HYDROLOGICAL PROCESSESHydrol. 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 integratingspatial 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 China2 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 ofclimate change and regional water resources planning. Traditionally, monthly models adopt a conceptual, lumped-parameterapproach and cannot account for spatial variations of basin characteristics and climatic inputs. A large requirement for dataoften 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 runoffgeneration and developed a monthly model that is able to account for their influences in the spatial and temporal dynamics ofwater balance. As a hybrid of the Xinanjiang model and TOPMODEL, the new model is constructed by innovatively makinguse of the highly acclaimed simulation techniques in the two existing models. A major contribution of this model developmentstudy is to adopt the technique of implicit representation of soil moisture characteristics in the Xinanjiang model and usethe TOPMODEL concept to integrate terrain variations into runoff simulation. Specifically, the TOPMODEL topographicindex ln�a/ tan ˇ� is converted into an index of relative difficulty in runoff generation (IRDG) and then the cumulativefrequency distribution of IRDG is used to substitute the parabolic curve, which represents the spatial variation of soil storagecapacity in the Xinanjiang model. Digital elevation model data play a key role in the modelling procedures on a geographicalinformation system platform, including basin segmentation, estimation of rainfall for each sub-basin and computation of terraincharacteristics. Other monthly data for model calibration and validation are rainfall, pan evaporation and runoff. The new modelhas only three parameters to be estimated, i.e. watershed-average field capacity WM, pan coefficient � and runoff generationcoefficient ˛. Sensitivity analysis demonstrates that runoff is least sensitive to WM and, therefore, it can be determined by aprior estimation based on the climate and soil properties of the study basin. The other two parameters can be determined usingoptimization methods. Model testing was carried out in a number of nested sub-basins of two watersheds (Yuanjiang Riverand Dongjiang River) in the humid region in central and southern China. Simulation results show that the model is capableof describing spatial and temporal variations of water balance components, including soil moisture content, evapotranspirationand runoff, over the watershed. With a minimal requirement for input data and parameterization, this terrain-based distributedmodel 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 bal-ance with varying degrees of complexity have been devel-oped and applied extensively around the world over thepast half century. The earliest models are probably thoseusing a simple accounting procedure of water budgetto estimate soil moisture fluctuation and runoff produc-tion based on climatic inputs, i.e. rainfall and tempera-ture (e.g. Thornthwaite, 1948; Thornthwaite and Mather,1955, 1957). With the advent of digital computers in theearly 1960s, hydrologists began to develop conceptualhydrological models into which more sophisticated waterbalance analysis could be incorporated. Later attemptswere made to develop more physically based models thatwere supposedly able to keep track of water movement

* Correspondence to: Yongqin David Chen, Department of Geographyand Resource Management, The Chinese University of Hong Kong,Shatin, Hong Kong. E-mail: ydavidchen@cuhk.edu.hk

and budget in a discretized spatial domain using physicallaws. The advancement of geoinformation technologies,such as geographical information systems and remotesensing, has offered a great impetus for the developmentof distributed hydrological models. However, the avail-ability of basin characteristics and meteorological inputdata with sufficiently fine resolutions is usually still acritical constraint for applying distributed models. Overthe history of model development, hydrological modelshave been adopted, modified, and applied to solve a widespectrum of hydrological problems (e.g. Gabos and Gas-parri, 1983; Alley, 1984; Vandewiele et al., 1992; Xuet al., 1996). In the past two decades, one major area ofmodel applications is hydrological impact studies of cli-mate change (e.g. Aston, 1984; Gleick, 1987; Arnell andReynard, 1996; Guo et al., 2002). Hydrological modelshave also been widely utilized for long-range stream-flow forecasting (e.g. Alley, 1985; Xu and Vandewiele,1995). Hydrological model runs at monthly time-steps

Copyright 2006 John Wiley & Sons, Ltd.

A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL 243

are often sufficient for assessing the long-term climaticchange impact on water resources.

The majority of the conceptual hydrological modelsbased on the water balance concept were developed inthe 1960s and 1970s. Examples include the StanfordWatershed Model (Crawford and Linsley, 1964), theSacramento Soil Moisture Accounting Model (Burnashet al., 1973), the HBV model (e.g. Bergstrom, 1976) andthe Xinanjiang model (Zhao et al., 1980). The structuresof these models have been improved by dividing runoffand state variables such as soil moisture storage intodifferent components (e.g. Gleick, 1987; Mimikou et al.,1991; Mohseni and Stefan, 1998). Such models containcomplex nonlinear functions defining moisture fluxesbetween a number of conceptual storage zones. Theyare usually operated on time-steps of a day or an evenshorter period and require more data and parameters incomparison with monthly models.

