Agricultural and Forest Meteorology 98±99 (1999) 295±304
Operational testing of a water balance model
for predicting climate change impacts
Chong-yu Xu
Institute of Earth Sciences, Hydrology, Uppsala University, Villavagen 16, S-752 36 Uppsala, Sweden
Abstract
The ability of water balance models to incorporate month±month or seasonal variations in climate, snowfall and snowmelt,
groundwater ¯uctuations, soil moisture characteristics, and natural climatic variability makes them especially attractive for
water resources studies of climatic changes. The use of conceptual models to explore the impact of climate changes has
increased in recent years. Because of the success claimed for these studies, it is likely that computer simulation of catchments
will increasingly be used by and for water resource managers as an aid to decision-making. There is therefore a need for a
generally accepted method for demonstrating a model's ®tness for such use. The simple split-sample test method may be
reasonable in the simplest case of the `®lling-in missing data' problem but certainly not if the express purpose of the model is
to simulate records for conditions different from those corresponding to the calibration record, such as the problem with
predicting the effects of climate changes where the data on the changed system are not (and cannot be) available for
comparison with the model predictions. Thus, model validation must demonstrate `®tness for the said purpose'.
In this paper, available model validation methods are reviewed and the hierarchical scheme for systematic testing of
hydrological simulation models according to the modelling tasks, proposed by Klemes (1986) (Klemes, V., 1986. Hydrol. Sci.
J. 31, 13±24) is discussed in detail and exempli®ed using the NOPEX water balance model (Xu, C.-Y., Seibert, J., Halldin, S.,
1996. J. Hydrol. 180, 211±236) and NOPEX data. # 1999 Elsevier Science B.V. All rights reserved.
Keywords: Water balance models; Validation methods; Climate change impacts; NOPEX
1. Introduction
In recent years, hydrologists have been increasingly
involved in studies of land-surface-atmosphere interactions in the context of climate change studies.
Several major international programmes have been
established, and NOPEX is one of them with the
primary aim of investigating ¯uxes of energy, momentum, water, and CO2 and associated dynamics between
the soil, the vegetation and the atmosphere, between
lakes and the atmosphere as well as within the soil and
atmosphere on local to regional scales ranging from
centimetres to tens of kilometres (Halldin et al., 1999).
Water balance investigations on different time and
spatial scales and prediction of the effects on water
availability of changes in climate are among the major
objectives of the NOPEX project.
Quantitative estimates require modelling, since
simulation is one of the most widely used techniques
in operations research and management (Bouraoui and
Wolfe, 1990). Conceptual catchment models have
been formulated to varying degrees of complexity,
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 6 - 9
296
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
operated with various time steps, and applied to a wide
spectrum of hydrological problems. Recently, they
have been employed to explore the impact of climate
changes (e.g. Gleick, 1987; Arnell, 1992; Xu and
Halldin, 1997). The state-of-the-art reviews including
those of Mein and McMahon (1982),Todini (1988),
and Xu and Singh (1997) have identi®ed the following
®ve major applications of catchment models: (1)
extension of stream¯ow records, (2) generation of
runoff statistics, (3) assessment of the effects of land
use changes, (4) prediction at ungauged catchments,
and (5) prediction of the effects of climate changes on
hydrologic regime. Because of the success claimed by
these studies, it is likely that computer simulation of
catchments will increasingly be used by water
resource managers as an aid to decision-making.
There is therefore a need for a generally accepted
method for demonstrating a model's ®tness for such
use. In current practice, it is usually the goodness of ®t
of the model output to the historic record in a calibration period, combined with an assumption that conditions under which the model will be used will be
similar to those under calibration. This may be reasonable in the simplest cases of the `®lling-in missing
data' problem but certainly not if the express purpose
of the model is to simulate records for conditions
different from those corresponding to the calibration
record, e.g. in studying the impact of climate changes.
