geospatially based distributed rainfall-runoff modelling for simulation of internal and outlet...

HYDROLOGICAL PROCESSESHydrol. Process. (2011)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.8271

Geospatially based distributed rainfall-runoff modellingfor simulation of internal and outlet responses in a

semi-forested lower Himalayan watershed

RAAJ Ramsankaran,a* U. C. Kothyari,b S. K. Ghosh,b A. Malcherekc and K. Murugesanda Department of Civil Engineering, Birla Institute of Technology & Sciences Pilani, Pilani, India

b Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, Indiac Institute of Hydro sciences, German Federal Armed Forces University Neubiberg, Munich, Germany

d Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India

Abstract:This study presents a Geographic Information System (GIS)-based distributed rainfall-runoff model for simulating surfaceflows in small to large watersheds during isolated storm events. The model takes into account the amount of interceptionstorage to be filled using a modified Merriam (1960) approach before estimating infiltration by the Smith and Parlange (1978)method. The mechanics of overland and channel flow are modelled by the kinematic wave approximation of the Saint Venantequations which are then numerically solved by the weighted four-point implicit finite difference method. In this modelling thewatershed was discretized into overland planes and channels using the algorithms proposed by Garbrecht and Martz (1999).The model code was first validated by comparing the model output with an analytical solution for a hypothetical plane. Thenthe model was tested in a medium-sized semi-forested watershed of Pathri Rao located in the Shivalik ranges of the GarhwalHimalayas, India. Initially, a local sensitivity analysis was performed to identify the parameters to which the model outputs likerunoff volume, peak flow and time to peak flow are sensitive. Before going for model validation, calibration was performedusing the Ordered-Physics-based Parameter Adjustment (OPPA) method. The proposed Physically Based Distributed (PBD)model was then evaluated both at the watershed outlet as well as at the internal gauging station, making this study a first of itskind in Indian watersheds. The results of performance evaluation indicate that the model has simulated the runoff hydrographsreasonably well within the watershed as well as at the watershed outlet with the same set of calibrated parameters. The modelalso simulates, realistically, the temporal variation of the spatial distribution of runoff over the watershed and the same hasbeen illustrated graphically. Copyright 2011 John Wiley & Sons, Ltd.

KEY WORDS blind validation; distributed runoff model; distributed runoff validation; event oriented; kinematic wave routing;GIS; watershed model

Received 4 November 2010; Accepted 1 July 2011

INTRODUCTION

The hydrology of a watershed is complex, involvinginteractions amongst many natural processes. Conduct-ing comprehensive field studies for monitoring watershedresponse to design and to evaluate the impact of manage-ment strategies requires huge funds. Difficulties in datacollection, field personnel and automated equipment oftenmake repeated field studies unfeasible. Faced with theselimitations, mathematical hydrologic models are power-ful alternatives to quantify storm runoff to design andevaluate alternative landuse and best management prac-tices (BMPs), the implementation of which can help inreducing the damaging effects of runoff on land produc-tivity and water bodies. The design of strategies to controlsoil erosion caused by runoff requires spatially distributedrunoff quantities, often on a minute-by-minute basis dur-ing different storm events for predicting the amount andtiming of peak discharges of water from small watersheds

* Correspondence to: RAAJ Ramsankaran, Department of Civil Engineer-ing, Birla Institute of Technology & Sciences Pilani, Pilani, India.E-mail: ramsankaran [email protected]

to rivers. In order to provide better representation ofrunoff processes which are strongly dependent on soil,vegetation and topographic characteristics of the water-shed. In recent years, researchers have concentrated ondeveloping Physically Based Distributed (PBD) models,capable of simulating temporal as well as spatial distri-bution of runoff at the watershed scale.

A number of such hydrological models with vari-ety of structures and data requirements that are capableof simulating runoff, including soil erosion and sed-iment transport processes, are available in the litera-ture (Singh and Woolhiser, 2002). Some of those areANSWERS (Beasley et al., 1980), CREAMS (Knisel,1980), SHETRAN (Ewen et al., 2000), an enhancedversion of the SHE/SHESED model (Abbott et al.,1986a,b; Bathurst et al., 1995; Wicks and Bathurst,1996); KYERMO (Hirshi and Barfield, 1988), WEPP(Nearing et al., 1989; Flanagan et al., 2007), AgNPS(Young et al., 1989), KINEROS-2, an enhanced versionof KINEROS (Woolhiser et al., 1990), LISEM (De Rooet al., 1996), SWAT (Arnold et al., 1998), EUROSEM(Morgan et al., 1998), and other models developed by

Copyright 2011 John Wiley & Sons, Ltd.

RAAJ RAMSANKARAN ET AL.

Jain et al. (2005), Rai and Mathur (2007), Reddy et al.(2008), Naik et al. (2009), among others.

Comparative assessments of some of the models showthat no single model works well in every situationof runoff and sediment yield on the watershed scale(Bingner et al., 1989). Many of the models are sitespecific and contain simplifications and assumptions thatpreclude their use universally. Hence, in such conditionswhen the availability of data is limited, like in theIndian sub-continent, it becomes difficult to adapt thesemodels. In India, Sharda (1990), Sharda and Singh(1994), Jain et al. (2004) and Bhardwaj and Kaushal(2009) presented their work on development of process-based mathematical models for simulation of runoff frompredominantly agricultural watersheds. It is observed thatthese models have the limitation that they do not considerthe process of channel flow routing which is a majorcomponent of the hydrological processes in mediumto large-sized watersheds. Therefore, these models maybe applicable only for micro level watershed or field-size plots where the channel flow is not a dominantfactor. So these models cannot be effectively used forthe design and implementation of conservation efforts,which are generally carried out at the watershed scale.In addition, these models neglect the interception storagewhich can have a considerable effect on runoff volumeand erosion of soil due to raindrops in the watershedswhere vegetative cover is predominant.

Developments in Geographic Information System(GIS) techniques have enhanced the capabilities to han-dle large databases describing the heterogeneities in landsurface characteristics (Julien et al., 1995). Also, remotesensing (RS) techniques can be used to obtain spatialinformation in digital form on landuse and soil type atregular grid intervals with repetitive coverage. Together,the tools of RS and GIS have provided the means ofidentifying the physical factors that control the process ofpartitioning of rainfall into runoff and other components,hence, they are useful in distributed modelling. This hasbrought about a new trend in hydrological modellingwith the models becoming distributed in nature. Sev-eral distributed models are available in the literature andmany of these have been modified and recently combinedwith GIS during the past decade (Beasley et al., 1980;Palacious-Velez and Cuevas-Renaud, 1992; Srinivasanand Arnold, 1994; Wigmosta et al., 1994; Desconnetset al., 1996; Olivera and Maidment, 1999; Miller et al.,2002; Jain et al., 2004; Flanagan et al., 2007; Winchellet al., 2007; Reddy et al., 2008). Many of these modelsare multipurpose, requiring extensive data inputs whichneed to be calibrated, or are too complex for parame-terisation (Ramsankaran, 2010). These models have beenmainly developed for selected areas of the world with theaim to operate under specific conditions.

The above mentioned reasons compel researchers tofurther develop distributed models for attempting tominimize the mentioned limitations. Furthermore, mostmodel evaluation studies (Wang and Hjelmfelt, 1998;Saghafian et al., 2000; Jain et al., 2004; Du et al., 2007;

Reddy et al., 2008) still focus strongly on comparingobserved and predicted watershed response in terms ofsediment and water output at the watershed outlet. Onlya few studies (for example, the studies by Bathurst,1986; Ambroise et al., 1995; Bathurst et al., 1996, 2004;Anderton et al., 2002a,b; Figueiredo and Bathurst, 2002;Nunes et al., 2005) are available where a deliberateattempt has been made to compare spatial distribution ofpredictions from PBD models with spatially distributedobservations. However, most of such studies report modelvalidation using data at an internal gauge site only formicro watersheds, i.e. of the order of less than 1 km2and not for a relatively large watershed. At the sametime, as far as the authors are aware, especially for thewatersheds in the Indian sub-continent, no such study hasbeen reported so far in the scientific literature even at themicro watersheds level.

The present study, therefore, has been planned withthe objectives to develop a GIS-based one-dimensionalprocess-oriented distributed numerical model to simulaterunoff from small to large watersheds on a storm-eventbasis using a relatively fewer number of calibrationparameters, and to evaluate the developed model usingreal-world data at more than one location inside arelatively large semi-forested hilly watershed having anarea of about 38 km2.

