Agricultural and Forest Meteorology 98±99 (1999) 257±277
Validation of a distributed hydrological model
against spatial observations
Yuri G. Motovilova,*,1, Lars Gottschalka, Kolbjùrn Engelanda, Allan Rodheb
a
Department of Geophysics, University of Oslo, PO Box 1022, Blindern, 0315 Oslo, Norway
b
Department Hydrology, Institute of Earth Sciences, Uppsala, Sweden
Abstract
In connection with climate change studies a new hydrologic ®eld has evolved Ð regional hydrological modelling or
hydrologic macro modelling, which implies repeated application of a model everywhere within a region using a global set of
parameters. The application of a physically based distributed hydrological model ECOMAG to river basins within the NOPEX
southern region with this purpose in mind is presented.
The model considers the main processes of the land surface hydrological cycle: in®ltration, evapotranspiration, heat and
water regime of the soil, snowmelt, formation of surface, subsurface and river runoff and groundwater. The spatial integration
of small and meso-scale non-homogeneity of the land surface is a central issue both for the de®nition 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 re¯ects topography, soil, vegetation and land use. As a
®rst step the model was calibrated using standard meteorological and hydrological data for 7 years from regular observation
networks for three basins. An additional adjustment of the soil parameters was performed using soil moisture and groundwater
level data from ®ve small experimental basins. This step was followed by validation of the model against runoff for 14 years
from six other drainage basins, and synoptic runoff and evapotranspiration measurements performed during two concentrated
®eld efforts (CFEs) of the NOPEX project in 1994 and 1995. The results are promising and indicate directions for further
research. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Hydrological model; Evapotranspiration; NOPEX
1. Introduction
Hydrological models account for the storage and
¯ow 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 sophis*
1
Corresponding author.
On leave from Institute for Applied Ecology, Moscow, Russia.
tication and complexity. Most of these models apply to
geographical areas smaller than the area represented
by a typical GCM grid square, although some basinscale 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
0168-1923/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 1 9 2 3 ( 9 9 ) 0 0 1 0 2 - 1
258
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
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 these hydrological
models. Ultimately, it must be possible to apply the
model globally. There are no data to calibrate macroscale 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. Among the
general requirements of hydrological models designed
to assess the sensitivity of water resources to climate
processes (Klemes, 1985) are the following:
1. They must be geographically transferable and this
has to be validated in the real world;
2. 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 and this is the scheme
followed here.
Most 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 approaching the issue of scale (aggregation/
disaggregation) that is the focal scienti®c problem.
Thus, a new hydrologic research ®eld has evolved Ð
regional hydrological modelling or hydrologic macromodelling. This new concept implies an application
of a hydrological model over a large spatial domain
(at least 105 km2) or, more precisely, the 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 modi®cations, Korzun, 1978, more recent ones
are provided by VoÈroÈsmarty et al., 1989; VoÈroÈsmarty and Moore, 1991; DuÈmenil and Todini,
1992, Sausen et al., 1994).
2. `Bottom-up' which identi®es 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 realising
that 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 scienti®c 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 us with such data.
Here data from the northern hemisphere climate
processes land-surface experiment (NOPEX) (Halldin
et al., 1995, 1999) are utilised for calibration and
validation of a physically based distributed hydrological model ECOMAG (Motovilov et al., 1999). The
NOPEX study region is chosen to represent northern
landscapes such as the boreal forests, which play an
important role in global hydrological and biogeochemical cycles (Thomas and 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.
The validation of the ECOMAG model performed
here is a test of its ability to live up to the demands for
a macro hydrological model. The following steps have
been de®ned:
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Calibration of the model against runoff for three
basins with one global set of parameters.
Adjustment of the soil parameters of the model
against soil moisture and groundwater level data
from five small experimental sub-basins.
Validation against synoptic measurements of
runoff.
Validation against runoff in six other basins that are
not 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 tests undertaken. The results of the validation
will however point to critical issues indicating how the
model process formulation and parameterisation can
be improved.
An introductory part of the paper presents in brief
the main features of the ECOMAG model and the
basic datasets used for model calibration and validation. The scale issue is of importance for de®nition of
the spatial grid resolution of the model and for comparing data measured at `points' with modelled data
representing grid cells. These aspects are discussed
®rst to give a background to the model formulation
and also to the description of the validation procedure.
Finally, some conclusions based on the gained experience are drawn.
