a numerical modeling system of the hydrological cycle for

A Numerical Modeling System of the Hydrological Cycle for Estimation of WaterFluxes in the Huaihe River Plain Region, China

XI CHEN

State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China

YONGQIN DAVID CHEN

Department of Geography and Resource Management, and Institute of Space and Earth Information Science, The Chinese Universityof Hong Kong, Hong Kong, China

ZHICAI ZHANG

State Key Laboratory of Hydrology–Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China

(Manuscript received 13 April 2006, in final form 6 December 2006)

ABSTRACT

To analyze the water budget under human influences in the Huaihe River plain region in China, theauthors have developed a numerical modeling system that integrates water flux algorithms into a platformcreated by coupling a soil moisture model with the modular three-dimensional finite-difference groundwa-ter flow model (MODFLOW). The modeling system is largely based on physical laws and employs anumerical method of the finite difference to simulate water movement and fluxes in a horizontally dis-cretized watershed or field. The majority of model parameters carry physical significance and can bedetermined by field and laboratory measurements or derived from watershed characteristics contained inGIS and remote sensing data. Several other empirical parameters need to be estimated by model calibra-tion. The numerical modeling system is calibrated in the Linhuanji catchment (2 560 km2) to estimatesurface runoff, groundwater recharge, and groundwater loss for evapotranspiration and stream baseflow.Model validation is conducted at a small runoff experimental field (1.36 km2) in the Wuduogou Hydro-logical Experimental Station to test the model’s capability to simulate hydrological components and esti-mate water fluxes using observed stream stage and groundwater data, as well as lysimeter-measured pre-cipitation recharge and groundwater loss. As proven by the promising results of model testing, this physi-cally based and distributed-parameter model is a valuable contribution to the ever-advancing technology ofhydrological modeling and water resources assessment.

1. Introduction

In the highly populated Huaihe River plain region inChina (Fig. 1), human activities, especially agriculture,influence the hydrological processes, and water re-sources management must focus on sustainability,tracked based on an accurate understanding of waterdistribution and fluxes. In other words, water storage inand movement among all dynamically linked reservoirsmust be estimated in order to evaluate water availabil-

ity caused by human impact. This task of modeling thewater transfer among the atmosphere, watershed sur-face, soil column, and groundwater aquifers has pro-vided hydrologists many challenges in understandingand evaluating the dynamic interactions of these reser-voirs (National Research Council 2004). Scientists andengineers in different disciplines often focus on certainparts of the hydrological system and treat other waterbalance components in a more simplified manner. Inengineering and earth science investigations there hasbeen a long tradition of treating soil moisture below theroot zone as groundwater, which is used as a “boundarycondition” in the simulation of soil moisture dynamics.In river hydraulics and hydrodynamics of open chan-nels, a porous subsurface is seldom considered to be an

Corresponding author address: Xi Chen, State Key Laboratoryof Hydrology–Water Resources and Hydraulic Engineering, Ho-hai University, Nanjing 210098, China.E-mail: [email protected]

702 J O U R N A L O F H Y D R O M E T E O R O L O G Y — S P E C I A L S E C T I O N VOLUME 8

DOI: 10.1175/JHM604.1

© 2007 American Meteorological Society

JHM604

active participant of in-channel processes and dynam-ics. In atmospheric science, soil moisture and ground-water are represented as “buckets” of limited sizes inwhich water movement is not coupled with streamflowdynamics. For other scientists and resource managers,groundwater is represented as an infinitely large reser-voir in which the slow-flow process is unlikely to play asignificant role in the hydrological cycle at the timescales of regular human activities (Duffy et al. 2006). Asa result of the strong emphasis by water resources man-agers and decision makers recently put on integrated(i.e., large scale) and sustainable (i.e., long term) waterresource management, integrated assessment and mod-eling techniques have increasingly gained in popularitysince the mid-1990s (Fedra and Jamieson 1996; Jamie-son and Fedra 1996a,b; Dunn et al. 1996; Reitsma 1996;Andreu et al. 1996; Parker et al. 2002).

Traditionally, hydrologists developed and appliedconceptual hydrological models to simulate the rain-fall–runoff relationship based on simplified and empiri-cal descriptions of the runoff generation processes [seean excellent summary by Singh (1995)]. Because of thelack of data on physical basin characteristics and thelimitations of computing power, conceptual and oftenlumped-parameter models mainly focus on the simula-tion of aggregated output (total streamflow) at the wa-tershed outlet and usually cannot offer sufficient detailsand accurate estimation of water fluxes in a spatiallyheterogeneous domain. Although these watershed hy-drological models have been widely and successfullyused in flood forecasting and regional water resourcesplanning (Shen 1992; Guo et al. 1997; Xu and Guo1994), they cannot simulate the physical processes ofwater transfer in a spatially discretized system, and thusoffer us a quantitative evaluation of water dynamics.