MATHEMATICAL FORMULATION

In the present modelling effort it is assumed that duringstorm events in a watershed, a part of the rainfallis intercepted by the vegetal cover and subsequentlyevaporates. A part of the rainfall that reaches the groundsurface, after meeting the requirements of interceptionloss, infiltrates into the soil. The remaining part of therainfall which is not lost to infiltration is transformedinto surface runoff. Surface runoff has been divided intooverland flow and channel flow and is assumed to beone-dimensional in the present formulation. The modelstructure consists of two components: runoff generationcomponent and runoff routing component. The numericalsolutions for each computational element are performedin a GIS environment and have been coded in as amodular computer program using the FORTRAN 90programming language.

Runoff generation componentInterception storage estimation. As rain falls on a

vegetated surface, part of it is held on the foliageby surface tension forces. This portion of the rainfallevaporates directly (Rojas et al., 2003) and does nottake part in the formation of runoff. Accordingly, theinterception depth is subtracted from the rainfall beforeinfiltration is calculated. Here the interception loss ismodelled empirically without making an allowance forcanopy evaporation using the modified form of Merriam

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. (2011)

DISTRIBUTED HYDROLOGICAL MODELLING IN A LOWER HIMALAYAN WATERSHED

(1960) as follows:

Ic D cf.sc[

1 eRcumsc

]1

where Ic D cumulative interception depth [L]; cf Dvegetative canopy cover fraction (%); sc D maximuminterception storage capacity for a crop or vegetationcover [L]; Rcum D cumulative rainfall [L].

The interception loss (I) for every time step is calcu-lated as follows:

It D IctCt Ict 2

where t is time [T] and t is time step [T]. Theinterception rate from the interception loss is calculatedand is deducted from rainfall intensity (i) [L T1] to getthe effective rainfall intensity (ieff) [L T1], which is usedto calculate infiltration and subsequent runoff.

Infiltration simulation and estimation of rainfall excess.For the estimation of excess rainfall from total rainfall,the Smith and Parlange (1978) infiltration model is usedto compute the infiltration rate in an element. It is atwo-parameter infiltration model applicable to rainfallor ponded boundary conditions on a homogeneous soil,based on the physics of the soil-water movement. Theinfiltration capacity fc as a function of cumulativeinfiltrated depth (F) is given by the following relationship(Smith and Parlange, 1978):

fc D Ks eFBeFB 1

3

where fc D infiltration capacity [L T1], F D cumulativeinfiltration to time t [L]; Ks D saturated hydraulic con-ductivity [L T1] and B D GSmax Sini, the saturationdeficit of the soil [L], where G D net capillary drive [L]; D porosity of the soil []; Smax and Sini are the max-imum and initial values of relative saturation [D (watercontent/porosity)] [], respectively.

The net capillary drive parameter G (Smith and Par-lange, 1978) is given in terms of the conductivity (K)-soilmatric potential () relationship as follows:

G D 0

1

K

Ksd . 4

Since the infiltration rate f D dF/dt, integratingEquation (3) with respect to time t (Smith and Parlange,1978) gives

F D B(

1 eFB

)CKst. 5

For pulsed rainfall data, cumulative infiltration andinfiltration between times t and t (Smith and Parlange,

1978) may be written as

Ft Ct D FtC B(e

FtB e

FtCtB

)CKst 6

ft Ct D Ks eFtCtBe

FtCtB 1

. 7

The ponding time and cumulative infiltration at pond-ing (Smith and Parlange, 1978) are expressed as

tp D Bieff

ln(

ieffieff Ks

)ieff > Ks 8

Fp D iefftp. 9Equations (6) and (7) are solved to find the infiltration

and consequently excess rainfall if soil parameters B (i.e.G, ) and Ks, and rainfall pattern are known.

Runoff routing componentAssessment of flow dynamics involves the process of

routing the estimated rainfall excess, i.e. surface runoff.As mentioned, the one-dimensional depth-averagedunsteady flow equations (Saint Venant equations) with thekinematic wave (KW) approximation, were selected andused herein for the simulation of overland flow and chan-nel runoff flow. Henderson (1966) noted that kinematicwaves behave closely to observed natural flood waves insteep rivers (slopes >0002), a common scenario in mosthilly watersheds such as those used in the present studywhere slope generally does not fall below 0002. Manyresearches suggest that for most cases of hydrologicalsignificance, the KW solution provides reasonable results(Singh and Woolhiser, 2002).

Overland flow routing. The continuity and momentumequations for the KW approximation in one-dimensionalform are given as follows (Chow et al., 1988).

Continuity equation:

q

xC ht

D re 10

Momentum equation:

S0 D Sf 11

where q D discharge per unit width [L2 T1]; h D depthof flow [L]; t D time [T]; x D distance along the flowdirection [L]; re D rainfall excess intensity (re D ieff f)[L T1]; S0 D bed slope of the overland plane [] andSf D friction slope of the flow plane [].

At a larger scale, the overland flow can be viewed asa one-dimensional flow process in which flux is relatedto the unit area storage by a simple power relation asfollows (Chow et al., 1988):

q D h 12



where parameters and are related to slope, surfaceroughness and flow regime which can be derived using aresistance equation like that of Mannings and are givenas D pSf/no and D 5/3, where no D Manningsroughness coefficient for overland flow.

For the overland flow equation, Equation (12) may besubstituted into Equation (10) to obtain

ht C

qx D re

q D h}

) ht

C h

xD re. 13

Initial and boundary conditionsThe most commonly used initial condition for overland

flow is a dry surface and this is represented as

hx, 0 and qx, 0 D 0, for t D 0 14The upstream boundary condition for overland flow isassumed to be zero inflow. So

h0, t and q0, t D 0, for t 0 15The initial and boundary conditions (Equations (14) and(15)) imply that the hydraulic head at any point in thedomain is zero at the start of the simulation and it remainszero at the uppermost points of the computational domainfor the entire duration of the simulation.

Channel flow routing. Unsteady, free surface flow inchannels is also represented by the KW approximation ofthe equations of unsteady, gradually varied flow. Channelsegments may receive uniformly distributed but time-varying lateral inflow from overland flow elements oneither or both sides of the channel, from one or twochannels at the upstream boundary, or from an area atthe upstream boundary. The flow equations for a channelwith lateral inflow are

Continuity equation:

Q

xC At

D qx, t 16

Momentum equation:

Sc D Sfc 17

where A D flow cross-sectional area [L2]; Q D channeldischarge [L3 T1]; qx, t D net lateral inflow per unitlength of the channel [L2 T1]; Sc D bed slope of thechannel [] and Sfc D friction slope of the channel [].

The KW assumption is demonstrated in the relation-ship between channel discharge and flow cross-sectionalarea using a flow resistance equation such as Manningsequation (Reddy et al., 2008) as given below.

Q D R1A 18where D Sfc/nc; D 5/3, nc D channel flow Man-nings roughness coefficient and R D hydraulic radius

(A/P) [L]; where P D wetted perimeter [L]. By substi-tuting for , and R in Equation (18) gives

Q D (

1P

) 23 A 19

For the channel flow equation, Equation (19) may besubstituted into Equation (16) to obtain

Qx C

At D q

Q D (

1P

) 23 A ) At C

(1P

) 23 Ax

D q.

20

Initial and boundary conditionsFor channel flow, the initial condition is prescribed

keeping in mind the fact that stream flow in small tropicalwatersheds is mostly ephemeral with negligible or nobase flow and is represented as

Qx, 0, Ax, 0 and qx, 0 D 0, for t D 0 21The upper boundary condition is a specified discharge,

given as a function of time. i.e. the outflow from the unitwidth of upstream channels and/or overland planes.

Numerical simulationThe governing equations of the KW model developed

for overland flow and channelized flow are solved byemploying a weighted four-point implicit finite differencenumerical technique. The solutions obtained from theabove mentioned techniques are unconditionally stable.

