Manual 21504497

Manual 21504497
Journal of Hydrology (2007) 336, 316– 333
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jhydrol
Comparison of hydrological impacts of climate
change simulated by six hydrological models in the
Dongjiang Basin, South China
Tao Jiang a, Yongqin David Chen b, Chong-yu Xu
Xi Chen d, Vijay P. Singh e
c,f,*
, Xiaohong Chen a,
a
Department of Water Resources and Environment, Sun Yat-sen University, Guangzhou, China
Department of Geography and Resource Management, Institute of Space and Earth Information Science, The
Chinese University of Hong Kong, Hong Kong
c
Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, N-0316 Oslo, Norway
d
State Key Laboratory of Hydrology, Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China
e
Department of Biological and Agricultural Engineering, Texas A&M University, Scoates Hall, 2117 TAMU,
College Station, TX 77843-2117, USA
f
Department of Earth Sciences, Uppsala University, Sweden
b
Received 5 February 2006; received in revised form 2 January 2007; accepted 9 January 2007
KEYWORDS
Climate change;
Water balance models;
Model comparison;
Hydrological impacts
Large differences in future climatic scenarios found when different global circulation models (GCMs) are employed have been extensively discussed in the scientific literature. However, differences in hydrological responses to the climatic scenarios resulting
from the use of different hydrological models have received much less attention. Therefore, comparing and quantifying such differences are of particular importance for the
water resources management of a catchment, a region, a continent, or even the globe.
This study investigates potential impacts of human-induced climate change on the water
availability in the Dongjiang basin, South China, using six monthly water balance models,
namely the Thornthwaite–Mather (TM), Vrije Universitet Brussel (VUB), Xinanjiang (XAJ),
Guo (GM), WatBal (WM), and Schaake (SM) models. The study utilizes 29-year long records
of monthly streamflow and climate in the Dongjiang basin. The capability of the six models
in simulating the present climate water balance components is first evaluated and the
results of the models in simulating the impact of the postulated climate change are then
analyzed and compared. The results of analysis reveal that (1) all six conceptual models
have similar capabilities in reproducing historical water balance components; (2) greater
differences in the model results occur when the models are used to simulate the hydrolog-
Summary
* Corresponding author. Tel.: +47 22 855825; fax: +47 22 854215.
E-mail address: [email protected] (C.-y. Xu).
0022-1694/$ - see front matter ª 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2007.01.010
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
317
ical impact of the postulated climate changes; and (3) a model without a threshold in soil
moisture simulation results in greater changes in model-predicted soil moisture with
respect to alternative climates than the models with a threshold soil moisture. The study
provides insights into the plausible changes in basin hydrology due to climate change, that
is, it shows that there can be significant implications for the investigation of response
strategies for water supply and flood control due to climate change.
ª 2007 Elsevier B.V. All rights reserved.
Introduction
Climate change associated with global warming induced by
the increase in carbon dioxide and other radiative trace gases
in the atmosphere has been the focus of a multitude of scientific investigations for over the past two decades (e.g., Xu
et al., 2005). These investigations are driven by the recognition that climate change has significant implications for the
environment, ecosystems, water resources and virtually
every aspect of human life. One of the most important and
immediate effects of global warming would be the changes
in local and regional water availability, since the climate system is interactive with the hydrologic cycle. Such effects may
include the magnitude and timing of runoff, the frequency
and intensity of floods and droughts, rainfall patterns, extreme weather events, and the quality and quantity of water
availability; these changes, in turn, influence the water supply system, power generation, sediment transport and deposition, and ecosystem conservation. Some of these effects
may not necessarily be negative, but they need to be evaluated as early as possible because of the great socio-economic
importance of water and other natural resources.
Modelling the hydrologic impacts of global climate
change involves two issues: climate change and the response of hydrologic systems. Climate change is a complex
problem involving interactions and feedbacks between
atmosphere, oceans, and land surface. In order to better
understand this problem it has been customary to use climate models which are mathematical descriptions of
large-scale physical processes governing the climate system. Currently general circulation models (GCMs) are considered to be the most comprehensive models for
investigating the physical and dynamic processes of the
earth surface-atmosphere system and they provide plausible
patterns of global climate change. However, it is not yet
possible to make reliable predictions of regional hydrologic
changes directly from climate models due to the coarse resolution of GCMs and the simplification of hydrologic cycle in
climate models (e.g., Arora, 2001). An investigation of climate-change effects on regional water resources, therefore, consists of three steps (e.g., Xu, 1999): (1) using
climate models to simulate climatic effects of increasing
atmospheric concentration of greenhouse gases, (2) using
downscaling techniques to link climate models and catchment-scale hydrological models or to provide catchment
scale climate scenarios as input to hydrological models,
and (3) using hydrological models to simulate hydrological
impacts of climate change. Errors occur at every step of
the investigation (Xu et al., 2005). Large differences in global and regional climate change scenarios, as calculated by
the use of different GCMs and downscaling techniques, have
been widely discussed in the literature (e.g., Arnell, 1995;
Arora, 2001). For a given study region, the range of diversity
obtained when different hydrological models are used for a
given climate scenario has not been widely investigated and
reported in the literature. A few examples of studying the
differences in hydrological impacts of climate change obtained by different hydrological models include Boorman
and Sefton (1997) who investigated the range of diversity
resulting from the use of two conceptual hydrological models. The study concluded that both models exhibited similar
capabilities in reproducing historical flow indices; however,
significant differences existed in the simulated flow indices
of the changed climate even for the same climate scenario
and for the same catchment. The study also suggested that
more studies on comparing the impacts due to different
hydrological models need to be carried out; this would help
quantify the differences resulting from different hydrological simulation models and provide useful guidelines for
water resources planners and managers. Panagoulia and Dimou (1997a,b) examined the differences in predictions of
two hydrological models under both historical and alternative climate conditions. The models for comparison were a
monthly water balance (MWB) model and the snow accumulation-ablation (SAA) and soil moisture accounting (SMA)
models of the US National Weather Service (US NWS). It
was shown that the models had small differences in monthly
runoff values and greater interannual variability for the
SAA–SMA models under historical climate conditions. When
the alternative climates were used as input to the hydrological models, greater differences were obtained with different models. The MWB model showed a greater runoff
increase in winter and a greater decrease in summer as
compared with the SAA–SMA model. Whereas the SMA model soil moisture varied substantially, the MWB model soil
moisture remained unaffected for any climate during winter. The soil moisture reduction predicted from the MWB
model was greater than that predicted from the SMA model
in late spring and summer.
The concept of using regional hydrologic models for
assessing the impact of climate change has several attractive
features (Gleick, 1986; Schulze, 1997). First, models tested
for different climatic/physiographic conditions as well as
models structured for use at various spatial scales and dominant process representations are readily available. This
affords flexibility in identifying and choosing the most appropriate approach to evaluate any specific region. Second,
hydrological models can be tailored to fit the characteristics
of available data. The GCM-derived climate perturbations (at
different levels of downscaling) can be used as model input. A
variety of responses to climate change scenarios can hence
be modelled. Third, regional-scale hydrological models are
318
considerably easier to manipulate than general circulation
models. Fourth, such regional models can be used to evaluate
the sensitivity of specific watersheds to both hypothetical
changes in climate and to changes predicted by large-scale
GCMs. Finally, the models that can incorporate both detailed
regional hydrologic characteristics and output from largescale GCMs will be well situated to take advantage of continuing improvements in the resolution, regional geography, and
hydrology of global climate models.
