HYDROLOGICAL PROCESSES
Hydrol. Process. 21, 242– 252 (2007)
Published online 24 April 2006 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/hyp.6187
A distributed monthly hydrological model for integrating
spatial variations of basin topography and rainfall
Xi Chen,1 Yongqin David Chen2 * and Chong-yu Xu3
1
State Key Lab of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, People’s Republic of China
2 Department of Geography and Resource Management, The Chinese University of Hong Kong, Shatin, Hong Kong
3 Department of Geosciences, University of Oslo, Oslo, Norway
Abstract:
Hydrological models at a monthly time-scale are important tools for hydrological analysis, such as in impact assessment of
climate change and regional water resources planning. Traditionally, monthly models adopt a conceptual, lumped-parameter
approach and cannot account for spatial variations of basin characteristics and climatic inputs. A large requirement for data
often severely limits the utility of physically based, distributed-parameter models. Based on the variable-source-area concept,
we considered basin topography and rainfall to be two major factors whose spatial variations play a dominant role in runoff
generation and developed a monthly model that is able to account for their influences in the spatial and temporal dynamics of
water balance. As a hybrid of the Xinanjiang model and TOPMODEL, the new model is constructed by innovatively making
use of the highly acclaimed simulation techniques in the two existing models. A major contribution of this model development
study is to adopt the technique of implicit representation of soil moisture characteristics in the Xinanjiang model and use
the TOPMODEL concept to integrate terrain variations into runoff simulation. Specifically, the TOPMODEL topographic
index lna/ tan ˇ is converted into an index of relative difficulty in runoff generation (IRDG) and then the cumulative
frequency distribution of IRDG is used to substitute the parabolic curve, which represents the spatial variation of soil storage
capacity in the Xinanjiang model. Digital elevation model data play a key role in the modelling procedures on a geographical
information system platform, including basin segmentation, estimation of rainfall for each sub-basin and computation of terrain
characteristics. Other monthly data for model calibration and validation are rainfall, pan evaporation and runoff. The new model
has only three parameters to be estimated, i.e. watershed-average field capacity WM, pan coefficient and runoff generation
coefficient ˛. Sensitivity analysis demonstrates that runoff is least sensitive to WM and, therefore, it can be determined by a
prior estimation based on the climate and soil properties of the study basin. The other two parameters can be determined using
optimization methods. Model testing was carried out in a number of nested sub-basins of two watersheds (Yuanjiang River
and Dongjiang River) in the humid region in central and southern China. Simulation results show that the model is capable
of describing spatial and temporal variations of water balance components, including soil moisture content, evapotranspiration
and runoff, over the watershed. With a minimal requirement for input data and parameterization, this terrain-based distributed
model is a valuable contribution to the ever-advancing technology of hydrological modelling. Copyright  2006 John Wiley
& Sons, Ltd.
KEY WORDS
monthly hydrological model; digital elevation model; distributed model; Xinanjiang model; TOPMODEL
Received 11 April 2005; Accepted 16 November 2005
INTRODUCTION
Numerous hydrological models of watershed water balance with varying degrees of complexity have been developed and applied extensively around the world over the
past half century. The earliest models are probably those
using a simple accounting procedure of water budget
to estimate soil moisture fluctuation and runoff production based on climatic inputs, i.e. rainfall and temperature (e.g. Thornthwaite, 1948; Thornthwaite and Mather,
1955, 1957). With the advent of digital computers in the
early 1960s, hydrologists began to develop conceptual
hydrological models into which more sophisticated water
balance analysis could be incorporated. Later attempts
were made to develop more physically based models that
were supposedly able to keep track of water movement
* Correspondence to: Yongqin David Chen, Department of Geography
and Resource Management, The Chinese University of Hong Kong,
Shatin, Hong Kong. E-mail: ydavidchen@cuhk.edu.hk
Copyright  2006 John Wiley & Sons, Ltd.
and budget in a discretized spatial domain using physical
laws. The advancement of geoinformation technologies,
such as geographical information systems and remote
sensing, has offered a great impetus for the development
of distributed hydrological models. However, the availability of basin characteristics and meteorological input
data with sufficiently fine resolutions is usually still a
critical constraint for applying distributed models. Over
the history of model development, hydrological models
have been adopted, modified, and applied to solve a wide
spectrum of hydrological problems (e.g. Gabos and Gasparri, 1983; Alley, 1984; Vandewiele et al., 1992; Xu
et al., 1996). In the past two decades, one major area of
model applications is hydrological impact studies of climate change (e.g. Aston, 1984; Gleick, 1987; Arnell and
Reynard, 1996; Guo et al., 2002). Hydrological models
have also been widely utilized for long-range streamflow forecasting (e.g. Alley, 1985; Xu and Vandewiele,
1995). Hydrological model runs at monthly time-steps
A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL
are often sufficient for assessing the long-term climatic
change impact on water resources.