The weighted four-point implicit finite differenceapproximations of the one-dimensional KW overland(Equation 13) and channel flow (Equation 20) equationsare given by Chow et al. (1988) as

For spatial derivatives:

h

xD

[hjC1iC1 hjC1i

xi

]C1

[hjiC1 hjixi

]22

A

xD

[AjC1iC1 AjC1i

xi

]C1

[AjiC1 Ajixi

]23

For temporal derivatives:

h

tD 1

2

[hjC1i hjitj

]C[hjC1iC1 hjiC1

tj

]24

A

tD 1

2

[AjC1i Ajitj

]C[AjC1iC1 AjiC1

tj

]25

The non-derivative terms such as re, and q are estimatedbetween adjacent time lines as

re D [rjC1ei C rjC1eiC1

2

]C 1

[rjei C rjeiC1

2

]



D rejC1i C 1 reji 26

q D [qjC1i C qjC1iC1

2

]C 1

[qji C qjiC1

2

]

D qjC1i C 1 qji 27where D a weighting parameter for the spatial deriva-tives at the advanced time step. A scheme using D 06is adopted in this modelling for which the solution isunconditionally linearly stable for any time step with afirst order accuracy (Fread, 1974). The variables re i andqi indicate the rainfall excess rate and lateral flow rateaveraged over the reach xi.

By substituting the approximations listed inEquations (22), (24) and (26) in Equation (13), the finitedifference form of the one-dimensional KW overlandflow equation is produced as given below:[

hjC1iC1 hjC1i C hjiC1 hji]

C 2tjxi

{

[(hjC1iC1

) (hjC1i )]

C1 [(hjiC1

) (hji )]}

tj[re

jC1i

C 1 reji] D 0 28

Similarly, by substituting the approximations listed inEquations (23), (25) and (27) in Equation (20), the finitedifference form of the one-dimensional KW channel flowequation is produced as given below:[

AjC1iC1 AjC1i C AjiC1 Aji]

C 2tjxi

(

1PjC1

)( 23

) [(AjC1iC1

) (AjC1i )]

C1 (

1Pj

)( 23

) [(AjiC1

) (Aji )]

tj[qjC1i C 1 qji

]D 0 29

The terms having superscript j in Equations (28) and(29) are known either from the initial conditions orfrom a solution of the KW equation for a previoustime line. The terms xi, tj, , need to be knownand must be specified independently of the solution.The unknown terms in Equations (28) and (29) are hjC1iC1and AjC1iC1 , respectively, which vary nonlinearly. Thesenonlinear equations are then solved for each time step byusing the NewtonRaphson method. The computationalprocedure for time jC 1 starts by assigning trial valuesfor the unknowns at that time. These trial values of hand Q can be the known values at time j from theinitial condition (if j D 1) or from calculations duringthe previous time step. This procedure continues until

the downstream-most discharge for the last time step iscomputed. Although unconditional stability is one of theadvantages of implicit schemes, to maintain accuracy theCourantFriedrichsLewy (CFL) criterion is specified inthe numerical solution algorithms.

DISCRETISATION OF WATERSHEDThe spatially distributed nature of watershed character-istics such as topography, soil, landuse and precipitationnecessitates the division of the watershed into smallerand relatively homogeneous units for the present mod-elling. The watershed discretisation involves breaking aheterogeneous and complex geometry into simple rela-tively homogeneous units while retaining the similitudewith the natural watershed. Several schemes for water-shed discretisation are in vogue at present. The choiceof the discretisation method is governed by many fac-tors including nature and type of input data, size of thewatershed, purpose of modelling, etc.

To represent a watershed, uniform/non-uniform grid-based approaches have been used extensively (Onstad andBowie, 1977; Beasley et al., 1980; Hadley et al., 1985;Gupta and Solomon, 1977; Vieira and Wu, 2002; Ren-schler, 2003; Jain et al., 2004; Reddy et al., 2008). Inthe present work, the discretisation using TOpographicPArameteriZation (TOPAZ) (Garbrecht and Martz, 1999)has been adopted, which is an automated digital land-scape analysis tool for drainage identification, watershedsegmentation and subcatchment parameterisation. Shapesof the overland planes derived using TOPAZ are eithersquare or rectangular depending on the length and widthof the plane. A detailed description of the algorithmsadopted in the TOPAZ tool is available in Garbrecht andMartz (1999); therefore, only a brief summary of the sig-nificant capabilities is presented for completeness.

The Digital Elevation Model (DEM) processing inTOPAZ is based on the D8 method, the downslope flowrouting concept, and the Critical Source Area (CSA)concept. The D8 method (Douglas, 1986; Fairfield andLeymarie, 1991) defines landscape properties for eachindividual raster cell by the evaluation of itself and its8 immediately adjacent cells. The downslope flow rout-ing concept defines the drainage and flow direction onthe landscape surface as the steepest downslope pathfrom the cell of interest to one of its 8 adjacent cells(Mark, 1984; OCallaghan and Mark, 1984; Morris andHeerdegen, 1988). The CSA concept defines the chan-nels draining the landscape as those raster cells thathave an upstream drainage area greater than a thresholddrainage area, called the critical source area. The CSAvalue defines a minimum drainage area below which apermanent channel is defined (Mark, 1984; Martz andGarbrecht, 1992). The CSA concept controls the water-shed segmentation and all resulting spatial and topologicdrainage network and subcatchment characteristics.

TOPAZ is designed to provide interrelated landscapeanalysis functions and to rely on an external, user-selected GIS for image display, as well as for additional



0

0.0005

0.001

0.0015

0.002

0.0025

0 42 84 126 168 210 252 294Time (min)

Dis

char

ge (m

2 /s)

AnalyticalNumerical

Figure 1. Comparison of analytical and numerical-based simulated hydro-graphs

data manipulation and raster algebra operations. Withinthis general framework, the digital elevation data isprocessed in TOPAZ by a system of interdependentcomputational programs.

MODEL VERIFICATION AND APPLICATION

The model concepts and the computer code were firstvalidated by comparing the hydrograph resulting fromthe analytical solution of the KW approximation forrunoff flow over a hypothetical watershed with that fromthe proposed model. For this purpose, a hypotheticalrectangular watershed having an area of 02 km2 with aflow plane of length 400 m at a uniform slope of 00005,a Mannings roughness value of 002 and steady rainfallexcess occurring at a rate of 198 mm h1 for 3 h 20 min,was considered as per Jaber and Mohtar (2003). The totalduration of the storm was taken as 5 h. A computationaltime step of 1 min was used for the simulation. Theresulting simulated hydrograph was found to be identicalto that from the analytical solution as shown in Figure 1,thus ensuring that the model formulation represents therouting process correctly and the developed computationcode is error free. However, it is to be noted that themodel code was not tested for cell-to-cell routing or thegeneration of overland flow from rainfall excess overinfiltration.

To test the predictive ability and performance of theproposed model, it has been applied for simulation offew storm events observed in the Pathri Rao watershedlocated in the Shivalik ranges of the Garhwal Himalayas,India.

Watershed descriptionThe experimental watershed selected for validating the

developed model is located about 17 km northeast ofRoorkee, Uttarakhand, India. It lies between the latitudesof 28550N and 30050N and longitudes of 78 and 78050.The catchment area of the watershed up to the gaugingstation at the watershed outlet is about 38 km2. Elevationof the watershed ranges between 272 and 730 m. The

lower tracts of the watershed area have flat slopes andare therefore, densely inhabited while the upland areasconsist of mostly hilly terrain having steep slopes. Theseare densely forested and form a part of Rajaji NationalPark which lies in the Shivalik foothills of the GarhwalHimalayas as depicted in Figure 2. In the lower part ofthe watershed a wheatmaize crop rotation is followed.The watershed receives an average annual rainfall of1300 mm with an average of 50 rain days, with morethan 90% of it occurring during the monsoon season, i.e.between June and September. High-intensity and short-duration storms are very common in the area. The meanminimum and maximum temperatures in the region are3 and 42 C, respectively. The mean relative humidityvaries from a minimum of 40% in April to a maximumof 85% in the month of July. The overall climate ofthe area can be classified as semi-arid to humid sub-tropical. The major soil groups found in the watershedare loam, sandy loam, loamy sand, coarse sandy loamand silt loam. The average soil depth ranges from 0 to100 cm. The river is of influent type which has flows onlyduring the storm events. The watershed has never beengauged before. For the purpose of the present study, fieldobservations on rainfall, runoff and sediment yield weremade during the monsoon storm events of the year 2005(Kothyari and Ramsankaran, 2010; Kothyari et al., 2010).In order to produce a comparison of the model outputsin a distributed manner, temporal variation of runoffdischarges have been measured both at the watershedoutlet as well as at the internal location shown in Figure 2(Ramsankaran et al., 2009).

Preparation of databaseThe proposed runoff model requires several parameters

which have been generated from various datasets throughthe use of documented procedures as briefly explainedbelow.