Models developed before the early 1980s have alumped structure and the spatial variation of hydrologicalvariables and model parameters is generally not taken intoaccount. However, some models do consider heterogene-ity of rainfall and basin characteristics such as infiltrationcapacity to some extent. Examples include the Hydro-logic Simulation Program–FORTRAN, which accountsfor the spatial variations by dividing the watershed intosub-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 het-erogeneity by adopting a statistical distribution of soilwater characteristics. Since the mid 1980s, given the needof explicit spatial representation of hydrological compo-nents and variables, distributed-parameter models basedon physical laws describing water movement have beendeveloped (e.g. the SHE model as described in Abbottet al. (1986a,b)). These models contain detailed simula-tion algorithms that are often partial differential equationsand numerical solution of the equations requires a tremen-dous amount of input data. Model applicability is seri-ously limited by data availability, especially for largebasins. Thus, a distributed hydrological model having theflexibility to deal with different conditions in a wide rangeof geographical regions is required. TOPMODEL (Bevenand Kirkby, 1979) has provided hydrologists with a pow-erful tool to simulate analytically the hillslope responseof site-specific topography without the need of makinguse of any finite-element model. A unique feature ofTOPMODEL is its capability to operate at large water-shed scales by using the statistics of the topography,rather than the details of the topography itself. A modelcomparison study by Guo et al. (2000) shows that thestatistical curve of spatial field capacity (FC) distribu-tion in the Xinanjiang model can be approximated bya curve derived from TOPMODEL’s topographic index.This approximation means that the spatial variability ofhydrological components and variables may be simu-lated by the Xinanjiang model if terrain information cansomehow be incorporated into the model. Moreover, at

a monthly time-scale, the Xinanjiang model is computa-tionally efficient in runoff simulation, and soil moisturecontent calculation based on a simple water balance isable to characterize spatial variations of FC.

The main objective of this study was to develop a sim-ple distributed water balance model that can make use ofreadily available meteorological and topographic data tosimulate spatial distribution of hydrological variables forthe purpose of planning and management of environmentand water resources over large geographical regions. Thesimplicity here is not a virtue in itself, but is a pragmaticresponse to a desire to produce a modelling approach thatis capable of being applied operationally, whilst reflectingthe necessary accuracy and physical relevance. The newmodel characterizes and combines the TOPMODEL topo-graphic index and the mechanism of runoff generationemployed in the Xinanjiang model. The model was testedon two watersheds, namely Yuanjiang and Dongjiang, inthe humid region in China.

THE MODEL

The following mass balance equation in a continuumform is essential for the development of hydrologicalmodels (Beven, 2002):

ds

dtD rq C p � e �1�

where s is a local mass storage, rq is the divergence inlocal mass flux, p is a local source term (such as pre-cipitation) and e is a local loss term (such as evapotran-spiration). More sophisticated mathematical equations forhydrological dynamics can be formulated if spatial vari-ations of basin topography are taken into consideration.Based on the fundamental principle of mass balance, aset of equations describing water balance and movementin a three-dimensional space can be used to developa watershed hydrological model in discrete space andtime increments. The spatial discretization at the scale offinite elements or finite volumes represents spatially vari-able soil properties and hillslope profiles. This methodrequires a tremendous amount of data and involves ahighly time-consuming process. An alternative approachis to find mathematical functions to describe the spatialvariations. This method is relatively easy in application.However, selection of a proper mathematical function torepresent the spatial distribution of hydrological compo-nents is difficult because of heterogeneity and variabilityof catchment characteristics and hydrological responses.Rodriguez-Iturbe (2000) pointed out that the final productfrom Equation (1) should be a probabilistic description ofsoil moisture at a point as a function of climate, soil, andvegetation. Soil moisture is a key variable in hydrologi-cal modelling. Viable attempts to link the spatial structureof the soil moisture field and inherent temporal fluctua-tions with organization and scaling have been made tosimulate successfully the hydrological processes in aninterlocked system of hillslopes and channels that make

Copyright 2006 John Wiley & Sons, Ltd. 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 theprobability distribution of soil moisture content and itscorrelation structure in time.