2. NOPEX
The model development is centred on data from the
NOPEX experiment, performed north of the city of
Uppsala in southern Sweden. The southern NOPEX
region is an area of low relief with heterogeneous
surface cover, represented by coniferous and mixed
forest (57%), open land (mainly agricultural) (35.8%),
mires (2.6%), lakes (2.6%) and urbanised areas (2.0%)
(evaluated from digital maps of the National Land
Survey of Sweden). The area is therefore very suitable
for studying the inter- and intra-patch variability of
energy and mass exchange processes.
An extensive amount of meteorological and hydrological data collected during the NOPEX concentrated
®eld efforts (CFE) CFE1 (27 May±23 June 1994) and
CFE2 (18 April±14 July 1995) has been utilised in the
259
process of setting up the model, its calibration and
validation:
Geographical data including a digital terrain model
with a resolution of 50 m and land use data with
25 m resolution (both datasets from the National
Land Survey of Sweden) and a comprehensive
digitised soil map with a resolution of 2 km (from
Seibert, 1994).
The regular hydrological discharge observation
network run by 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 (Fig. 1)
which provided 24 h average values for the period
1981±95.
Data (daily values) from 25 precipitation stations, 7
temperature stations and 5 stations for vapour
pressure deficit for the period 1981±95 from the
regular climatic observation network run by SMHI
were used. The temperature and vapour pressure
deficit were interpolated to a regular 2 km grid by
inverse distance weighting and the precipitation
was interpolated by kriging.
Detailed hydrological studies concentrated in five
experimental basins (see Fig. 1 for location) during
the NOPEX 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, and
nose) within the experimental basins. This dataset
comprises about 2000 individual measurements of
groundwater levels and about 16 000 measurements of soil moisture content (the measurements
were also performed outside CFE periods) (Tallaksen et al., 1999).
Synoptic discharge measurements at 38 sites in the
FyrisaÊn river basin on four occasions during recession. The procedure for these measurements followed that reported by Krasovskaia (1988) and
Rodhe et al. (1999).
3. Scale issues
An ambition within the NOPEX project is to bring
insight into the scale of variation. For this purpose
260
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Fig. 1. The NOPEX area showing the nine gauged drainage basins and five experimental basins.
spatial data for the NOPEX area (digital terrain data:
topography, land use, 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 (Sulebakk,
1997). Soil moisture, groundwater and synoptic runoff
measurements were analysed with the aim of identifying spatial scales (patches, representative areas) of relevanceforaggregationapproaches(Beldringetal.,1999).
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
respect. 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 suf®cient
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 those
characteristics but only of their distribution. The
underlying variability may still be important in controlling both discharges and evaporation ¯uxes, but the
patterns are less important. The scale at which this
happens de®nes 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 ¯uxes. In the REA the
distribution of characteristics may still be important in
determining the ¯uxes.
Fig. 2 shows examples of plots used to identify the
REA for terrain with till soils. The soil moisture and
groundwater level data were obtained by the measurements in the NOPEX area during CFEs periods. A
preliminary conclusion is that for this type of terrain
the main part of the spatial variability in soil moisture
and groundwater ¯uctuations is contained in the 2 km
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
261
Fig. 2. Spatial variation of soil moisture and groundwater levels as a function of scale of aggregation (from Beldring et al., 1999).
grid size used for modelling (Beldring et al., 1999).
Theoretical distribution functions have been developed that can take into account this variability.
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
2 km runoff is delivered to the river network and that
rivers provide the only exchange between grid cells in
this type of landscape. The exchange through groundwater ¯ow is of negligible order, as there are no runoff
formation factors acting at a between grid cell scale
(no signi®cant gradients in soil moisture content and
groundwater levels between grid cells at this 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 re¯ect the full small
scale variability as illustrated by the left-hand side of
the diagrams in Fig. 2. Measured data must be averaged to the REA scale to be able to match model
output.
4. Hydrological model formulation
Distributed hydrological models allow the determination of the water balance and its variation across
river basins. Several such models are in common use
(i.e. SHE-model, Abbott et al., 1986; TOPMODEL,
Beven and Kirkby, 1979; WATBAL Knudsen et al.,
1986) but none of them explicitly contains components re¯ecting important characteristics of the boreal
landscape like mires, lakes and the close relationship
between soil moisture and groundwater in the till soil.
