Hydrological Sciences Journal
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Stability of model performance and parameter
values on two catchments facing changes in
climatic conditions
Hong Li, Stein Beldring & Chong-Yu Xu
To cite this article: Hong Li, Stein Beldring & Chong-Yu Xu (2015) Stability of model
performance and parameter values on two catchments facing changes in climatic conditions,
Hydrological Sciences Journal, 60:7-8, 1317-1330, DOI: 10.1080/02626667.2014.978333
To link to this article: http://dx.doi.org/10.1080/02626667.2014.978333
Accepted online: 23 Oct 2014.Published
online: 12 Aug 2015.
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Date: 03 October 2015, At: 03:36
Hydrological Sciences Journal – Journal des Sciences Hydrologiques, 60 (7–8) 2015
http://dx.doi.org/10.1080/02626667.2014.978333
Special issue: Modelling Temporally-variable Catchments
1317
Stability of model performance and parameter values on two
catchments facing changes in climatic conditions
Hong Li1, Stein Beldring2 and Chong-Yu Xu1
1
Department of Geosciences, University of Oslo, Blindern, N-0316 Oslo, Norway
chongyu.xu@geo.uio.no
2
Norwegian Water Resources and Energy Directorate, Majorstua, N-0301 Oslo, Norway
Downloaded by [University of Oslo] at 03:36 03 October 2015
Received 5 April 2014; accepted 11 September 2014
Editor D. Koutsoyiannis; Guest editor G. Thirel
Abstract Hydrological models are often used for studying the hydrological effects of climate change; however,
the stability of model performance and parameter values under changing climate conditions has seldom been
evaluated and compared. In this study, three widely-used rainfall–runoff models, namely the SimHYD model, the
HBV model and the Xin’anjiang model, are evaluated on two catchments subject to changing climate conditions.
Evaluation is carried out with respect to the stability in their performance and parameter values in different
calibration periods. The results show that (a) stability of model performance and parameter values depends on
model structure as well as the climate of catchments, and the models with higher performance scores are more
stable in changing conditions; (b) all the tested models perform better on a humid catchment than on an arid
catchment; (c) parameter values are also more stable on a humid catchment than on an arid catchment; and (d) the
differences in stability among models are somewhat larger in terms of model efficiency than in model parameter
values.
Key words climate change; conceptual models; hydrological regime; non-stationarity; rainfall–runoff models
Stabilité des performances de modèles et des valeurs de leurs paramètres dans deux bassins
versants confrontés à des changements de conditions climatiques
Résumé Les modèles hydrologiques sont souvent utilisés pour étudier les effets hydrologiques du changement
climatique ; cependant, la stabilité des performances des modèles et des valeurs de leurs paramètres sous des
conditions climatiques changeantes a rarement été évaluée et comparée. Dans cette étude, trois modèles pluie–
débit largement utilisés, les modèles SimHYD, HBV et Xin’anjiang, ont été évalués sur deux bassins versants
soumis à une évolution des conditions climatiques. On effectue une évaluation de la stabilité de leurs performances et des valeurs de leurs paramètres au cours de périodes de calage différentes. Les résultats montrent que
(a) la stabilité des performances d’un modèle et les valeurs de ses paramètres dépendent de la structure du modèle
ainsi que du climat des bassins versants, et que les modèles les plus performants sont plus stables dans des
conditions changeantes ; (b) tous les modèles testés fonctionnent mieux sur un bassin versant humide que sur un
bassin aride ; (c) les valeurs des paramètres sont aussi plus stables sur un bassin versant humide que sur un bassin
aride ; et (d) les différences de stabilité entre les modèles sont un peu plus importantes en termes d’efficacité du
modèle qu’en ce qui concerne les valeurs des paramètres.
Mots clefs changement climatique ; modèles conceptuels ; régime hydrologique ; non-stationnarité ; modèles pluie–débit
1 INTRODUCTION
Climate change is one of the most serious environmental threats that humanity has ever been confronted
with (Hofgaard 1997, Xu 1999a, Xu et al. 2005,
O’Brien et al. 2006). To comprehend the hydrological
impacts of climate change, scientists use hydrological
models driven by different climate change scenarios.
Hydrological models transform climate conditions to
© 2015 IAHS
hydrological responses at catchment, regional and global scales (Widén-Nilsson et al. 2007, Kizza et al.
2013, Li et al. 2013). Therefore, projections can be
made for water resources and floods under future
climate conditions by hydrological models taking
inputs from global or regional climate models.