It would not be unfair to say that all kinds of models find
their usefulness in different applications. Physically-based
distributed-parameter models are complex in terms of structure and input requirements and can be expected to provide
adequate results for a wide range of applications. On the
other hand, simpler models which have a smaller range of
applications can yield adequate results at greatly reduced
cost, provided that the objective function is suitable. The
distinction between simple and physically-based distributed-parameter models is not only one of lesser or greater
sophistication, but is also intimately linked with the purpose
for which such models are to be used. Thus, choosing a suitable model is equivalent to distinguishing the situation between when simple models can be used and when complex
model must be used. The choice of a model for a particular
study depends, therefore, on many factors (Gleick, 1986),
amongst which the purpose of study and model and data
availability have been the dominant ones (Ng and Marsalek,
1992; Xu, 1999). For example, for assessing water resources
management on a regional scale, monthly rainfall-runoff
(water balance) models were found useful for identifying
hydrologic consequences of changes in temperature, precipitation, and other climate variables (e.g., Gleick, 1986;
Schaake and Liu, 1989; Mimikou et al., 1991; Arnell, 1992;
Xu and Halldin, 1997; Xu and Singh, 1998). For detailed
assessments of surface flow and other water balance components, conceptual lumped-parameter models are used. One
of the more frequently used models in this group is the Sacramento Soil Moisture Accounting Model (Burnash et al.,
1973). Many researchers have used the same model or similar
models for studying the impact of climate change (e.g., Nemec and Schaake, 1982; Gleick, 1987; Lettenmaier and Gan,
1990; Schaake, 1990; Nash and Gleick, 1991; Cooley, 1990;
Panagoulia, 1992; Leavesley, 1994; Panagoulia and Dimou,
1997a,b). In Nordic countries the HBV model is widely used
as a tool to assess the climate change effects (e.g., Vehviläinen and Lohvansuu, 1991). For simulation of spatial patterns
of hydrological response within a basin, process-based distributed-parameter models are needed (Beven, 1989;
Thomsen, 1990; Running and Nemani, 1991; Bathurst and
O’Connell, 1992). For estimating changes in the average annual runoff for different climate change scenarios simple
empirical and regression models have been used, as for
example, the models by Revelle and Waggoner (1983) in
the United States, and Arnell and Reynard (1989) in the UK.
The studies reported in the literature and discussed
above have used one or a limited number of hydrological
models (2 models in some cases) to simulate the impact of
postulated climate changes; these studies represent the results of the selected models only. It is therefore desirable to
compare the differences in hydrological impacts of alternative climates resulting from the use of more hydrological
models. In this study, six monthly water balance models
T. Jiang et al.
(i.e., Thornthwaite–Mather model (Alley, 1984), VUB model
(Vandewiele et al., 1992), the monthly Xinanjiang model
(Hao and Su, 2000), Guo model (Guo, 1992), WatBal model
(Kaczmarek, 1993; Yates, 1996) and Schaake model
(Schaake, 1990)) are used and their capabilities in reproducing historical water balance components and in predicting
hydrological impacts of alternative climates are compared.
The choice of these six models is based on the following
considerations: First, climate change scenarios at a monthly
time scale are easily available and more reliable. Second,
water resources management and planning for a large basin
or region are generally on a monthly time scale. Third, large
scale observed hydrological data on a monthly scale are
more easily available for calibrating and validating hydrological models, especially in developing countries.
Thus the main objective of this study is to quantify how
large the difference one can expect when using different
hydrological models to simulate the impact of climate
change as compared to the model capabilities in simulating
historical water balance components. The study is performed in two steps: First, the performance of models in
reproducing historical water balance components is evaluated; and second, the differences in the simulated hydrological consequences of changed climate by various
models are evaluated and compared.
Study area and data
The study area is the Dongjiang (East River) catchment, a
tributary of the Pearl River in southern China. The Dongjiang
catchment is located in the Guangdong and Jiangxi provinces (see Fig. 1). Originating in the Xunwu county of Jiangxi
province, the river flows from north-east to south-west and
discharges into the Zhujiang (the Pearl River) estuary with
an average gradient of 0.39&. The Dongjiang water is being
transferred out of the basin to Hong Kong since the mid
1960s. The proportion of the Dongjiang water in Hong
Kong’s annual water supply has steadily increased from only
8.3% in 1960 to about 70% or even slightly over 80% in recent
years. However, the water resources of the Dongjiang basin
are already heavily committed. Rapid economic development and growth of population in this region have caused
serious concerns over the adequacy of the quantity and
quality of water withdrawn from the Dongjiang River in
the future. Any significant change in the magnitude or timing of runoff or soil moisture in the Dongjiang basin induced
by changes in climate variables would thus have important
implications for the great economic success and prosperity
of the Pearl River Delta region and Hong Kong. Therefore,
a modelling study is urgently needed that can evaluate the
potential impacts of future climate change on the water
availability in this basin.
The Dongjiang basin has a sub-tropical climate with a
mean annual temperature of about 21 C and only occasional
incidents of winter daily air temperature dropping below
0 C in the mountainous areas of the upper basin. The average annual rainfall for the period of 1960–1988 is 1747 mm,
and the average annual runoff is 935 mm, or roughly 54% of
the annual rainfall. Precipitation is generated mainly by
two types of storms: frontal type and typhoon-type rainfalls.
There are large seasonal changes in rainfall and runoff in the
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
Figure 1
319
Location of the Dongjiang basin and the hydro-meteorological stations.
catchment: about 80% of the annual rainfall and runoff occur
in the wet season from April to September, and about 20%
occurs during the dry period of October to March. The geology of the catchment is complex. Precambrian, Silurian, and
Quaternary geological formations are encountered at the
surface with granites, sandstone, shale, limestone, and alluvium. The landscape is characterized by hills and plains,
comprising 78.1% and 14.4% of the basin area, respectively.
Forest covers upper elevations and intensive cultivation
dominates hills and plains.
The data for model calibration and validation include
monthly air temperature, pan evaporation, rainfall and
streamflow. All the data were obtained from the published
Yearly Hydrological Books of China for the period from
1960 to 1988. In this study, 46 major stations, almost
evenly distributed over the whole basin with 29-year continuous records (1960–1988), were selected for model calibration and validation. Many methods are available for
estimating mean areal rainfall over an area (e.g., a catchment) based on the results of meteorological observations
(Naoum and Tsanis, 2004), which include Spline (Regularized & Tension), Inverse Distance Weighting (IDW), Trend
Surface, Kriging, and Thiessen Polygons. The density of
the gauge stations and their distribution are important
for the accuracy of all the methods. In this study, the
model input of areal rainfall was calculated from the records of the 46 stations using the Thiessen polygon method. This is mainly because (1) the Thiessen polygons are
probably the most common approach for modeling the
spatial distribution of rainfall and the Thiessen method is
known to provide good results when used for relatively
dense networks (Naoum and Tsanis, 2004); and (2) the
rainfall stations are rather dense and evenly distributed
(see Fig. 1) in the catchment that makes the differences
resulting from using different interpolation and area averaging methods small. Pan (U80 cm) evaporation data of 3
meteorological stations were averaged to estimate areal
potential evaporation, i.e., PE = kEpan, where coefficient
k is calibrated in the study and an average value of
k = 0.64 was obtained. The use of a constant coefficient
is based on two considerations. First, the study by Xu
and Vandewiele (1994) has shown that this type of
monthly water balance model is much less sensitive to
the evaporation input than to precipitation. Second, the
main objective of the study is to compare the simulation
capabilities of the six chosen water balance models under
historical climate and alternative climate with respect to
the same input data series. The monthly streamflow data
were from the Boluo stream gauging station, above which
the drainage area is 25,325 km2. Fig. 2 presents areal
320
T. Jiang et al.
50.0
350.0
Run off
45.0
Depth of water (mm)
Pan Evaporation
Air Temperature
250.0
40.0
35.0
30.0
200.0
25.0
150.0
20.0
100.0
15.0
Air temperature oC
Rainfall
300.0
10.0
50.0
0.0
5.0
0.0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
Figure 2
Mean monthly pan evaporation, rainfall, runoff and air temperature of the Dongjiang basin.
mean monthly values over the 29-year record for observed
pan evaporation, rainfall, runoff, and air temperature for
the Dongjiang basin.