Here, we have to do with the problem of general model
transposability which has long been recognised as the
major aim and the most dif®cult aspect of hydrological
simulation models. Despite this fact, very little effort
has been expended on the testing of this most important aspect, certainly by orders of magnitude less than
on many rather peripheral problems like manual versus automatic calibration, optimisation, etc. (Klemes,
1986). This point, and in particular the fact that
modellers seem to spend most of their time developing
and upgrading their models rather than testing them in
the way they would actually be used by water resource
managers, has also been noted by Dooge (1986).
Despite the low priority they assign to validation,
however, modellers consider their models to be accurate. For example, as Ewen and Parkin (1996) pointed
out, in a survey of over 20 modellers (American
Society of Civil Engineers (ASCE), 1985), only one
described the accuracy of his model as poor. It is
probably fair, though, to say that most modellers
recognise the need for proper validation, but do not
give it the high priority it deserves, and are unclear
about what proper validation involves.
In this paper, existing methods of model validation
are reviewed and the hierarchical scheme for the
systematic testing of hydrological simulation models,
proposed by Klemes (1986) are discussed in detail and
exempli®ed using the NOPEX water balance model
(Xu et al., 1996) and NOPEX data. More attention is
paid to the validation of models towards the use in
predicting the impacts of climate change.
2. Problems and use of hydrological models in
climate change studies
One of the most signi®cant potential consequences
of changes in climate may be alterations in regional
hydrological cycles and subsequent changes in river
quantity and quality regimes. Such hydrologic
changes will affect nearly every aspect of human
well-being, from agricultural productivity and energy
use to ¯ood control, municipal and industrial water
supply, and ®sh and wildlife management. The tremendous importance of water in both society and
nature underscores the necessity of understanding
how a change in global climate could affect regional
water supplies. Global atmospheric general circulation models (GCMs) have been directly used to simulate stream¯ow under present climate and to predict
the impact of future climatic change in macroscale
watersheds. The analysis of GCM predicted runoff
showed that the representation of the hydrologic cycle
within a global model of general atmospheric circulation leads to poor hydrologic predictive skill (e.g. Kuhl
and Miller, 1992; Miller and Russell, 1992). Because
the current generation of global climate models is not
well suited to the evaluation of detailed water
resources problems, a variety of other impact assessment techniques and tools must be developed and
tested. Hydrologic models provide a framework in
which to conceptualise and investigate the relationships between climate and water resources. Various
methodologies for simulating hydrological responses
to global climate change by using hydrologic models
have been reported, which may be described using
three categories: (1) Coupling high-resolution regional climate models (RCM) with hydrologic models.
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
Hostetler and Giorgi (1993) used the output from a
RCM to drive a lake model and a stream¯ow model.
The results of the simulations indicated that it may be
feasible to use directly, output data from RCM simulations as input to hydrological models in climate
change research aimed at, for example, assessing
potential changes in various components of the basin
hydrologic budget under increased levels of atmospheric CO2. Nash and Gleick (1993) studied the
hydrological impact of climate change on the Colorado River basin in the western United States. By
linking atmospheric, hydrologic, and river simulation
models Nash and Gleick (1993) were able to assess the
potential impacts of greenhouse warming in the Colorado River basin. However, more experiments of regional climates are needed to assess how well RCMs will
be able to simulate changed climate states, as suggested by Hostetler and Giorgi (1993). (2) Coupling
GCMs with hydrologic models through statistical
downscaling techniques. General circulation models
(GCMs) suggest that rising concentrations of greenhouse gases may have signi®cant consequences for the
global climate. What is less clear is the extent to which
local (sub-grid) scale meteorological processes will be
affected. So-called `downscaling' techniques have
subsequently emerged as a means of bridging the
gap between what climate modellers are currently
able to provide and what impact assessors require.