Rainfall–runoff models are mathematical tools
that describe the relationship between the precipitation
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Hong Li et al.
over a catchment area or a region and the resulting
runoff by means of mathematical equations. The constants of these equations, i.e. parameters of the models,
are estimated based on observations of precipitation
and runoff with the help of other meteorological variables and basin physical data. However, climate and
land-use change can change or modify the rainfall–
runoff relationship (Lavabre et al. 1993, Zhang et al.
2011b). The most distinct indicator of climate change
is the increase in global average temperature and/or
the change in precipitation. Runoff is simultaneously
modified by climate change (e.g. precipitation and
temperature) and human activities (land use, water
consumption and construction of dams) (Milly et al.
2008, Zhang et al. 2011a, Zeng et al. 2014).
In mathematics, strict stationarity of a time series
requires that all moments of its probability distribution function are identical across time, whereas a time
series is non-stationary if one of its moments is not
constant over time. A less strict type of stationarity,
called ‘weak’ or ‘second-order’ stationarity, is that in
which the first- and second-order moments are constant over time (Chen and Rao 2002, Murphy and
Ellis 2013). Due to the limited length of hydrological
records, normally 50 years or less, only the first and
second order moments can be reliably estimated.
Therefore, a stationary hydrological time series is
actually only weakly stationary in mathematical
terms (Chen and Rao 2002).
To substantiate applicability of hydrological
models in changing conditions, the models have to
pass rigorous tests. Klemeš (1986) prescribed a differential split-sample method for testing the transferability of hydrological models under non-stationary
conditions. Time series of data are subdivided into
two sub-periods with contrasting climatic conditions,
like warm and cold, dry and wet. Validation on the
period that has different climate conditions from the
calibration period can test the dependence of model
parameters on climate and transferability of parameters in various climate conditions (Brigode et al.
2013). Using this method, Xu (1999b) evaluated the
WASMOD model on two Swedish catchments with
two sub-periods having different climate conditions.
Seibert (2003) used this method to assess the ability
of the HBV model on simulating peak flow on four
Swedish catchments. Li et al. (2012) tested the
DWBM model and the SimHYD model on 30 unimpaired catchments in Australia with two sub-periods
of changing climate conditions. In these studies, only
two sub-periods classified as dry or wet act as
calibration and verification by turn and these
studies show deterioration in model performance of
validations.
If longer records of data are available, this test
can be generalized or modified to multiple calibration
periods and yields multiple optimized parameter sets.
The statistics of the optimized parameter values and
all possible validations in independent periods give
insights about uncertainty in calibrations and stability
of parameters (Coron et al. 2012, Brigode et al.
2013). This test can be seen as an extension or
modification of the differential split-sample test
(Coron et al. 2012). Thus the modified differential
split-sample test method provides a possibility for
examining model stability under changing climate
conditions.
In general, parameter values in dynamic models
are assumed to represent stable catchment conditions,
while rainfall, temperature and other inputs are timevarying boundary conditions (Merz et al. 2011).
Therefore, calibrated parameters are expected to be
insensitive to changes in climatic conditions. This is
a fundamental assumption for any hydrological
model to be used in simulating climate change impact
on hydrological variables (Schulze 2000, Zeng et al.
2014). However, using the aforementioned method,
Merz et al. (2011) found that parameters of snow and
soil moisture are more sensitive to climatic conditions of calibration periods than other parameters.
Moreover, Coron et al. (2012) found that the transferability of model parameters is more affected by a
change in precipitation than in temperature
and potential evaporation by three models of different
structures. However, no universal conclusions can be
drawn and further studies are always recommended.
A large number of rainfall–runoff models of
varying degrees of complexity have been developed,
ranging from empirical black-box models to conceptual quasi-physical models and physically-based distributed models (Shamseldin et al. 1997, Singh 2002,
Xu and Singh 2004). Comparisons of models with
different degrees of complexity demonstrated that
there is no single model that performs better than
other models for all types of catchments and under
all circumstances (Refsgaard and Knudsen 1996,
Shamseldin et al. 1997, Butts et al. 2004,
Georgakakos et al. 2004, Reed et al. 2004, Duan
et al. 2007, Habets et al. 2009). Furthermore, hydrological simulations of different water balance components by different models are different even though
runoff simulations exhibit the same pattern. Alley
(1984) was probably the first to notice the ‘invisible’
discrepancies. He found that after calibration,
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Stability of model performance and parameter values
different monthly models reproduced similar runoff
series, but simulated values of state variables such as
soil moisture storage were substantially different
among models. More recently, using six conceptual
models, Jiang et al. (2007) demonstrated that even
though these six models had similar capabilities in
reproducing historical water balance components,
greater differences occurred in simulating impacts
of the postulated climate changes on different water
balance components.
The above mentioned studies revealed that each
model has its own strengths in capturing different
aspects of real world processes (Duan et al. 2007).