Methodology
Selected monthly water balance models
Almost all monthly water balance models share the same
general structure which includes the water balance equation at the monthly time scale:
Sðt þ 1Þ ¼ SðtÞ þ PðtÞ EðtÞ Q ðtÞ
ð1Þ
in which S(t) represents the amount of soil moisture stored
at the beginning of the time interval t; S(t + 1) represents
the storage at the end of that interval; and the flow across
the control surface during the interval consists of precipitation P(t), actual evapotranspiration, E(t), and soil moisture
surplus, Q(t), which supplies streamflow and groundwater
recharge. Solution of this equation requires dealing with
time series of four variables: S, P, E, Q, and possibly of
other variables related to them.
Monthly water balance models represent the entire
catchment hydrology as a series of moisture storages and
flows. The water balance models differ in how E and Q are
Table 1
conceptually considered and mathematically represented.
In order to estimate the actual evapotranspiration in the
soil–water budget method many investigators have used a
soil–moisture extraction function or coefficient of evapotranspiration which relates the actual rate of evapotranspiration E to the potential rate of evapotranspiration PE based
on some function of the current soil moisture content and
moisture retention properties of the soil (Xu and Singh,
2004).
It was desired to consider a broad spectrum of hydrological models and therefore six monthly models (i.e.,
Thornthwaite–Mather model (Alley, 1984), VUB model (Vandewiele et al., 1992), the monthly Xinanjiang model (Hao
and Su, 2000), Guo model (Guo, 1992), WatBal model (Kaczmarek, 1993; Yates, 1996) and Schaake model (Schaake,
1990)) with 2–5 parameters, all of which have been widely
employed in simulating water resources of stationary and
changed climate conditions, were employed in this study.
All six models are described in the Appendix (a complete list
of equations can be found in the cited references); only
their similarities and differences are briefly discussed here
in order to provide background information in interpreting
and understanding the similarities and differences in the
simulation results. The structural characteristics of the
models employed are shown in Table 1.
Characteristics of the selected models
Model
No. of
soil zones
No. of
storages
(deficit)
Types of storage (deficit)
Runoff components
TM
VUB
XAJ
1
1
3
2
1
5
Runoff
Fast runoff, Slow runoff
Fast runoff, Slow runoff
GM
WM
1
1
2
1
Soil moisture storage, Water surplus
Soil moisture storage
Upper layer tension storage,
Lower layer tension storage,
Deep layer tension storage,
Free water storage, Groundwater storage
Soil moisture storage, Groundwater storage
Relative soil moisture storage
SM
1
1
Soil moisture deficit
Surface runoff, Interflow, Groundwater flow
Direct runoff, Surface flow, Sub-surface flow,
Baseflow
Surface runoff, Groundwater flow
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
In all of the aforementioned models, three distinct
components can be identified: monthly streamflow, evapotranspiration and soil moisture accounting, which are
treated differently in each model. Soil moisture accounting is the most important component which expresses
the balance between soil moisture content, incoming (precipitation), and outgoing (evapotranspiration and runoff)
quantities.
Actual evapotranspiration in all of the models is treated
as a function of potential evapotranspiration and soil moisture storage. The Thornthwaite–Mather (called TM model
hereafter) Guo (called GM model hereafter) models assume that evapotranspiration takes place at potential rate
for a given month when precipitation is equal to or greater
than the potential evapotranspiration. In the WatBal
(called WM model hereafter) and Schaake (called SM model
hereafter) models, evapotranspiration is assumed to be
equal to the potential evapotranspiration when soil moisture storage reaches the maximum capacity. The Belgium
(called VUB model hereafter) model is an exceptional case,
in which evapotranspiration is equal to the potential
evapotranspiration in the case when the available water
(precipitation plus available storage) is greater than the
potential evapotranspiration. In all of these models, when
precipitation or available water is less than the potential
evapotranspiration, soil moisture deficit occurs. Then,
the actual evapotranspiration is determined by using a
non-linear function of potential evapotranspiration and soil
moisture content in TM, VUB, GM and WM models. On the
other hand, the SM model calculates actual evapotranspiration as a proportion to the ratio of the soil moisture content to the maximum storage capacity. In all of these five
models soils are considered to be a one layer medium for
moisture accounting. The monthly Xinanjiang (called XAJ
model hereafter) model is the only one in which actual
evapotranspiration is estimated from detailed relationships
with plant root characteristics and moisture content distribution in the soil profile. Evapotranspiration in the monthly
Xinanjiang model may decrease from the potential rate in
the upper layer of very thin top soil to actual rate in the
lower layers. The approaches used in all of these models
do not consider the influence of vegetation and the interaction between vegetation and atmosphere. However, they
have the advantage of minimal input data requirement and
ease of application.
In the treatment of soil moisture accounting there are
large differences among the models. All the models, except
the VUB model, adopt a threshold value of soil moisture
storage capacity and rainfall in excess of this value would
become runoff. In the TM, GM and XAJ models, the precipitation for the current month does not produce any runoff
unless soil moisture content reaches the storage capacity.
In the WM model baseflow is a pre-determined threshold value and surface runoff emerges only when the current
monthly effective precipitation exceeds the baseflow. In
the SM model the threshold controls the generation of
groundwater runoff.
In each model, with the exception of the TM model, the
remaining content of soil moisture after evapotranspiration
eventually contributes to various runoff components. The
TM model does not differentiate surface runoff from
groundwater flow.
321
A distinction is made between quick runoff and slow runoff in both the VUB model and the XAJ model. Quick (or
fast) runoff and slow runoff correspond to surface runoff
and groundwater flow, respectively, in the SM model.
Although the two runoff components in all three models
are the same, the mechanisms of runoff generation are
completely different. In the VUB model, the mechanism of
quick runoff can be seen as a translation of the variablesource-area concept of runoff generation: the greater the
available water, the wetter the catchment; the larger the
‘source-area’ of surface runoff, the greater the part of
the ‘active’ precipitation running off rapidly. The slow runoff component is proportional to the soil moisture content
at the beginning of the month.
The runoff generation process described in the monthly
XAJ model is based on the concept of soil moisture storage
repletion. Specifically, runoff generation results from the
soil moisture in the excess of field capacity in the aeration
zone. Part of the generated runoff contributes to quick flow
through a free water storage reservoir, and the rest is added
to the groundwater storage. Groundwater contributes to
the formation of slow flow through a linear reservoir with
a time lag of one month.
In the SM model surface runoff is generated by the effective precipitation after evapotranspiration and replenishing
soil moisture. The infiltration process is described simply as
a linear function of the soil moisture storage deficit. The
groundwater runoff is derived from the aquifer through a
non-linear reservoir.
The GM and WM models consider more runoff components than other models. Surface runoff and interflow are
generated when the soil moisture capacity is reached. Part
of the excess water contributes to surface runoff and another part flows to the river as interflow, and the remaining
percolates to the groundwater storage. Groundwater discharges to the river as baseflow with a time lag of one
month. Runoff in the WM model is divided into four parts:
direct runoff, surface runoff, sub-surface runoff, and baseflow. Baseflow is given a pre-set value, while direct runoff is
a fraction of precipitation. Surface runoff and sub-surface
runoff are expressed as functions of relative soil moisture
storage. Actually there is no obvious distinction between
surface runoff and interflow/sub-surface runoff at a
monthly time interval, because the distribution of precipitation is unified over time as a result of the extended time
scale.
Only the XAJ model considers a certain spatial variation
of the basic variables used for the computation of surface
runoff. This model assumes two parabolic distributions of
tension water capacity and free water storage capacity over
the catchment. None of the models, except the SM model,
includes any infiltration or percolation equations for
describing the movement of water from the surface detention storage to soil moisture storage and consequently to
groundwater storage.
River flow routing is not considered in the models, and
all the flow components run off directly at the basin outlet. This is because compared with daily or event-based
hydrological models, monthly hydrological models may
not make a distinction between runoff production and
runoff routing, and therefore have a relatively simple
framework.