Even if global climate models in the future are run at
high resolution there will remain the need to `downscale' the results from such models to individual sites
or localities for impact studies (Wilby and Wigley,
1997). The present generation of downscaling tools
include the general limitations, theory and practice are
well described in the literature (see, for example,
Grotch and MacCracken, 1991; von Storch et al.,
1993; Wilby and Wigley, 1997), and are beyond the
scope of the present paper. (3) Use hypothetical
scenarios as input to hydrologic models. Ideally, the
climate simulations from the GCMs could be used
directly to drive hydrologic models, which in turn
could be used to evaluate the hydrologic and water
resources effects of climate change. However, the
performance of GCMs in the control simulation and
the magnitude of the predicated climate change signal
is not certain. Moreover, different GCMs are still
giving different values of climate variable changes
and so do not provide a single reliable estimate that
297
could be advanced as a deterministic forecast for
hydrological planning. Accordingly, methods of simple alteration of the present conditions are often used.
Therefore, the results obtained should be interpreted
as a sensitivity analysis to alternative climates rather
than as predictions. Many published works were done
in this way (e.g. Nemec and Schaake, 1982; Gleick,
1986, 1987; Schaake and Liu, 1989; Lettenmaier and
Gan, 1990; VehvilaÈinen and Lohvansuu, 1991; Arnell,
1992; Xu and Halldin, 1997). Various scenarios have
been used and climate predictions for `double CO2'
conditions have become a standard (e.g. Loaiciga
et al., 1996).
3. Validation methods of hydrologic models for
climate impact assessment
Hydrologic models (either for forecasting or simulation) were designed for stationary conditions. In
either of the three categories discussed in the previous
section, hydrologic models are to be used under
changing conditions. Special validation (testing)
methods have to be used. Most of the types of validation tests in current use were discussed by Klemes
(1986). He considered the general problem of validating catchment hydrological models and proposed a
testing framework. The proposed scheme is called
hierarchical because the modelling tasks are ordered
according to their increasing complexity, and the
demands of the test increase in the same direction.
Four major categories, corresponding modelling tasks
and test methods are summarised in Table 1.
Simple split-sample testing involves dividing the
available measured time-series data for the test catchment into two sets, each of them should be used in turn
for calibration and validation, and results from both
arrangements compared. For differential split-sample
testing, the same approach is followed, but the data are
divided according to rainfall rate or some other variable in an attempt to show that the model has general
validity in that it can predict the values of the output
variables for conditions different from those for which
it was calibrated. For example, if the model is intended
to simulate stream¯ow for a wet climate scenario then
it should be calibrated on a dry set of the historic
record and validated on a wet set. If it is intended to
simulate ¯ows for a dry climate scenario, the opposite
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C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
Table 1
Hierarchical approach for operational testing of hydrological simulations
Number
Proposed categories
Examples of modelling tasks
Testing methods
1
Stationary conditions,
the same basin
Stationary conditions,
a different basin
Nonstationary conditions,
the same basin
filling-in a missing segment of, or
extending, a stream-flow record
simulation of a streamflow record in
an ungauged basin
simulation of a streamflow record in
an gauged basin for conditions after
a change in land use, climate or both
simulation of a streamflow record in
an ungauged basin for conditions after
a change in land use, climate or both
Split-sample test
2
3
4
Nonstationary conditions,
a different basin
should be done. In general, the model should demonstrate its ability to perform under the transition
required: from drier to wetter conditions or the opposite. The importance of such a test is shown in Fig. 1
Proxy-basin test
Differential split-sample test
Proxy-basin differential split-sample
test
taken from Klemes (1986). The example illustrates the
potential danger of using a simulation model in studies
involving climate change without subjecting it to a
differential split-sample test.
Fig. 1. Example of differential split-sample test for a simulation model for monthly flows for the Gers River at Layrac, France (from Klemes,
1986).
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
Proxy-catchment tests use data for two catchments.
These tests can be used to show the model has even
greater general validity as they involve calibrating the
model against data for one catchment and then running
a validation test using data for the other catchment. For
differential proxy-catchment testing, the available
measured time-series data for each catchment are
divided into two sets according to rainfall rate or
some other variable. The model is then calibrated
against one of the sets (e.g. the dry period data for
the ®rst catchment) and a validation test run using a
contrasting set (e.g. the wet period data for the second
catchment). Calibration is required in all the four
validation methods discussed above.