No model is likely to perform satisfactorily at all
times or under all conditions (e.g. perhaps not all of
its structural assumptions are valid or the conditions
under which it is assumed to operate are not entirely
fulfilled) (Shamseldin et al. 1997). It is, therefore,
crucially important to investigate the different performance of the models under different conditions and
to explore the reasons for the differences among the
models.
To involve as many models as possible in studies
of non-stationary hydrological relationships, a workshop entitled “Testing simulation and forecasting
models in non-stationary conditions” was organized
as a special session during the IAHS/IAPSO/IASPEI
Joint Assembly in Gothenburg, Sweden in July 2013.
Time series of precipitation, temperature, discharge
and other variables of 14 catchments with significant
changes in land cover, climate and dam construction
were provided as a common database. Twenty four
models, including black-box models, conceptual
models and physically-based models, were set-up
on these catchments by research groups around the
world. The modellers were asked to follow a similar
calibration and validation protocol and results were
analysed using common criteria, such as the NashSutcliffe efficiency and the bias (Thirel et al. 2015).
Besides these common criteria, participants also put
forward their own insights and solutions to hydrological modelling on the catchments.
This paper originates from one of the 30 presentations made at the workshop, and follows the
guidance of the workshop. As a contribution to the
session, the objective of this study is to compare and
quantify the differences in model performance and
stabilities of parameters of three widely-used rainfall–runoff models in estimating runoff and water
balance for two catchments located in very different
climate zones. In the two catchments, distinct
changes are detected in precipitation and runoff.
1319
2 STUDIED CATCHMENTS
2.1 The Lianshui catchment
The Lianshui catchment at the Xiangxiang gauging
station is located in the humid zone in southern China
(Fig. 1). The mean altitude is 209 m a.m.s.l. ranging
from 52 to 1033 m a.m.s.l.. The upstream part of the
catchment is mountainous (altitude >200 m) and
comprises approximately 36% of the total area. The
midstream area is dominated by hills (100 m < altitude ≤ 200 m), and covers around 55% of the catchment. Plains in the downstream (altitude ≤ 100 m)
cover the rest of the area. As for land-use, forest and
cropland, cover 48 and 47% of the total area of the
catchment, respectively. This catchment is heavily
influenced by a monsoon climate, which brings
heavy rainfall from the south. Annual precipitation
is around 1360 mm year-1; yearly average temperature is 17°C; and the annual runoff is 660 mm. The
rainy season is from April to September accounting
for almost 70% of annual precipitation.
Time series of precipitation, temperature, potential evaporation and runoff at a daily time step are
available from 1963 to 2003, with one year (1963)
kept for warming up the models. Thus, the whole
simulation period is from 1964 to 2003. The eight
sub-periods, of 5-years each are: 1964–1968 (P1),
1969–1973 (P2), 1974–1978 (P3), 1979–1983 (P4),
1984–1988 (P5), 1989–1993 (P6), 1994–1998 (P7),
and 1999–2003 (P8). One year before the start of
every sub-period is used for model warming up.
2.2 The Wimmera catchment
The Wimmera catchment at the Glenorchy Weir Tail
gauging station is located in the arid zone in southeast Australia (Fig. 2). The mean altitude is 300 m a.
m.s.l. Around 13% of the total area is above 413 m,
mainly located in the east; approximately 83% of the
total area is between 187 and 413 m. Cropland covers
60% of the total area, with forests and grassland over
the remainder (Hansen et al. 2000). Annual precipitation is 560 mm year-1; yearly average temperature
is 13.5°C; and annual runoff is 40 mm.
Time series of precipitation, temperature, potential evaporation and runoff at a daily time step from
1960 to 2005 were used. The period from 1960 to
1965 was kept for warming up the models. There
were five sub-periods of 8-years each: 1966–1973
(P1), 1974–1981 (P2), 1982–1989 (P3), 1990–1997
(P4), and 1998–2005 (P5). Six years before the start
of each sub-period are used for model warming up.
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Hong Li et al.
Fig. 1 Altitude and location of the Lianshui catchment at
the Xiangxiang gauging station. The black line is the
Lianshui River and the black dot is the Xiangxiang gauging station.
The division of sub-periods is the same as in Thirel
et al. (2015), except that the whole period is defined
from 1966 to 2005. Very low runoff was recorded
from 1997 to 2005. These years, called the
“Millennium Drought”, completely covered subperiod P5. Because the Wimmera catchment is
located in an arid region and as the climate has a
larger inter-annual variability than the Lianshui
catchment, a longer sub-period and warming-up
period were used in model evaluation.