322
T. Jiang et al.
Methods of model calibration and validation
Some of the parameters of the six selected models cannot
be directly determined from field measurement or estimated from catchment characteristics and must, therefore, be estimated by model calibration. There are many
objective functions that have been used for model calibration. In this study, model parameters were optimized by
minimizing the values of the objective function given by
Eq. (2):
OF ¼
n
X
ðqobst qsimt Þ2
ð2Þ
t¼1
where qobst and qsimt are the observed streamflow and simulated streamflow, respectively, of month t, and n is the total number of months of simulation. The main reasons for
using this criterion include: (1) it is simple and directly
applicable to any model, as stated by Sorooshian and Dracup
(1980); and (2) the main objective of the study is to compare the model performance with respect to a common criterion rather than to compare the advantages and
disadvantages of the objective functions.
The Simplex method of Nelder and Mead (1965) was chosen for parameter optimization in this study. The Simplex
method is a local, direct search algorithm that has been
commonly used for conceptual hydrological models (e.g.,
Johnston and Pilgrim, 1976; Gan and Biftu, 1996; Hendrickson et al., 1988). In order to test the accuracy of modelling
results, it is a common practice to employ some criterion
for judging model performance. The first requirement of a
model is that it should have the ability to reproduce the
mean of observed streamflow. However, the mean value
cannot fully indicate how well individual simulated values
match observed values. To overcome this limitation, the
root mean squared error (RMSE) and the coefficient of efficiency or the Nash–Sutcliffe efficiency E (Nash and Sutcliffe, 1970) were employed.
RMSE is simply the average of the squared errors for all
simulation results and provides an objective measure of
the difference between observed and simulated values:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u 1
1 uX
RMSE ¼ t ðqobst qsimt Þ2
ð3Þ
n t¼1
E, as shown in Eq. (4), is a dimensionless coefficient for
measuring the degree of association between observed
and simulated values:
Pn
Pn
2
2
t¼1 ðqobst qobsÞ t¼1 ðqobst qsimt Þ
;
ð4Þ
E¼
Pn
2
t¼1 ðqobst qobsÞ
where qobs is the mean of observed discharges. The value of
E is always less than unity. A value of E equalling unity represents a perfect agreement between observed and simulated streamflows.
Determination of climate change scenarios
In simulating future water resources scenarios, future climate change scenarios are needed. Climate scenarios are
sets of time series or statistical measures of climatic vari-
ables, such as temperature and precipitation, which define
changes in climate. Many methods have been developed for
generating climate scenarios for the assessment of hydrologic impacts of climate change, which include downscaled
general circulation model (GCM) simulations and hypothetical methods. GCMs are used to generate projections of future climate change on a large spatial and temporal scale
(several decades). Even as GCM grid sizes tend towards
one or two degrees, there is still a significant mismatch with
the scale at which many hydrologic and water resources
studies are conducted (Varis et al., 2004). Given the limitations of GCMs grid-point predictions for regional climate
change impact studies, an alternative option is to downscale
GCM’s climate output for use in hydrological models. Two
categories of climatic downscaling, namely, dynamic approaches (in which physical dynamics are solved explicitly)
and empirical (the so called ‘statistical downscaling’) are
commonly employed.
Dynamic downscaling techniques have been used to develop regional climate models (RCMs) to attain a horizontal
resolution on the order of tens of kilometres over selected
areas of interest. This nested regional climate modelling
technique consists of using initial conditions, time-dependent lateral meteorological conditions derived from GCMs
(or analyses of observations) and surface boundary conditions to drive high-resolution RCMs (e.g., Cocke and LaRow,
2000; von Storch et al., 2000). Thus, the basic strategy is to
use a global model to simulate the response of global circulation to large-scale forcings and an RCM to (a) account for
sub-GCM grid-scale forcing (e.g., complex topographical
features and land-cover inhomogeneity) in a physicallybased way; and (b) enhance the simulation of atmospheric
circulations and climate variables at fine spatial scales (upto
10–20 km or less). The main theoretical limitations of this
technique that remain to be improved include (Hay et al.,
2002; Varis et al., 2004): (1) the inheritance of systematic
errors in the driving fields provided by global models. For
example, boundary conditions from a GCM might themselves
be so biased that they impact the quality of regional simulation, complicating the evaluation of the regional model itself (e.g., Hay et al., 2002); (2) lack of two-way interactions
between regional and global climate; and (3) the algorithmic limitations of the lateral boundary interface. Other limitations are: (1) depending on the domain size and
resolution, RCM simulations can be computationally
demanding, which has limited the length of many experiments to date, and (2) there will remain the need to downscale the results from such models to individual sites or
localities for impact studies (Wilby and Wigley, 1997; Xu,
1999). It is essential that the quality of GCM large-scale
driving fields continues to improve, as those impact regional
climate simulations (Varis et al., 2004).
A second, less computationally demanding, approach is
statistical downscaling. In this approach, regional-scale
atmospheric predictor variables (such as area-averages of
precipitation or temperature, and circulation characteristics (such as mean sea level pressure or vorticity) are related to station-scale meteorological series (Hay et al.,
1991, 1992; Karl et al., 1990; Kim et al., 1984; Wigley
et al., 1990). The statistics involved can be simple or extensive, but the final relationships typically arrived at are as
with some form of regression analysis. Statistical downscal-
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
Table 2
323
Hypothetical climate change scenarios
Scenario no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
DT (C)
DP (%)
1
20
1
10
1
0
1
10
1
20
2
20
2
10
2
0
2
10
2
20
4
20
4
10
4
0
4
10
4
20
Hypothetical scenarios are based on reasonably but arbitrarily specified changes in climate variables. Changes in climate variables, such as temperature and precipitation, are
adjusted, often according to a qualitative interpretation of
climate model predictions or the analyses of changes in climate characteristics that occurred in the past during particularly warm or cool periods of hydrometeorological
observations. Adjustments might include, for example,
changes in mean annual temperature of 1 C, 2 C, 3 C,
4 C or changes in annual precipitation of 5%, 10%, 15%,
20%, 25%, relative to the baseline climate. Adjustments
can be made in temperature and precipitation independently or the combination thereof.
In this study hypothetical scenarios were used which
were drawn from the analysis of the state-of-the-art estimates of future climate change for the region (IPCC,
2001). In order to cover a wide range of climate variability,
fifteen hypothetical climate change scenarios were derived
from combinations of three temperature increases and five
precipitation changes (Table 2).
ing methods can be classified into three categories (Wilby
and Wigley, 1997; Xu, 1999), namely, regression methods
(e.g., Kim et al., 1984; Wigley et al., 1990; von Storch
et al., 1993); weather-pattern based approaches (e.g.,
Lamb, 1972; Hay et al., 1991; Bardossy and Plate, 1992; Wilby, 1995); and stochastic weather generators (e.g., Richardson, 1981; Wilks, 1992; Gregory et al., 1993; Katz, 1996). In
reality, many downscaling approaches embrace the attributes of more than one of these methods and therefore tend
to be hybrid in nature. Compared with dynamic downscaling, statistical downscaling methods have the following
advantages (von Storch et al., 2000): (1) they are based
on standard and accepted statistical procedures, (2) they
are computationally inexpensive, (3) they may flexibly be
crafted for specific purposes, and (4) they are able to directly incorporate the observational record of the region.
However, the following disadvantages have also been summarized by Goodess et al. (2001): (1) They assume that predictor/predictand relationships will remain unchanged in
the future, (2) they require long/reliable observed data series, and (3) they are affected by biases in the underlying
GCM. The last point also exists in the dynamic downscaling
methods. Furthermore, the skill of statistical downscaling
depends on climatic region and season (Wetterhall et al.,
2006, 2007).