Beven et al. (1984) and Loague (1990) used an
another type of test in which the model is not calibrated, and predictions are simply compared against
measurements. Recently, Ewen and Parkin (1996)
proposed a method, namely a `blind' approach. The
central feature of this method is that it involves
making predictions for a test catchment as if it were
a hypothetical catchment. The modeller is, therefore,
not allowed sight of the output data for the test
catchment (i.e. the method involved `blind' testing),
and, as a result, cannot calibrate the model for the test
catchment.
Considering the fact that the present generation of
hydrological simulation models is in the category of
conceptual models, which describe conceptually landbased hydrologic processes which are spatially averaged or lumped, calibration of some parameters is still
useful and needed. The hierarchical scheme for the
systematic testing of hydrological simulation models,
proposed by Klemes (1986) will be used in this study.
Although it is true that, to make the best use of a data
set collected for a test catchment, several validation
methods, each for a different set of speci®ed features,
may be carried out in parallel. The selection of the
method to be used in this study is based on the
consideration of the nature of the model and the
availability of data.
4. Brief description of the model and the test
catchments
Both model and test catchments are discussed in
detail by Xu et al. (1996). A brief summary is given
299
below. A monthly water balance model requires as
inputs monthly values of areal precipitation, potential
evapotranspiration and air temperature. The model
outputs are river ¯ow and other water balance components, such as actual evapotranspiration, slow and
fast components of river ¯ow, soil-moisture storage
and accumulation of snowpack, etc. The model works
as follows: precipitation pt is ®rst split into rainfall rt
and snowfall st by using a temperature-index function,
snowfall is added to the snowpack spt (the ®rst storage) at the end of the month, of which a fraction mt
melts and contributes to the soil-moisture storage smt.
Snowmelt is calculated by using a temperature-index
method. Before the rainfall contributes to the soil
storage as `active' rainfall, a small part is subtracted
and added to interception evaporation loss. The soil
storage contributes to evapotranspiration et, to a fast
component of ¯ow ft and to base ¯ow bt. The principal
equations of the model are summarised in Table 2.
Observed precipitation, runoff and land-use data
were available for 11 catchments located within or
close to the NOPEX region (Fig. 2). Fourteen years
(1981±1994) of monthly precipitation, air temperature
and runoff data were available for use. Table 3 contains brief summary details about the 11 catchments.
5. Results of validation
There are two fundamental assumptions in using
hydrologic models to evaluate the impacts of climatic
changes on runoff, i.e. the model will be able to (1)
Table 2
Summary of the principal equations of the monthly water-balance
modela
n
o‡
2
Snowfall
St ˆ pt 1ÿe‰…ct ÿa1 †=…a1 ÿa2 †Š
Snowpack
spt ˆ sptÿ1n‡ st ÿmt
o‡
2
Snowmelt
mt ˆ sptÿ1 1ÿeÿ‰…ct ÿa2 †=…a1 ÿa2 †Š
Rainfall
rt ˆ pt ÿst
Actual evapotranspiration
et ˆ min fwt …1ÿeÿa3 ept †; ept g
2
Baseflow
bt ˆ a4 …sm‡
tÿ1 †
‡ 2
Fast flow
ft ˆ a5 …smtÿ1 † …mt ‡ nt †
Total runoff
dt ˆ bt ‡ ft
Water balance equation
smt ˆ smtÿ1 ‡ rt ‡ mt ÿet ÿdt
a
‡
where: wt ˆ rt ‡ sm‡
tÿ1 is the available water; smtÿ1 ˆ
max …smtÿ1 ; 0† the available storage; nt ˆ rt ÿept …1ÿert =ept † the
active rainfall; pt, ept and ct are monthly precipitation, potential
evapotranspiration and air temperature, respectively; ai (i ˆ 1,
2,. . ., 5) are model parameters.
