S-E.Gryning, M.Heikinheimo, U.Högstrom,
A.Jochum and L-C. Lundin (1998) NOPEX - a northern hemisphere climate processes land
surface experiment. Accepted for publication in a BACH special issue of Journal of
Hydrology.
Klemes, V. (1985) Sensitivity of water-resources systems to climate variations. WCP
Report 98, WMO, Geneva.
Klemes, V. (1986) Operational testing of hydrological simulation models. Hydrological
Sciences Journal 31(1):13-24.
Knudsen,J., A.Thomsen and J.Chr.Refsgaard (1986) WATBAL: a semi-distributed
physically based hydrological modelling system. Nordic Hydrology 17:347-362.
Korzun,V.I. (ed.) (1978) World water balance and water resources of the Earth.
UNESCO, Studies and Reports in Hydrology 25.
References
- 85 -
Krasovskaia, I. (1988) A study of mesoscale runoff varaibility. Geografiska Annaler 70A:
191-201.
Kuchment, L.S., V.N.Demidov and Yu.G.Motovilov (1983) Formirovanie rechnogo stoka:
fisiko-matematicheskie modeli (River runoff formation: physically based models) (in
Russian). Nauka, Moscow.
Kuchment, L.S., V.N.Demidov and Yu.G.Motovilov (1986) A physically based model of the
formation of snowmelt and rainfall runoff. In: Modelling Snowmelt-Induced Processes
(Proc. Budapest Symp., July 1986), IAHS Publ., 155:27-36.
Kuchment, L.S., Yu.G.Motovilov and N.A.Nazarov (1990) Chuvstvitelnost’ gidrologicheskih
system – vliyanie antropogennyh izmeneny rechnyh basseinov i klimata na gidrologicheski tsikl
(Sensitivity of hydrological systems - effects of human activity and climate changes on
hydrological cycle) (in Russian). Nauka, Moscow.
Maidment D.R., ed. (1993) Handbook of hydrology. McGraw-Hill, Inc, USA.
Motovilov, Yu.G. (1986) A model of snow cover formation and snowmelt processes. In:
Modelling Snowmelt-Induced Processes (Proc. Budapest Symp., July, 1986), IAHS Publ.,
155:47-57.
Motovilov, Yu.G. (1987) Modelling the effects of agrotechnical measures on spring runoff
and water erosion. In: Large Scale Effects of Seasonal snow Cover (Proc. of the Vancouver
Symp., August 1987), IAHS Publ., 166:241-251.
Motovilov, Yu.G. (1993) The modelling of snowcover formation and snowmelt. In: The
Modelling of the Hydrological Cycle for River Basins. Results of Research on the
International Geophysical Projects. Russ. Nat. Geoph. Comm., Moscow:27-42.
References
- 86 -
Motovilov Yu.G. (1995) ECOMAG: Regional model of hydrological cycle and pollution
transformation in river basins (Application to the NOPEX region). Oslo, Moscow 1995.
Motovilov,Yu.G., and A.S.Belokurov (1997) Modelirovanie ptotsessov perenosa i
transformatsii zagrjaznenii v rechnom basseine dlja zadach ecologicheskogo
monitoringa (Modeling of a transfer processes and pollution transformation in river
basin for ecological monitoring) (in Russian). Inst. Appl. Geophys. Publ., 81:49-60.
Motovilov, Yu.G., and N.A.Nazarov (1991) Modelled estimates of changes in the water
balance of forested northern river basins. In: Northern Hydrology: Selected Perspectives
(Proc. North. Hydr. Symp., July, 1990, Saskatoon, Saskatchewan, Canada), NHRI
Symp., 6: 499-513.
Motovilov,Yu.G., L.Gottschalk, K.Engeland and A.Rodhe (1998) Validation of a distributed
hydrological model against spatial observations. Accepted for publication in the NOPEX special
issue of Journal of Agricultural and Forest Meteorological Research.