Preliminary analyses of surveys of runoff data indicate
that the main factors, which explain the spatial variation in runoff, are the frequency of lakes and mires in
upstream areas (Erichsen et al., 1995). Consequently,
a distributed hydrological model ECOMAG (Motovilov and Belokurov, 1997; Motovilov et al., 1999)
developed for application to boreal conditions was
used. The model describes the processes of soil in®ltration, evapotranspiration, thermal and water regimes
of the soil, surface and subsurface ¯ow, groundwater
262
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
and river ¯ow, snow accumulation and snowmelt. In
its original form a drainage basin is approximated by
irregular triangular or trapezoidal elements, taking
into consideration peculiarities of topography (size,
form and slope), soil types (peat, clay, sand, till,
bedrock), vegetation and land use (open area, forest,
lake, mire, urban area) in a GIS framework. This
version of the model has already been applied and
tested in Russia. It is based on 15-year's experience of
the development and application of distributed physically based hydrological models (Kuchment et al.,
1983, 1986, 1989; Motovilov, 1986, 1987, 1993).
A second version of the model is now under
development (Gottschalk et al., 1998) and the present
paper is a step in this new direction. The main change
is the use of a regular grid network (2 km 2 km)
in order to, with further development, allow direct
coupling with a meso-scale meteorological model
and the use of radar-evaluated precipitation data
(Crochet, 1999).
The basic assumption of the model is that a river
basin can be sub-divided into a mosaic of irregular or
regular elements, each to be viewed as a landscape
hydrological unit. The REA concept referred to above
is of vital importance here as it constitutes a minimum
size for such an element. The speci®c characteristics
of topography, structure of river network, soil types,
land use etc. for each element are determined in a GIS
framework.
The hydrological model for a landscape unit was
constructed in conformity with the following scheme
taking into account the processes of hydrological
cycle (Fig. 3). During a summer period the rain
partially in®ltrates into the soil and penetrates into
Fig. 3. Block-scheme of the ECOMAG model structure for a fundamental landscape unit.
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
deeper soil layers. The soil is divided into a top layer
(horizon A), an intermediate layer (horizon B) and a
bottom layer (groundwater storage). The total porosity
of the soil is divided into two parts: a capillary zone
(the upper limit of which is the ®eld capacity) and a
noncapillary zone (the difference between total porosity and ®eld capacity).
After the ®lling of depressions on the surface, the
excess of water, not absorbed by the soil, runs off on
the sloping land surface to the river network (surface
¯ow). A part of the water, which was in®ltrated into
the soil, follows a temporary, relatively impermeable,
boundary along the slopes as shallow groundwater
(subsurface) ¯ow. Another part is transported in the
groundwater zone and forms base ¯ow. The subsurface and groundwater ¯ow is modelled as a Darcy
¯ow, while the surface and river runoff is described by
a simpli®ed version of the kinematic wave equation
(Rose et al., 1983).
Under the condition of high soil moisture content,
the actual evaporation equals the potential, and then
linearly decreases with the decay of the soil moisture
content to a certain lowest level, being zero at the soil
moisture content equal to the wilting point (Feddes
et al., 1974).
Lake-element in the area is described as a storage
with recession coef®cient de®ned on the basis of the
kinematic wave equation. The actual evaporation is
taken equal to the potential one.
During cold periods of the year, the scheme is
supplemented by hydrothermal processes Ð snow
cover formation, snowmelt, freezing and thawing of
the soil, and in®ltration of snowmelt water into the
frozen soil. The phase composition of precipitation is
determined by the daily average air temperature. The
snowmelt rate is calculated using the degree-day
method. Evaporation of solid and liquid phases of
snow is estimated using data on vapour pressure
de®cit.
It is assumed that the vertical temperature pro®les 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).
In®ltration of rain and meltwater into the frozen soil is
calculated, taking into account the in¯uence of ice
263
content in the frozen soil on the hydraulic conductivity
of the soil.
The landscape information extracted from the GIS
only grasps large scale features. Small scale ¯uctuations 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 simpli®cation is to
use the same distribution for all elements only allowing its mean value to vary between elements. In
ECOMAG the within element variability is taken into
consideration in this manner for three parameters Ð
the vertical saturated hydraulic conductivity of soils,
surface depression storage and soil ®eld capacity. For
the ®rst two parameters an exponential function is
applied (Popov, 1979; Vinogradov, 1988) and for the
third Ð a parabolic function (BergstroÈm, 1976;
DuÈmenil and Todini, 1992).
5. Model calibration procedure
Many of the equations in a physically based model
contain parameters and coef®cients that have a direct
physical interpretation and, in principal, can be measured in the ®eld. Such parameters of the ECOMAG
model are, in particular, the soil parameters with the
exception of the horizontal hydraulic conductivity
(Table 1). The initial values of these parameters for
the different soil types were determined on the basis of
regional information of agrohydrological properties of
soils, supplemented by data from Nyberg (1995) and
StaÈhli et al. (1996).