As a result of technological advancements, develop-ment of physically based and distributed-parametermodels have dominated the field over the past two de-

cades. Several commercially available products such asthe Danish Hydraulic Institute’s European Hydro-logical System’s derivative MIKE SHE (Refsgaardand Storm 1995), the Swiss Federal Institute of Tech-nology’s Water Balance Simulation Model (WaSiM-ETH) (Schulla and Jasper 2001), and HydroGeoSphere(Therrien et al. 2004) have become internationally wellknown and gained popularity for use in applications tosolve many kinds of water resources problems. MIKESHE and WaSiM-ETH dynamically link the unsatu-rated zone model (Richard’s equation) and a 2D or 3Dgroundwater model in a numerical method that cansimulate the entire land phase of the hydrologic cy-cle. MIKE SHE has become a more popular tool andhas a proven track record in numerous consultancyand research applications around the world. Hydro-GeoSphere is a fully integrated 3D model that cansimulate water flow, heat flow, and advective–disper-sive solute transport on a 2D land surface and in a 3Dsubsurface domain under variably saturated, heteroge-neous geologic conditions. Full coupling of surface andsubsurface flow regimes is accomplished implicitly bysimultaneously solving one system of nonlinear discreteequations describing flow and transport in both flowregimes. Obviously these full-fledged and well-pack-aged models can offer powerful modeling capabilitiesfor sophisticated simulation of watershed hydrologicalprocesses. However, their applicability in a large water-shed is sometimes seriously limited because physicalparameters of basin characteristics are simply not avail-able. Furthermore, hydrologists may find it difficult tomodify or expand these models in order to build a com-prehensive tool for water resource management. Sinceour ultimate goal is to develop such a tool for HuaiheRiver Water Resources Commission, in this study wefound it impossible to use these existing models.

Soil layers and groundwater aquifers are the twomain regulators of water movement and fluxes. Giventhe background and motivation of this study, we for-mulated our modeling strategies and adopted an ap-proach to integrating a soil moisture model with agroundwater model for numerical simulation of the hy-drological cycle in a vertically and horizontally dis-cretized domain at the watershed or field scale. Manyresearchers have used numerical methods to solve theRichard’s equation and thus construct soil hydrologicalmodels for 1D, 2D, or 3D soil moisture simulation(Lappala et al. 1987; Ross 1990; Stothoff 1995; Simuneket al. 1998; Hsieh et al. 2000; Fayer 2000). In a plainregion, soil moisture movement in the vertical directionplays a dominant role and therefore a 1D model shouldbe sufficient. Chen and Hu (2004) developed such amodel to investigate groundwater influences on soil

FIG. 1. Plain region of the Huaihe River basin and location ofthe two study sites.

AUGUST 2007 C H E N E T A L . 703

moisture and surface evaporation. This model wasadopted in the present study to simulate the downward(infiltration and percolation) and upward (evapotrans-piration) movement of soil moisture. Since these waterfluxes interact with groundwater dynamics, a ground-water model must be integrated with the soil moisturemodel. The modular three-dimensional finite-differ-ence groundwater flow model (MODFLOW), a widelyused groundwater model of the U.S. Geological Survey,has a modular structure and open environment (Mc-Donald and Harbaugh 1988). It was selected for themodel integration in order to link its three packages forsimulating water exchanges between aquifer and otherhydrological components (i.e., recharge, evapotranspi-ration, and river) with the soil moisture model andstreamflow routing algorithms.

The modeling system was calibrated in the Linhuanjicatchment of the Huaihe River basin to estimate sur-face runoff, groundwater recharge, and groundwaterlosses for evapotranspiration and stream baseflow. Itwas further tested at the Wudaogou Hydrological Ex-perimental Station for validating the model’s capabilityin simulation of hydrological components and estima-tion of water fluxes using observed stream water stageand groundwater data, as well as lysimeter-measuredprecipitation recharge and groundwater loss. Modeltesting and application have demonstrated its accuracyand usefulness for quantitative assessment of the dy-namics of water movement and storage, which is con-trolled by both meteorological conditions and agricul-tural land use in the plain region of the Huaihe Riverbasin.

2. Model components and algorithms

a. Soil moisture model

Soil moisture dynamics driven by climate fluctuationsplay a key role in the simulation of water transferamong ground surface, unsaturated zones, and aquifer.Soil moisture variation in the model is described byRichard’s equation. Integrating Richard’s equationthrough four soil layers under the assumption of verti-cally homogeneous soil hydraulic properties withineach layer yields the following equations (Chen andDudhia 2001; Chen and Hu 2004):

d1

��1

�t� �D��

�z�1� K1 � Pd � Ir � Rs � Edir � ET1,

�1�

d2

��2

�t� D��

�z�1� D��

�z�2� K1 � K2 � ET 2, �2�

d3

��3

�t� D��

�z�2� D��

�z�3� K2 � K3 � ET3, �3�

and

d4

��4

�t� D��

�z�3� D��

�z�4� K3 � K4, �4�

where subscript i � 1, 2, 3, and 4 is soil layer index; di

is thickness of the ith soil layer; �i is soil moisture con-tent; Pd is precipitation P falling on the ground; Ir is theirrigated water from stream and aquifer; Rs is surfacerunoff; Ki is vertical unsaturated soil hydraulic conduc-tivity; and D the soil water diffusivity. Both K and Dare functions of soil moisture content � and are com-puted from K(�) � Ks(� /�s)