Nash, J. E. and J.V.Sutcliffe, (1970) River flow forecasting through conceptual models
part 1 - A discussion of principles. Journal of Hydrology 10: 282-290
National Research Council (1991) Opportunities in the Hydrological Sciences. National
Academy Press, Washington D.C..
Nyberg, L. (1995) Soil- and Groundwater Distribution, Flowpaths, and Transit Times in
a Small Till Catchment. Acta Universitatis Upsaliensis, Uppsala, Sweden.
Popov, E.G. (1979) Gidrologicheskie prognozy (Hydrological forecasts) (in Russian).
Gidrometeoizdat, Leningrad.
References
- 87 -
Refsgaard J.C. (1997) Model and data requirements for simulation of runoff and land. NATO
ASI Series 1: Global Environmental Change, 46:423-452.
Rose, C.W., J.-Y. Parlange, G.C. Sander, S.Y. Campbell and D.A. Barry (1983)
Kinematic flow approximation to runoff on a plane: an approximate analytic solution.
Journal of Hydrology, 62: 363-369.
Rosenbrock, H.H. (1960) An automatic method for finding the greatest or least value of
a function. Computer Journal, 17(3):175-184.
Sausen, R., S.Schubert and D.Dümenil. (1994) A model for river runoff for use in
coupled atmosphere - ocean models. Journal of Hydrology, 155: 337-352.
Seibert, P. (1994) Hydrological characteristics of the NOPEX research area. NOPEX
Technical Report No 3, Institute of Earth Sciences, Uppsala University.
Stähli, M., K.Hessel, J.Eriksson and A.Lindhal (1996) Physical and chemical
description of the soil at the NOPEX central tower site. NOPEX Technical Report No
16, Institute of Earth Sciences, Uppsala University
Sulebak, J.R. (1997) Geomorphometric studies of different topographic regions: analyses
and applications from Norway and Sweden. Department of Geography, University of Oslo
Tallaksen, L. and B. Erichsen (1995) Intercalibration of soil moisture measurements using
oscilloscope and TDR devices. Internal report Department of Geography, University of Oslo
Thomas, G., and P.R.Rowntree (1992) The boreal forest and climate. Q. J. R. Meteorol.
Soc. 118: 469-497.
Tourula, T., A.Heikinheimo, B.Vehvilainen and S.Tattari 1997:Micrometeorological
measurements on lakes Tämnaren and Råksjö during CFE1 and CFE2. 25 pp. Finnish
References
- 88 -
Meteorological Institute, Helsinki, Finland.
Vehvilainen B. and Yu.G.Motovilov (1989) Simulation of soil frost depth and effect on
runoff. Nordic Hydrology, 20:9-24.
Vinogradov Yu.B. (1988) Matematicheskoe modelirovanie protsessov formirovanija
stoka (Mathematical modelling of runoff formation processes) (in Russian),
Gidrometeoizdat, Leningrad.
Vörösmarty,C.J., and B.Moore (1991) Modelling basin-scale hydrology in support of
physical climate and global geochemical studies: an example using the Zambezi River,
Surveys in Geophysics 12:271-311.
Vörösmarty,C.J., B.Moore, A.L.Grace, M.P.Gildea, J.L.Melillo, B.J.Peterson, E.B.Rastetter
and P.A.Steudler (1989) Continental scale models of water balance and fluvial transport: an
application to South America. Global Biogeochemical Cycles 3:241-265.
Wood, E.F., M.Sivapalan and K.J.Beven (1990) Similarity and scale in catchment storm
response. Rev. Geophys. 28:1-18.
Wood, E.F., M.Sivapalan, K.J.Beven and L.Band (1988) Effects of spatial variability and
scale with implications to hydrological modelling. Journal of Hydrology 102:29-47.
Yosida Z. et al. (1955) Physical studies on deposited snow. Contrib. Inst. Low Temp.
Sci. Sapporo, 7:19-74.