In this study, a spatially distributed hydrological modelis developed by adopting and combining the techniquesof two well-known hydrological models, namely theXinanjiang model and TOPMODEL. Specifically, themodel is composed of three major components. The firstcomponent uses the TOPMODEL concept to estimatethe spatial distribution of soil moisture deficit fromterrain characteristics. The second component simulatesrunoff based on the runoff generation theory adoptedin the Xinanjiang model, i.e. runoff generation afterfilling up the FC of soils. In the third component,streamflow from a sub-basin outlet is routed by a simplestorage routing technique. In total there are only threeparameters that need to be determined. For the sake ofcompleteness, some important equations of TOPMODEL,the Xinanjiang model and the newly developed model arebriefly summarized below.

TOPMODEL concept used in this study

TOPMODEL, developed by Beven and Kirkby (1979),is a physically based watershed model based on thevariable-source-area concept of streamflow generation.This model requires digital elevation model (DEM) dataand a sequence of rainfall and potential evapotranspira-tion data for predicting, among others, stream discharge.

Since the theoretical basis of TOPMODEL has beenclearly reported in the literature (e.g. Beven and Kirkby,1979; Beven and Wood, 1983; Beven, 1997b), we onlydiscuss that part of TOPMODEL used in constructing thenew model. TOPMODEL makes use of a topographicindex of hydrological similarity based on an analysisof DEM data. Mathematically, the topographic index isequal to ln�a/ tan ˇ�, in which a is the cumulative areadrained through a unit length of contour line and ˇ is theslope of the unit area.

In general, TOPMODEL predicts the catchment respo-nses following a series of rainfall events and maintainsa continuous accounting of the storage deficit, whichidentifies the saturated source areas within a catchment.This model involves a number of important hydrologicalequations and variables for its simulation purpose.

The local soil moisture deficit is calculated by:

Si D S C m[ � ln�a/ tan ˇ�i] �2�

where S is the average storage deficit, m is a scalingparameter, and is the areal average of ln�a/ tan ˇ�.Equation (2) is used to predict the saturated contributingarea at each time step. A negative value of Si indicatesthat the area is saturated and saturation overland flow isgenerated, whereas a positive value of Si indicates thatthe area is unsaturated. Unsaturated zone calculations aremade for each ln�a/ tan ˇ� increment.

The subsurface flow rate per unit width of contourlength qi, the vertical flow to the zone, and the outflow

from the saturated zone Qb are all dependent on the topo-graphic index. Therefore, TOPMODEL is a distributedmodel and can calculate spatial variations of hydrologicalcomponents based on the distribution of the topographicindex.

The Xinanjiang model algorithms

The Xinanjiang model was first developed in 1973and published in English in 1980 (Zhao et al., 1980). Itis a well-known lumped watershed model and has beenwidely used in China. In comparison with other lumpedhydrological models, the Xinanjiang model describeswatershed heterogeneity using a parabolic curve of FCdistribution (Zhao et al., 1980):

f

FD 1 �

(1 � WM0

WMM

)b

�3�

where WM0 is the FC at a point, which varies from zeroto the maximum of the whole watershed WMM, and b isa power index. The f/F versus WM0 curve is shown inFigure 1. WM, the watershed average FC, is the integralof (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 timet, is the integral of 1 � f/F between zero and WMŁ

t , acritical FC at time t (Figure 1):

Wt D∫ WMŁ

t

0

(1 � f

F

)d�WM0� D WM

ð[

1 �(

1 � WMŁt

WMM

)1Cb]

�5�

Thus, the critical FC WMŁt corresponding to watershed-

average soil moisture storage Wt is

WMŁt D WMM

[1 �

(1 � Wt

WM

)1/�1Cb�]

�6�

Runoff occurs where soil moisture reaches FC. Asshown in Figure 1, if the net rainfall amount (rainfall less

f/F 10

WMM

Wt

WM∗

P-ER

∆Wt

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 watershedarea in excess of FC; WMŁ

t is FC at a point in the watershed; Rt is runoffyield at time t; wt is soil moisture storage deficit at time t and is equalto WM � Wt; Wt is watershed-average soil moisture storage at time t

Copyright 2006 John Wiley & Sons, Ltd. Hydrol. Process. 21, 242–252 (2007)DOI: 10.1002/hyp

A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL 245

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 timeinterval Rt can be calculated as follows.