For other parameters, experimental results have
allowed the establishment of empirical relations (heat
conductivity of soil and snow) or indicated reasonably
well de®ned limits for parameter values (degree-day
factor for snowmelt). In still other cases, the limits are
not so well de®ned (for example, horizontal hydraulic
conductivity for the calculation of shallow groundwater ¯ow) and these parameter values must be
determined by calibration. The fact that not all parameters are well de®ned originates from scale issues
and inadequacies in the model description. The various groups of parameters in the model may be
calibrated in separate steps using only data about
the dynamics of evapotranspiration, soil moisture,
264
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Table 1
Model calibration parametersa
Snow routine
Degree-day factor
Threshold temperature*
Water holding capacity*
Parameter of snow compaction*
Soil routine
Depth of horizon A
Porosity
Field capacity
Wilting point
Vertical hydraulic conductivity
Horizontal hydraulic conductivity
Factor for potential evaporation*
Surface runoff routine
Surface retention storage
Surface roughness (Manning coefficient)
River runoff routine
River bed roughness (Manning coefficient)*
a
Parameters with asterisk (*) have one unique value for the
whole NOPEX area, while the others have different values for
different soil and land use types.
groundwater, snow cover, frozen soil and river runoff,
respectively. As a ®rst step in the calibration procedure
the soil water parameters for different soil types were
adjusted using soil moisture and groundwater level
data on ®ve experimental river basins in the NOPEX
area during 1994±95 including CFE periods. These
basins were considered as the REA units representing
different landscapes. The adjustment was carried out
by manual inspection by means of a visual comparison
of simulated and observed dynamics of soil moisture
and groundwater levels. In a second step, the remaining model parameters were calibrated against runoff.
This latter calibration and evaluation of the performance of ECOMAG were done using the Nash±Sutcliffe ef®ciency measure R2 (Nash and Sutcliffe,
1970). InP
this the sum of squared residuals is de®ned
q0 ÿq†2 where F2 is the index of disagreeas: F 2 ˆ
ment and q and q0 are the observed and computed
discharges at corresponding times. F2 is analogous to
the residual variance of a regression analysis. The sum
is taken over a selected time period.
The initial
P
qÿ
q†2 where q
variance,F02 , is de®ned by F02 ˆ
is the mean of the observed q and the sum is taken as
before. It can be interpreted as the total variance of the
data. This enables the ef®ciency of a model to be
de®ned by R2 as the proportion of the initial variance
accounted for by that model.
R2 ˆ
F02 ÿF 2
F02
(1)
This R2 is analogous to the explained variance (the
squared multiple correlation coefficient) in multiple
regression. In regression analysis R2 can take values
between zero and one only. Zero is the worst model fit
when all the computed values are equal to the mean
value q. The best value, one, is gained when the sum of
squared residuals is zero. The calibration of a dynamic
model is not directly analogous to a regression problem and the squared sum of residuals can, in principle, be higher than the variance of the data. The
possible theoretical range for R2 is thus from minus
infinity to one. A negative value would indicate a very
bad model performance while values near to one
indicate a good performance.
The calibration of the model parameters against
discharge data was done simultaneously for a number
of river basins with different conditions of runoff
formation to ®nd a global parameter set for the whole
NOPEX area. The calibration was performed using a
Rosenbrock optimisation procedure (Rosenbrock,
1960). The criterion of optimisation was calculated
as a mean value of R2 for these river basins during the
optimisation period.
6. Results of calibration and validation
6.1. Runoff at gauging stations
Calibration of model parameters against runoff was
carried out in three river basins, different in size and
conditions of ¯ow formation: FyrisaÊn (at Ulva Kvarn)
with an area of 950 km2; LillaÊn (at GraÈnvad) with an
area of 168 km2and StabbybaÈcken (at Stabby) with an
area of 6.2 km2. Seven years of observation were used
in the calibration: 1986±93. These years were the most
dif®cult for modelling with the presence a number of
years with low annual ¯ow and unstable winters. The
remaining 7 years of observations were used for the
validation purposes. Table 2 contains an overview of
the model ef®ciency R2 for all basins and all years, a
total of 136 station years. Of these 21 have been used
for calibration (marked with bold in the table) and the
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
265
Fig. 4. Calibration model runs for FyrisaÊn, LillaÊn and StabbybaÈcken.
rest for validation. Fig. 4, showing observed and
modelled hydrographs, illustrates the model performance for basins and years used for calibration.