Given the deficiencies of GCM predictions and downscaling techniques, the use of hypothesized scenarios as input
to catchment-scale hydrological models is widely used
(e.g., Nemec and Schaake, 1982; Xu, 2000; Graham and Jacob, 2000; Engeland et al., 2001; Arnell and Reynard, 1996;
Leavesley, 1994; Boorman and Sefton, 1997; Panagoulia and
Dimou, 1997). Various hypothetical climate-change scenarios have been adopted and the techniques for developing
climate scenarios are continuously progressing. Hulme and
Carter (1999), as cited by Varis et al. (2004), have presented
a typology for scenario construction, which consists of the
following eight stages: Scenarios based on expert judgment;
Equilibrium 2 · CO2 scenarios; Time-dependent climate
change; Multiple forcing scenarios; Climate system unpredictability; Natural climate variability; Scenarios combining
uncertainties based on Bayesian logic; and Sub-grid scale
variability.
Table 3
Results
Comparison of models results in reproducing
historical records
Statistical comparisons and visual comparisons of observed
and simulated values were conducted to evaluate the performance of the selected models. Table 3 gives a summary
of statistics of simulations by the selected models for both
calibration and validation periods. The values of RMSE and
E in Table 3 indicate that all the models produce good results for calibration and validation periods and the XAJ model has the highest E value and the lowest RMSE value,
followed by GM, VUB, TM, SM and WM. The values in Table
3 demonstrate the basic capability of each model to reproduce long-term mean annual observed runoff in the Dongjiang basin.
Comparison of mean monthly values of simulated runoff,
evapotranspiration and soil moisture content for the period
1960–1988 are shown in Fig. 3. It is seen that (1) all six mod-
Comparison of the results of the six models in reproducing historical discharge in the Dongjiang basin (1960–1988)
Calculation and validation
QOBS
TM
VUB
XAJ
GM
WM
SM
Calibration 1960–1974
Q (mm/month)
RMSE
E (%)
73.3
71.4
23.61
90.9
72.2
24.65
90.1
71.3
21.88
92.2
70.5
22.28
91.9
77.4
29.01
86.3
75.3
27.03
88.1
Validation 1975–1988
Q (mm/month)
RMSE
E (%)
82.8
83.4
22.57
89.9
83.2
22.44
89.9
83.3
20.19
91.8
82.6
21.01
91.1
86.4
27.34
85.0
81.8
25.15
87.3
T. Jiang et al.
runoff (mm/month)
324
250
200
150
100
50
0
1
2
3
4
5
6
7
8
9 10 11 12
month
OBS
TM
VUB
GM
WM
SM
XAJ
actual ET (mm/month)
120
100
80
60
40
20
0
1
2
3
4
5
6
7
8
9
10 11 12
month
TM
VUB
XAJ
GM
WB
SM
soil moisture (mm)
400
and correlated with observed values using a linear regression equation Y = mX + c. In the equation, Y represents the
model calculated runoff, and X is the observed runoff, and
m and c are constants representing the slope and intercept,
respectively. The scatter plot and the results of regression
analysis are shown in Fig. 4. It is seen from Fig. 4 that: (1)
as far as the R2 values are concerned, all model predictions
correlated well with observed values resulting in R2 values
P0.90 in all cases. (2) When the values of slope and intercept are compared, the differences among the models are
also not so great. The values of intercept are generally less
than 10% of the mean monthly values, and the slopes (m)
are all within ±10% of the 1:1 line. A close look at the differences among the models reveals that the TM and GM models
have the smallest bias in the regression slope, while the GM
and SM models have the smallest bias in the intercept. (3)
When looking at the monthly peak values, it is found that
the TM, GM and WM models exhibit a bigger negative bias
when compared with observed values.
Generally speaking, the results show that all six models
can reproduce historical monthly runoff series with an
acceptable accuracy. It must, however,be kept in mind that
the purpose here is not to discuss in detail which model is
superior. The main purpose is to check how diverse the
models’ results are with respect to historical and alternative climates.
Differences of models results in predicting
hydrological response of changed climate
300
200
100
0
1
2
3
4
5
6
7
8
9
10 11 12
month
TM
VUB
XAJ
GM
WM
SM
Figure 3 Comparison of mean monthly runoff (upper), actual
evapotranspiration (middle) and soil moisture (lower) simulated by the six models for the period of 1960–1988.
els simulate quite well the mean monthly runoff except the
WM model for the months of June and July, and the SM model for the months of October and November (Fig. 3 upper).
(2) There is a good agreement in the mean monthly evapotranspiration simulated by the six models, except that the
WM and SM models yield smaller values for winter and spring
months (Fig. 3 middle). (3) Larger differences are found for
the simulated monthly soil moisture. Similar results have
been reported by Alley (1984) and Vandewiele et al.
(1992) that ‘state variables simulated by the conceptual
monthly water balance models may be quite different’,
and this is partially because the soil depth is usually not
explicitly defined in such models.
In order to compare the models’ capabilities in simulating the dynamics of monthly runoff series, the monthly runoff values computed using different models are analyzed
It is important for water resources managers to be aware of
and prepared to deal with the effects of climate change on
hydrological variables. Obviously, streamflow is essential in
order to provide an indication of the extent of impacts of
climatic change on water resources, which represents an
integrated response to hydrologic inputs on the surrounding
drainage basin area and therefore affords a good spatial
coverage. Since it is expected that climate change will result in a diversity of environmental responses, actual evapotranspiration and soil moisture are also included in this
study.
Mean annual changes
The mean annual response of hydrological variables to the
15 climate scenarios is first evaluated. The percent changes
of mean annual runoff in response to the 15 climate change
scenarios are shown in Fig. 5. In general, Fig. 5 shows that
even on the annual level there is a wide range of differences
between runoff responses simulated by the six models when
perturbed climate scenarios are used to drive the models.
The runoff changes in response to temperature changes
for a given precipitation change are shown in Fig. 5a. Six
lines in each branch of lines represent the results of six
models. The slope of each line represents the changing rate
for runoff as temperature increases. The differences between the five branches represent the influence of different
precipitation changing scenarios. It is seen that (1) when
there is no change in precipitation (six middle branch lines),
one, two and four degree increase in the air temperature result in a reduction in annual runoff of about 3%, 5–8% and
8–15%, respectively, depending on the model. When precip-
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
400
1:1
Y = 1.03X - 6.00
R2 = 0.91
300
200
100
Monthly runoff by VUB (mm/month)
Monthly runoff by TM (mm/month)
400
1:1
Y = 0.94X + 5.30
R2 = 0.91
300
200
100
0
0
0
100
200
300
400
0
Observed monthly runoff (mm/month)
Y = 1.09X - 7.11
R2 = 0.91
300
Monthly runoff by GM (mm/month)
Monthly runoff by XAJ (mm/month)
200
300
400
400
1:1
200
100
1:1
Y = 0.98X - 2.37
R2 = 0.91
300
200
100
0
0
0
100
200
300
400
0
Observed monthly runoff (mm/month)
100
200
300
400
Observed monthly runoff (mm/month)
400
Monthly runoff by SM (mm/month)
400
Monthly runoff by WM (mm/month)
100
Observed monthly runoff (mm/month)
400
1:1
Y = 0.96X + 8.15
R2 = 0.90
300
200
100
1:1
Y = 0.93X + 4.76
R2 = 0.90
300
200
100
0
0
0
100
200
300
400
Observed monthly runoff (mm/month)
Figure 4
325
0
100
200
300
400
Observed monthly runoff (mm/month)
Scatter plot and regression equations of the monthly runoff calculated by the six models with the observed runoff.