If Pt � Et � WMŁt < WMM

Rt D Pt � Et � Wt

D Pt � Et �∫ Pt�EtCWMŁ

t

WMŁt

(1 � f

F

)d�WM0� �7�

D Pt � Et � WM C WtCWM[1 � �Pt � Et � WMŁ

t �/WMM]1Cb

If Pt � Et � WMŁt ½ WMM

Rt D Pt � Et � WM C Wt �8�

DEM-based FC distribution and runoff generation

In Equation (3), the f/F versus WM0 curve describesthe 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 significantspatial variation) and it is usually determined by modelcalibration. Therefore, the Xinanjiang model is a lumpedhydrological model used in a watershed where streamflowdischarge and meteorological data are available.

In a hilly mountain area, the topographic index canbe used to represent the influences of terrain on thespatial variations of soil wetness. A larger topographicindex in a local area means less soil moisture deficit oreasier runoff generation in response to rainfall input. Onthe contrary, a larger WM0 means a larger soil moisturestorage capacity in a local area and more difficult runoffgeneration. Comparing the spatial distribution of WM0

and ln�a/ tan ˇ�, Guo et al. (2000) demonstrated thatf/F versus WM0/WMM (normalized f/F versus WM0

curve in Figure 1) in Equation (3) can be substitutedby a curve of f/F versus IRDG (normalized f/Fversus ln�a/ tan ˇ� curve) defined as an index of relativedifficulty of runoff generation, calculated by

IRDG D max[ln�a/ tan ˇ�] � ln�a/ tan ˇ�

max[ln�a/ tan ˇ�] � min[ln�a/ tan ˇ�]�9�

where max[ln�a/ tan ˇ�] and min[ln�a/ tan ˇ�] rep-resent the maximum and minimum topographic indexrespectively. Thus, curves of f/F versus WM0/WMMin 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/Nand the fraction of area in excess of FC is fi/F.Then, WM, the watershed-average FC of the basin, inEquation (4) can be written as

WM D WMM

N

N∑iD1

(1 � fi

F

)�10�

Then Equation (5) for determining the relationshipbetween WMŁ

t and Wt is substituted by

Wt DNWMŁ

t∑iD1

(1 � fi

F

)WMM

N�11�

where NWMŁt

is the NWMŁt

th segment of WMM, and theWMŁ

t corresponding to that segment is given by

WMŁt D NWMŁ

t

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∫ Pt�EtCWMŁ

t

WMŁt

f

Fd�WM0� ³

NP∑NWMŁ

t

fi

F

WMM

N

when Pt � Et C WMŁt < WMM �13�

where NP is calculated by solving Equations (11) and(12) if WMŁ

t in these two equations is substituted forPt � Et C WMŁ

t .

Rt D Pt � Et��WM � Wt� when Pt � EtCWMŁ

t ½ WMM �14�

where Wt is the watershed-average soil moisture storageat time t in the unsaturated zone and can be calculated bythe following water balance equation (Zhao et al., 1980):

Wt D Wt�1 C Pt � Et � Rt �15�

where Et is actual evapotranspiration and is estimatedusing

Et D �Ep

[1 �

(1 � Wt

WM

)1/Be]

�16�

where � is a conversion coefficient from pan evaporationto potential evapotranspiration, Ep is pan evaporation andBe ³ 0Ð6 (Ripple et al., 1972).

As illustrated above, using the terrain-based indexIRDG as a surrogate to represent the spatial patternsof runoff generation is a major invention for the newmodel. Based on the distribution of rainfall stations andbasin topography, the study basin will first be divided intosub-basins and then a rainfall amount and a curve of f/Fversus WM0/WMM can be obtained for each sub-basin.Depending on the distribution of rainfall stations, basintopography and river channel network as characterizedby DEM data, a modeller may design a segmentationscheme to divide the basin into a certain number ofsub-basins. Whereas the basin segmentation reflects thespatial distribution of rainfall, a curve of f/F versusWM0/WMM for each sub-basin takes the effects of terrainon soil moisture storage and runoff yield into account. Inother words, these procedures and algorithms have beendeveloped to integrate the spatial variations of rainfall

Copyright 2006 John Wiley & Sons, Ltd. 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 hydrologicalmodel.

