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


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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


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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.


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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

0

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1 10 100 1000 10000 100000

Square root of area (m)

Vol

umet

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oist

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19. June 1996

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Gro

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Gro

undw

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tabl

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(m)

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


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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


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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


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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


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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):


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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


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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.


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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.


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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):


- 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


- 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


- 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.


- 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.


- 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.


- 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).


- 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


- 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.


- 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:


- 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:


- 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


- 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)


- 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):


- 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:


- 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):


- 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)


- 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;


- 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


- 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


- 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

�

��−

−−−=

QQ

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


- 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


- 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


- 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


- 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


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


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


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


Figure 5.6 Observed and simulated runoff at Ulva Kvarndam, Fyrisån, for calibrated years


- 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


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


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


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


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


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


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


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


- 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


- 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.


- 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


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


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


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


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


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


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


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


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


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


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


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


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


- 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


- 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).


- 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


- 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


- 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


- 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).


- 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


- 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


- 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.


- 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


- 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.


- 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.


- 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.


- 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


- 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.


- 74 -

a)


- 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


- 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


- 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


- 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

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