itation decreases by 20% (six left branch lines), annual runoff decreases by about 25–40%, 28–45% and 30–50%,
respectively, for temperature increases of 1 C, 2 C and
4 C, depending on the model. When precipitation increases
by 20% (six right branch lines), annual runoff increases by
about 20–35%, 17–27% and 15–20%, respectively, for temperature increases of one, two and four degrees, depending
on the model; (2) the differences between models increase
as the precipitation change increases in both directions. The
decrease in precipitation results in larger differences than
40
ΔP=20%
% change in runoff
30
20
ΔP=10%
10
0
1
2
3
4
1
3
4
1
2
3
4
1
2
3
4
1
2
3
4
ΔP=0%
-20
-30
ΔP=-10%
-40
-50
VUB
XAJ
GM
WM
% change in runoff
10
0
-30
0
ΔP=20%
10
5
0
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1 2
3 4
10
20
-20
ΔT=1˚C
-10
0
10
20
-20
ΔT=2˚C
-10
Temperature increase in˚C
TM
20
-10
ΔP=-10%
ΔP=-20%
ΔP=10%
ΔP=0%
15
SM
30
-20
20
-10
Temperature increase in ˚C
40
-20
25
ΔP=-20%
TM
-10
30
-5
-60
b
2
-10
a
0
10
20
ΔT=4˚C
-40
b
30
% change in evaporation
a
T. Jiang et al.
% chnage in evaporation
326
25
VUB
XAJ
GM
WM
SM
ΔT=4˚C
20
15
ΔT=2˚C
10
ΔT=1˚C
5
0
-20
-10
0
10
20
-20
-10
0
10
20
-20
-10
0
10
20
-5
-50
-60
-10
%change in precipitation
TM
VUB
XAJ
GM
WM
SM
% change in precipitation
TM
VUB
XAJ
GM
WM
SM
Figure 5 Comparison of mean annual changes in runoff in
response to temperature increases for a given precipitation
change (a) and comparison of mean annual changes in runoff in
response to mean annual changes in precipitation for a given
temperature change (b).
Figure 6 Comparison of mean annual changes in evapotranspiration in response to temperature increases for a given
precipitation change (a) and comparison of mean annual
changes in evapotranspiration in response to mean annual
changes in precipitation for a given temperature change (b).
the increase in precipitation by the same amount; (3) the
TM, XAJ and GM models behave similarly and produce more
changes in runoff for a given climate change scenario, while
the SM model produces the smallest changes. The runoff
changes in response to precipitation changes for a given
temperature change are shown in Fig. 5b. The slopes of
the lines in each branch of lines reveal the changing rate
of runoff in response to precipitation changes. The
difference between the three branches represents the
influence of different temperature change scenarios. Comparing Fig. 5a with Fig. 5b it can be seen that runoff changes
are more sensitive to precipitation changes than to
temperature.
Similar to Fig. 5, evapotranspiration changes in response
to the climate change scenarios are shown in Fig. 6. This figure also shows that even on the annual level there is a wide
range of differences between the evapotranspiration responses simulated by the six models when perturbed climate scenarios are used to drive the models. From Fig. 6a
and b, two groups of model simulated evapotranspiration
changes in response to climate change scenarios can be distinguished. The first group consists of three models, i.e.,
TM, XAJ and GM, which respond almost identically in all
the climate change scenarios. The other models show different responses.
Each branch of lines in Fig. 6a represents the difference
of evapotranspiration changes caused by precipitation
changes. Comparing Fig. 6a with Fig. 5a it is seen that the
effect of precipitation changes on evapotranspiration is less
than on runoff. Comparing Fig. 6b with Fig. 5b one can see
that the effect of temperature changes on evapotranspiration and runoff has a different sign. For example, when precipitation has no change, one, two and four degree
increases in temperature cause an increase in evapotranspiration of about 3%, 6–8% and 12–17%, respectively.
The percent changes of mean annual soil moisture in response to the 15 climate change scenarios are shown in
Fig. 7. In general, Fig. 7 shows that (1) the differences in soil
moisture changes simulated by the VUB model are larger
than those simulated by other five models when perturbed
climate scenarios are used to drive the models. This is probably due to the fact that the VUB model is the only model
under comparison that does not have an upper threshold
limit for soil moisture. The soil moisture can change freely
in the VUB model, while this is not the case in other five
models. (2) The differences in soil moisture changes under
alternative climates are smaller than the runoff changes
in the five models (exclude VUB model), when an upper
threshold limit is used for soil moisture simulation in the
model equations.
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
1
ΔP=20%
20
ΔP=10%
10
ΔP=-10%
ΔP=-20%
0
1
2
3
4
1
2
3 4
1 2
3
4
1 2
3 4
1 2
3
4
-10
-20
0
-10
-20
-30
-40
-50
-60
-70
2
3
4
5
7
8
9 10 11 12
month
TM
-40
1
Temperature increase in ˚C
VUB
XAJ
GM
WM
SM
% change in runoff
TM
b
6
a
-30
-50
% change in soil moisture
ΔP=0%
% change in runoff
30
30
20
10
ΔT=1˚C
ΔT=2˚C
ΔT=4˚C
0
-20
-10
-10
0
10
20
-20 -10 0
10
20 -20 -10
0
10
20
0
VUB
2
XAJ
3
4
5
GM
6 7
8
WM
SM
9 10 11 12
b
-10
-20
-30
-40
month
-20
TM
VUB
XAJ
GM
WM
SM
-30
-40
-50
% change in precipitation
TM
VUB
XAJ
GM
WM
SM
Figure 7 Comparison of mean annual changes in soil moisture
in response to temperature increases for a given precipitation
change (a) and comparison of mean annual changes in soil
moisture in response to mean annual changes in precipitation
for a given temperature change (b).
% change in runoff
% change in soil moisture
a
327
50
c
40
30
20
10
0
1
TM
Mean monthly changes
To evaluate seasonal and inter-annual changes, differences
in mean monthly runoff, actual evapotranspiration and soil
moisture simulated by the six models with various climate
change scenarios are compared. Due to the limit of the
length of the paper and for illustrative purposes, changes
in mean monthly runoff, actual evapotranspiration and soil
moisture simulated by the six models for three climate
change scenarios (i.e., combination of temperature increases by 2 C (DT =+2 C) and precipitation changes by
±20% and 0%) are plotted in Figs. 8–10, respectively.
Fig. 8 shows that (1) the differences in model predicted
mean monthly runoff resulting from the use of different
hydrological models are large. The figure shows a great
diversity in the simulation results. (2) The larger differences
in percent changes in runoff for winter months may be
caused by smaller absolute values in runoff in winter months
(see Fig. 2). (3) The TM, XAJ and GM models respond similarly in predicted changes in monthly runoff, while other
three models show a similar pattern of seasonal variation
in the predicted changes of monthly runoff for changing
climate. (4) On average, when temperature increases by
2 C the mean monthly runoff changes by 30 50%,
5 10%, and 10 30%, respectively for precipitation
changes of 20%, 0% and 20%, depending on the model.
Fig. 9 shows that (1) the differences in model predicted
mean monthly actual evapotranspiration resulting from
2
3
VUB
4
5
6 7 8
month
XAJ
GM
9 10 11 12
WM
SM
Figure 8 Comparison of mean monthly changes in runoff
simulated by the six models for three climate change scenarios
(a) DT = +2 C and DP = 20%, (b) DT = +2 C and DP = 0%, and
(c) DT = +2 C and DP = 20%.
the use of different hydrological models are also remarkable. (2) Two groups of evapotranspiration reaction behaviour with respect to climate changes can be distinguished.
The first group of models (i.e., TM, XAJ and GM ) react very
similarly, while differences among other three models are
considerable. (3) In summer months (rainy season in the region) the model-predicted actual evapotranspiration does
not change significantly with the change in precipitation.
A two degree increase in air temperature causes about a
10% increase in evapotranspiration in all three cases, meaning that actual evapotranspiration is energy controlled in
the rainy season in the humid area.