Storage routing of watershedPoint or local runoff is regulated by watershed surface,

subsurface and stream channel systems before it reacheswatershed outlet. All surface runoff and a portion ofsubsurface runoff in a shallow layer will flow out of thewatershed within a calculation time interval of 1 month;the rest will be stored in the subsurface soil and flowout in successive months. If the watershed regulation ona monthly scale is treated as a linear reservoir, then thefollowing simple storage routing approach can be usedto simulate streamflow:

Qt D Qt�1 e�˛ C It�1 � e�˛� �17�

andIt D RtF/t �18�

where Qt and Qt�1 are the discharges at time t andt � 1 respectively, ˛ is a parameter used to describethe watershed regulation of monthly runoff, and F iswatershed area.

Model parametersThere are only three parameters that need to be

determined, i.e. WM, � and ˛. The first two parametersinfluence runoff generation, and ˛ influences the slopeof the streamflow hydrograph. Previous studies (Zhao,1984; Zhao and Wang, 1988; Huang, 1993) indicate thatthe watershed-average FC WM is mainly dependent onclimatic dryness or wetness. It is smaller in the humidregion and larger in the dry region of China. Zhao(1984) demonstrated that runoff generation is insensitiveto WM and a certain value can be set depending onthe climatic zone. Approximate values of 120 mm forregions south of the Yangtze River and 160 mm forregions north of the Yanshan Mountains and northeasternChina are recommended by Zhao (1984; Zhao and Wang,1988). According to the Ministry of Water Resources(1992), the parameter � varies between 0Ð72 and 1Ð00for an evaporation pan of 80 cm in diameter and variesbetween 0Ð53 and 0Ð80 for an evaporation pan of 20 cmin diameter, with the larger values for the humid climatein the southeastern China and the smaller values forthe dry climate in the northwestern China. Therefore,values of WM and � are fairly consistent for basinslocated in the same climatic zone. As shown later, theresults of model validation using the same parametersWM, �, and ˛ for nested basins from upstream todownstream not only confirm the validity of the abovefindings and recommendations, but also demonstrate thatthe watershed regulation parameter ˛ varies very littlespatially across a large basin on a monthly interval.

STUDY WATERSHEDS AND DATA FOR MODELTESTING

Two watersheds were selected to test the model throughcalibration and validation. Yuanjiang watershed and

Dongjiang watershed are major tributaries of the YangtzeRiver (Changjiang) and the Pearl River (Zhujiang)respectively, two large rivers in China. As shown inFigure 2, both watersheds are located in southern China.

Yuanjiang watershed

Yuanjiang River, originating from Yunwu Mountainin Guizhou province, has a length of 1033 km and adrainage area of 78 595 km2 above the Yuanling hydro-logical station (Changjiang Water Resources Commis-sion, 2002). Mean annual rainfall, potential evapotran-spiration (from 20 cm diameter evaporation pan) andrunoff for the period 1971–85 are 1302 mm, 1152 mmand 695 mm respectively. Owing to the dominance ofmonsoon climate, more than 73% of the annual rain-fall occurs in the wet season from April to September.Significant variations of topography from 90 m abovethe mean sea level in the downstream region to over2000 m in the upstream mountainous areas (Figure 2)result in a remarkable spatial variation of annual rain-fall from 927 mm to 1657 mm. Therefore, spatial vari-ations of topography and rainfall play an essential rolein runoff generation and distribution of hydrological pro-cesses throughout the watershed.

The description of the spatial variations of rainfall isbased on monthly precipitation data recorded at 121 pre-cipitation stations from 1971 to 1985. Basin topographyis characterized by DEM data with 50 m grid resolu-tion. Monthly streamflow data recorded at four hydrolog-ical stations, i.e. Jingping, Anjiang, Pushi, and Yuanlingfrom upstream to downstream, are used for model cal-ibration and validation. Basic information for the fournested basins in the Yuanjiang watershed is presented inTable I.

Dongjiang watershed

Dongjiang River has a length of 439 km and drainsan area of 25 325 km2 above Boluo, the lowest hydro-logical station of the study watershed. It is located in asubtropical region dominated by a monsoon climate withsignificant seasonal variations in rainfall and wind. Meanannual precipitation is 1768 mm. Spatial and temporalvariations of rainfall are remarkable. About 76–86% ofannual rainfall falls in the wet season (from April toSeptember). Frontal rainfall mainly occurs from Aprilto June, and rainfall brought by typhoons occurs fromJune to September mainly in the southern part of theregion near the coast. Rainfall decreases from the south-west to the northeast within the watershed. For all ofthe rainfall stations, the coefficient of variation (CV) ofannual rainfall falls between 0Ð20 and 0Ð25, and the ratioof maximum to minimum annul rainfall varies from 2Ð03to 3Ð48.