The watershed boundary was extracted from the digitalSurvey of India (SOI) topographical maps at a scale of1 : 50 000 having a contour interval of 20 m and storedwithin the GIS environment as a polygon map. Next, a50 m 50 m DEM (Figure 3) of the extracted watershedwas generated using contour interpolation techniquesavailable in ArcGIS software and, subsequently, a slopemap of the watershed was also generated. The value ofthe channel initiation threshold and CSA were determinedin such a manner that only the cells coinciding withthe prominent channels seen on topographic maps getassigned as the channel cells.

Using the derived DEM as an input to the TOPAZ, withcriteria of 50 ha CSA and 500 m minimum source chan-nel length, the watershed of Pathri Rao was discretizedinto 75 overland planes and 31 channels (Figure 4). Thenetwork of discretized watershed elements in the com-putational grid along with their order of hydrologicalsequencing is given in Table I.

The landuse/landcover map (Figure 5) for the simula-tion year was generated using remote sensing techniques



Figure 2. Location map of the Pathri Rao watershed

Figure 3. DEM of the Pathri Rao watershed Figure 4. Spatial discretisation of the Pathri Rao watershed



Table I. Discretized elements of the computational grid and their hydrological sequencing order for the Pathri Rao watershed

Sequence No. Stream No. Contributing elements

Overland planes Streams

Upland source ele. no. Right lateral ele. no. Left lateral ele. no. Top left Top right

1 284 281 282 283 Null Null2 234 231 232 233 Null Null3 224 221 222 223 Null Null4 184 181 182 183 Null Null5 164 161 162 163 Null Null6 104 101 102 103 Null Null7 74 71 Null Null Null Null8 54 51 52 53 Null Null9 84 Null 82 83 54 7410 114 Null 112 113 84 10411 154 Null 152 153 114 16412 44 41 42 43 Null Null13 24 21 22 Null Null Null14 34 Null 32 33 24 4415 144 Null 142 143 34 15416 174 Null 172 173 144 18417 194 191 192 193 Null Null18 214 Null 212 213 194 17419 64 61 62 63 Null Null20 14 11 12 13 Null Null21 124 Null 122 123 14 6422 94 91 92 93 Null Null23 134 Null 132 133 94 12424 204 Null 202 203 134 21425 244 Null 242 243 204 22426 254 Null 252 253 244 23427 264 261 262 263 Null Null28 274 Null 272 273 264 25429 294 Null 292 293 274 28430 304 301 302 303 Null Null31 314 Null 312 313 304 294

Figure 5. Landuse/landcover map of the Pathri Rao watershed

as described in Kothyari and Ramsankaran (2010) andKothyari et al. (2010). The accuracy of the prepared dig-ital landuse map is 84%. Then, based on the landusecategories the initial base values of parameters like no asper Engman (1986) and Vieux (2001), Sc as per Morganet al. (1998) and Cf from previously published look-up tables of Woolhiser et al. (1990) and Sunil Chandra(Forest Survey of India, personal communication) wereassigned to each class. On the basis of this, Sc and Cfvalues for this watershed vary in the range 02 mm and065%, respectively. The soil texture map (Figure 6) wasprepared based on the data supplied by the Indian Insti-tute of Remote Sensing (IIRS), Dehradun. Owing to adearth of field measurements, for each soil texture, theinitial base value of various infiltration parameters likeKs, G, were estimated based on the guidelines given inRawls and Brakensiek (1989) and Rawls et al. (1991). Itis to be mentioned that the mean values from the abovecited literature are chosen as the initial base value foreach mentioned parameter of the model.

With the discretized watershed elements map obtainedthrough TOPAZ analysis, the slope, soil texture and lan-duse maps were overlaid. Then by using the Zonal Statis-tics option in the Spatial Analyst module of ArcGIS



Figure 6. Soil texture map of the Pathri Rao watershed (source: IIRSDehradun)

software, the mean values of the mentioned inputparameters related to soil characteristics and landuse pat-terns were determined for each element of the compu-tational grid. The attribute table of the grid containingthe element number and mean values of the mentionedparameters was then exported as a database file to inputto the developed distributed rainfall-runoff model. Thechannel widths at different locations within the watershedwere determined by the empirical relationship based onthe watershed area and channel order proposed by Milleret al. (2003). They were then slightly revised as per fieldobservations and were approximated with side slope of1H:1V for all channels. Similarly, from the field observa-tions, and based on literature (Arcement and Schneider,1992), initial base values for channel roughness (nc) weredetermined. However, due to the inaccessibility of theupstream part of the watershed, a single roughness valueof 0035 is assigned for all the steeply sloping upstreamriver channels (those located in the forested area abovethe internal gauge station) that may contain gravel orboulder river beds, followed by a relatively smaller uni-form roughness value of 0025 for mild sloped down-stream channels. It is to be noted that the above initialnc values have been calibrated before attempting a fieldapplication of the model.

Hydro-meteorological data like rainfall intensity andhydrographs were obtained through the field measure-ments mentioned in the section on Watershed descrip-tion. In this study, we have used only those storm eventsfor which the full event data on runoff hydrograph (i.e.starting from beginning of the rainfall to end of the

Table II. Hydro-meteorological parameters of the selected stormevents

Date of thestorm event

Rainfall depth(mm)

Duration(h)

Initial soilmoisture indexa

26.06.05 (v) 3607 25 02003023.07.05 (c) 4034 25 05006004.08.05 (v) 3904 3 01504006.08.05 (c) 2487 15 07008010.09.05 (v) 1793 1 025050a A likely initial estimate based on antecedent daily rainfall records.

surface runoff) at the watershed outlet as well as theinternal gauge station were available. Another importanthydro-meteorological and soil condition-related piece ofinformation is the initial soil moisture status before thestart of a particular storm event. However, quantificationof the exact degree of initial soil moisture status is dif-ficult and no real-time observations on it are generallyavailable. Therefore, in the present study, likely rela-tive values of initial soil saturation (initial soil moistureindex) (Sini) at the beginning of each storm were deter-mined by analysing the daily rainfall records (antecedentrainfall patterns) prior to the simulated storm events asdescribed in Jain (2002) and Jain et al. (2004). Details ofthe hydro-meteorological parameters including the likelyestimate of Sini for those selected storm events are givenin Table II.

COMPUTATIONS, ANALYSIS AND DISCUSSIONOF RESULTS

Sensitivity analysisBefore attempting calibration and field application of

the developed model for the Pathri Rao watershed, it isconsidered essential to know the sensitivity of simula-tions to the model parameters related to soil texture andlanduse. Following Foglia et al. (2009) (who advocatethat it is advantageous to consider local sensitivity analy-sis in model evaluation, possibly as a preliminary step toprovide insights, such as identifying insensitive param-eters), Jain et al. (2004, 2005), Bathurst et al. (2004),Nunes et al. (2005), Rai and Mathur (2007), Al-Qurashiet al. (2008), Reddy et al. (2008), Bhardwaj and Kaushal(2009) and Naik et al. (2009), we have carried out alocal sensitivity analysis as a preliminary step to pro-vide insights. The sensitivity analysis was performed forthe parameters, viz. initial moisture index (Sini), saturatedhydraulic conductivity (Ks), capillary drive coefficient(G), soil porosity (), Mannings roughness coefficients(no and nc) and maximum interception storage capac-ity (Sc) to determine their level of influence on runoffhydrograph variables like runoff volume, peak flow andtime to peak flow. For this purpose, several model runswere made in a distributed manner (i.e. by consideringall the existing different soil and landuse types) usingthe 6 August 2005 storm event by varying one of theseparameters at a time and keeping the others fixed. Vari-ations of 10 and 20% from the initial base values



60.0

40.0

20.0

0.0

20.0

40.0

60.0

20 10 0 10 20

20 10 0 10 2020 10 0 10 20

20 10 0 10 20

Percent change in Sini

Perc

ent c

hang

e in

mo

del o

utpu

ts

Runoff volumePeak dischargeTime to peak discharge

Runoff volume

Peak dischargeTime to peak discharge


Runoff volume

Peak discharge

Time to peak discharge

80.060.040.020.0

0.020.040.060.0

Percent change in Ks

Perc

ent c

hang

e in

mo

del o

utpu

ts

15.0

10.0

5.0

0.0

5.0

10.0

15.0

Percent change in G

perc

ent c

hang

e in

mo

del o

utpu

ts

20.015.010.0

5.00.05.0

10.015.020.0

Percent change in h

Perc

ent c

hang

e in

mo

del o

utpu

ts

Sensitivity to capillary drive coefficient (G)