The area of the Lianshui catchment is twice as
large as the Wimmera catchment; it also experienced
twice as much as precipitation. However, the
Lianshui catchment has a six times larger runoff
coefficient than the Wimmera catchment as shown
in Fig. 3. More information about the two catchments
is tabulated in Table 1.
3 METHODS AND MODELS
Fig. 2 Altitude and location of the Wimmera catchment at
the Glenorchy Weir Tail gauging station. The black line is
the Wimmera River and the black dot is the Glenorchy
Weir Tail gauging station.
In this study three models were compared on the two
catchments. The models are programmed in different
computer languages and calibrated by different algorithms. Successful applications of these models by
others and ourselves have verified the merits of the
models and their calibration packages. Since the main
objective of the study is not to compare the calibration routines, differences induced by the calibration
algorithms are not considered. The calibration routines are discussed in Sections 3.2–3.4.
Moreover, the results presented herein are
obtained with different initial parameter and state
values in order to ensure that globally optimal parameter values are obtained. Occasionally the optimization results are not satisfactory with limited predefined initial parameter values especially on the
Wimmera catchment.
Fig. 3 Mean annual precipitation (grey bars) and runoff coefficients (solid line) during each sub-period in the Lianshui
catchment (left) and the Wimmera catchment (right). The bold dashed lines are the average annual precipitation for the
whole period, and the dotted lines are the average runoff coefficients for the whole period. The ticks on the x-axis are the
starting years of the sub-periods.
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Stability of model performance and parameter values
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Table 1 Summary information of the two catchments. No. refers to the number of sub-periods and Length is the duration of
each sub-period.
Catchment
(Longitude, Latitude)
Area (km2)
Whole period
No.
Length
Lianshui
Wimmera
(112.52°E, 27.72°N)
(142.79°E, 36.98°S)
5499
2000
1964–2003
1966–2005
8
5
5 years
8 years
3.1 Model performance criteria
The objective function of calibration used in the
study is the Nash-Sutcliffe coefficient (NSE) (Nash
and Sutcliffe 1970). Even though this criterion is
sensitive to the peak and underestimates the variability (Gupta et al. 2009, Vansteenkiste et al. 2014),
it is still the most widely used objective function in
general hydrological modelling (Perrin et al. 2001,
Chiew and Siriwardena 2005, Pechlivanidis et al.
2011, Pushpalatha et al. 2012). In the model evaluation, two criteria, i.e. NSE and the relative mean
error (RME), are adopted as requested in the guidance of the workshop. Their formulas are shown in
Table 2.
If N is the number of sub-periods, the models are
first calibrated on each sub-period resulting in N sets
of parameter values and model performance scores.
Each calibration is then validated in all other sub-
Table 2 Evaluation criteria and their corresponding formulations (Oi and Si are the observed and simulated flow,
respectively; i is the time series index; and n is the total
number of time steps).
Criterion
Formula
n
P
NSE
1
RME
n
P
i1
i1
n
P
ðOi Si Þ2
Perfect value
ð1; 1
1
ð1; þ1Þ
0
2
ðOi OÞ
i1
ðSi Oi Þ
n
P
Range
Oi
periods. Thus, there are N calibrations and N*(N-1)
validations for the sub-periods plus one calibration
for the whole period.
3.2 The SimHYD model
The SimHYD model is a lumped conceptual rainfall–
runoff model. It simulates daily runoff (surface runoff
and baseflow) using daily precipitation and potential
evaporation as input data. This model is one of the
most commonly used hydrological models in
Australia for climate change studies (Jones et al.
2006). More details and algorithms of the model
can be found in Chiew and Siriwardena (2005).
Nine parameters need to be calibrated and the
five most sensitive parameters (Chiew and
Siriwardena 2005) plus correction factors of rainfall
and potential evaporation are selected to analyse
their stabilities in different calibration periods. The
ranges of the parameters are primarily determined
from Chiew and Siriwardena (2005) and adjusted
accordingly in the study to better suit the two catchments. The final parameter ranges are tabulated in
Table 3.
The SimHYD in Fortran is automatically calibrated by a global optimization procedure entitled the
shuffled complex evolution (SCE-UA) method developed by Duan et al. (1992). The SCE-UA method
indeed estimates the global optimization values
(Duan et al. 1992, Doherty and Johnston 2003,
Coron et al. 2012).
i1
Table 3 Meanings and ranges of nine parameters in the SimHYD model. The analysed parameters are underlined.