Monthly meteorological and hydrological data recor-ded from 1971 to 1985 were used for model testing,including rainfall at 52 stations, 80 cm diameter panevaporation at three stations, and streamflow at fourstations. DEM data of 50 m grid resolution are used to

Copyright 2006 John Wiley & Sons, Ltd. Hydrol. Process. 21, 242–252 (2007)DOI: 10.1002/hyp

A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL 247

Chi

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Yua

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200

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600

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800

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<100

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100

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0 m

200

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300

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5025

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Copyright 2006 John Wiley & Sons, Ltd. 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

Area (km2) 13 485 40 305 54 144 78 595 5 151 7 699 15 750 25 325Length of mainstem (km) 177 530 712 1 033 112 165 293 439No. of rainfall stations 15 31 83 121 11 15 31 52No. of evaporation stations 1 1 2 3 1 1 2 3Mean annual rainfall (mm) 1 190 1 240 1 275 1 302 1 548 1 622 1 718 1 768Mean annual pan evaporation (mm) 1 164 1 187 1 162 1 152 1 393 1 393 1 407 1 391Mean annual runoff (mm) 615 619 645 695 796 795 893 912

describe the spatial variations of topography (Figure 2).Basic information for the Dongjiang watershed and itsnested basins is given in Table I.

RESULTS AND DISCUSSION

Watershed division and calculation of IRDG

In the Yuanjiang and the Dongjiang watersheds, spatialvariations of topography and rainfall, which dominate therainfall–runoff relationship, can be described by dividingthe two watersheds into a number of sub-basins. TheYuanjiang watershed was divided into 49 sub-basins andthe Dongjiang watershed into 17 sub-basins. Monthlyrainfall in each of the sub-basins was calculated fromobservation 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 sub-basins are shown in Figures 3 and 4 for the Yuanjiangand Dongjiang watersheds respectively.

Model calibration and validation

The model was calibrated and validated based onstreamflow discharges observed in the whole watershedoutlet in calibration and validation periods respectively.Further validation for different spatial scales was madebased on streamflow discharges observed in nested water-shed outlets.

For the monthly model, the watershed-average FC ofsoil moisture WM is set as 130 mm in the Yuanjiang and115 mm in the Dongjiang. The other two parameters need

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Cumulative frequency (f/F)

IRD

G

Figure 3. Cumulative frequency of IRDG for Yuanjiang watershed andits sub-basins. Each curve represents an f/F versus IRDG relationshipfor one of the 49 sub-basins. In the Xinanjiang model, f/F is a fraction

of the watershed area in excess of FC

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Cumulative frequency (f/F)

IRD

G

Figure 4. Cumulative frequency of IRDG for Dongjiang watershed andits sub-basins. Each curve represents an f/F versus IRDG relationshipfor 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 usingthe simplex acceleration technique with respect to theobjective function of maximizing the Nash–Sutcliffe effi-ciency coefficient (NSC) between observed and simulatedmonthly discharges. Another measure of model perfor-mance used in the study is the root-mean-squared error(RMSE) of monthly discharge.

For the Yuanjiang watershed, the calibration periodis 1971–79 and the validation period is 1980–85. Thesimulated streamflow from 1971 to 1985 in each of thethree observation stations (Jingping, Anjiang and Pushi)was further compared with the observed data. Modelcalibration and validation results are shown in Table II.The calibrated model parameter values are 0Ð55 and0Ð991 for � and ˛ respectively. The NSC values are0Ð91 and 0Ð87 respectively for the calibration period andthe validation period for Yuanling. NSC values in thethree nested watersheds of Anjiang, Pushi and Jingpingare 0Ð75, 0Ð89 and 0Ð89 respectively. For illustrativepurposes, monthly simulated and observed runoff inYuanling for the calibration period 1971–79 and for thevalidation period 1980–85 are shown in Figures 5 and 6respectively. These results demonstrate that the modelis capable of reproducing both the magnitude and thedynamics of the monthly discharge at different spatialscales.

For the Dongjiang watershed, the model calibrationwas done for the period 1960–74 and the validation for1975–88. Model validation at spatial scales was executedfor the three observation stations (Fengshuba, Longchuanand Heyuan) for the period 1960–88.