Sensitivity to initial soil moisture index (Sini) Sensitivity to saturated hydraulic conductivity (Ks)

Sensitivity to soil porosity (h)

(a) (b)

(c) (d)

Figure 7. Sensitivity of computed runoff hydrograph variables to soil infiltration parameters: (a) initial soil moisture content (Sini), (b) saturatedhydraulic conductivity (Ks), (c) capillary drive coefficient (G), and (d) soil porosity () for the 6 August 2005 storm event in the Pathri Rao

watershed

Sensitivity to Mannings roughness coefficient (no & nc) Sensitivity to maximum interception storage capacity (sc)

30.0

20.0

10.0

0.0

10.0

20.0

30.0

20 10 0 10 20

20 10 0 10 20

Percent change in no& ncPer

cent

cha

nge

in m

odel

out

puts


0.5

0.8

0.3

0.0

0.3

0.5

Percent change in scPerc

ent c

hang

e in

mod

el o

utpu

ts Runoff volumePeak discharge

(a) (b)

Figure 8. Sensitivity of computed runoff hydrograph variables to landuse parameters: (a) Mannings roughness coefficient (n), and (b) maximuminterception storage capacity (sc) for the 6 August 2005 storm in the Pathri Rao watershed

were used following Bhardwaj and Kaushal (2009). Theresults obtained in respect of all the tested parameters arediscussed in the following sections and are also shownin Figures 7(a)(d) and 8(a)(b). To assess the sensi-tivity, the level of sensitivity has been categorized asfollows: a high sensitivity refers to a percentage changein the hydrological output (O), exceeding the percent-age change of the model input variable, (I), while amoderate sensitivity implies O 1020% change,relatively low sensitivity refers O 510% change,trivial sensitivity refers O


Table III. Sensitivity of computed runoff hydrograph variables to initial soil moisture index (Sini)

Runoff model outputs Effect of change in model input parameter (Sini) Level of sensitivity to Sini20% 10% C10% C20%

Runoff volume 4894 1998 2057 3709 HighPeak discharge 4034 2308 2561 4952 HighTime to peak discharge 1938 875 250 1063 Moderate

Table IV. Sensitivity of computed runoff hydrograph variables to saturated hydraulic conductivity (Ks)

Runoff model outputs Effect of change in model input parameter (Ks) Level of sensitivity to Ks20% 10% C10% C20%

Runoff volume 3800 1918 2659 4517 HighPeak discharge 4780 2541 3316 5506 HighTime to peak discharge 313 188 938 1938 Moderate

Table V. Sensitivity of computed runoff hydrograph variables to net capillary drive (G)

Runoff model outputs Effect of change in model input parameter (G) Level of sensitivity to G20% 10% C10% C20%

Runoff volume 1021 506 522 1137 ModeratePeak discharge 1290 740 776 1243 ModerateTime to peak discharge 1250 063 625 813 Moderate

Table VI. Sensitivity of computed runoff hydrograph variables to soil porosity ()

Runoff model outputs Effect of change in model input parameter () Level of sensitivity to 20% 10% C10% C20%

Runoff volume 1082 567 609 1205 ModeratePeak discharge 1460 830 863 1395 ModerateTime to peak discharge 125 125 625 813 Less

change in Sini. The high sensitivity of the model outputslike runoff volume and peak flow to Sini shows the needfor its accurate monitoring in the watershed prior to theoccurrence of the storm to be simulated.

Sensitivity to saturated hydraulic conductivity (Ks).Sensitivity of runoff hydrograph variables to variationin Ks is given in Table IV and graphically shown inFigure 7(b). It is found that runoff volume and peakdischarge are highly sensitive and that the nature ofvariation (Figure 7(b)) is inversely proportional to Ks.Similarly, in the case of time to peak discharge, it ismoderately sensitive and directly proportional to Ks.Thus, it requires a careful calibration of Ks for derivingreliable results.

Sensitivity to net capillary drive (G). Sensitivity ofrunoff hydrograph variables to variation in G is shownin Table V and graphically represented in Figure 7(c),which shows a similar behaviour to Ks. However, theorder of magnitude of the change in outputs is noticed tobe less. It is observed that runoff volume, peak discharge

and time to peak discharge are moderately sensitive toG. The trends of variation of runoff volume and peakdischarge are inversely proportional to the variation inG, while time to peak discharge is directly proportionalto the variation in G. The magnitude of change inrunoff hydrograph variables with respect to change in Gsuggests careful calibration is needed for deriving reliableresults.

Sensitivity to soil porosity (). Sensitivity of runoffhydrograph variables to variation in is shown inTable VI and graphically represented in Figure 7(d).Table VI shows that runoff volume and peak dischargeare moderately sensitive and time to peak discharge iscomparatively less sensitive to the variations in . Thevariation in is inversely proportional to runoff volumeand peak discharge, while it is directly proportionalto time to peak discharge (Figure 7(d)). Though themagnitude of change in runoff hydrograph variables withrespect to change in is not so high compared with othersoil infiltration input parameters, it is still significant andshows the need for careful calibration.



Table VII. Sensitivity of computed runoff hydrograph variables to Mannings overland and channel bed roughness parameters (noand nc)

Runoff model outputs Effect of change in model input parameter (no & nc) Level of sensitivity to (no & nc)20% 10% C10% C20%

Runoff volume 938 367 588 968 LessPeak discharge 2564 1130 1330 2381 HighTime to peak discharge 1375 313 1063 2250 High

Table VIII. Sensitivity of computed runoff hydrograph variables to maximum interception storage capacity (sc)

Runoff model outputs Effect of change in model input parameter (sc) Level of sensitivity to sc20% 10% C10% C20%

Runoff volume 013 011 031 066 TrivialPeak discharge 029 001 027 059 TrivialTime to peak discharge 000 000 000 000 Insensitive

Sensitivity to overland and channel bed Manningsroughness parameters (no and nc). Landuse-related over-land and channel bed roughness parameters which signifythe smoothness of the land surface that affects the flowbehaviour were studied for their combined effect on therunoff hydrograph variables. This was done by varyingthe initial base values of no and nc by 20%. The initialbase values of no and nc were taken based on the detailsgiven in the section on Preparation of database. Theeffect of variation in no and nc (Figure 8(a)) indicatesthat the runoff volume is relatively less sensitive, whilepeak discharge and time to peak discharge are highly sen-sitive (Table VII). As expected, the runoff volume andpeak discharge are inversely proportional to variations inno and nc (Figure 8(a)), while time to peak discharge isdirectly proportional to variations in no and nc. For exam-ple, with increasing no and nc up to 20% from their initialbase values, there is about 23% decrease in peak flowrate, which is attributed to the fact that increased rough-ness reduces flow velocity and, hence, the flow rate. It isalso observed that an increase in no and nc increases thetime base of the runoff hydrograph and causes only a rel-atively small change in the volume of runoff, indicatingit to be less sensitive to variations in no and nc values.

Sensitivity to maximum interception storage capacity(sc). Sensitivity of the model outputs like runoff volumeand peak discharge to the variations in sc is found tobe trivial as the model outputs vary by less than 1%(Table VIII). In the case of time to peak discharge, it isinsensitive to the variation in sc, even while altering scup to 20%, and hence, is not shown in the graph. Thevariation in sc is inversely proportional to runoff volumeand peak discharge (Figure 8(b)).

On the basis of the above analysis, it is thus concludedthat the model outputs related to runoff hydrographvariables are relatively more sensitive to changes in thevalues of Sini and Ks, followed by G, , no and nc. Themodel outputs on runoff are also sensitive to sc although

to a lesser degree. Similar trends were also noticed fordata of all other simulated storm events in the studywatershed. Therefore, it can be said that the above modelparameter values except sc need to be carefully estimatedto minimize the model prediction errors.