The majority of the conceptual hydrological models
based on the water balance concept were developed in
the 1960s and 1970s. Examples include the Stanford
Watershed Model (Crawford and Linsley, 1964), the
Sacramento Soil Moisture Accounting Model (Burnash
et al., 1973), the HBV model (e.g. Bergström, 1976) and
the Xinanjiang model (Zhao et al., 1980). The structures
of these models have been improved by dividing runoff
and state variables such as soil moisture storage into
different components (e.g. Gleick, 1987; Mimikou et al.,
1991; Mohseni and Stefan, 1998). Such models contain
complex nonlinear functions defining moisture fluxes
between a number of conceptual storage zones. They
are usually operated on time-steps of a day or an even
shorter period and require more data and parameters in
comparison with monthly models.
Models developed before the early 1980s have a
lumped structure and the spatial variation of hydrological
variables and model parameters is generally not taken into
account. However, some models do consider heterogeneity of rainfall and basin characteristics such as infiltration
capacity to some extent. Examples include the Hydrologic Simulation Program–FORTRAN, which accounts
for the spatial variations by dividing the watershed into
sub-basins (Bicknell et al., 1993), the Xinanjiang model
(Zhao et al., 1980) and the VIC model (Liang et al.,
1994), which can implicitly simulate hydrological heterogeneity by adopting a statistical distribution of soil
water characteristics. Since the mid 1980s, given the need
of explicit spatial representation of hydrological components and variables, distributed-parameter models based
on physical laws describing water movement have been
developed (e.g. the SHE model as described in Abbott
et al. (1986a,b)). These models contain detailed simulation algorithms that are often partial differential equations
and numerical solution of the equations requires a tremendous amount of input data. Model applicability is seriously limited by data availability, especially for large
basins. Thus, a distributed hydrological model having the
flexibility to deal with different conditions in a wide range
of geographical regions is required. TOPMODEL (Beven
and Kirkby, 1979) has provided hydrologists with a powerful tool to simulate analytically the hillslope response
of site-specific topography without the need of making
use of any finite-element model. A unique feature of
TOPMODEL is its capability to operate at large watershed scales by using the statistics of the topography,
rather than the details of the topography itself. A model
comparison study by Guo et al. (2000) shows that the
statistical curve of spatial field capacity (FC) distribution in the Xinanjiang model can be approximated by
a curve derived from TOPMODEL’s topographic index.
This approximation means that the spatial variability of
hydrological components and variables may be simulated by the Xinanjiang model if terrain information can
somehow be incorporated into the model. Moreover, at
Copyright  2006 John Wiley & Sons, Ltd.
243
a monthly time-scale, the Xinanjiang model is computationally efficient in runoff simulation, and soil moisture
content calculation based on a simple water balance is
able to characterize spatial variations of FC.
The main objective of this study was to develop a simple distributed water balance model that can make use of
readily available meteorological and topographic data to
simulate spatial distribution of hydrological variables for
the purpose of planning and management of environment
and water resources over large geographical regions. The
simplicity here is not a virtue in itself, but is a pragmatic
response to a desire to produce a modelling approach that
is capable of being applied operationally, whilst reflecting
the necessary accuracy and physical relevance. The new
model characterizes and combines the TOPMODEL topographic index and the mechanism of runoff generation
employed in the Xinanjiang model. The model was tested
on two watersheds, namely Yuanjiang and Dongjiang, in
the humid region in China.
THE MODEL
The following mass balance equation in a continuum
form is essential for the development of hydrological
models (Beven, 2002):
ds
D rq C p e
dt
1
where s is a local mass storage, rq is the divergence in
local mass flux, p is a local source term (such as precipitation) and e is a local loss term (such as evapotranspiration). More sophisticated mathematical equations for
hydrological dynamics can be formulated if spatial variations of basin topography are taken into consideration.
Based on the fundamental principle of mass balance, a
set of equations describing water balance and movement
in a three-dimensional space can be used to develop
a watershed hydrological model in discrete space and
time increments. The spatial discretization at the scale of
finite elements or finite volumes represents spatially variable soil properties and hillslope profiles. This method
requires a tremendous amount of data and involves a
highly time-consuming process. An alternative approach
is to find mathematical functions to describe the spatial
variations. This method is relatively easy in application.
However, selection of a proper mathematical function to
represent the spatial distribution of hydrological components is difficult because of heterogeneity and variability
of catchment characteristics and hydrological responses.
Rodriguez-Iturbe (2000) pointed out that the final product
from Equation (1) should be a probabilistic description of
soil moisture at a point as a function of climate, soil, and
vegetation. Soil moisture is a key variable in hydrological modelling. Viable attempts to link the spatial structure
of the soil moisture field and inherent temporal fluctuations with organization and scaling have been made to
simulate successfully the hydrological processes in an
interlocked system of hillslopes and channels that make
Hydrol. Process. 21, 242– 252 (2007)
DOI: 10.1002/hyp
244
X. CHEN, Y. D. CHEN AND C.-Y. XU
up a drainage basin. The description involves both the
probability distribution of soil moisture content and its
correlation structure in time.