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A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL 249

0

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1971 1972 1973 1974 1975 1976 1977 1978 1979

Time (year)

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off (

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Figure 5. Monthly calibrated and observed runoff of Yuanjiang watershedfor the period 1971–79

020406080

100120140160180200

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Time (year)

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off (

mm

)

SimulationObservation

Figure 6. Monthly validated and observed runoff of Yuanjiang watershedfor the period 1980–85

The calibrated model parameter values at Boluo are0Ð67 and 0Ð917 for � and ˛ respectively. NSC is 0Ð89 inthe calibration period and 0Ð90 in the validation period(Table II). The NSC values in the three nested water-sheds Fengshuba, Longchuan and Heyuan are 0Ð81, 0Ð85and 0Ð88 respectively. Monthly observed and simulatedrunoffs at the Boluo station for the calibration period1960–74 and for the validation period 1975–88 areshown in Figures 7 and 8 respectively. Again, the resultsdemonstrate that the model is reliable for runoff simula-tion at different spatial scales.

Successful application of the model in the nestedwatersheds using the same values of WM, � and ˛ indi-cates that these parameters are less spatially variable forthe monthly hydrological model applied at the watershedscale.

Sensitivity analysis

Sensitivity analysis was carried out on both watershedsto evaluate and quantify the effect of the parameter varia-tions on model output. Relative changes of annual stream-flow (the ratio of streamflow changes to annual meanstreamflow dR/R) resulting from the relative changes of

0

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450

1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974

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off (

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Figure 7. Monthly calibrated and observed runoff of Dongjiang water-shed for the period 1960–74

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Figure 8. Monthly validated and observed runoff of Dongjiang watershedfor the period 1975–88

each parameter (the ratio of parameter changes to thecalibrated model parameter dP/P) are used as an indica-tor of the sensitivity of runoff to parameter changes. Forillustrative purposes, the relationship between parameterchanges and the corresponding streamflow changes in theDongjiang watershed is shown in Figure 9. For the threeparameters, ˛ has the most significant effect on stream-flow. A 10% change in parameter ˛ results in approxi-mately the same percentage of streamflow changes, com-pared with 5Ð8% for � and only 0Ð5% for WM. The resultsshow that parameter WM is least sensitive to streamflow,and using fixed values of 130 mm and 115 mm respec-tively for the Yuanjiang and the Dongjiang watershedsis warranted. Similar results were obtained in the Yuan-jiang watershed. The effect of change of rainfall amounton model output was also tested; as expected, rainfall hadthe most significant effect on annual streamflow. A 5%change in rainfall changed streamflow by approximately10% in the two watersheds.

Spatial variation of hydrological components

Basin topography, soil and vegetation cover affecthydrological processes; consequently, they influence theenergy balance, which is a key component in globalclimate 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 Dongjiang watershed

Yuanling Anjiang Pushi Jingping Boluo Fengshuba Longchuan Heyuan

Annual runoff (mm)Simulated 716a 664 642 620 642 890a 986 806 823 912Observed 710a 678 647 620 646 880a 993 797 830 936

NSC 0Ð91a 0Ð87 0Ð75 0Ð89 0Ð89 0Ð89a 0Ð90 0Ð81 0Ð85 0Ð88RMSE (mm) 16Ð2a 17Ð0 22Ð8 15Ð7 15Ð8 26Ð7a 22Ð6 26Ð7 24Ð0 25Ð7a Calibration results.

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250 X. CHEN, Y. D. CHEN AND C.-Y. XU

describe the spatial variations of hydrological compo-nents, and parameterizations of hydrological models aremade for a successful assessment of climate-changeimpacts on hydrology and water resources and estima-tion of rainfall-runoff in ungauged areas. For hydrologicalmodelling, the distribution of the three water budget com-ponents, i.e. soil moisture content, actual evapotranspira-tion and runoff, is vital for water resources management,environmental protection and assessment of land use andclimate-change impacts on hydrology. A major strengthof the monthly model is its capability of simulating thespatial variations of these components.