Satisfactory agreement between the observed and
simulated runoff has been obtained. The model performance is better for 1986/87 than for 1988/89 in all
three catchments. This re¯ects that when the simulations are wrong, often the same error can be found in
all catchments. Especially in the period around day
241 in 1988/89 can be noted. The simulated runoff
values are too low for all three catchments, probably
due to error in the modelling of snow cover. This is
also re¯ected in the period after day 301 where the
simulated runoff values are all too high. It is also
interesting to note the differences between the catchments. For example, the ¯ow peak between day 61 and
121 in 1986/87 is wrongly simulated in all three
catchments. In FyrisaÊn it is too low, in LillaÊn it is a
266
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Table 2
Model performance efficiency (R2) for the gauged river basins in the NOPEX areaa
Year
Basin
FyrisaÊn
SagaÊn
LillaÊn
È rsunO
daaÊn
HagaaÊn
SaÈvaaÊn
SaÈvja-aÊn
StalbobaÈcken
StabbybaÈcken
Total gauged
area
1981/82
1982/83
1983/84
1984/85
1985/86
1986/87
1987/88
1988/89
1989/90
1990/91
1991/92
1992/93
1993/94
1994/95
0.73/0.76
0.81/0.84
0.72/0.78
0.78/0.84
0.83/0.88
0.88/0.94
0.86/0.91
0.70/0.84
0.91/0.93
0.77/0.92
0.80/0.87
0.90/0.94
0.70/0.87
0.72/0.78
0.60/0.64
0.56/0.60
0.57/0.61
0.83/0.86
0.50/0.28
0.48/0.46
0.48/0.51
0.25/0.33
0.69/0.76
0.35/0.19
±
±
±
±
0.72/0.72
0.62/0.70
0.65/0.81
0.75/0.90
0.69/0.74
0.57/0.71
0.72/0.85
0.32/0.46
0.66/0.77
0.62/0.84
0.60/0.77
0.74/0.78
0.40/0.76
0.61/0.78
0.83/0.88
0.52/0.73
0.64/0.72
0.84/0.94
0.80/0.81
0.69/0.72
0.76/0.85
0.22/0.60
0.77/0.85
0.62/0.74
0.52/0.70
0.71/0.73
0.39/0.71
0.53/0.91
0.64/0.75
0.43/0.83
0.56/0.82
0.77/0.96
0.76/0.81
0.53/0.71
0.56/0.66
0.26/0.64
0.70/0.92
0.53/0.62
0.19/0.44
0.64/0.78
0.59/0.74
0.24/0.70
0.76/0.83
0.62/0.80
0.69/0.75
0.90/0.96
0.82/0.91
0.73/0.84
0.75/0.80
0.27/0.64
0.80/0.89
0.71/0.78
0.57/0.80
0.65/0.72
0.55/0.75
0.69/0.91
0.65/0.73
0.53/0.61
0.50/0.63
0.82/0.93
0.86/0.90
0.69/0.77
0.66/0.77
0.19/0.58
0.83/0.88
0.60/0.65
0.63/0.77
0.78/0.85
0.61/0.80
0.69/0.84
0.14/0.29
0.70/0.72
0.84/0.83
0.75/0.88
0.30/0.20
0.45/0.54
0.75/0.83
0.62/0.76
0.85/0.90
0.60/0.68
0.57/0.58
0.73/0.79
0.46/0.50
0.67/0.66
0.58/0.72
0.59/0.60
0.61/0.66
0.68/0.93
0.57/0.81
0.54/0.75
0.57/0.77
0.26/0.44
0.75/0.91
0.71/0.85
0.44/0.70
0.76/0.85
0.54/0.75
0.65/0.95
0.79/0.81
0.76/0.80
0.74/0.78
0.90/0.95
0.88/0.90
0.77/0.79
0.77/0.83
0.48/0.68
0.86/0.90
0.72/0.75
0.81/0.91
0.84/0.87
0.67/0.88
0.80/0.92
1981±91
0.81/0.87
0.57/0.60
0.69/0.81
0.75/0.83
0.63/0.81
0.77/0.86
0.71/0.80
0.57/0.67
0.61/0.78
0.81/0.85
1981±95
0.81/0.87
±
0.67/0.80
0.71/0.83
0.60/0.80
0.76/0.85
0.71/0.81
0.59/0.68
0.62/0.79
0.82/0.88
a
Numerator: R2 day; Denominator: R2 month; 0.00: data included in calibration; 0.00: validation.
bit too high and in StabbybaÈcken it is much too low.
This shows that the parameterisation of the model
does not manage to re¯ect all the differences between
the catchments.
Numerical experiments have shown that the calibration results could 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. 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 will be transferable to other basins. A
good model performance can be obtained for many
different combinations of optimised parameters. It
was easy to check that the parameters obtained for
one basin did not provide a good performance of the
model when applied in another basin.