Index
Parameter
Meaning (unit)
Range
1
2
3
4
5
6
7
8
9
INSC
SMSC
SUB
CRAK
K
SQ
COEFF
PC
EC
Interception storage capacity (mm)
Soil moisture storage capacity (mm)
Constant of proportionality in interflow equation
Constant of proportionality in groundwater recharge equation
Log_10 of baseflow linear recession parameter
Infiltration loss exponent
Maximum infiltration loss (mm)
Rainfall multiplier
Potential evaporation multiplier
[0, 20]
[20, 500]
[0, 1]
[0, 1]
[−2.5, −0.5]
[0, 6]
[20, 400]
[0.5, 2.0]
[0.2, 5.0]
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Hong Li et al.
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3.3 The HBV model
The HBV model is a conceptual rainfall–runoff model
aimed at the Scandinavian countries (Bergström 1992,
Lindström et al. 1997). The model is also widely used
in other countries (more than 80 worldwide), especially in northern Europe. The model version used in
this study was developed by Beldring et al. (2003).
The inputs are daily precipitation and air temperature;
the outputs are daily runoff, groundwater and other
water balance components. More details of the model
can be found in Li et al. (2014).
Thirteen parameters need to be calibrated
(Table 4) and the seven most sensitive parameters
(Seibert 1997, 1999) are selected to analyse their
stabilities. The ranges of the parameters were primarily determined by Seibert (1997) and Li et al. (2014),
and were adjusted accordingly in the study to better
suit the two catchments. The final parameter ranges
are tabulated in Table 4.
The HBV model in C++ is calibrated by a free
package called PEST (Model-Independent Parameter
Estimation & Uncertainty Analysis) (Doherty and
Johnston 2003). It is based on the GaussMarquardt-Levenberg algorithm, which combines
advantages of the inverse Hessian matrix and the
steepest gradient method to allow a fast and efficient
convergence towards to the best value of the objective function (Doherty and Johnston 2003, Wrede
et al. 2013).
3.4 The Xin’anjiang model
The Xin’anjiang model (XAJ) was developed in 1973
(Zhao 1992). The model has been applied successfully over a very large range of areas including the
agricultural, pastoral and forested lands of China
except the loess (Zhang and Lindström 1996, Jiang
et al. 2007, Xu et al. 2013). The inputs are daily
precipitation and potential evaporation and the outputs are daily runoff and other water balance
components.
Fifteen parameters need to be calibrated and
seven of them are sensitive parameters as recommended by Zhao (1992). The ranges of the parameters are determined by the study of Chen et al.
(2012) and are adopted herein. The parameters underlined in Table 5 are analysed for time stability.
The XAJ model in Fortran is optimized by three
algorithms (Chen et al. 2012), namely the
Rosenbrock, simplex and genetic algorithms (Wang
1991). Chen et al. (2012) successfully applied the
XAJ model as well as the calibration routines to
study the impacts of climate change on runoff on
the Hanjiang basin in China.
4 RESULTS
4.1 Changes of model performance in different
sub-periods
4.1.1 The Lianshui catchment The results of
the RME values are presented in Fig. 4. It is seen that
as far as RME is concerned, the XAJ model and the
HBV model perform better than the SimHYD model
on the Lianshui catchment, since the RME values
concentrate around zero and no significant bias is
seen. The SimHYD model shows negatively biased
results.
Results of the NSE values are shown in Fig. 5. It
shows that the XAJ model gives the highest NSE
values both in calibrations and validations, and the
SimHYD model gives the lowest NSE values.
Table 4 Meanings and ranges of 13 parameters in the HBV model. The analysed parameters are underlined.
Index
Parameter
Meaning (unit)
Range
1
2
3
4
5
6
7
8
9
10
11
12
13
PREC
INTER_MAX
EPO
WETCORR
FCA
FCD
BETA
INFM
KUZ
ALFA
PERC
KLZ
DRAW
Precipitation correction
Maximum interception storage (m)
Potential evaporation capacity (m/d)
Transpiration correction
Field capacity (m)
Maximum evaporation efficiency
Shape coefficient of soil moisture
Infiltration capacity (m)
Recession coefficient of the upper zone
Nonlinear drainage coefficient of the upper zone
Percolation from upper zone to lower zone
Recession coefficient of the lower zone
Draw up coefficient from lower zone to soil moisture
[0.5, 2.0]
[0.001, 0.100]
[10-4, 5 × 10-3]
[0, 1]
[0.05, 1.50]
[0.005, 1.000]
[0.5, 15.0]
[0.5, 1.5]
[0.05, 1.00]
[0.2, 2.0]
[0, 1]
[0, 1]
[0, 1]
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Stability of model performance and parameter values
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Table 5 Meanings and ranges of 15 parameters in the XAJ model. The sensitive parameters are underlined.