2b�3 and D(�) � K(�)(��/��), where is soil water tension function and �(�) ��s /(� /�s)

b in which b is a curve-fitting parameter(Cosby et al. 1984); Edir is the evaporation from the topsoil surface, and ETi in Eqs. (1)–(3) is the transpirationby vegetation through roots. The groundwater effect onsoil moisture is taken into account in Eq. (4) by allow-ing upward soil moisture exchange between the deepestmodel soil layer and the groundwater table [D(��/�z)4](Chen and Hu 2004). The vertical derivative of D(�� /�z)i

is approximated by D[(�i�1 � �i)/di].

b. Groundwater model

Interactions between unsaturated and saturatedzones (e.g., the groundwater recharge and loss, and be-tween stream water and groundwater including base-flow), depend on the groundwater dynamics, which isdescribed by the governing equation:

�

�x �Kx

�h

�x��

�y �Ky

�h

�y��

�z �Kz

�h

�z�� Ss

�h

�t� Ws,

�5�

where h is the hydraulic head; Kx, Ky, and Kz are thehydraulic conductivities along the x, y, and z axes; Ss isthe specific storage of the aquifer (specific yield Sy di-vided by the aquifer thickness); and Ws is a volumetricflux per unit area representing sources and/or sinks ofwater. It includes groundwater recharge from soil mois-ture Prg and groundwater loss through capillary flowupward Gup, water exchanges between stream channeland aquifer Qg, and groundwater pumping rate Wg. InMODFLOW, this equation is numerically solved usinga finite-difference method and the FORTRAN sourcecodes of MODFLOW-2000 can be easily modified formodel integration and other customized applications(McDonald and Harbaugh 1988; Harbaugh et al. 2000).


c. Simulation of water fluxes

The two models can simulate the water movementand dynamics within the unsaturated and saturatedzones, respectively. The key for integrating the twomodels is to simulate the water fluxes, which link thetwo storage reservoirs together. The entire hydrologicalcycle involves water fluxes at three major interfaces: 1)evapotranspiration and surface runoff at the interfacebetween atmosphere and soils; 2) groundwater re-charge and loss at the interface between unsaturatedand saturated zones; and 3) water exchanges (baseflowor groundwater recharge) at the interface betweenaquifer and stream channel.

1) EVAPOTRANSPIRATION

In the soil moisture model, total evapotranspiration(ET) is the sum of 1) direct evaporation from the topshallow soil layer, Edir; 2) transpiration via canopy androots, ET ; and 3) evaporation of precipitation inter-cepted by the canopy, Ec.

A simple linear method is used to calculate Edir

(Mahfouf and Noilhan 1991):

Edir � �1 � �f��Ep, �6�

where f is the green vegetation fraction (cover); � �(�1 � �w /�ref � �w), in which �ref and �w is field capacityand wilting point, respectively; Ep is the potentialevaporation calculated using a Penman-based energybalance approach that includes a stability-dependentaerodynamic resistance (Mahrt and Ek 1984). Here ET

is calculated by

ET � �fEpBc�1 � �Wc

S �n�, �7�

where Bc is a function of canopy resistance, Wc is in-tercepted canopy water content estimated from thebudget for intercepted canopy water, S is the maximumcanopy capacity, and n � 0.5. Finally, the third compo-nent of ET, Ec, can be estimated by

Ec � �fEp�Wc

S �n

. �8�

The budget for intercepted canopy water is

�Wc

�t� �fP � Dp � Ec, �9�

where P is total precipitation. If Wc exceeds S, the ex-cess precipitation or drip, Dp, reaches the ground [notethat Pd � (1�f)P � Dp in Eq. (1)].

2) SURFACE RUNOFF

In the semihumid region of China, infiltration excessoverland flow and saturation overland flow can be gen-

erated from precipitation. The former surface runoff,Rs, is defined as the excess of precipitation, which doesnot infiltrate into the soil (Rs � Pd � Imax). The maxi-mum infiltration, Imax, is formulated as

Imax � min�K1, If , �10�

where K1 is the upper-layer soil hydraulic conductivityand If is the infiltration capacity related to precipitationintensity, soil moisture deficit, and rainfall duration(Chen and Dudhia 2001).

In the wet season, the upper layer of soil may becomesaturated during a rainfall event, resulting in overlandflow (Rs � max{Pd � Dx1, 0}, where Dx1 is the upper-layer soil moisture deficit per unit area in a simulationtime step).

3) GROUNDWATER RECHARGE AND LOSS

Water flux that crosses the interface between satu-rated and unsaturated zones is either groundwater re-charge from soil moisture driven by gravity or ground-water loss in soil layers driven by capillary force. Thewater flux We can be estimated by the following equa-tion:

We � K��

�z� 1�

4� D��

�z�4� K4, �11�

where D((�� /�z))4 � D(�4 � �s /Zg), and Zg is the dis-tance between the groundwater table and the midpointof the soil layer located immediately above the ground-water table. A positive We represents groundwater re-charge Prg and a negative We represents groundwaterloss Gup.