In the case where a global set of parameters have to
be found for a number of basins with different conditions of ¯ow formation, the probability of ®nding the
`correct' values, which can be reasonable in the physical sense, increases. This was proved by the results
of simulations using the same parameters in other
basins in the NOPEX area (see Table 2). Fig. 5 shows
the observed and simulated discharge values for a few
basins in the NOPEX area for 2 years: one with
`satisfactory' agreement (with respect to R2) Ð
1986±87, and the other with `the worst' agreement
Ð 1988±89. The visual impression is that the simulation results are not worse for the catchments used for
validation than for those used for calibration. Here the
same differences between the two years can be seen
for the catchments used for validation as those used for
calibration. Also here it is interesting to note the
differences between the catchments. For example,
the observed response for the event between day 61
and 121 is different in SaÈvjaaÊn than in all the other
catchments. This is not re¯ected in the simulation
results. It is also seen that StalbobaÈcken is the only
catchment for which the simulations of the last days of
1988/89 are comparable to the observed runoff. As a
summary these ®gures shows that the differences
between the catchment are not totally accounted for
in the model structure and that some years are more
dif®cult to model than others and that the estimation of
global parameters is possible.
Sensitivity analysis has shown that the best model
performance for separate basins was achieved when at
least the one parameter Ð horizontal hydraulic con-
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
267
Fig. 5. Validation of the model performance; comparing observed and modelled runoff at independent basins not used in the calibration of
regional parameters.
ductivity of the soil, which de®nes the rate of subsurface ¯ow, slightly differs from the `global' value for
different river basin usually not more than two times.
However for SagaÊn basin this difference was about
®ve times.
According to common practice (e.g. Popov, 1979)
simulation results are considered to be good for values
of R2 0.75, while for values of R2 between 0.75 and
0.36 the simulation results are considered to be satis-
factory. This would correspond to multiple correlation
coef®cients of R ˆ 0.86 and 0.60, respectively, in a
regression problem. In this gradation good simulation
results, based on daily observations, were obtained
for FyrisaÊn, SaÈvaaÊn 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 SagaÊn and StalbobaÈcken, where
268
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
they were satisfactory. It should also be mentioned,
however, that the gradation referred to is as a rule
applied for individually calibrated basins, while in this
study we are dealing with regional hydrological calculations with a global set of parameters for the whole
NOPEX area. Experience will show what are reasonable accuracy demands for this more demanding
situation.
Comparing the diagrams in Figs. 4 and 5 it is also
seen that the simulated curves are as a rule more
peaked 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 ¯ow transformation in the channel
is not considered. For small and medium-sized basins
with a lag time of less than the one day used in the
simulations, this does not make any signi®cant difference. A consideration of the transformation in the
channel would smooth the hydrographs and possibly
increase the R2 for daily values in the case of larger
basins. It should also be noted, that when hydrological
and meteorological models are to be coupled, the
instantaneous values of 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 ef®ciency criterion re¯ects the agreement of
observed and calculated hydrographs, i.e. the
dynamics of discharge and to a less extent ¯ow
volumes. Table 3 shows the results of a comparison
of the simulated water balance characteristics with the
observed values from Seibert (1994). It is seen that the
precipitation values used in simulations and those
de®ned 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. In the ECOMAG model precipitation values
for each basin were obtained by weighted averages of
the observations at the nearest stations. A correction
factor of 1.2 was used to compensate for loss of
precipitation catch due turbulence for all the stations
with precipitation less than 40 mm per day and 1.0 for
higher daily precipitation. 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.
A comparison of the runoff values in Table 3 shows
that the simulated values were unsatisfactory for
SagaÊn. No obvious reasons for such a discrepancy
were found as physiographic conditions of runoff
formation in SagaÊn are similar to those for other river
basins in the NOPEX area, in particular FyrisaÊn, for
which the agreement was good. At the same time, the
difference between the measured average annual
values for FyrisaÊn and SagaÊn 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 SagaÊn
need a thorough analysis to sort out this problem.