It is seen from Fig. 10 that (1) the differences in modelpredicted mean monthly soil moisture content resulting
from the use of different hydrological models are also
considerable. (2) Again, two groups of model reaction
behaviour with respect to climate changes can be distinguished. The first group of models (i.e., TM, XAJ and GM )
react very similarly, while differences among the other
three models are considerable, especially the VUB model
behaves very differently from other models. As discussed
a
20
10
a
0
-10 1
2
3
4
5
6
7
8
9 10 11 12
-20
-30
-40
-50
month
TM
VUB
XAJ
GM
WM
% change in soil moisture
T. Jiang et al.
% change in evap
328
10
0
-10 1
6
4
2
0
TM
% change in evap.
c
4
VUB
5
6 7 8
month
XAJ
9 10 11 12
GM
WM
% change in soil moisture
8
SM
5
6
7
8
9 10 11 12
-60
month
VUB
XAJ
GM
WM
SM
5
0
-5 1
2
3
4
5
6
7
8
9 10 11 12
-10
-15
-20
-25
month
TM
VUB
XAJ
GM
WM
SM
25
c
20
15
10
5
0
1
TM
2
3
VUB
4
5
6 7 8
month
XAJ
GM
9
10 11 12
WM
SM
Figure 9 Comparison of mean monthly changes in actual
evapotranspiration simulated by the six models for three
climate change scenarios (a) DT = +2 C and DP = 20%, (b)
DT = +2 C and DP = 0%, and (c) DT = +2 C and DP = 20%.
in the last section, this is because the VUB model is the only
one that does not have an upper threshold limit in the calculation of soil moisture.
Summary and conclusions
In this study, six monthly water balance models are used
and their differences in reproducing historical water balance components and in predicting hydrological impacts of
15 perturbed climate change scenarios are compared. The
study is performed in the Dongjiang catchment, a tributary
of the Pearl River (Zhujiang) located in a subtropical humid
region in southern China. The main focus of the study is to
test how large differences one can expect when using different rainfall-runoff models to simulate hydrological response of climate changes as compared to their capacities
in simulating historical water balance components.
This study shows that when using the class of models considered in this paper for hydrological simulation of changing/changed climate the following conclusions can be
drawn.
% change in soil moisture
% change in evap.
b
10
3
4
-40
-50
TM
2
3
SM
b 12
1
2
-20
-30
20
15
10
5
0
-5 1
2
3
4
5
6
7
8
9 10 11 12
month
TM
VUB
XAJ
GM
WM
SM
Figure 10 Comparison of mean monthly changes in soil
moisture simulated by the six models for three climate change
scenarios (a) DT = +2 C and DP = 20%, (b) DT = +2 C and
DP = 0%, and (c) DT = +2 C and DP = 20%.
• All the six tested models can reproduce almost equally
well the historical runoff data series, while large differences exist in the model simulated soil moisture.
• Using alternative climates as input to the tested models,
large differences exist in model predicted runoff, actual
evapotranspiration and soil moisture. The differences
depend on the climate scenarios, the season, and the
hydrological variables under examination.
• Using an upper threshold limit in the soil moisture simulation by the models has a significant influence on the
model simulated soil moisture under both historical and
alternative climates. The model without a threshold in
soil moisture simulation results in greater changes in
model predicted soil moisture with respect to alternative climates than the models with a threshold soil
moisture.
The results confirm the findings of the previous studies
using fewer models than the present study. Boorman and
Sefton (1997) compared two rainfall-runoff models and con-
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
cluded that ‘‘Clearly the two models do little to support
each other in estimating the possible effects of a changed
climate’’. Panagoulia and Dimou (1997) also reported that
significant differences exist in the predicted runoff and soil
moisture with respect to alternative climates by using two
different models, and the differences depend on the climate scenarios and on the seasons.
This study suggests that attention must be paid when
using existing hydrological models for simulating hydrological responses of climate changes. Future water resources
scenarios predicted by any particular hydrological model
represent only the results of that model. More studies using
different hydrological models on different catchments need
to be carried out in order to provide more general
conclusions.
Acknowledgements
The work presented in this paper was partly supported by
the Swedish Research Council, the Research Grants Council
of the Hong Kong Special Administrative Region, China (Project no. CUHK4247/03H), the National Natural Science
Foundation of China (Project no. 50579078) and the Outstanding Overseas Chinese Scholars Fund from CAS (The Chinese Academy of Sciences). The authors express their
thanks to the three referees for their constructive and helpful comments, which greatly improved the quality of the
paper.
Appendix A. Model description
The Thornthwaite–Mather model (called TM model hereafter) was developed by Thornthwaite and Mather (1955)
and a detailed study of the model was done by Alley
(1984). It is a model with two storages (Fig. A1): ‘soil moisture index’ and ‘water surplus’. The model has two parameters: soil moisture capacity and storage constant. In this
model, the soil is assumed to have a maximum soil moisture
capacity, Smax. Moisture is either added to or subtracted
from the soil, depending on whether the precipitation of
PET
month t, P(t), is greater or less than the potential evapotranspiration for the month, PET(t). When P(t) P PET(t),
the soil moisture content is updated byS(t) = min
[P(t) PET(t) + S(t),Smax], and the excess precipitation is
assumed to contribute to water surplus, DQ = [P(t) PET(t)] + S(t 1) Smax]. When P(t) < PET(t), the soil moisPETðtÞPðtÞ
ture storage is described by SðtÞ ¼ Sðt 1Þe Smax and
DQ = 0. Actual evapotranspiration is computed by Ea(t) =
PET(t), when P(t) P
PET(t). Otherwise, E a ðtÞ ¼ PðtÞþ
PETðtÞPðtÞ
Sðt 1Þe Smax 1. Streamflow is derived from the water
surplus. This model assumes that a fraction k of the water
surplus remains in the soil and recharges the groundwater
storage. Thus runoff for month t is R(t) =
(1 k)[Q(t 1) + DQ], and the water surplus at the end of
the month is updated by Q(t) = k[Q(t 1) + DQ]. Parameter
k varies with the depth and texture of the soil, size and
physiography of the basin, and characteristics of
groundwater system. Parameters that need to be calibrated
are Smax and k.
A.2. Belgium model (VUB)
Vandewiele et al. (1992) proposed a series of monthly water
balance models on a basin scale. One of the models, referred to here as VUB model (Fig. A2), is selected for use
in the study. The model is based on the water balance
equation S(t) = S(t 1) + P(t) Ea(t) R(t). S(t) and S(t 1)
represent the states of the soil moisture storage at the
end and beginning of month t, respectively. P(t), Ea(t),
R(t) are precipitation, actual evapotranspiration, and discharge during month t, respectively.
h Actual evapotranspirai
tion is computed as E a ðtÞ ¼ min WðtÞð1 e
A.1. Thornthwaite–Mather model (TM)
P
329
PETðtÞ
a1
Þ; PETðtÞ ,
where a1 is a non-negative parameter and W(t) =
P(t) + S(t 1) is the available water. Monthly discharge is
distinguished between slow runoff Rs(t) = a2[S(t 1)+]0.5
and quick runoff Rf(t) = a3 (S(t 1)+)0.5N(t), where NðtÞ ¼
h
i
PðtÞ
PðtÞ PETðtÞ 1 e maxðPETðtÞ;1Þ is defined as the effective precipitation. The total runoff is R(t) = Rs (t) + Rf(t). Parameters that need to be calibrated are a1, a2, and a3.
A.3. The monthly xinanjiang model (XAJ)
The Xinanjiang model was originally developed on a hourly
time scale for flood forecasting or on a daily time scale
for continuous hydrological simulation (Zhao, 1992). Various
Ea
Soil Moisture Storage
(S)
PET
ΔQ
Water Surplus
(Q)
R
Available Water Storage
(S)
Rf
Simulated
Streamflow
Figure A1 Schematic representation of Thornthwaite–
Mather model (TM).
P
Ea
Rs
Simulated
Streamflow
Figure A2
Schematic representation of Belgium model (VUB).
330
T. Jiang et al.
simplified model versions for monthly simulation were reported (e.g., Hao and Su, 2000) according to the characteristics of monthly runoff hydrograph for basin hydrological
modeling and water resources assessment (Fig. A3).
In the monthly Xinanjiang model, the soil moisture storage during month t, W(t), is divided into three layers: WU(t)
in the upper layer, WL(t) in the lower layer, and WD(t) in
the deep layer, of which the upper threshold limit values
are WUM, WLM and WDM, respectively. Soil moisture storage is depleted and replenished, respectively, through
evapotranspiration and precipitation.