Index
Parameter
Meaning (unit)
Range
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
WM
X
Y
KE
B
SM
EX
CI
CG
IMP
C
KI
KG
N
NK
Areal tension water capacity (mm)
Fraction of upper water in WM
Fraction of upper water in (1–X) × WM
Evaporation coefficient
Tension water distribution index
Areal free water capacity (mm)
Free water distribution index
Fraction of free water to interflow
Fraction of free water to groundwater
Impermeable coefficient
Deep layer evaporation coefficient
Interflow recession coefficient
Groundwater recession coefficient
Number of reservoirs of the Nash model
Storage constant of the Nash model
[50, 250]
[0, 1]
[0.1, 1.5]
[0.5, 1.5]
[0.01, 1.00]
[5, 100]
[0.05, 50.00]
[0, 1]
[0, 1]
[0, 1]
[0, 1]
[0, 1]
[0.5, 1]
[1, 10]
[0.5, 50]
Fig. 4 Histogram of the RME values on the Lianshui catchment. The total number of occurrences is 64, including all
calibrations and validations for all the sub-periods.
The NSE range of validations (the length of the
red bars in Fig. 5) is a measure of the sensitivity of
models to climate conditions. There are seven validations for each sub-period. The ranges are the largest
in the SimHYD model. The performance scores of
the HBV model and the XAJ model are similar.
Additionally, the length of the ranges reflects to
some extent the problem of parameter equifinality
and uncertainty. The range bars are very short,
especially those of the HBV model and the XAJ
model, indicating that the uncertainty caused by parameters is low.
Normally, the highest NSE is obtained during
the calibration. However, in the XAJ model, in
some sub-periods, for example, P2 and P6, the maximum NSE values of the validations are slightly
larger than those of the calibration. This is mainly
caused by the fact that the calibration procedures
Fig. 5 NSE values of the three models on the Lianshui catchment. Circles represent the NSE values of calibrations for
every sub-period and the error bars are the NSE values of validations, with crosses indicating the mean. The performance
scores of calibrations and validations exhibit a similar pattern.
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Hong Li et al.
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occasionally cannot find the global optimal parameters. However, the differences are very small and
therefore they are not considered to be significant.
4.1.2 The Wimmera catchment The results
of RME are presented in Fig. 6 for the Wimmera
catchment. The HBV model performs best in terms
of RME, since the RME values concentrate around
zero with small deviation. The XAJ model and the
SimHYD model show biased RME values.
Figure 7 shows that the XAJ model gets the highest
NSE values both in the calibrations and the validations,
and the SimHYD model gets the lowest NSE values
during the sub-periods P1 to P4. All models failed to
give satisfactory simulation in the sub-period P5.
The ranges of NSE are the largest in the
SimHYD model. The performance scores of the
HBV model and the XAJ model are still very similar.
The calibrated parameters on sub-period P5 also
work on other sub-periods, whereas the calibrated
parameters on other periods do not work on the
sub-period P5. This can be seen from the NSE values
of the HBV model and the XAJ model in Fig. 7. The
sub-period P1 is also relatively dry, but model performances are different from the sub-period P5.
Compared with the Lianshui catchment, the performance scores of the three models are much lower
and the ranges of NSE are larger on the Wimmera
catchment. The reasons for model inefficiency are
explained in Section 5. The larger ranges reveal
larger parameter uncertainty than on the Lianshui
catchment.
4.2 Stability of parameters in different
calibration periods
The values of the optimized parameters in different
sub-periods are an indicator of the stability of the
parameters. The optimized parameter sets on the
whole period are assumed to be most robust and
most representative of catchment characteristics
(Brigode et al. 2013), acting as a benchmark of
parameters calibrated in the sub-periods. The changes
of parameters are defined as the deviations in percent
from their respective benchmark values, computed by:
Pi Pw 100; Pw Þ 0
Di ¼ Pw where i is the index of the sub-period; Pi is the
calibrated parameter value on the ith sub-period; Pw
is the calibrated parameter value on the whole period.
The SUB parameter of the SimHYD model (Table 3)
Fig. 6 Histogram of the RME values on the Wimmera catchment. The total number of occurrences is 25, including all the
calibrations and validations during all the sub-periods.
Fig. 7 NSE values of the three models on the Wimmera catchment (see Fig. 5 for explanation). NSE values of less than
zero are not shown.
Stability of model performance and parameter values
1325
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Fig. 8 Cumulative frequency of deviations of parameters calibrated on all sub-periods on the Lianshui catchment (left) and
the Wimmera catchment (right). The optimized parameters on the whole period are the benchmark values.
calibrated on the whole period is zero, and hence this
formula is not valid. However, the values of this
parameter calibrated on all sub-periods on the two
catchments are also zero. Therefore the deviations of
SUB are zero. The cumulative frequencies of all the
selected parameters (Tables 3, 4 and 5) within every
10% deviation intervals are shown in Fig. 8.