4) WATER EXCHANGES BETWEEN AQUIFER AND

STREAM CHANNEL

The river package of MODFLOW simulates the wa-ter fluxes between stream channel and aquifers that areprimarily controlled by the hydraulic conductivity andthickness of the bottom sediments and the head differ-ences between streamflow and aquifer at the streamchannel. The flow rate Qg between the stream channeland aquifer is calculated by the difference in hydraulicheads in the stream and the adjacent aquifer using thefollowing equation (McDonald and Harbaugh 1988):

Qg � Criv�Hriv � h�, �12�

where Criv is the hydraulic conductance of the stream–aquifer interconnection, h is the head at the node in thecell underlying the stream reach, Hriv is the head in thestream channel. Obviously positive and negative values ofQg represent groundwater recharge from river channelRr and baseflow discharge from aquifer Rg, respectively.


d. Routing of surface runoff and streamflow

Movement of surface runoff and streamflow ismainly regulated by the basin’s terrain and the chan-nel’s characteristics. For runoff-generating stormevents, surface runoff governs the peak discharge rate,time to peak, and volume of observed downstream out-flows. Since the ground surface is relatively flat in aplains region, surface runoff generated in each grid cellflows into its nearby ditches and then concentrates inthe stream channel. A simplified surface runoff routingmethod called a time lag approach, as described by theequation below, was used to represent the ground sur-face regulation:

Qs�t� � CSQs�t � �t� � �1 � CS�Rs�t � Lag�, �13�

where Qs(t) and Qs(t � �t) is the discharge at an outletat time t and t � �t, respectively, Rs is average value ofsurface runoff Rs between time t and t � �t, CS iscoefficient of surface runoff concentration, and Lag istime lag.

Stream channels are divided into reaches for stream-flow routing. Besides upstream inflow, each river reachmay receive surface runoff and baseflow from the ad-jacent land segments. Stream discharge may also beinfluenced by water diversion, direct precipitation, andET. Water balance analysis for each river reach pro-vides an estimate of reach storage and thus its corre-sponding stage at each time step. The estimated storageand stage determine the discharge at each cross section,and streamflow is thus routed from upstream to down-stream.

3. Model integration and implementation

The numerical modeling system is essentially an in-tegration of the water flux algorithms described above,

which are tightly coupled into the soil moisture modeland the groundwater model. In practice, water fluxesare either inputs or outputs for the two models and thusthey are numerically simulated through an iterativeprocess. The physically based simulation of water fluxesamong the atmosphere, stream channel, soil layers, andthe aquifer is implemented using a finite-difference ap-proach. A study site (watershed or field) is divided intorectangular or square cells, each of which is consideredto be hydrologically and hydrogeologically uniform inland use, soil, and predominant depth of the watertable.

Figure 2 schematically presents the water fluxesthroughout the hydrological cycle and how they areinteractively linked with reservoirs as represented inour modeling system. After precipitation is interceptedby vegetation a portion of it, Pd reaches the groundsurface. Water may become surface runoff, Rs, or infil-trate the soil and then further percolate into a ground-water aquifer, Prg. Part of the water is returned to theatmosphere through evapotranspiration, ET. Drivenby capillary force, groundwater may be pulled up tomove into the bottom layer of the soil profile and thenthe moisture (Gup) may move farther upward as a re-sult of a soil moisture gradient and finally return tothe atmosphere through evapotranspiration. Humanactivities may introduce additional water fluxes into thehydrological cycle, namely, groundwater pumping, Wg,stream water diversion for irrigation, and storing andpercolation from artificial ponds.

Water fluxes interact with soil moisture dynamics,groundwater table fluctuations, and streamflow re-gimes. The modeling system simulates these interac-tions between each reservoir and their related waterfluxes. Given the inputs of rainfall, potential ET, andland-cover and soil characteristics, the coupling of

FIG. 2. A schematic representation of the modeling system.


water flux algorithms with the soil moisture model cansimulate the soil moisture dynamics and thus produceestimates of infiltration, surface runoff, groundwaterrecharge, and actual ET. For groundwater simulation,algorithms of the two vertical fluxes—groundwater re-charge, Prg, and loss, Gup—are inserted into the re-charge (RCH) package and evapotranspiration (EVT)package of MODFLOW, respectively. The two waterfluxes can be estimated by coupling the modifiedMODFLOW with the soil moisture model for iterativesimulation based on the objective function of minimiz-ing the errors between the observed and simulated val-ues of streamflow and the groundwater table, as well assoil moisture contents if available. The horizontal fluxof water exchanges between the aquifer and the stream

channel is simulated directly by the river (RIV) pack-age. Computational codes in FORTRAN and computerinterfaces in Visual Basic have been developed to inte-grate all the algorithms into the modeling system.

The modeling system contains two types of param-eters. The majority of parameters carry certain physicalsignificance and they can be measured through experi-ments in the field or laboratory. These parameters pri-marily represent the soil and vegetation characteristicssuch as saturated hydraulic conductivity, water contentsat wilting point, field capacity and saturation, andcanopy capacity and reflectivity. Other empirical pa-rameters such as the coefficient of surface runoff con-centration, CS, time lag, storage capacity of smallponds, and hydraulic conductance, Criv, need to be cali-

FIG. 3. (a) Ground surface elevation in the LHJ catch-ment; (b) location of groundwater observation wells in theLHJ catchment; and (c) geological materials of aquifers inthe LHJ catchment.


brated against the observed streamflow and thegroundwater table. Finally, human influences on thewater fluxes must be accounted for and irrigation isoften the most important input into the soil waterbucket or the output from an aquifer and stream chan-nel. The amount of irrigation water can be estimatedeither by the difference between vegetation demandand the water available from rainfall and soil moisturestorage or by using the records of water usage.