Actual evapotranspiration is related to both potential
evapotranspiration and soil moisture status. In the upper
layer, evapotranspiration of month t, EU(t), takes place at
the rate of potential evapotranspiration. Once the moisture
content in the upper layer has been depleted, evapotranspiration proceeds to the lower layer, EL(t), depending on the
ratio of the moisture content to the storage capacity. When
the lower layer storage falls below some pre-set fraction of
WLM, evapotranspiration is assumed to continue at a rate
ED(t). The actual evapotranspiration is the total of the
evapotranspiration of the three layers.
Precipitation first satisfies the demand for evapotranspiration and runoff generation depends on the difference between precipitation and potential evapotranspiration. If
the difference is positive, runoff generates; otherwise,
there is no runoff production. It is proposed that the runoff
production is based on the partial area concept by considering the non-uniform distribution of soil moisture storage
capacity over the basin. The remainder of runoff production becomes an addition to the groundwater storage.
The groundwater storage contributes to the slow runoff.
The simulation procedures of the monthly Xinanjiang model are outlined in Fig. A3. The model has 7 parameters, of
which 4 parameters are sensitive ones and need to be
calibrated.
PET
P
Ea
EU
Upper Layer Soil Moisture
Storage (WU)
EL
Low Layer Soil Moisture
Storage (WL)
ED
A.4. Guo model (GM)
Guo (1992) developed a five-parameter monthly water balance model. The basic structure of this model is presented
in Fig. A4. At a monthly time step, the model divides runoff
into surface runoff, interflow, and groundwater flow. Rainfall first satisfies the demand for evapotranspiration and
replenishes soil moisture, and the remaining amount would
become surface runoff and interflow.
If precipitation is greater than potential evapotranspiration, then the soil moisture is calculated as S(t) =
PETðtÞPðtÞ
S(t 1) + P(t) PET(t), otherwise SðtÞ ¼ Sðt 1Þ e Smax .
When precipitation exceeds potential evapotranspiration
and soil moisture storage attains its capacity, the excess
water is equal to S(t) minus Smax, a part of which contributes
to surface runoff Rs(t) = c[S(t) Smax], and c is the surface
runoff coefficient. The remaining amount of excess water
is determined from WS(t) = (1 c)[S(t) Smax], and the
interflow is Ri(t) = k1WS(t). Where k1is a watershed lag coefficient. Groundwater is assumed to behave like a reservoir
receiving a part of the excess water and discharging at a
specified rate to the river with a time lag of one month.
The groundwater flow is calculated by Rg(t) = k2G(t 1),
where k2 is a groundwater reservoir coefficient, and
G(t 1) is the groundwater storage at the beginning of
the month. At the end of each month t, groundwater storage is updated by G(t) = G(t 1) + (1 k1)WS(t) k2G(t 1) for WS(t) P 0, and G(t) = G(t 1) k2G(t 1),
for WS(t) < 0. The total monthly runoff TR(t) is the sum of
surface runoff, interflow, and groundwater flow
TR(t) = Rs(t) + Ri(t) + Rg(t). Parameters that need to be calibrated are maximum soil moisture storage, Smax, surface
runoff coefficient, c, watershed lag coefficient, k1 and
groundwater reservoir coefficient, k2.
A.5. WatBal model (WM)
The WatBal model was originally developed for Colorado
Subalpine watersheds (Leaf and Brink, 1973). Sequentially
it was modified for assessing the hydrological impact of
climate change. The conceptualization of the WatBal model
is shown in Fig. A5. The uniqueness of the WatBal model is
the use of continuous functions of relative storage to
represent surface outflow, sub-surface outflow, and evapo-
Deep Layer Soil Moisture
Storage (WD)
R
PET
Ea
Free Water Storage
(S)
Rs
Rf
Groundwater Storage
(GS)
Rs
Ri
Rg
Simulated
Streamflow
Figure A3 Schematic representation of the monthly Xinanjiang Model (XAJ).
P
Soil Moisture Storage
(S)
WS
Groundwater Storage
(GS)
Simulated
Streamflow
Figure A4
Schematic representation of Guo model (GM).
Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin
T
PET
PET
331
P
Pxx
P
Ea
Peff
Ea
Soil Moisture Deficit
(D)
Relative Soil Moisture
Storage(Z)
Rs
Rss
Rb
Groundwater Storage
Rd
Rg
Simulated
Streamflow
Figure A5
Schematic representation of WatBal model (WM).
transpiration. Given direct runoff Rd(t) = bPeff(t), the water
balance is written as Smax dz
¼ P eff ðtÞð1 bÞ Rs ðz; tÞ
dt
Rss ðz; tÞ E a ðz; tÞ Rb ; where t is time, b is a direct runoff
coefficient, Smax is the maximum storage capacity, Peff(t)
is the effective precipitation, Rs(z,t) is the surface runoff,
Rss(z,t) is the sub-surface runoff, Ea(z,t) is the evapotranspiration, Rb is the baseflow, z = S(t)/Smax is the relative soil
moisture storage, and S(t) is the soil moisture storage. This
differential equation can be solved by using a predictor-corrector method.
Evapotranspiration is a function of potential evapotrans2
piration and the relative storage, E a ðz; tÞ ¼ PETðtÞ 5z2z
.
3
Surface runoff and subsurface runoff are calculated as
functions of relative storage and effective precipitation,
respectively. The model has four parameters that need calibration, i.e., maximum storage capacity, Smax, direct runoff coefficient, b, a parameter related to surface runoff,
e, and a parameter related to sub-surface runoff, a.
Rs
Simulated
streamflow
Figure A6
Schematic representation of Schaake model (SM).
trols infiltration of precipitation through the surface of
the earth. If Pxx(t) is positive, surface runoff is calculated
xx ðtÞ
as Rs ðtÞ ¼ P xx ðtÞ Pxx PðtÞþD
. Groundwater runoff is assumed
max
to vary with deficit D(t). It is assumed that the groundwater
table rises to streams and groundwater runoff generates
when D(t) is less than a certain value. The equation used
to compute groundwater runoff is Rg(t) = kk[Gmax D(t)],
where kk is a parameter, and Gmax is a threshold value. If
D(t) exceeds Gmax, Rg(t) is zero and streams would percolate
to groundwater. However, no attempt is made in the model
to account for such losses from streams to groundwater.
The storage deficit at the end of the month is computed
by mass balance as D(t + 1) = D(t) Pxx(t) + Ea (t) + Rs(t).
Parameters that need to be calibrated are maximum limit
of soil moisture storage deficit, Dmax, infiltration parameter, z, proportion of Ea(t) that must be satisfied before runoff or infiltration can occur, H, groundwater parameter, kk,
and a threshold parameter, Gmax.
A.6. Schaake model (SM)
Schaake and Liu (1989) developed a simple water balance
model for assessing the impact of climate change. Schaake
(1990) improved groundwater algorithms of the linear model
using a nonlinear reservoir. The enhanced model, referred
to as the SM model, has the ability to simulate runoff over
a range of climate conditions. The uniqueness of the model
is to introduce soil moisture deficit in the expression of
runoff and evapotranspiration. Runoff is divided into surface
runoff and groundwater flow. The schematic representation
of the Schaake model is given in Fig. A6.
In the SM model, actual evapotranspiration is assumed to
occur at a potential rate when the storage deficit is zero,
whereas actual evapotranspiration is zero in the case when
the storage deficit reaches the maximum limit. In the intermediate case, actual evapotranspiration Ea(t) in month t is
DðtÞ
calculated as E a ðtÞ ¼ PETðtÞ DmaxDmax
, and Dmax is the maximum limit of soil moisture storage deficit, and D(t) is the
current deficit.
To compute surface flow, the effective precipitation,
Pxx ðtÞ, is defined as Pxx(t) = P(t) HEa(t) zD(t), H is a
parameter representing the proportion of Ea(t) that must
be satisfied from precipitation in the current month before
runoff or infiltration can occur; z is a parameter that con-
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