The comparisons between the two catchments
indicate that the parameters of the three models are
more stable on the Lianshui catchment than on the
Wimmera catchment. On average, approximately
50% of the parameter values calibrated in the sub-
periods are ±10% deviations from the benchmark
values on the Lianshui catchment, whereas this number on the Wimmera catchment is only ~30%. Within
±50% deviation, cumulative frequency of parameters
on Lianshui catchment can reach about 80–90%,
whereas on the Wimmera catchment it is about
60–80%. Additionally, the ranks of the three models
on the two catchments show a similar pattern. The
differences between the models are smaller on the
Lianshui catchment than on the Wimmera catchment.
For illustrative purposes, the parameter values
are shown in Figs 9 and 10, for the Lianshui and
Fig. 9 Selected parameters (short, solid, red lines) of the SimHYD model (left), the HBV model (middle) and the XAJ
model (right) calibrated for each sub-period on the Lianshui catchment. The solid (blue) lines are the benchmark values, the
parameter values calibrated on the whole period; the dashed (blue) lines are the ±50% deviations from the benchmark
values. A cross indicates that parameter value is out of limits of the y-axis for the corresponding sub-period. The ±50%
deviations of parameter SUB are not shown, since SUB is zero for the eight sub-periods and the whole period. The +50%
deviations of KUZ and KG are not shown, since they are larger than the upper limit values.
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Hong Li et al.
Fig. 10 Selected parameters of the SimHYD model (left), the HBV model (middle) and the XAJ model (right) calibrated
for every sub-period on the Wimmera catchment. See Fig. 9 for explanation. The +50% deviations of FCD and KG are not
shown, because they are larger than the upper limit values.
Wimmera catchments, respectively. They show that
some parameters do not change at all and some are
varying in different manners between the two catchments. For the SimHYD model, SUB keeps stable
on both catchments during all sub-periods; CRAK,
K and PC are within ±50% deviations on the
Lianshui catchment during all sub-periods, whereas
such parameter behaviour occurs for the parameters
SMSC and K on the Wimmera catchment. For the
HBV model, KUZ keeps stable on the Lianshui
catchment during all sub-periods; PREC and EPO
are within ±50% deviations on both catchments
during all sub-periods. For the XAJ model, KE,
SM, KG and NK are within ±50% deviations on
the Lianshui catchment during all sub-periods,
whereas such behaviour occurs for the parameters
KE and KG on the Wimmera catchment. This means
that the parameter values of the three models are
more stable on the Lianshui catchment than on the
Wimmera catchment.
5 DISCUSSION
The methods that split data series into various calibration and validation periods were put forward by
Klemeš (1986) for testing hydrological models under
non-stationary climate conditions. Using a modified
differential split-sample test, three widely used
hydrological models, namely the SimHYD model,
the HBV model and the XAJ model are evaluated
on two catchments with changing climate conditions.
On the Lianshui catchment, runoff and precipitation
increased from 1989, whereas on the Wimmera
catchment a severe drought started in 1997.
All models performed better on the Lianshui
catchment with a humid climate than on the
Wimmera catchment with an arid climate. This confirmed that hydrological modelling on arid and semiarid areas is much more difficult than on humid areas
(Michaud and Sorooshian 1994, Zhang and
Lindström 1996, Hughes 2008). In arid and semi-
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Stability of model performance and parameter values
arid areas, precipitation generally is characterized as
short duration storms of high intensity. Associated
with relatively thin vegetative cover and high evaporation rates, the dominant runoff generation
mechanism is infiltration-excess overland flow.
Rainfall and consequently runoff generation have
large spatial variability, frequently occurring at local
scales. This local scale character leads to some runoff, generated on some of the slopes, not always
surviving to contribute to runoff at the outlet of
catchments due to infiltration and evaporation.
However, it is also possible that water penetrates
into deep groundwater aquifers, and finally contributes to runoff at the outlet of catchments (Ye et al.
1997). The complex spatial pattern and runoff generation mechanism would be a main reason for less
model efficiency on the Wimmera catchment than on
the Lianshui catchment.
If trading space for time, by these models,
increasing precipitation would lead to higher model
efficiency and vice versa. The two case studies
clearly demonstrate this statement. On the Lianshui
catchment, the NSE values of the three models
increased during P6, P7 and P8 compared with P4
and P5 (Fig. 5). Conversely on the Wimmera catchment, the NSE values of three models decreased
during the dry sub-period P5.