In this study, a spatially distributed hydrological model
is developed by adopting and combining the techniques
of two well-known hydrological models, namely the
Xinanjiang model and TOPMODEL. Specifically, the
model is composed of three major components. The first
component uses the TOPMODEL concept to estimate
the spatial distribution of soil moisture deficit from
terrain characteristics. The second component simulates
runoff based on the runoff generation theory adopted
in the Xinanjiang model, i.e. runoff generation after
filling up the FC of soils. In the third component,
streamflow from a sub-basin outlet is routed by a simple
storage routing technique. In total there are only three
parameters that need to be determined. For the sake of
completeness, some important equations of TOPMODEL,
the Xinanjiang model and the newly developed model are
briefly summarized below.
TOPMODEL concept used in this study
TOPMODEL, developed by Beven and Kirkby (1979),
is a physically based watershed model based on the
variable-source-area concept of streamflow generation.
This model requires digital elevation model (DEM) data
and a sequence of rainfall and potential evapotranspiration data for predicting, among others, stream discharge.
Since the theoretical basis of TOPMODEL has been
clearly reported in the literature (e.g. Beven and Kirkby,
1979; Beven and Wood, 1983; Beven, 1997b), we only
discuss that part of TOPMODEL used in constructing the
new model. TOPMODEL makes use of a topographic
index of hydrological similarity based on an analysis
of DEM data. Mathematically, the topographic index is
equal to lna/ tan ˇ, in which a is the cumulative area
drained through a unit length of contour line and ˇ is the
slope of the unit area.
In general, TOPMODEL predicts the catchment responses following a series of rainfall events and maintains
a continuous accounting of the storage deficit, which
identifies the saturated source areas within a catchment.
This model involves a number of important hydrological
equations and variables for its simulation purpose.
The local soil moisture deficit is calculated by:
Si D S C m[ lna/ tan ˇi ]
The Xinanjiang model algorithms
The Xinanjiang model was first developed in 1973
and published in English in 1980 (Zhao et al., 1980). It
is a well-known lumped watershed model and has been
widely used in China. In comparison with other lumped
hydrological models, the Xinanjiang model describes
watershed heterogeneity using a parabolic curve of FC
distribution (Zhao et al., 1980):
b
f
WM0
3
D1 1
F
WMM
where WM0 is the FC at a point, which varies from zero
to the maximum of the whole watershed WMM, and b is
a power index. The f/F versus WM0 curve is shown in
Figure 1. WM, the watershed average FC, is the integral
of (1 f/F) between WM0 D 0 and WM0 D WMM,
obtaining
WM D WMM/1 C b
4
Wt , the watershed-average soil moisture storage at time
t, is the integral of 1 f/F between zero and WMŁt , a
critical FC at time t (Figure 1):
WMŁt f
Wt D
1
dWM0 D WM
F
0
WMŁt 1Cb
ð 1 1
5
WMM
Thus, the critical FC WMŁt corresponding to watershedaverage soil moisture storage Wt is
1/1Cb W
t
6
WMŁt D WMM 1 1 WM
Runoff occurs where soil moisture reaches FC. As
shown in Figure 1, if the net rainfall amount (rainfall less
WMM
2
where S is the average storage deficit, m is a scaling
parameter, and  is the areal average of lna/ tan ˇ.
Equation (2) is used to predict the saturated contributing
area at each time step. A negative value of Si indicates
that the area is saturated and saturation overland flow is
generated, whereas a positive value of Si indicates that
the area is unsaturated. Unsaturated zone calculations are
made for each lna/ tan ˇ increment.
The subsurface flow rate per unit width of contour
length qi , the vertical flow to the zone, and the outflow
Copyright  2006 John Wiley & Sons, Ltd.
from the saturated zone Qb are all dependent on the topographic index. Therefore, TOPMODEL is a distributed
model and can calculate spatial variations of hydrological
components based on the distribution of the topographic
index.
R
P-E
∆Wt
WM∗
Wt
0
f/F
1
Figure 1. FC curve of soil moisture and rainfall–runoff relationship.
WMM is maximum FC in a watershed; f/F is a fraction of the watershed
area in excess of FC; WMŁt is FC at a point in the watershed; Rt is runoff
yield at time t; wt is soil moisture storage deficit at time t and is equal
to WM Wt ; Wt is watershed-average soil moisture storage at time t
Hydrol. Process. 21, 242–252 (2007)
DOI: 10.1002/hyp
245
A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL
actual evapotranspiration) in a time interval [t 1, t]
is Pt Et and initial watershed-average soil moisture
(tension water) is Wt , then runoff yield in the time
interval Rt can be calculated as follows.
If Pt Et WMŁt
t fi WMM
Wt D
1
F
N
iD1
NWMŁ
< WMM
Rt D Pt Et Wt
Pt Et CWMŁt f
D Pt Et 1
dWM0 7
F
WMŁt
D Pt Et WM C Wt C
WM[1 Pt Et WMŁt /WMM]1Cb
If Pt Et WMŁt ½ WMM
Rt D Pt Et WM C Wt
8
In Equation (3), the f/F versus WM0 curve describes
the watershed heterogeneity of FC in a statistical way.