Model calibrationCalibration of the proposed model was performed

based on systematic minimisation of the differencebetween actual and simulated outflow hydrographs at thewatershed outlet using the Ordered-Physics-based Param-eter Adjustment (OPPA) method (Vieux and Moreda,2003). The results of the model sensitivity analysis car-ried out in the previous section were taken into accountwhile selecting/estimating the input parameter values forcalibration of the model. Since we derive parameters fromGIS maps related to soils and landuse, it is usual to adjustthe parameter map values for purposes of calibration.Adjusting those spatially distributed parameter magni-tudes is done using multipliers as described in Vieux(2001) while preserving their spatial pattern. By meansof this approach, it is intended to reduce the differencesbetween observed and simulated hydrographs by simplyadjusting multipliers of the input parameters. Also, it hasbeen ensured that the input parameter values lie within thephysically realistic ranges specified by Rawls and Brak-ensiek (1989) for each soil type, and by Woolhiser et al.(1990), Morgan et al. (1998), Engman (1986) and Vieux(2001) for each landuse pattern.

Of the 5 storms observed during the monsoon seasonof 2005, only 2 storms were used for calibration of themodel. The storms which occurred on 26 June 2005 and6 August 2005 were arbitrarily selected and also ensuredthat they cover the whole monsoon season and representhigh-intensity short-duration storms which are commonin this area.

As quantification of the exact degree of initial soilmoisture status is difficult and no real-time observa-tions on it are available, in the present study, Sini has



Table IX. Calibrated optimum values of initial soil moistureindex (Sini)

Date of the storm event Sini

26.06.05 02523.07.05 05604.08.05 03506.08.05 08010.09.05 050

been treated as an event-dependent calibration param-eter satisfying the condition of equality of the volumeof the computed and observed runoff values during theselected storm events. Such an assumption is commonin isolated storm events-based modelling (Julien et al.,1995; Wang and Hjelmfelt, 1998; Folly et al., 1999; Mol-nar and Julien, 2000; Jain et al., 2004). The calibratedvalues of Sini for each storm event are given in Table IX.It can be noted that the calibrated values fall within therange of likely initial estimates (Table II), which justi-fies the method adopted for estimating Sini in the absenceof field measurements. However, if exact values of Siniare available it would be possible to use the proposedmodel without treating Sini as a calibration parameter,which would eventually allow the model to be used in apredictive way.

For matching the volume of observed and computedrunoff, the other parameters Ks, G and related to soilwere also varied but within the range of values specifiedby Rawls and Brakensiek (1989). The hydrograph shapeand time to peak were matched through variation of the

Table X. Calibrated optimum values of soil related infiltrationparameters for the Pathri Rao watershed

Soil texturalclass

Ks(mm/h)

Capillarydrive G (mm)

Porosity

Silt loam 245 609 0501Loam 468 324 0463Sandy loam 936 381 0453Coarse Sandy Loam 936 381 0453Loamy sand 2196 189 0437

Mannings parameters no and nc. Through several trialsusing the OPPA method, both events were optimizedtogether using a common set of optimum parametervalues of Ks, G, , no and nc for the study watershed.The calibrated optimum values of the soil texture-relatedmodel infiltration parameters for the two calibration stormevents are listed in Table X. Similarly, the calibratedoptimum values of landuse parameters like no and ncincluding the values of non-calibration parameters Scand Cf are listed in Table XI. Basing on calibration, thevalue of nc D 003 has been assigned to the channelsin the upstream forested zone and a value of 0025has been assigned to the downstream channels. Themodel output in the form of runoff hydrographs wasobtained and analysed for the two storm events used inthe calibration. For graphical comparison, the computedhydrographs for these storm events are plotted alongwith the corresponding observed hydrographs. Theseplots (Figure 9(a) and (b)) indicate that the proposedmodel generally well simulated the overall shape ofthe hydrographs. In addition, some statistical parameterssuggested by Janssen and Heuberger (1995) and Krauseet al. (2005) were also worked out to determine thecalibration accuracy and are summarized in Table XII.

For the 2 storms used for calibration of the model,percentage errors (PE) in prediction of runoff volume(Vstorm), peak discharge (Qp) and time to peak dis-charge (Tpeak) are noticed to range between 1605 andC2109%. The averaged absolute errors (AAE) in pre-dicting Vstorm, Qp and Tpeak are 1857, 1217 and 1111%,respectively. The values of the coefficient of determi-nation (R2) for the 23 July 2005, and 6 August 2005storm events are 097 and 096, respectively, while itsweighted form wR2 is 086 and 078, respectively. TheNashSutcliffe efficiency (NSEF) is 9526 and 8596%,respectively, for each calibrated storm event. Likewise,the Alternate Index of Agreement (AIoA) which over-comes the insensitivity of NSEF and R2 is found tobe 092 and 086 for the 2 calibrated storm events, indi-cating better agreement between the model simulationsand observations. The root mean square error (RMSE), awell accepted absolute error goodness-of-fit indicator that

Table XI. Calibrated optimum values of landuse related model parameters for the Pathri Rao watershed

Landuse category Mannings roughnesscoefficients, n0 and nc

Max. interception storagecapacity, Sc (mm)a

Canopy cover fraction,Cf (%)a

Dense scrubs 004 15 025River 0025/003nc Dry deciduous forests 011 0575 05Mango plantation 003 14 07Wastelands without scrubs 003 0 0Wastelands with scrubs 003 02 025Forest plantations 003 14 07Double crop lands 003 2 075Forest blank 003 02 025Fallow lands 003 0 0Habitations 001 005 015a Non-calibration parameter.



Event: 23 July, 2005

05

101520253035404550

0 210 315 420 525 630 735Time (min)

Dis

char

ge (m

3 /sec

)

05

101520253035404550

Dis

char

ge (m

3 /sec

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

RainfallComputed runoffObserved runoff

Event: 6 August, 2005

RainfallComputed runoff Observed runoff

(a) (b)

105 0 210 315 420 525 630 735Time (min)

105

Figure 9. Computed and observed runoff hydrographs of the calibration storms: (a) 23 July 2005, and (b) 6 August 2005

Table XII. Summary of parametric statistics results for the calibration storms at the watershed outlet (Vstorm - Volume of storm; Qp- peak flow; Tpeak - Time to peak flow)

Date of storm Percentage error in prediction R2 wR2 NSEF (%) AIoA RMSEevents

Vstorm Qp Tpeak

23.07.05 1605 470 C1111 097 088 9526 092 00806.08.05 C2109 C1965 1111 096 076 8596 086 007

Table XIII. Summary of parametric statistics results for the validation storms at the watershed outlet. (Vstorm - Volume of storm; Qp- peak flow; Tpeak - Time to peak flow)

Date of storm Percentage error in prediction R2 wR2 NS-EF (%) AIoA RMSEevents

Vstorm Qp Tpeak

26.06.05 2058 1294 C588 086 073 7904 084 00404.08.05 1926 1003 C833 098 085 9196 086 00710.09.05 2076 1224 00 097 089 9183 086 002

describe differences in observed and simulated values inthe appropriate units was also calculated and is found tobe 008 and 007, respectively, for each calibrated stormevent.

These various statistical results indicate that the simu-lated hydrographs are not significantly different from theobserved hydrographs, and model predictions are reason-ably accurate, and the errors of prediction are also wellwithin the limits proposed by Wang et al. (2006) andLove and Donigian (2002) for such studies.

Model validationThe calibrated model was applied to the remaining

3 selected storm events observed during the monsoonseason of the year 2005 (Table II). The results and thestatistical evaluation of the model validity with respectto the observation made at watershed outlet for the val-idation storm events are summarized in Table XIII. Forillustration purpose, the observed and simulated runoffhydrographs are shown in Figure 10(a)(c). The discus-sions of results with respect to each parameter of thehydrographs simulated by the model are presented below.

Volume of runoff (Vstorm). The model slightly under-computes the volume of runoff for all the storm events

used for validation. The value of PE ranges from 2076to 1926% (Table XIII). The AAE is 202% for all thosestorm events. The under estimation of volume of runoffmay be due to the difficulty in establishing the initialsoil saturation which may spatially vary significantlyover the entire watershed. Nevertheless the differences insimulated and observed flow volumes are not consideredto be significant given the cartographic and measurementerrors that are endemic in such analysis (Love andDonigian, 2002).

Peak flow (Qp). The model simulated the peak flowfor all the storms reasonably well, with PE value rang-ing from 1003 to 1294% (Table XIII) which alsoindicates that the model under-predicts the Qp for all the3 validation storm events considered in this study. TheAAE for those storm events is 1174%. The overall modelaccuracy is, however, good (Love and Donigian, 2002)for the peak discharge as well.