4. Model testing and application

a. Study sites and model testing approach

The model was tested in two sites located in the Hua-ihe River basin where climate conditions vary fromsemihumid in the southeast to semiarid in the north-west (Fig. 1). The first site is the Linhuanji (LHJ) catch-ment with an area of 2 560 km2. This catchment hasmeteorological and hydrological data covering a 10-yrperiod (1986–95), as well as spatial data of soil, vegeta-tion, aquifer, and land characteristics. Therefore, it waschosen for model calibration and water budget analysis.Model validation was conducted in a runoff experimen-tal field of 1.36 km2 surrounded by drainage ditches atthe Wuduogou Hydrological Experimental Station(WHES). For this field, the available data include notonly those required for model calibration againststreamflow and the groundwater table for a 7-yr period(1994–2000), but also values of soil moisture content, as

well as lysimeter-measured groundwater recharge andloss, which can be used to further evaluate the model’saccuracy.

In the LHJ catchment, average annual precipitationduring 1986–95 is 713 mm and approximately 60%–70% of the precipitation occurs in the summer seasonfrom June to September. The annual potential evapo-transpiration is 960 mm. Figure 3 shows the terrain lo-cation of groundwater observation wells and aquifercomposition for this study basin. The ground surfaceelevations vary from 45 m above sea level in the northto 28 m above sea level in the south. The spatial distri-bution of the groundwater table demonstrates a similarpattern: 37–38 m above sea level in the north to 26–27m above sea level in the south. The depth to ground-water table is as deep as 7–8 m in the north and de-creases to only 2 m in the south. The groundwater tablefluctuates about 1–2 m annually.

Data from the 10-yr period (1986–95) for the LHJcatchment includes daily precipitation recorded at 25stations, pan evaporation from one station, groundwa-ter table depths at 5-day intervals from 30 observationwells (Fig. 3b), and the daily streamflow discharge atthe catchment outlet. The geological materials fromaquifers in the northern part of LHJ, mostly sand andsilty sand, came from the alluvial deposits of the aban-doned Yellow River. In the southern part of the catch-ment, the aquifer sources are mostly silty sand, which islocally called “calcic concretionary black soil,” a main

FIG. 4. Observed and simulated discharges in the LHJ catchment.


type of soil in this plain region of the Huaihe Riverbasin (Fig. 3c). In the upper cultivated soils of unsatu-rated zone, sandy loam dominates in the north andsandy clay loam becomes more common in the south.Wheat, maize, and sorghum are the main crops in theregion.

WHES has been a site for studies of the hydrologicalcycle in the Huaihe River plain region since the early1950s. Regularly observed meteorological variables in-clude precipitation, air temperature, soil temperature,humidity, wind speed, solar radiation, and pan evapo-ration. Other data collected at the experimental runofffield site include the water level in drainage ditches, thegroundwater table, and soil moisture contents adjacentto the observation well at the depths of 5, 25, 55, and 90cm below the ground’s surface. Observations indicate

the average depth from the ground surface to the watertable is 1.5 m. Additionally, 60 sets of lysimeters for soilcolumns of different depths were installed to measuregroundwater recharge and loss. Soils at WHES repre-sent a typical composition of the silty sand that is mostcommon in the Huaihe River plain region. Wheat is thedominant crop at the experimental runoff field. Soilparameters for silty sand estimated in LHJ catchmentwere used for model validation in the field.

b. Model calibration and validation

The LHJ catchment is discretized into 2356 gridunits, each 1047 m long and 1048 m wide. The simula-tion time step for model calibration is one day. Resultsof the soil analysis by Song (2003) provide physical pa-

FIG. 5. Simulated and observed groundwater table at observation wells in the LHJcatchment.


rameters of soil moisture dynamics, for example, volu-metric water content at saturation �s, field capacity �f,and wilting point �w in the unsaturated zone. Accordingto Cosby et al. (1984), hydraulic conductivity of sandyloam and sandy clay loam is 0.41 and 0.29 m day�1,respectively. In the saturated zone, hydraulic conduc-tivity and the specific yield in the sandy region are 4.4m day�1 and 0.055 and are 2.8 m day�1 and 0.045 in thesilty sand region, respectively (Song 2003). Hydraulicconductivity of a riverbed deposit and channel cross-sectional characteristics determine the hydraulic con-ductance Criv, ranging from 200 to 1500 m2 day�1.Other parameters are calibrated against the observedstream discharge and the groundwater table using atrial and error method. The calibrated coefficient of thesurface runoff concentration, CS, and time lag is 0.35and 1 day, respectively; the storage capacity of smallponds with an area of about 1% of the LHJ catchmentis 2.5 mm.

The simulated and observed discharge for 1990–91and 1994–95 examples are given in Fig. 4, showing thatthe two time series match each other reasonably well.The Nash–Sutcliff index for the entire calibration pe-riod (1986–95) is 0.79, and RMSE is 4.0 m3 s�1. Modelperformance is also evaluated by comparing the simu-lated and observed groundwater table. As shown in Fig.5, the groundwater table is simulated quite accuratelyfor individual observation wells such as 13, 29, and 35.Averages of the simulated and observed water table forall of the 30 wells at each time step during the 10-yrcalibration period are plotted in Fig. 6. Simulated andobserved values of the water table at each well areaveraged over the whole calibration period, and thecorrelation coefficient for the two sets of data is 0.81(Fig. 7). These two figures further prove the model’saccuracy. Although the results of model calibration aregenerally satisfactory, it should be pointed out that

some significant discrepancies between the observedand simulated values of discharge and the groundwatertable do exist. We believe that these errors are unavoid-able because the amount, timing, and location of hu-man interferences on regional water fluxes and distri-bution, such as artificial pond storage and irrigationpumping, cannot be accurately estimated.