Parameter b represents the spatial heterogeneity of FC
(b D 0 for uniform distribution and large b for significant
spatial variation) and it is usually determined by model
calibration. Therefore, the Xinanjiang model is a lumped
hydrological model used in a watershed where streamflow
discharge and meteorological data are available.
In a hilly mountain area, the topographic index can
be used to represent the influences of terrain on the
spatial variations of soil wetness. A larger topographic
index in a local area means less soil moisture deficit or
easier runoff generation in response to rainfall input. On
the contrary, a larger WM0 means a larger soil moisture
storage capacity in a local area and more difficult runoff
generation. Comparing the spatial distribution of WM0
and lna/ tan ˇ, Guo et al. (2000) demonstrated that
f/F versus WM0 /WMM (normalized f/F versus WM0
curve in Figure 1) in Equation (3) can be substituted
by a curve of f/F versus IRDG (normalized f/F
versus lna/ tan ˇ curve) defined as an index of relative
difficulty of runoff generation, calculated by
max[lna/ tan ˇ] lna/ tan ˇ
max[lna/ tan ˇ] min[lna/ tan ˇ]
9
where max[lna/ tan ˇ] and min[lna/ tan ˇ] represent the maximum and minimum topographic index
respectively. Thus, curves of f/F versus WM0 /WMM
in Equation (3) can be calculated from DEM data.
If the FC of the basin varies from zero to WMM,
which can be divided into N segments, then the FC WM0
corresponding to the ith segment is equal to iWMM/N
and the fraction of area in excess of FC is fi /F.
Then, WM, the watershed-average FC of the basin, in
Equation (4) can be written as
N WMM fi
WM D
1
N iD1
F
Copyright  2006 John Wiley & Sons, Ltd.
10
11
where NWMŁt is the NWMŁt th segment of WMM, and the
WMŁt corresponding to that segment is given by
WMŁt D NWMŁt
WMM
N
12
NWMŁt and WMŁt can be obtained from Equations (11)
and (12) using an iteration method.
When Pt Et > 0, runoff emerges and its amount is
calculated using equations (13) and (14).
Rt D
DEM-based FC distribution and runoff generation
IRDG D
Then Equation (5) for determining the relationship
between WMŁt and Wt is substituted by
Pt Et CWMŁt
WMŁt
NP
f
fi WMM
0
dWM ³
F
F N
N Ł
WM
when Pt Et C
WMŁt
t
< WMM
13
where NP is calculated by solving Equations (11) and
(12) if WMŁt in these two equations is substituted for
Pt Et C WMŁt .
Rt D Pt Et WM Wt when Pt Et C
WMŁt ½ WMM
14
where Wt is the watershed-average soil moisture storage
at time t in the unsaturated zone and can be calculated by
the following water balance equation (Zhao et al., 1980):
Wt D Wt1 C Pt Et Rt
15
where Et is actual evapotranspiration and is estimated
using
Wt 1/Be
16
Et D Ep 1 1 WM
where is a conversion coefficient from pan evaporation
to potential evapotranspiration, Ep is pan evaporation and
Be ³ 0Ð6 (Ripple et al., 1972).
As illustrated above, using the terrain-based index
IRDG as a surrogate to represent the spatial patterns
of runoff generation is a major invention for the new
model. Based on the distribution of rainfall stations and
basin topography, the study basin will first be divided into
sub-basins and then a rainfall amount and a curve of f/F
versus WM0 /WMM can be obtained for each sub-basin.
Depending on the distribution of rainfall stations, basin
topography and river channel network as characterized
by DEM data, a modeller may design a segmentation
scheme to divide the basin into a certain number of
sub-basins. Whereas the basin segmentation reflects the
spatial distribution of rainfall, a curve of f/F versus
WM0 /WMM for each sub-basin takes the effects of terrain
on soil moisture storage and runoff yield into account. In
other words, these procedures and algorithms have been
developed to integrate the spatial variations of rainfall
Hydrol. Process. 21, 242– 252 (2007)
DOI: 10.1002/hyp
246
X. CHEN, Y. D. CHEN AND C.-Y. XU
and basin topography into the distributed hydrological
model.
Storage routing of watershed
Point or local runoff is regulated by watershed surface,
subsurface and stream channel systems before it reaches
watershed outlet. All surface runoff and a portion of
subsurface runoff in a shallow layer will flow out of the
watershed within a calculation time interval of 1 month;
the rest will be stored in the subsurface soil and flow
out in successive months. If the watershed regulation on
a monthly scale is treated as a linear reservoir, then the
following simple storage routing approach can be used
to simulate streamflow:
Qt D Qt1 e˛ C It 1 e˛ 17
It D Rt F/t
18
and
where Qt and Qt1 are the discharges at time t and
t 1 respectively, ˛ is a parameter used to describe
the watershed regulation of monthly runoff, and F is
watershed area.