Time to peak flow (Tpeak ). The error in predicting thetime to peak flow for the 3 validation storm events rangefrom 0 to 20 min which is not considered as significantgiven the much larger time bases of the individualhydrograph. The PE value lies between 0 and C833%(Table XIII) and the AAE is 473% for all the validation



Event: 26 June, 2005



Rainfall

Computed runoff

Observed runoff

05

101520253035404550

Dis

char

ge (m

3 /sec

)

(a)

0 210 315 420 525 630 735Time (min)

105 0 210 315 420 525 630 735Time (min)

10505

101520253035404550

Dis

char

ge (m

3 /sec

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

Event: 10 September, 2005

Rainfall rate

Computed runoffObserved runoff

05

101520253035404550

Dis

char

ge (m

3 /sec

)

(c)

0 210 315 420 525 630 735Time (min)

105

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

(b)

Figure 10. Comparison of computed and observed runoff hydrographs of the validation storms: (a) 26 June 2005, (b) 4 August 2005, and (c) 10September 2005

storm events. The time to peak flow prediction for thestorm event of 10 September 2005 is excellent having PEequal to 0%. Hence, the level of agreement in predictingthe time to peak flow is termed very good as per Loveand Donigian (2002).

For all the validation storm events, the values of R2range between 086 and 098, the wR2 between 073and 089, NSEF between 7904 and 9196%, AIoAbetween 084 and 086 and RMSE between 002 and007 (Table XIII). It may also be noted that the statisticalresults obtained as above satisfy the criteria proposed byChung et al. (1999, 2002) and Wang et al. (2006) forassessing the performance of a hydrological model. Thisindicates the good performance of the proposed modelfor the simulated storm events.

Likewise, through visual inspection of the simulatedand observed hydrographs shown in Figure 10(a)(c),one can see that the model has generally simulated theoverall shape of the hydrographs well for all the threevalidated storm events. Keeping in view the complexnature of the runoff process, the relatively long narrowshape of the watershed and the large variability in thevalues of model parameters in the actual system, theresults presented above indicate the models performanceand efficiency in general to be good in the Pathri Raowatershed for the simulated storm events.

Model evaluation using internal gauge dataSeveral authors like Dunne (1983), Grayson et al.

(1992), OConnell and Todini (1996) have suggested that

an effective method for reducing uncertainty in parameteridentification in PBD models might be through their eval-uation against a number of responses representing differ-ent aspects of hydrological functioning of the watershed.This would allow rejection of those parameterisationsfor which the correct outlet discharge is being erro-neously simulated as a result of internal compensatingerrors. The explicit representation of internal processesand the distributed structure of PBD models make themparticularly amenable to such internal evaluation. Anumber of examples of the use of multi-response eval-uation of semi-distributed or fully distributed modelshave appeared in the literature (for example, Ambroiseet al., 1995; Franks et al., 1998; Vertessy and Elsenbeer,1999; Bathurst et al., 2004; Nunes et al., 2005) to demon-strate that the uncertainty in parameter estimates could bereduced substantially.

In this article too, such an evaluation of the developedmodel against a number of responses representing dif-ferent aspects of hydrological functioning (like volumeof runoff, peak discharge, time to peak discharge) of thewatershed is presented for the simulated storm eventsboth at the outlet as well as at an internal gauge sta-tion. Details of the evaluation of the internal responseare discussed briefly below.

To verify the model outputs and their predictabilityat locations within the watershed, we used the hydro-graphs observed at the internal gauging station shownin Figure 2. Results and the statistical evaluation of themodel outputs at the internal gauging station are listed in



05

101520253035404550

Dis

char

ge (m

3 /sec

)(a)

05

1015

2025

30354045

50

Dis

char

ge (m

3 /sec

)

(c)

05

101520253035404550

Dis

char

ge (m

3 /sec

)

(b)

05

101520253035404550

Dis

char

ge (m

3 /sec

)

(d)

0

5

10

15

20

25

30

35

40

45

50

Dis

char

ge (m

3 /sec

)

(e)

0 210 315 420 525Time (min)

105 0 195 300 405 510 615Time (min)

105

0 195 300 405 510Time (min)

105

0 195 300 405 510Time (min)

105

0 195 300 405 510Time (min)

105

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

05

1015

2025

30354045

50

Rai

nfal

l rat

e (m

m/hr

)

0

5

10

15

20

25

30

35

40

45

50

Rai

nfal

l rat

e (m

m/hr

)

05101520253035404550

Rai

nfal

l rat

e (m

m/hr

)

Event: 26 June, 2005 Event: 23 July, 2005


Event: 10 September, 2005







Figure 11. Comparison of computed and observed runoff hydrographs of the simulated storms at the internal gauge station: (a) 26 June 2005, (b) 23July 2005 (c) 4 August 2005, (d) 6 August 2005, and (e) 10 September 2005

Table XIV and are illustrated in Figure 11(a)(e). Thestatistical results shows that the volume of runoff, peakflow and time to peak flow computed from the modelcompare reasonably well with the corresponding obser-vations for all the simulated events and these lie within20% error bands for most of the simulated storm events.Likewise, visual inspection of the hydrographs shown inFigure 11 indicates that the proposed model generallysimulates well the overall shape of hydrographs at theinternal gauging station as well. At this point, it is to bementioned that the model parameters values were not cal-ibrated against observations at the internal gauge stationfor producing results related to internal gauge site. Hence,somehow, it can be said that this study also demonstrates

a kind of blind validation (Bathurst et al., 2004) of theinternal responses in the study watershed.

From the hydrographs shown in Figures 9, 10 and 11one can observe that there seems to be some variationin the ratio of the measured peak discharges for the twogauging stations. For example, for the 23 July 2005 event,the outlet discharge (Figure 9(a)) is rather higher thanthe discharge at the internal station (Figure 11(b)), whilefor the 6 August 2005 event, the discharge is higherat the internal station (Figure 11(d)) than at the outlet(Figure 9(b)). The interesting fact is that the model seemsto represent these variations in the ratio of the measuredpeak discharges for the two stations quite well. All theabove validations highlight the excellent performance



Table XIV. Summary of parametric statistics results for the simulated storms at the internal gauging station. (Vstorm - Volume ofstorm; Qp - peak flow; Tpeak - Time to peak flow)

Date of storm Percentage error in prediction R2 wR2 NS-EF (%) AIoA RMSEevents

Vstorm Qp Tpeak

26.06.05 208 C902 769 093 078 8990 090 00423.07.05 782 C1878 C312 081 073 6298 079 01404.08.05 1906 C437 400 086 085 7602 081 01406.08.05 C942 1582 869 077 063 7243 079 01510.09.05 C1418 C2958 1600 074 068 5824 078 008

of the model in computing the distributed variation ofsurface runoff hydrographs within the watershed.

The satisfactory results obtained both at the outletas well as at the internal gauge station indicate thatthe calibrated parameter values can certainly be used tosimulate outlet discharges without inducing any internalcompensating errors. Hence, it can be said that thismethod of evaluation at different locations against thewatershed responses representing different aspects ofhydrological functioning of the watershed can aid inreducing the uncertainty in parameterisation, which inturn would reduce the uncertainties in simulations. Thismanner of evaluation is also a method of testing thedistributed hydrological models. Also, it is noteworthyto mention here that, as far as the authors are aware, thistype of validation of a PBD hydrological model both atwatershed outlet as well as at an internal gauging stationfor such a medium-sized watershed makes this study afirst of its kind in Indian watersheds.

Physical interpretation of the model parametersA qualitative study was made to assess the variation of

the model parameters within the watershed with regard tosoil type, landuse, slope, etc. The infiltration parametersKs, G and which were optimized for the two calibrationstorm events are found to remain constant for all thevalidation storm events and are found to vary onlywith the soil type of the computational elements of thewatershed as listed in Table X. The above soil parametershave been obtained as per the procedure of Rawls andBrakensiek (1989) and Rawls et al. (1991) and thencalibrated for use in modelling. It may be noted thatthe values of Ks, G and obtained through calibrationof the two storm events are constrained to vary withinthe range specified by Rawls and Brakensiek (1989) andRawls et al. (1991) for all the simulated storm events.