Model validation for the runoff experimental field inWHES also produces promising results. The correla-tion coefficient between the simulated and observedditch stage is 0.80, and the correlation coefficient be-tween the simulated and observed groundwater table is0.85. The measurement of soil moisture contents,groundwater recharge, and loss at the field allows us toevaluate how accurately the model can simulate thewater storage and fluxes within the soil–aquifer con-tinuum. Figure 8 presents the observed and simulatedsoil moisture contents averaged for the four soil layersin each year from 1994 to 2000, indicating that the

FIG. 6. Averages of simulated and observed groundwater table for 30 wells at each timestep in the LHJ catchment.

FIG. 7. Scatterplot of simulated vs observed groundwater tableaveraged over the 10-yr period at each well in the LHJ catchment.


FIG. 8. Simulated (dot) and observed (solid line) variations of soil moisture content(SMC, m3 m�3) in WHES.


model simulation can capture the seasonal variations ofsoil moisture contents throughout the year. The annualmean recharge coefficient Prg/P is the ratio of ground-water recharge to precipitation aggregated for oneyear. Corresponding to a certain groundwater depth,the coefficient of groundwater loss Gup/Ep is the ratioof the loss to potential ET averaged over the wholesimulation period. As shown in Figs. 9 and 10, the simu-lated and observed values of these two coefficientsmatch quite well in most cases except for the modelwarm-up period, which directly affects the result of thedry year, 1994. These results prove the accuracy andreliability of water flux simulation.

c. Water budget analysis

After calibration and validation, the model can beused to simulate water fluxes and storage rates withinthe hydrological system to investigate the water trans-fer process and evaluate available water resources. Forthe LHJ catchment, simulation results of the annualwater budget are given in Table 1. On average over the10-yr period, the sum of precipitation and groundwaterwithdrawal that is primarily for agricultural utilization(column 2 � column 6 in Table 1) is 769.46 mm everyyear, and approximately 87% of this amount, that is,

669 mm (column 3), is lost through soil evaporation andvegetation transpiration. About 8.2% of precipitation,that is, 57.86 mm in column 9, becomes streamflow. Inother words, the annual mean runoff coefficient equals0.082 on average, and it varies from 0.02 in the dry yearof 1994 to 0.24 in the wet year of 1991. About 15% ofprecipitation, that is, 103.60 mm (column 4), enters thegroundwater aquifer, which means an annual mean re-charge coefficient of 0.15, and it varies from 0.03 to0.20. More than half of the recharge amount is losteither through evapotranspiration or as baseflow thatdischarges into the stream channel (column 5 � column8), and the remaining amount stays in the aquifer. Thetotal of the surface runoff and baseflow (column 7 �column 8) equals the simulated runoff (column 9). Theyearly relative errors between the observed and simu-lated runoff fall within the range of 1.94%–22.84%. Themajority of larger simulation errors occur primarily inthe dry years because the artificial influences on thewater balance become more significant. For the wholesimulation period over the 10 yr, the relative error ofsimulated runoff is only 1.75%.

Water balance should be maintained for each storagereservoir of the hydrological system. Theoretically, in-put minus output for each reservoir should be equal tothe storage change. Because of computational approxi-

TABLE 1. Water budget analysis for the LHJ catchment based on simulated water fluxes (mm). The relative error between Qsim andQobs is RE.

Year (1) P (2) ET (3) Prg (4) Gup (5) Wg (6) Rs (7) Rg (8) Qsim (9) Qobs (10) RE (%) (11)

1986 571 648 47.38 64.93 63.06 21.45 8.70 30.16 32.36 7.321987 713 653 65.25 48.37 31.39 18.19 9.00 27.19 27.72 1.941988 572 723 63.63 39.06 74.20 8.60 16.22 24.82 29.91 20.501989 813 647 28.47 49.83 26.17 165.49 41.64 90.84 104.5 15.041990 887 667 163.78 69.46 39.46 73.13 19.32 92.45 96.25 4.121991 883 638 174.74 86.43 60.91 168.49 39.88 208.4 195.91 �5.981992 751 726 111.16 46.11 49.91 42.67 12.70 55.37 48.52 �12.381993 616 593 29.79 25.29 79.03 12.97 3.38 16.35 17.12 4.691994 610 716 71.72 6.93 58.74 8.64 3.18 11.82 10.36 �12.381995 723 684 143.01 19.06 56.29 15.65 5.55 21.20 26.04 22.84Mean 714 669 103.60 45.55 55.46 43.22 14.64 57.86 58.88 1.75

FIG. 9. Simulated and measured recharge coefficient Prg/P inWHES.