Model parameters
There are only three parameters that need to be
determined, i.e. WM, and ˛. The first two parameters
influence runoff generation, and ˛ influences the slope
of the streamflow hydrograph. Previous studies (Zhao,
1984; Zhao and Wang, 1988; Huang, 1993) indicate that
the watershed-average FC WM is mainly dependent on
climatic dryness or wetness. It is smaller in the humid
region and larger in the dry region of China. Zhao
(1984) demonstrated that runoff generation is insensitive
to WM and a certain value can be set depending on
the climatic zone. Approximate values of 120 mm for
regions south of the Yangtze River and 160 mm for
regions north of the Yanshan Mountains and northeastern
China are recommended by Zhao (1984; Zhao and Wang,
1988). According to the Ministry of Water Resources
(1992), the parameter varies between 0Ð72 and 1Ð00
for an evaporation pan of 80 cm in diameter and varies
between 0Ð53 and 0Ð80 for an evaporation pan of 20 cm
in diameter, with the larger values for the humid climate
in the southeastern China and the smaller values for
the dry climate in the northwestern China. Therefore,
values of WM and are fairly consistent for basins
located in the same climatic zone. As shown later, the
results of model validation using the same parameters
WM, , and ˛ for nested basins from upstream to
downstream not only confirm the validity of the above
findings and recommendations, but also demonstrate that
the watershed regulation parameter ˛ varies very little
spatially across a large basin on a monthly interval.
STUDY WATERSHEDS AND DATA FOR MODEL
TESTING
Two watersheds were selected to test the model through
calibration and validation. Yuanjiang watershed and
Copyright  2006 John Wiley & Sons, Ltd.
Dongjiang watershed are major tributaries of the Yangtze
River (Changjiang) and the Pearl River (Zhujiang)
respectively, two large rivers in China. As shown in
Figure 2, both watersheds are located in southern China.
Yuanjiang watershed
Yuanjiang River, originating from Yunwu Mountain
in Guizhou province, has a length of 1033 km and a
drainage area of 78 595 km2 above the Yuanling hydrological station (Changjiang Water Resources Commission, 2002). Mean annual rainfall, potential evapotranspiration (from 20 cm diameter evaporation pan) and
runoff for the period 1971–85 are 1302 mm, 1152 mm
and 695 mm respectively. Owing to the dominance of
monsoon climate, more than 73% of the annual rainfall occurs in the wet season from April to September.
Significant variations of topography from 90 m above
the mean sea level in the downstream region to over
2000 m in the upstream mountainous areas (Figure 2)
result in a remarkable spatial variation of annual rainfall from 927 mm to 1657 mm. Therefore, spatial variations of topography and rainfall play an essential role
in runoff generation and distribution of hydrological processes throughout the watershed.
The description of the spatial variations of rainfall is
based on monthly precipitation data recorded at 121 precipitation stations from 1971 to 1985. Basin topography
is characterized by DEM data with 50 m grid resolution. Monthly streamflow data recorded at four hydrological stations, i.e. Jingping, Anjiang, Pushi, and Yuanling
from upstream to downstream, are used for model calibration and validation. Basic information for the four
nested basins in the Yuanjiang watershed is presented in
Table I.
Dongjiang watershed
Dongjiang River has a length of 439 km and drains
an area of 25 325 km2 above Boluo, the lowest hydrological station of the study watershed. It is located in a
subtropical region dominated by a monsoon climate with
significant seasonal variations in rainfall and wind. Mean
annual precipitation is 1768 mm. Spatial and temporal
variations of rainfall are remarkable. About 76–86% of
annual rainfall falls in the wet season (from April to
September). Frontal rainfall mainly occurs from April
to June, and rainfall brought by typhoons occurs from
June to September mainly in the southern part of the
region near the coast. Rainfall decreases from the southwest to the northeast within the watershed. For all of
the rainfall stations, the coefficient of variation (CV) of
annual rainfall falls between 0Ð20 and 0Ð25, and the ratio
of maximum to minimum annul rainfall varies from 2Ð03
to 3Ð48.
Monthly meteorological and hydrological data recorded from 1971 to 1985 were used for model testing,
including rainfall at 52 stations, 80 cm diameter pan
evaporation at three stations, and streamflow at four
stations. DEM data of 50 m grid resolution are used to
Hydrol. Process. 21, 242–252 (2007)
DOI: 10.1002/hyp
Copyright  2006 John Wiley & Sons, Ltd.