Table 3
Annual water balance of the gauged river basins in the NOPEX area (1981±91) according to Seibert (1994): observed precipitation (P*),
observed runoff (Q*) and evapotranspiration as residual term (E*); and according to ECOMAG modelling: observed precipitation (P),
calculated evapotranspiration (E) and calculated runoff (Q). Q ˆ Qmodel ÿ Qobserved
Basin
Station
P* (mm)
E* (mm)
Q* (mm)
P (mm)
E (mm)
Q (mm)
Q (mm)
|Q/Q*| (%)
FyrisaÊn
SagaÊn
LillaÊn
È rsundaaÊn
O
HaÊgaaÊn
SaÈvaaÊn
SaÈvjaaÊn
StalbobaÈcken
StabbybaÈcken
Ulva Kvarn
SoÈrsaÈtra
GraÈnvad
HaÈrnevi
Lurbo
Ransta
SaÈvja
TaÈrnsjoÈ
Stabby
755
729
726
738
750
734
732
733
639
534
384
481
448
436
456
488
462
458
222
346
245
290
313
278
245
272
235
731
720
709
715
716
715
719
728
709
502
484
461
468
450
464
464
472
463
229
237
249
248
265
251
254
257
246
7
ÿ109
4
ÿ42
ÿ48
ÿ27
9
ÿ15
11
3
31
2
14
15
10
4
6
5
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Fig. 6. Validation of the model performance; (a) synoptic runoff observations at 12 sites in the Fyris river and (b) comparison with those modelled from four different campaigns.
269
270
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
6.2. Synoptic runoff measurements
An impression of the spatial variability of river
runoff can be obtained through synoptic runoff measurements (Krasovskaia, 1988). Four surveys of runoff
were performed in the FyrisaÊn river basin at 38 sites
during ¯ow recession, 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. 6a). Fig. 6b shows a comparison of the simulated
and measured river runoff for these 12 sites on the four
occasions. In general the agreement is good especially
when considering that the synoptic data have not at all
been involved in the calibration. The range of variation and the variance are not signi®cantly different for
both datasets. The discrepancies that appear in a more
detailed analysis cannot at present be fully explained.
The main reason is probably due to inaccuracy in
determination of the areas of small tributaries and the
spatial interpolation of meteorological characteristics,
especially rainfall. Besides, it should be noted that the
synoptic runoff measurements, describing instantaneous discharge values, were carried out over 2 or 3
days. The modelled discharges, on the other hand, give
the average for a certain day. This might also cause
discrepancies.
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 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 offers information about the number of observation points in
each basin including their soil and land surface cover
type. Table 5 gives information of the model performance for soil moisture and groundwater levels in
terms of the R2 ef®ciency measure and Fig. 7 allows a
Table 4
Number of observation points of soil moisture and groundwater
levels within experimental drainage basins
Basin
Number of observation points Soil type Land use
Soil moisture Groundwater
Buddby
151
DansarhaÈllarna 75
È stfora
O
50
Marsta
25
TaÈrnsjoÈ
50
16
16
19
±
±
till
till
till/sand
clay
sand
forest
forest
forest
open area
forest
comparison of observed and simulated values of these
variables.
The modelled and averaged observed soil moisture
contents are in general in good agreement. R2 is
greater than 0.83 for four of the sites. TaÈrnsjoÈ has
the poorest agreement, which can be explained by the
small variance in the observed values. The ®gure
shows that there is only one observation in the relatively wet period in springtime. TaÈrnsjoÈ is also very
special for the NOPEX-area, placed at the top of an
esker. It can be noted, that soil moisture measurements
were carried out in the top soil layer, 15±20 cm thick
on average, while soil moisture content has been
modelled for an averaged 40±60 cm thick soil layer
(horizon A). This difference might contribute to making the observed soil moisture content much more
sensitive to external factors (rain, evaporation) than
the more integrated modelled results, causing discrepancies between the curves.
The modelled values of groundwater levels also
follow well the averaged values of the groundwater
level measurements. R2 is greater than 0.48 for all
sites. The agreement is, however, not as good as for the
soil moisture content. This is mainly explained by the
Table 5
The model performance for soil moisture and groundwater levels in
terms of the R2 efficiency measure
Experimental catchment
R2 soil moisture R2 groundwater
Buddby
DansarhaÈllarna
Marsta
È stfora
O
TaÈrnsjoÈ
0.87
0.83
0.84
0.83
0.42
0.55
0.52
±
0.48
±
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
271
Fig. 7. Comparing observed and modelled soil moisture content at five experimental basins and observed and modelled groundwater levels at
three experimental basins (Each cross represents a spatial average, compare Table 4).
272
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
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 fact in¯uences the calculated
averages so that they are systematically underestimating the average groundwater depth. The modelled
groundwater depth is accordingly deeper than the
observed averages for till soils during dry conditions.