FIG. 10. Simulated and observed coefficient of groundwater lossGup/Ep related to groundwater depths in WHES.


mation, there might be a small difference between thetwo quantities, and this difference divided by the aver-age of input and output is defined as balance error.Table 2 shows the 10-yr (1986–95) average water bal-ance for unsaturated and saturated zones. For the un-saturated zone, the inputs include precipitation P, up-ward groundwater flux from the aquifer Gup, and irri-gation water Ir, and the outputs include soil moistureloss through evapotranspiration ET, surface runoff Rs,and groundwater recharge Prg. As noted earlier, the soilprofile is divided into only four layers for soil moisturesimulation. This approximation has caused a small bal-ance error of 0.37% as shown in Table 2. For the satu-rated zone, the inputs are the recharge from the bottomof the unsaturated zone Prg, the streamflow rechargeinto aquifer Rr, and the horizontal inflow into the aqui-fer from outside of the simulation domain Bin. Regard-ing the outputs from the aquifer, groundwater is lostthrough upward capillary flow into the soil layers (Gup),discharge into the stream as baseflow (Rg), withdrawal(Wg) for irrigation and other consumption (domesticand industrial water use), and the horizontal outflow(Bout) on the aquifer boundary. For the 10-yr simula-tion period, the difference between inputs and outputsinto the saturated zone is exactly balanced by the stor-age change and therefore the error is zero in ground-water simulation using the MODFLOW.

5. Summary and conclusions

Estimation of water fluxes requires a modeling sys-tem that integrates algorithms for simulation of watermovement among the atmosphere, stream channel, soillayers, and groundwater aquifer. For the Huaihe Riverbasin where human activities, especially agriculture,have profound impacts on the hydrological cycle, sucha tool is needed to understand the processes and evalu-

ate the quantities of water being transferred from pre-cipitation to evapotranspiration, surface runoff, soilmoisture, groundwater, and streamflow. In this study,coupling a soil moisture model with the MODFLOWgroundwater model has created a platform for us tointegrate water flux algorithms into the numerical mod-eling system.

The modeling system is largely based on physicallaws and employs a finite-difference method to numeri-cally simulate water movement and fluxes in a horizon-tally discretized watershed or field. The majority ofmodel parameters carry physical significance and canbe determined by field and laboratory measurements orderived from watershed characteristics contained inGIS and remote sensing data. Several other empiricalparameters need to be estimated by model calibration.The model has been successfully tested in two steps attwo sites in the Huaihe River plain. First, it was cali-brated in the Linhuanji catchment against observationsof streamflow and the groundwater table in a 10-yr pe-riod (1986–95). Second, model validation against inten-sive measurements of soil moisture contents andgroundwater fluxes was conducted at a very small run-off experimental field in the Wudouguo HydrologicalExperimental Station. Calibration and validation re-sults prove the accuracy and reliability of the modelingsystem.

This study has developed a useful tool for water re-source managers to estimate water fluxes and evaluatewater distribution in the Huaihe River plain undernatural conditions and human perturbations. Thephysically based model offers promising applicabilitybecause it can be calibrated and customized with rela-tive ease. The distributed-parameter design allowsmodelers to predict the changes of a regional waterbudget resulting from any scenarios of land use prac-tices in different parts of the watershed. Water balanceanalysis based on model results will provide crucial in-formation for the optimization of water allocation, ir-rigation scheduling, and other tasks in water resourceassessment and planning.

Acknowledgments. This research was supported bythe Program for New Century Excellent Talents in Uni-versity, China (NCET-04-0492), and partially sup-ported by a grant from the Research Grants Council ofthe Hong Kong Special Administrative Region, China(Project CUHK4627/05H).

REFERENCES

Andreu, J., J. Capilla, and E. Sanchès, 1996: AQUATOOL, ageneralized decision support system for water-resources

TABLE 2. Average annual water balance in unsaturated andsaturated zones of the LHJ catchment during 1986–95 (mm).

Unsaturated zone

Input Output S Balance error (%)

P 714.00 ET 669.45 �17.70 0.37Gup 45.55 Rs 43.22Ir 42.00 Prg 103.60

Saturated zones

Input Output S Balance error (%)

Prg 103.60 Gup 45.55 �12.50 0Rr 4.10 Rg 14.64

Wg 55.46Bin 7.96 Bout 12.50


planning and operational management. J. Hydrol., 177, 269–291.

Chen, F., and J. Dudhia, 2001: Coupling an advanced land sur-face–hydrology model with the Penn State–NCAR MM5modeling system. Part I: Model implementation and sensitiv-ity. Mon. Wea. Rev., 129, 569–585.

Chen, X., and Q. Hu, 2004: Groundwater influences on soil mois-ture and surface evaporation. J. Hydrol., 297, 285–300.

Cosby, B. J., G. M. Hornberger, R. B. Clapp, and T. R. Ginn,1984: A statistical exploration of the relationships of soilmoisture characteristics to the physical proprieties of soil.Water Resour. Res., 20, 682–690.

Duffy, C., and Coauthors, 2006: Towards an integrated observingplatform for the terrestrial water cycle: From bedrock toboundary layer. Draft of SSG Whitepaper, 57 pp. [Availableonline at http://www.usgcrp.gov/usgcrp/Library/watercycle/ssg-whitepaper-dec2006.pdf.]