300
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
least some measure of con®dence that the initial model
calibration is valid.
5.1. Split-sample test
Fig. 2. Map of Sweden with the location of the NOPEX area.
reproduce reasonably well the historical stream¯ow
record and (2) simulate the stream¯ow under climatic
conditions that are different from conditions for which
the model has been calibrated. The ®rst assumption
concerning the ability of the model in reproducing the
historical stream¯ow record was usually validated by
the modellers and/or users by using simple splitsample test. Strictly speaking, the validation, concerning the second assumption, is not possible until the
climatic changes actually occur and the `experiment is
done' (e.g. Gleick, 1987). There are, however, certain
tests that can be (and should be) applied to provide at
In this study, the model is ®rst calibrated for each
catchment for the entire period (January 1981±
December 1994), and then calibrated using the ®rst
(last) 7 years of the available record, with the parameters optimised to simulate the ¯ows in the last (®rst)
7 years of the available record. For illustrative purpose, the calibration and veri®cation results for catchment SA are presented here in detail. There are no
agreed performance criteria because of the many
different types of models and model applications.
The criteria chosen for model veri®cation in this study
were the comparison between observed and simulated
mean annual and monthly runoff and R2 values (as
de®ned by Nash and Sutcliffe, 1970). In addition, two
different analyses were done on the deviations from
observed values to determine whether signi®cant
model bias existed for average ¯ows. These analyses
included the plotting and assessment of the residuals
and the computation of the relative error of simulated
and observed mean monthly ¯ows.
The calibrated parameter values with 95% con®dence interval for different calibration periods are
compared in Fig. 3. The observed and simulated mean
monthly runoff, the R2 values and relative error for
different calibration and simulation periods are shown
in Table 4. Fig. 4 presents the residuals versus the
simulated monthly discharge. It is seen from Table 4
and Figs. 3 and 4 that, (1) the optimised parameter
Table 3
Summary information of the NOPEX catchments
Station
Abbreviation
Area (km2)
Mean precepitation
(mm/month)
Mean discharge
(mm/month)
Lake (%)
Forest (%)
Field or
meadow (%)
GraÈnvad
HaÈrnevi
Lurbo
Ransta
SaÈvja
SoÈrsaÈtra
Stabby
TaÈrnsjoÈ
Ulva Kvarn
Vattholma
Ê kesta Kvarn
A
GR
HA
LU
RA
SA
SO
ST
TA
UL
VA
AK
168.0
305.0
124.0
198.0
727.0
612.0
6.6
14.0
950.0
284.0
730.0
59.41
60.21
60.84
59.79
59.70
59.70
56.43
59.70
61.21
60.65
60.12
19.91
22.80
25.60
22.44
19.73
28.28
20.22
22.20
16.70
20.30
21.64
0
1.0
0.3
0.9
2.0
1.1
0
1.5
3.0
4.8
4.0
41.0
55.0
77.7
66.1
64.0
61.0
87.0
84.5
61.0
71.0
69.0
59.0
44.0
27.0
33.0
34.0
37.9
13.0
14.0
36.0
24.2
27.0
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
301
Table 5
Comparison of hydroclimatic variables with different time periods
for catchment RA
Periods
1981±1994
1981±1987
1988±1994
Fig. 3. Comparison of optimised parameter values with the 95%
confidence interval for different calibration periods in catchment
SA. (line with circle for period 1982±1994; line with plus for
period 1982±1987; line with cross for period 1988±1994).
values for different calibration periods do not show
signi®cant difference. (2) There is a good comparison
between observed and simulated mean monthly runoff. (3) Residuals have no trends and homoscedasticity.
Fig. 4. Residual vs. computed discharge for catchment SA
(residual shows no trends and homoscedastic).