6.4. Vertical flux exchange and water balance
The NOPEX concentrated ®eld efforts during May±
June 1994 and April±July 1995 provide high quality
datasets for estimation of vertical ¯uxes, especially
evapotranspiration (latent heat ¯ux). 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 ¯ux estimates are not
directly comparable due to differences in temporal and
spatial scales. Local measurements from masts allow
calculation of `point' estimates of heat ¯uxes from
lakes and land surfaces (forest, mires, and agricultural
land) using eddy correlation, pro®le and sap ¯ow
methods. During events with airborne and radiosounding measurements, estimates of the ¯uxes are
also available along ¯ight transects. Regional ¯ux
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., 1999). The analysis of data within
the NOPEX project is in an early stage and the
methodological problem of comparison of different
¯ux estimates has been stressed in this comparison.
Table 6 shows components of the water balance
estimated with ECOMAG for 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 part of the water balance was 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 of the soil moisture and groundwater supply,
Table 6
Water balance of the NOPEX area during periods CFE1 and CFE2
according to ECOMAG
Period
Precipitation Evaporation
(mm)
(mm)
Runoff
(mm)
Wa
(mm)
CFE1 27 May±
23 June 1994
CFE2 18 April±
14 July 1995
64
74
6
ÿ16
215
289
82
ÿ156
a
W: Water supply changes in soil and groundwater zone.
accumulated during snowmelt and rain in winter and
spring.
Fig. 8a and b illustrate the patterns of the main
hydrologic elements for CFE1 and CFE2 periods,
respectively. The components show relatively large
variation across space. The smoothest variation is
revealed by precipitation, which is partly explained
by the method used for interpolation here (kriging).
An evaluation of precipitation from weather radar data
gives a more patchy result (Crochet, 1999). It is seen
that during both periods the lowest precipitation
amount is found in the southwestern part of the
NOPEX area, while the highest values are observed
in the northern part for CFE1 and northeastern part for
CFE2. The full daily data sets of all water balance
components for CFE1 and CFE2 are provided in
Gottschalk et al. (1999).
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. At 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 ¯ux 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
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
273
Fig. 8. The calculated water balance of the whole NOPEX area for (a) CFE1 (27 May±23 June 1994) and (b) CFE2 (18 April±14 July 1995).
The size of the pixels are 2 km 2 km.
by the model remains to be supported by independent
measurements.
Runoff patterns during CFE1 and CFE2 are nonhomogeneous due to the nonlinearity of the runoff
formation process involving factors such as precipitation, soil and land-use patterns, slopes etc. In general,
the highest speci®c 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 ¯ow 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 ¯at areas. Table 7 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 good agreement for the runoff
(with the exception of LillaÊn) and also for the
maximum daily discharges.
274
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
Fig. 8 (Continued )
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.
The main comparison is performed for regional ¯ux
estimates for the whole NOPEX area (Gottschalk
et al., 1999). 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 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 estimates of evapotranspiration by a weighted average of mast measurements
for CFE1 are 67 mm and CFE2 335 mm. The corresponding estimates by the ECOMAG model are 74
and 289 mm, respectively.
7. Conclusions
A physically-based distributed hydrological model
ECOMAG has been applied to nine river basins within
Y.G. Motovilov et al. / Agricultural and Forest Meteorology 98±99 (1999) 257±277
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 ®eld efforts
during 1994 (CFE1) and 1995 (CFE2) as well as
the continuous climate and runoff monitoring provide
high quality datasets for such a validation.
Most parameters of the ECOMAG model have a
physical interpretation, for example soil physical
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 acceptable performance for basins not used
in the calibration and for variables not included in the
calibration procedure. Evidence cited herein supports
this minimal calibration with some caveats.
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 ®ve small experimental sub-basins in
1994±95 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 FyrisaÊn during
CFE1 and CFE2. Finally, regional estimates of daily
evapotranspiration were compared with estimates
from ¯ux measurements, to give an independent
assessment of the water balance.
The performance of simulated runoff was evaluated
by the Nash±Sutcliffe ef®ciency 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 winter climatic conditions. Some
discrepancies in the model performance are suspected
to be caused by poor quality in regular runoff data.
However, the overall result must be considered to be
good as the simulations were performed without
calibration.
275
The ability of the ECOMAG model to simulate the
variation of average soil moisture for grid
2 km 2 km as showed by this study is also good.
The performance has been evaluated by the Nash±
Sutcliffe ef®ciency measure comparing 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 poorer 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 dif®culties with installing access
tubes to suf®cient 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 in 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
dif®cult 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 different simulated water balance components for grid cells show relatively high spatial variability and it has not been possible to con®rm this
variability from independent observations. This problem needs to be studied further.
When simulated water balance elements were integrated to the whole NOPEX area, independent estimates from vertical ¯ux 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.
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