Dunn, S. M., R. Mackay, R. Adams, and D. R. Oglethorpe, 1996:The hydrological component of the NELUP decision-supportsystem. J. Hydrol., 177, 213–236.

Fayer, M. J., 2000: UNSAT-H Version 3.0: Unsaturated soil waterand heat flow model, theory, user manual, and examples.Pacific Northwest National Laboratory Rep. PNNL-13249,184 pp.

Fedra, K., and D. G. Jamieson, 1996: The “WaterWare” decision-support system for river-basin planning. 2. Planning capabil-ity. J. Hydrol., 177, 177–198.

Guo D., Y. Wei, and B. Yan, 1997: Study on water transfer amongprecipitation, surface runoff, soil moisture and groundwaterin wet agriculture area (in Chinese). J. Water Resour. Hy-draul. Power, 5, 21–24.

Harbaugh, A. W., E. R. Bantaa, M. C. Hill, and M. G. McDonald,2000: MODFLOW-2000: The U.S. Geological Survey modu-lar groundwater model. User guide to modularization con-cepts and the ground-water flow process. U.S. GeologicalSurvey Open-File Rep. 00-92, 121 pp.

Hsieh, P. A., W. Wingle, and R. W. Healy, 2000: VS2DI: Agraphical software package for simulating fluid flow and sol-ute or energy transport in variably saturated porous media.U.S. Geological Survey Water-Resources Investigations Rep.99-4130, 16 pp.

Jamieson, D. G., and K. Fedra, 1996a: The “WaterWare” deci-sion-support system for river-basin planning. 1. Conceptualdesign. J. Hydrol., 177, 163–175.

——, and ——, 1996b: The “WaterWare” decision-support systemfor river-basin planning. 3. Example applications. J. Hydrol.,177, 199–211.

Lappala, E. G., R. W. Healy, and E. P. Weeks, 1987: Documen-tation of computer program VS2D to solve the equations offluid flow in variably saturated porous media. U.S. Geologi-cal Survey Water-Resources Investigations Rep. 83-4099, 184pp.

Mahfouf, J. F., and J. Noilhan, 1991: Comparative study of various

formulations from bare soil using in situ data. J. Appl. Me-teor., 30, 1354–1365.

Mahrt, L., and M. Ek, 1984: The influence of atmospheric stabilityon potential evaporation. J. Climate Appl. Meteor., 23, 222–234.

McDonald, M. G., and A. W. Harbaugh, 1988: A modular three-dimensional finite-difference ground-water flow model. U.S.Geological Survey Techniques of Water-Resources Investi-gations Rep. TWRI 6-A1, 586 pp.

National Research Council, 2004: Groundwater Fluxes Across In-terfaces. The National Academy Press, 85 pp.

Parker, P., R. Letcher, A. Jakeman, M. B. Beck, G. Harris, R. M.Argent, M. Hare, and C. PahlWostl, 2002: Progress in inte-grated assessment and modelling. Environ. Model. Software,17, 209–217.

Refsgaard, J. C., and B. Storm, 1995: MIKE SHE. Computer Mod-els of Watershed Hydrology, V. P. Singh, Ed., Water Re-sources Publications, 809–846.

Reitsma, R. F., 1996: Structure and support of water resourcesmanagement and decision-making. J. Hydrol., 177, 253–268.

Ross, P. J., 1990: SWIM: A simulation model for soil water infil-tration and movement. Commonwealth Scientific and Indus-trial Research Organisation, 59 pp.

Schulla, J., and K. Jasper, 2001: Model description WaSiM-ETH(Water balance Simulation Model ETH). EidgenössischTechnische Universität, 166 pp.

Shen, Z. R., 1992: Water resources experiments and analysis:Transfers among precipitation, surface water, soil moisture,and groundwater (in Chinese). China Science and Technol-ogy Press, 569 pp.

Simunek, J., M. Sejna, and M. T. van Genuchten, 1998: The Hy-drus-1D software package for simulating the one-dimen-sional movement of water, heat, and multiple solutes in vari-ably-saturated media. User’s manual, version 2.0, U.S. Sa-linity Laboratory, Agricultural Research Service, 178 pp.

Singh, V. P., Ed., 1995: Computer Models of Watershed Hydrol-ogy. Water Resources Publications, 1130 pp.

Song, J. C., 2003: Analysis of hydrologic and hydrogeologic pa-rameters from observation data at the Wudaogou experimen-tal site (in Chinese). Anhui and Hui River Water ResourcesResearch Institute Rep., 12 pp.

Stothoff, S. A., 1995: BREATH Version 1.1: Coupled flow andenergy transport in porous media. Simulator description anduser guide, U.S. Nuclear Regulatory Commission Rep.NUREG/CR-6333, 94 pp.

Therrien, R., R. G. McLaren, E. A. Sudicky, and S. M. Panday,2004: HydroGeoSphere: A three-dimensional numericalmodel describing fully integrated subsurface and surface flowand solute transport. Manual (Draft), HydroGeoLogic, Inc.,275 pp.

Xu, F., and Y. Guo, 1994: Study on water transfer among precipi-tation, surface runoff, soil moisture and groundwater in theplain region of Taihang Mountain frontier (in Chinese). J.Haihe Water Resour., 5, 53–55.


a numerical modeling system of the hydrological cycle for

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