Variables
Precipitation
(mm/month)
Temperature
(8C)
Discharge
(mm/month)
60.0
62.4
57.7
5.8
5.1
6.5
21.9
25.0
18.8
5.2. Differential split-sample test
The basic requirement of this test is a long record of
simultaneous precipitation, temperature and runoff
data from which different periods can be chosen with
different historical conditions, such as a period of high
average precipitation and/or temperature versus a
period of low average precipitation and/or temperature. If the climatic change to be modeled is a transition to a warmer wetter scenario, the model should be
calibrated on a dry, cool data set and then validated for
the other extreme. A differential split-sample test can
arise by default from a simple split-sample test if the
only meaningful way of splitting an available record is
such that the two segments exhibit markedly different
conditions. This is the case of the study. The longest
data set that we have for the NOPEX catchments is 14
years (1981±1994). However, an examination of existing data shows that, even with this relatively short data
set, two data periods with different climatic conditions
can be distinguished. Catchment RA is used as an
example. The mean monthly precipitation, temperature and runoff for the whole period, ®rst 7 years and
last 7 years are shown in Table 5. The annual variation
Table 4
Model verification: simple split-sample test catchment SAa
Calibration
Period
1982±1994
1982±1987
1988±1994
a
Verification
Mean discharge
(mm/month)
Obs.
Mod.
18.64
20.15
17.34
18.74
20.73
17.01
R
2
0.78
0.82
0.75
RE (Relative error) ˆ …Qmod ÿQobs =Qobs † 100.
RE (%)
0.57
2.9
ÿ1.9
Period
1988±1994
1982±1987
Mean discharge
(mm/month)
Obs.
Mod.
17.34
20.15
16.42
21.17
R2
RE (%)
0.70
0.79
ÿ5.3
5.1
302
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
Table 6
Model verification: differential split-sample test wet and dry years
for catchment RAa
Periods
Observed runoff
(mm/month)
Model runoff
(mm/month)
Relative
error (%)
Dry (1988±1994)
Wet (1981±1987)
18.8
25.0
20.2
23.9
7.4
ÿ4.5
a
Relative error (%) ˆ …Qmod ÿQobs =Qobs † 100.
Table 6. Residuals were also checked for each of 14year monthly averages in order to determine the
nature, e.g. the absence of trend and also homoscedasticity in model runoff. No trend is discernible and
residual is homoscedastic.
5.3. Proxy-catchment test
Fig. 5. Standardised air temperature and mean monthly discharge
for catchment HA. This figure shows a significant increase of
temperature and decrease of runoff for the second half of the
historical record.
of the standardised values (de®ned as the deviation
from the mean divided by the mean values) are plotted
in Fig. 5. A comparison between the ®rst and second
half of the data series shows that the mean temperature
increased by nearly one and half degree, mean
monthly discharge decreased from 25 to 18.8 mm.
Of course, it would have been more correct to choose a
record of suf®cient length, say 50 years, and select
several sets of extremes, but data limitations in the
present instance precluded this. This level of detail is
more typical of the situation that might be faced under
`applied' conditions.
This test measures the ability of the model to perform under conditions that may prevail after climatic
conditions shift. In this test, the model was calibrated
on 7 wetter years and tested on 7 drier years, and the
reverse procedure was also done. For both the drier
and wetter years, total simulated runoff was within 8%
of the observed values. Given an uncertainty of 5±10%
in the observed runoff values themselves, this test
suggests that the model is capable of operating under
both dry and wet conditions within acceptable margins
of error. The data and the results of this test are in
Simple proxy-catchment tests have the potential to
form part of a method which tests the ®tness of a
model for predicting the impact of changes in land-use
which may resulted from climate changes (Whitehead
et al., 1988). To perform this test, catchments HA and
SA were chosen because they have similar characteristics with respect to land use (see Table 3). The model
was ®rst calibrated on one of the catchments and
veri®ed on the other. The results of this test are shown
in Table 7. It is seen that for both catchments, total
model runoff were within 3% of the observed values.