50
Jingping
<200 m
200 ~ 400 m
400 ~ 600 m
600 ~ 800 m
800 ~ 1000 m
>1000 m
Elevation
Yuanjiang
Basin
N
0
Anjiang
Pushi
Yuanling
China
Beijing
Boluo
N
10 0 10 20 30 40 50 km
Dongjiang Basin
Figure 2. Location, topography and nested basins of the Yuanjiang and Dongjiang watersheds
25 50 75 100 km
N
<100 m
100 ~ 200 m
200 ~ 300 m
300 ~ 400 m
400 ~ 600 m
>600 m
Elevation
Heyuan
Longchuan
Fengshuba
A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL
247
Hydrol. Process. 21, 242– 252 (2007)
DOI: 10.1002/hyp
248
X. CHEN, Y. D. CHEN AND C.-Y. XU
Table I. Basin characteristics of the two study watersheds and their nested basins
Yuanjiang watershed
Dongjiang watershed
Jingping
Anjiang
Pushi
Yuanling
Fengshuba
Longchuan
Heyuan
Boluo
13 485
177
15
1
1 190
1 164
615
40 305
530
31
1
1 240
1 187
619
54 144
712
83
2
1 275
1 162
645
78 595
1 033
121
3
1 302
1 152
695
5 151
112
11
1
1 548
1 393
796
7 699
165
15
1
1 622
1 393
795
15 750
293
31
2
1 718
1 407
893
25 325
439
52
3
1 768
1 391
912
0.8
1.0
Area (km2 )
Length of mainstem (km)
No. of rainfall stations
No. of evaporation stations
Mean annual rainfall (mm)
Mean annual pan evaporation (mm)
Mean annual runoff (mm)
describe the spatial variations of topography (Figure 2).
Basic information for the Dongjiang watershed and its
nested basins is given in Table I.
1.0
IRDG
0.8
0.6
0.4
RESULTS AND DISCUSSION
0.2
Watershed division and calculation of IRDG
0.0
In the Yuanjiang and the Dongjiang watersheds, spatial
variations of topography and rainfall, which dominate the
rainfall–runoff relationship, can be described by dividing
the two watersheds into a number of sub-basins. The
Yuanjiang watershed was divided into 49 sub-basins and
the Dongjiang watershed into 17 sub-basins. Monthly
rainfall in each of the sub-basins was calculated from
observation data of rainfall stations within the sub-basin,
and IRDG was calculated using the DTM9704 program
(Beven, 1997a,b) and a DEM at 50 m grid resolution.
The calculated curves of f/F versus IRDG for all subbasins are shown in Figures 3 and 4 for the Yuanjiang
and Dongjiang watersheds respectively.
Model calibration and validation
The model was calibrated and validated based on
streamflow discharges observed in the whole watershed
outlet in calibration and validation periods respectively.
Further validation for different spatial scales was made
based on streamflow discharges observed in nested watershed outlets.
For the monthly model, the watershed-average FC of
soil moisture WM is set as 130 mm in the Yuanjiang and
115 mm in the Dongjiang. The other two parameters need
1.0
IRDG
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Cumulative frequency (f/F)
Figure 3. Cumulative frequency of IRDG for Yuanjiang watershed and
its sub-basins. Each curve represents an f/F versus IRDG relationship
for one of the 49 sub-basins. In the Xinanjiang model, f/F is a fraction
of the watershed area in excess of FC
Copyright  2006 John Wiley & Sons, Ltd.
0.0
0.2
0.4
0.6
Cumulative frequency (f/F)
Figure 4. Cumulative frequency of IRDG for Dongjiang watershed and
its sub-basins. Each curve represents an f/F versus IRDG relationship
for one of the 17 sub-basins. In the Xinanjiang model, f/F is a fraction
of the watershed area in excess of FC
to be calibrated, i.e. pan coefficient of evapotranspiration
and watershed regulation coefficient of the basin ˛.
The model parameters are calibrated automatically using
the simplex acceleration technique with respect to the
objective function of maximizing the Nash–Sutcliffe efficiency coefficient (NSC) between observed and simulated
monthly discharges. Another measure of model performance used in the study is the root-mean-squared error
(RMSE) of monthly discharge.
For the Yuanjiang watershed, the calibration period
is 1971–79 and the validation period is 1980–85. The
simulated streamflow from 1971 to 1985 in each of the
three observation stations (Jingping, Anjiang and Pushi)
was further compared with the observed data. Model
calibration and validation results are shown in Table II.
The calibrated model parameter values are 0Ð55 and
0Ð991 for and ˛ respectively. The NSC values are
0Ð91 and 0Ð87 respectively for the calibration period and
the validation period for Yuanling. NSC values in the
three nested watersheds of Anjiang, Pushi and Jingping
are 0Ð75, 0Ð89 and 0Ð89 respectively. For illustrative
purposes, monthly simulated and observed runoff in
Yuanling for the calibration period 1971–79 and for the
validation period 1980–85 are shown in Figures 5 and 6
respectively. These results demonstrate that the model
is capable of reproducing both the magnitude and the
dynamics of the monthly discharge at different spatial
scales.
For the Dongjiang watershed, the model calibration
was done for the period 1960–74 and the validation for
1975–88. Model validation at spatial scales was executed
for the three observation stations (Fengshuba, Longchuan
and Heyuan) for the period 1960–88.