The stability either in model performance or
parameter values obviously depends on how significant are the changes between the sub-periods. Less
stable model performance and parameter values on
the Wimmera catchment than on the Lianshui catchment are quite reasonable, since changes on the
Wimmera catchment were more distinct than on the
Lianshui catchment. Another possible reason is the
uncertainty in the inputs and runoff data. As aforementioned, precipitation and runoff generation are
highly localized and last for a short duration in arid
and semi-arid areas. High variability both in space
and time results in inadequate model presentation,
either by lumping or from sparse resolution of in
situ observations (Hughes 1995).
Data error or less efficiency is thought to be one
of the possible reasons for parameter instability
(Merz et al. 2011). Actually, at least one parameter
is designed for data error in precipitation and potential evaporation in the three models. In the SimHYD
model, PC and EC are multipliers respectively for
precipitation and potential evaporation as tabulated in
Table 3. On the Lianshui catchment, PC values were
within ±50% deviations during eight sub-periods (in
Fig. 9), whereas on the Wimmera catchment,
1327
calibrated PC values on four sub-periods were within
±50% deviations (in Fig. 10). Besides, on the
Lianshui catchment, PC values were approximately
one; whereas on the Wimmera catchment, PC values
were negatively biased from one. Higher stable
values of PREC in the HBV model and KE in the
XAJ model on the Lianshui catchment than on the
Wimmera catchment also substantiate this
supposition.
Though all three models are conceptual hydrological models, some routines indeed provide insights
for model development for arid and semi-arid areas.
Both the HBV model and the XAJ model use exponential curves for the relationship between net rainfall and runoff (Bergström 1992, Zhao 1992, Zhang
and Lindström 1996). This is very necessary and of
high value to represent the localized runoff generation response to precipitation. However, the evaporation routine and separation of runoff components are
more complex in the XAJ model than in the HBV
model. Soil evaporation was calculated by dividing
the soil into three layers in the XAJ model (Zhao
1992) whereas soil evaporation is only a nonlinear
function of available water and soil capacity in the
HBV mdoel (Bergström 1992). The fine representation of soil evaporation is considered for improving
evaporation modelling in a nonlinear soil system,
especially on the Wimmera catchment. There are
four runoff components in the XAJ model (Zhao
1992) and two in the HBV model (Lindström et al.
1997, Beldring et al. 2003).
6 CONCLUSIONS
Rainfall–runoff models are mathematical tools used
to describe the relationship between precipitation and
runoff. However, climate change significantly modifies this relationship. Hydrologists are required to
evaluate if hydrological models can behave successfully on catchments with changing conditions. To
contribute to such a study, we selected two catchments subject to changes in climate conditions, the
Lianshui catchment in the humid zone in southern
China and the Wimmera catchment in the arid zone
in southeast Australia. We compared three conceptual
models, the SimHYD model, the HBV model and the
XAJ model in terms of stabilities of model performance and parameter values.
The study shows that the XAJ model gives the
best model efficiency and the HBV model is very
similar to the XAJ model in this respect. The
SimHYD model has somewhat lower efficiency. All
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1328
Hong Li et al.
models have a higher efficiency on the Lianshui
catchment (wet) than on the Wimmera catchment (dry).
Performance scores as well as the stability of
parameter values of all the models are more stable
on the Lianshui catchment than on the Wimmera
catchment. However, this conclusion is partly caused
by the fact that runoff change on the Wimmera catchment is larger than on the Lianshui catchment.
Model structure determines model performance.
Among the three models, the structures of the HBV
model and the XAJ model are very similar and performance scores of the two models are also close on
both catchments. The high performance scores of the
models indicate that the structural assumptions are
valid on the two catchments.
The stability of model performance and parameter values highly depends on the climate of catchments. The models with higher performance scores
are more stable in changing conditions. This conclusion is drawn from the differences of individual
model performance on two catchments. All the models are more stable on the Lianshui catchment than on
the Wimmera catchment both in performance scores
and parameter values.
For the parameter stability comparisons, the
study shows that there is not much difference
between the three models. There is not enough evidence to generalize which model parameter values
are more stable although significant differences in
performance scores exist among the models.
Acknowledgements The provision of data for the
Lianshui catchment by Hua Chen in Wuhan
University, China and for land use of the Wimmera
catchment by Department of Geography, University
of Maryland are gratefully acknowledged. The helpful comments by Guillaume Thirel in Irstea, France
did motivate us to clarify our work and led to a
substantial improvement of this paper. The authors
are also grateful to the reviewers for their valuable
comments and suggestions.
Disclosure statement No potential conflict of interest was reported by the author(s).
Funding This research contributes to the projectJOINTINDNOR (project number 203867) funded
by the Research Council of Norway.
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