This test suggests that calibrated model parameter
values are transferable to another catchment with
similar land-use.
5.4. Proxy-catchment differential split-sample test
The most involved model test is the proxy-basin
differential split-sample test for geographic, land-use
Table 7
Model verification: simple proxy-catchment test (January 1982±
December 1994)a
Catchments
Observed runoff
(mm/month)
Model runoff
(mm/month)
Relative
error (%)
HA
SA
21.3
18.6
21.1
19.0
0.81
ÿ2.12
a
Relative error (%) ˆ …Qmod ÿQobs =Qobs † 100.
C.-y. Xu / Agricultural and Forest Meteorology 98±99 (1999) 295±304
and climatic transferability. Such broad transferability
is probably the ultimate objective of most hydrologic
models. The test aims, for example, at assessing
whether a model calibrated to a dry climate on basin
A can simulate stream¯ow for a wet climate on basin
B, and vice versa. The differential split-sample test
and the proxy-basin differential split-sample test are
clearly called for in testing hydrologic models
embedded in GCMs. Changes in climate justify using
these complex model testing methodologies (Loaiciga
et al., 1996). The obvious shortcoming here is the lack
of available data bases to conduct these tests over a
representative cross-section of regions and varying
climatic conditions.
This test was performed by using the same catchments as have been used in the simple proxy-catchment test, i.e. catchments HA and SA. As has been
discussed in the previous sections, these two basins
have similar characteristics and, segments with different climatic parameters, e.g. wet years and dry
years, are identi®ed in the historical records. The
model was calibrated and validated on the following
combinations:
1. Calibrated on HA wet years (1982±1987),
validated on SA dry years (1988±1994);
2. Calibrated on HA dry years (1988±1994),
validated on SA wet years (1982±1987);
3. Calibrated on SA wet years (1982±1987),
validated on HA dry years (1988±1994);
4. Calibrated on SA dry years (1988±1994),
validated on HA wet years (1982±1987).
The results are shown in Table 8. It is seen that for
all the testing combinations, total model runoff was
within 3.5% of the observed values which show
excellent agreement between observed and model
runoff in all validation runs.
Table 8
Model verification: proxy-catchment differential split-sample test
Combinations
calibrated/
validated
Observed
runoff
(mm/month)
Model
runoff
(mm/month)
Relative
error (%)
HAwet/SAdry
HAdry/SAwet
SAwet/HAdry
SAdry/HAwet
18.8
24.2
17.3
20.1
18.9
23.7
17.7
20.8
0.73
1.96
1.98
3.40
303
6. Conclusion
Hydrologic models, developed under stationary
conditions, have been used to explore the impact of
climate change. Existing model test methods
described so far were reviewed in this paper. Simple
split-sample test method is unable to test the applicability of hydrologic models under nonstationary conditions. The hierarchical scheme for systematic testing
of hydrological simulation models, proposed by
Klemes (1986), were discussed in detail and exempli®ed using the NOPEX water balance model (Xu
et al., 1996) and NOPEX data. The criterion chosen for
this model veri®cation was whether or not the model
could reproduce the means of monthly runoff within
the limits of the data themselves. In addition, two
different analyses were done on the model residuals to
determine whether signi®cant model bias existed for
averaged ¯ows. The model passed all four tests and is
capable of reproducing both the magnitude and timing
of monthly and seasonal runoff for both stationary and
changed conditions. This method of model testing
would increase the credibility of a simulation model
that will be used in climate change study.
Acknowledgements
The research is partially ®nanced by NFR (Swedish
Natural Science Research Council). The data used in
this investigation was provided from the SINOP (System for Information in NOPEX) data base. The Swedish Meteorological and Hydrological Institute (SMHI)
provided most of the data to SINOP and Ms. Petra
Seibert performed data checking, correction and calculation of the areal precipitation. The author wishes
to thank the two anonymous reviewers for their valuable comments. I am also thankful to Prof. V.P. Singh,
Lousisiana State University, for correcting this manuscript.
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