Hydrol. Process. 21, 242–252 (2007)
DOI: 10.1002/hyp
249
A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL
250
450
Simulation
Observation
Runoff (mm)
Runoff (mm)
200
150
100
400
Simulation
350
Observation
300
250
200
150
100
50
0
1971
50
1972
1973
1974
1975
1976
1977
1978
0
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974
Time (year)
1979
Time (year)
Figure 5. Monthly calibrated and observed runoff of Yuanjiang watershed
for the period 1971– 79
Figure 7. Monthly calibrated and observed runoff of Dongjiang watershed for the period 1960– 74
400
Simulation
Observation
350
Simulation
Observation
Runoff (mm)
Runoff (mm)
450
200
180
160
140
120
100
80
60
40
20
0
1980
300
250
200
150
100
50
0
1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
Time (year)
1981
1982
1983
1984
Figure 8. Monthly validated and observed runoff of Dongjiang watershed
for the period 1975– 88
1985
Time (year)
Figure 6. Monthly validated and observed runoff of Yuanjiang watershed
for the period 1980– 85
The calibrated model parameter values at Boluo are
0Ð67 and 0Ð917 for and ˛ respectively. NSC is 0Ð89 in
the calibration period and 0Ð90 in the validation period
(Table II). The NSC values in the three nested watersheds Fengshuba, Longchuan and Heyuan are 0Ð81, 0Ð85
and 0Ð88 respectively. Monthly observed and simulated
runoffs at the Boluo station for the calibration period
1960–74 and for the validation period 1975–88 are
shown in Figures 7 and 8 respectively. Again, the results
demonstrate that the model is reliable for runoff simulation at different spatial scales.
Successful application of the model in the nested
watersheds using the same values of WM, and ˛ indicates that these parameters are less spatially variable for
the monthly hydrological model applied at the watershed
scale.
each parameter (the ratio of parameter changes to the
calibrated model parameter dP/P) are used as an indicator of the sensitivity of runoff to parameter changes. For
illustrative purposes, the relationship between parameter
changes and the corresponding streamflow changes in the
Dongjiang watershed is shown in Figure 9. For the three
parameters, ˛ has the most significant effect on streamflow. A 10% change in parameter ˛ results in approximately the same percentage of streamflow changes, compared with 5Ð8% for and only 0Ð5% for WM. The results
show that parameter WM is least sensitive to streamflow,
and using fixed values of 130 mm and 115 mm respectively for the Yuanjiang and the Dongjiang watersheds
is warranted. Similar results were obtained in the Yuanjiang watershed. The effect of change of rainfall amount
on model output was also tested; as expected, rainfall had
the most significant effect on annual streamflow. A 5%
change in rainfall changed streamflow by approximately
10% in the two watersheds.
Sensitivity analysis
Sensitivity analysis was carried out on both watersheds
to evaluate and quantify the effect of the parameter variations on model output. Relative changes of annual streamflow (the ratio of streamflow changes to annual mean
streamflow dR/R) resulting from the relative changes of
Spatial variation of hydrological components
Basin topography, soil and vegetation cover affect
hydrological processes; consequently, they influence the
energy balance, which is a key component in global
climate models. Numerous efforts have been made to
Table II. Results of model calibration and validation of the two study watersheds and their nested basins
Yuanjiang watershed
Yuanling
Annual runoff (mm)
Simulated
716a
Observed
710a
NSC
0Ð91a
RMSE (mm)
16Ð2a
a Calibration
Dongjiang watershed
Anjiang
Pushi
Jingping
642
647
0Ð75
22Ð8
620
620
0Ð89
15Ð7
642
646
0Ð89
15Ð8
664
678
0Ð87
17Ð0
Boluo
890a
880a
0Ð89a
26Ð7a
986
993
0Ð90
22Ð6
Fengshuba
Longchuan
Heyuan
806
797
0Ð81
26Ð7
823
830
0Ð85
24Ð0
912
936
0Ð88
25Ð7
results.
Copyright  2006 John Wiley & Sons, Ltd.
Hydrol. Process. 21, 242– 252 (2007)
DOI: 10.1002/hyp
250
X. CHEN, Y. D. CHEN AND C.-Y. XU
describe the spatial variations of hydrological components, and parameterizations of hydrological models are
made for a successful assessment of climate-change
impacts on hydrology and water resources and estimation of rainfall-runoff in ungauged areas. For hydrological
modelling, the distribution of the three water budget components, i.e. soil moisture content, actual evapotranspiration and runoff, is vital for water resources management,
environmental protection and assessment of land use and
climate-change impacts on hydrology. A major strength
of the monthly model is its capability of simulating the
spatial variations of these components.