The newly developed model was executed for each ofthe segmented sub-basins with rainfall input and IRDGcurves. The hydrological components, i.e. soil moisture

-20

-15

-10

-5

0

5

10

15

20

-20 -15 -10 -5 0 5 10 15 20

dP/P (%)

dR/R

(%

)WMαη

Figure 9. Sensitivity of the model simulated discharge to the changeof model parameter values for Dongjiang watershed. The Y-axis is therelative change in the simulated discharge and the X-axis is the relative

change in parameter values

1300

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1000 Kilometers

N

Figure 10. Spatial variation of the mean annual rainfall in the Yuanjiangwatershed for the period 1971–85

Actual evaporation18 - 22mm22 - 25mm25 - 28mm28 - 31mm31 - 34mm34 - 37mm37 - 40mm40 - 43mm

N0 100 Kilometers

Figure 11. Spatial variation of the simulated actual evapotranspiration inYuanjiang watershed in November 1973

Soil moisture content75 - 80mm80 - 85mm85 - 90mm90 - 95mm95 - 100mm100 - 105mm105 - 110mm110 - 115mm115 - 120mm120 - 125mm125 - 130mm130 - 135mm

N0 100 Kilometers

Figure 12. Spatial variation of the simulated soil moisture storage in theYuanjiang watershed in November 1973

content, actual evapotranspiration and runoff, are sim-ulated for each sub-basin with their spatial variationstaken into account. For illustrative purposes, spatial vari-ations of mean annual precipitation (1971–85), actualevapotranspiration (November 1973), soil moisture con-tent (November 1973) and mean annual runoff (1971–85)simulated by the model for the Yuanjiang watershed areshown in Figures 10–13 respectively. Figure 10 showsthat precipitation is greater in the high mountain areaof the upper stream (the highest elevation is 2570 m)and smaller in the western centre of the watershed. Spa-tial variations of simulated actual evapotranspiration aresimilar to those of the soil moisture content (Figure 11).Simulation results indicate that soil moisture content inNovember 1973 is greater in the south and smaller in thewestern centre and the northern areas of the watershed(Figure 12). The runoff distribution in Figure 13 demon-strates that greater runoff occurs in the high mountainareas with greater precipitation and steeper slopes.

CONCLUSIONS

The Xinanjiang model is well known for its implicitdescription of watershed heterogeneity using a paraboliccurve of FC. Traditionally, the parabolic curve is cali-brated on the basis of observed stream discharges, and

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A DISTRIBUTED MODEL FOR INTEGRATING BASIN TOPOGRAPHY AND RAINFALL 251

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900800700

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500600

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Figure 13. Spatial variation of the simulated mean annual runoff in theYuanjiang watershed for the period 1971–85

thus the model could not be applied in an ungaugedwatershed. We consider rainfall and terrain to be thetwo dominant spatially variable factors that influencethe runoff generation processes. Segmentation of a studybasin into sub-basins will reflect the spatial distribution ofrainfall. A surrogate for the FC curve using a DEM-basedcurve of index of relative difficulty of runoff generationhas been successfully adopted to develop a distributedmonthly water balance model. The new model incorpo-rates the TOPMODEL topographic index into the mecha-nism of runoff generation of the Xinanjiang model, mak-ing it a distributed model with small data requirementsand high applicability. The model has three parameters,only two of which need to be calibrated. These twoparameters are less spatially variable for watersheds ofdifferent sizes located in the same climate zone, althoughthey are highly sensitive to the basin water yield. There-fore, the model can be applied successfully in those areaswhere rainfall and topography distribution dominate thespatial variation of runoff generation.

The model’s accuracy and reliability have been testedin four nested basins from upstream to downstream inthe Dongjiang watershed and the Yuanjiang watershedrespectively using monthly meteorological and hydrolog-ical series. Simulation results demonstrate that not onlyis the model capable of reproducing both the magnitudeand the dynamics of the monthly discharge for basins ofdifferent sizes, but it is also able to produce reasonablespatial variations of major water balance components,such as soil moisture storage and actual evapotranspi-ration. The study shows that, with prudent simplification,a distributed hydrological model based on terrain anal-ysis is appropriate for finding a reasonable solution ofregional hydrological problems associated with planning,optimal allocation and management of water resources.Based on the results of model testing, we believe thatthe conclusions reached in this paper can be extendedto other basins in humid regions. This is because both

TOPMODEL and the Xinanjiang model have been suc-cessfully used in humid regions worldwide. However, theuse of the proposed modelling approach in arid regionsis yet to be tested.

ACKNOWLEDGEMENTS

This research was substantially supported by a grant fromthe Research Grants Council of the Hong Kong SpecialAdministrative Region, China (project no. CUHK4247/03H) and the Scientific Research Foundation for theReturned Overseas Chinese Scholars, State EducationMinistry, China.

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