The newly developed model was executed for each of
the segmented sub-basins with rainfall input and IRDG
curves. The hydrological components, i.e. soil moisture
0
15
Figure 11. Spatial variation of the simulated actual evapotranspiration in
Yuanjiang watershed in November 1973
Soil moisture content
75 - 80mm
80 - 85mm
85 - 90mm
90 - 95mm
95 - 100mm
100 - 105mm
105 - 110mm
110 - 115mm
115 - 120mm
120 - 125mm
125 - 130mm
130 - 135mm
10
5
dP/P (%)
0
-20
-15
-10
-5
0
5
10
15
N
100 Kilometers
dR/R (%)
20
WM
α
η
Actual evaporation
18 - 22mm
22 - 25mm
25 - 28mm
28 - 31mm
31 - 34mm
34 - 37mm
37 - 40mm
40 - 43mm
20
-5
-10
0
100 Kilometers
N
-15
Figure 12. Spatial variation of the simulated soil moisture storage in the
Yuanjiang watershed in November 1973
-20
17
0
0
16
00
Figure 9. Sensitivity of the model simulated discharge to the change
of model parameter values for Dongjiang watershed. The Y-axis is the
relative change in the simulated discharge and the X-axis is the relative
change in parameter values
1400
00
0
15
130
16
00
150
0
13
00
1300
00
14
0
140
1300
00
11
1200
0
00
150
1400
0
0
130 140
0
150
1700
0
1400
14
1000
1100
1200
N
100 Kilometers
Figure 10. Spatial variation of the mean annual rainfall in the Yuanjiang
watershed for the period 1971– 85
Copyright  2006 John Wiley & Sons, Ltd.
content, actual evapotranspiration and runoff, are simulated for each sub-basin with their spatial variations
taken into account. For illustrative purposes, spatial variations of mean annual precipitation (1971–85), actual
evapotranspiration (November 1973), soil moisture content (November 1973) and mean annual runoff (1971–85)
simulated by the model for the Yuanjiang watershed are
shown in Figures 10–13 respectively. Figure 10 shows
that precipitation is greater in the high mountain area
of the upper stream (the highest elevation is 2570 m)
and smaller in the western centre of the watershed. Spatial variations of simulated actual evapotranspiration are
similar to those of the soil moisture content (Figure 11).
Simulation results indicate that soil moisture content in
November 1973 is greater in the south and smaller in the
western centre and the northern areas of the watershed
(Figure 12). The runoff distribution in Figure 13 demonstrates that greater runoff occurs in the high mountain
areas with greater precipitation and steeper slopes.
CONCLUSIONS
The Xinanjiang model is well known for its implicit
description of watershed heterogeneity using a parabolic
curve of FC. Traditionally, the parabolic curve is calibrated on the basis of observed stream discharges, and
Hydrol. Process. 21, 242–252 (2007)
DOI: 10.1002/hyp
10
00 11
00
A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL
TOPMODEL and the Xinanjiang model have been successfully used in humid regions worldwide. However, the
use of the proposed modelling approach in arid regions
is yet to be tested.
0
90
700
800 0
90
700
100
0
800
251
ACKNOWLEDGEMENTS
800
900
This research was substantially supported by a grant from
the Research Grants Council of the Hong Kong Special
Administrative Region, China (project no. CUHK4247/
03H) and the Scientific Research Foundation for the
Returned Overseas Chinese Scholars, State Education
Ministry, China.
500
600
700
800 900
0
900
800
900
700
400
600
500
800
N
100 Kilometers
Figure 13. Spatial variation of the simulated mean annual runoff in the
Yuanjiang watershed for the period 1971– 85
thus the model could not be applied in an ungauged
watershed. We consider rainfall and terrain to be the
two dominant spatially variable factors that influence
the runoff generation processes. Segmentation of a study
basin into sub-basins will reflect the spatial distribution of
rainfall. A surrogate for the FC curve using a DEM-based
curve of index of relative difficulty of runoff generation
has been successfully adopted to develop a distributed
monthly water balance model. The new model incorporates the TOPMODEL topographic index into the mechanism of runoff generation of the Xinanjiang model, making it a distributed model with small data requirements
and high applicability. The model has three parameters,
only two of which need to be calibrated. These two
parameters are less spatially variable for watersheds of
different sizes located in the same climate zone, although
they are highly sensitive to the basin water yield. Therefore, the model can be applied successfully in those areas
where rainfall and topography distribution dominate the
spatial variation of runoff generation.
The model’s accuracy and reliability have been tested
in four nested basins from upstream to downstream in
the Dongjiang watershed and the Yuanjiang watershed
respectively using monthly meteorological and hydrological series. Simulation results demonstrate that not only
is the model capable of reproducing both the magnitude
and the dynamics of the monthly discharge for basins of
different sizes, but it is also able to produce reasonable
spatial variations of major water balance components,
such as soil moisture storage and actual evapotranspiration. The study shows that, with prudent simplification,
a distributed hydrological model based on terrain analysis is appropriate for finding a reasonable solution of
regional hydrological problems associated with planning,
optimal allocation and management of water resources.
Based on the results of model testing, we believe that
the conclusions reached in this paper can be extended
to other basins in humid regions. This is because both
Copyright  2006 John Wiley & Sons, Ltd.
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