Variation of the parameters no and nc related to over-land and channel flow resistance are given in Table XIalong with the corresponding landuse. A close assessmentreveals that large values of no are found to be associatedwith overland areas having high vegetative cover likedry deciduous forest and dense scrubs. At the same time,a small uniform value of no D 003 is associated withlanduse like mango plantations, wastelands with/withoutscrubs, forest plantations, double crops, fallow lands, etc.wherein the topography is very mild. It can be notedthat during the field visits made between June 2005 and

September 2005, it was observed that in general, thesoil surface at the lower tracts of the watershed weresmooth. Therefore, it is reasonable to have low valuesof no for the above mentioned landuse classes. Also, itis to be noted that during the simulation period, most ofthe vegetations in the cropped lands were at their initialstages of growth. Because of this, lesser amounts of cropresidue were present on the soil surface, resulting in a rel-atively low value of no for that landuse class. A similarclose inspection of channel roughness parameter revealsthat large values of nc are found to be associated withsteeply sloping upstream channels in the forested areathat may contain gravel, or boulder river beds followedby a small uniform value of nc D 0025 for mild slopeddownstream channels. On the basis of the above facts, onecan say that these parameters values are in conformitywith physical conditions and are on the expected lines.While detailed measurement of hydraulic roughness overany large spatial extent is impractical, reclassifying a GISmap of landuse/landcover into a map of hydraulic rough-ness parameters is proved to be attractive for spatiallyrepresenting the location of hydraulically rough versussmooth landuse types.

Presentation of spatially distributed resultsEstimates of the spatial and temporal distribution of

model outputs such as velocity and flow rate are neededfor effective planning of a watershed development. Use ofGIS and the distributed nature of the present model allowthe generation and presentation of such information forall the model elements. For illustrating such capabilityof the model, the spatial and temporal distributions ofsurface runoff (mm/h) for the storm event that occurredon 10 September 2005, were generated and are presentedhere.

Model results used for generation of spatial distributionof surface runoff were retrieved at each time step from thebeginning of the storm event. For illustration purposes,maps are generated depicting the surface runoff (mm/h),respectively, at times of 30, 45, 60, 90 and 210 minfrom the commencement of the storm event and theseare shown in Figure 12(a)(f).

Figure 12(b) portrays the model-computed surfacerunoff (mm/h) at time equal to 30 min. It is evidentfrom the figure that practically no surface runoff has beengenerated from the commencement of storm event untilt D 30 min. The partially dry initial moisture condition



(a)

(c) (d)

(e) (f)

(b)

Figure 12. Spatial distribution of computed discharge during the 10 September 2005 storm event in the Pathri Rao watershed

(Sini D 05) prevailed (as per calibration) just prior to thestorm event, and a higher saturated conductivity of theexisting soils would have resulted in infiltration of mostof the rain they received during the given duration, andthe computed result, therefore, is understandable.

Figure 12(c) depicts the spatially distributed computedsurface runoff at time equal to 45 min. The hyetograph(Figure 12(a)) shows that during this period the water-shed receives rainfall at an intensity of 239 mm/h. Ascan be seen from Figure 12(c) such rainfall has resultedin a thin sheet of flow over almost the entire watershed.Also, it can be noted that flow in the channels is not

yet prominent except in some upstream channels whichreceives flow from smaller and steeper overland flowplanes that have shorter travel times for the flow to reachthose channels.

Figure 12(d) depicts the spatial distribution of com-puted surface runoff at time equal to 60 min. The rainfalloccurring during this time interval resulted in genera-tion of some overland flow across the whole watershed.Comparison of Figure 12(c) and Figure 12(d) indicatesthat the generated overland flow starts to become con-centrated, resulting in generation of channel flow atthe upstream locations. Figure 12(d) clearly portrays the



relative amount of overland flow between the elementswith higher and moderate saturated hydraulic conductiv-ity. Similarly, by comparing Figure 6 with Figure 12(d)it is found that the elements with loamy soil have gener-ated a slightly higher amount of overland flow than theelements having sandy loam, which is understandable.

The flow condition at time equal to 90 min is depictedin Figure 12(e). This figure clearly depicts the drainingprocess within the watershed after the end of rainfall.It indicates that most of the generated overland flowshave drained into channels and only the channel flow isoccurring over the entire watershed at this time except atsome portions in the downstream part of the watershed.This appears to be realistic since by this time the rainfallhas completely stopped and, hence, no further runoffgeneration would take place over the overland flowplanes. The presence of milder slopes in the overlandflow planes in the downstream part of the watershedmay be the reason for the overland flow still beingpresent at downstream locations. By visual comparison ofFigure 12(d) with Figure 12(e) one can clearly visualizethe downstream movement of flow.

The flow condition at time equal to 210 min is depictedin Figure 12(f). The comparison of Figure 12(e) andFigure 12(f) also clarifies the downstream propagationof the surface runoff. The corresponding computed andobserved runoff hydrographs at the watershed outletreveal that the surface runoff flow has attained its peakat 210 min since the beginning of the storm event. Itis also evident from Figure 12(f) that at time equal to210 min, the rate of flow has increased in the channelsnearer to the watershed outlet. By this time, in the restof the watershed, the draining of flow from the overlandplanes seems to be reduced significantly. This result isalso considered to be realistic.

After time equal to 210 min, still the draining processof the watershed continues beyond time equal to 735 min,as indicated by the base time of the runoff hydrographshown in Figure 12(a). Owing to non-availability ofobservations on spatial and temporal distribution ofrunoff for the whole watershed, the spatial outputscould not be evaluated in detail. However, with theobservation made at the internal gauge station (Figure 2),a quantitative assessment of model results at this locationhas been made and the results are listed in Table XIV,which seems satisfactory.

Also, a critical examination of Figure 12(b)(f) ismade in the flow pattern at the watershed outlet. Temporalvariation of flow accumulation (surface runoff) at thewatershed outlet is shown in Figure 12(a). In this figure,a small hike in the rising limb of the computed as wellas the observed hydrographs indicates that only flowfrom the areas surrounding the watershed outlet arrivesfirst. Flow from the upland areas does not reach theoutlet before the end of the rainfall, causing a dip inthe rising limb. However, the hydrograph limb starts torise immediately after the end of the rainfall because, bythis time, the channel flow from the upland areas hasreached the watershed outlet. For this particular event,

the above facts could be the most possible reasons forhaving two peaks in the computed and the observedhydrographs at the watershed outlet, although it is asingle peaked hydrograph at the internal gauging station.This interpretation of flow pattern accumulation at theoutlet of Pathri Rao watershed matches well with theknown process of storm runoff generation and watersheddraining characteristics as illustrated in Figure 12(b)(f).It may be mentioned here that this would hold true foranother similar event which occurred on 26 June 2005,which also has two peaks in the computed hydrograph atthe watershed outlet. However, the measured hydrographfor this event does not show two peaks. One possiblereason for this can be attributed to the measurementerrors, which is very likely in any field hydrologicalmeasurement. The analysis of results thus reveals thatthe model has simulated the physics of the rainfall-runoffprocess reasonably well for the Pathri Rao watershed.

SUMMARY AND CONCLUSIONS

In this article, a GIS-based distributed rainfall-runoffmodel capable of handling watershed heterogeneity interms of distributed information on topography, landuseand soil is presented. The developed model is event-based (i.e. it does not allow for continuous simulationsover a long period) and does not allow for runoffgeneration by upward saturation of the ground, whichlimits its application in the areas having saturation excessrunoff generation mechanism. The developed model wasfirst verified by comparing the model results with ananalytical solution for its correctness in coding. Beforefield application of the model in the study watershed,sensitivity analysis was performed. Sensitivity analysis ofthe model demonstrated that the Sini and Ks are the mostsensitive parameters, followed by G and in determiningrunoff volume and peak flow rate. It is also found that thetime to peak flow is moderately sensitive to Sini, Ks, Gand relatively less sensitive to . Likewise, the results arefound to be highly sensitive to the Mannings roughnesscoefficients no and nc for peak flow rate and the time topeak flow. Among the tested parameters Sc is found tohave the least effect on runoff volume and peak flow rateand no effect at all on time to peak flow.

It is significant to mention here that all the input param-eters of the model possess physical meaning, i.e. all theparameters can be measured in the field. In the case whereno measurements on soil and landuse input parametersare available (like in the present study) the correspondingvalues shall be obtained from various scientific literatureand should be calibrated for use in modelling, as demon-strated in this study. The calibrated form of the developedmodel was then applied for a few storm events thatoccurred in the Pathri Rao watershed, India. The resultsdemonstrate that the model predicts the physical pro-cesses adequately and realistically for the simulated stormevents that occurred in the Pathri Rao watershed locatedin the Shivalik ranges of the Garhwal Himalayas, India.



The qualitative evaluation of spatially and temporallydistributed model outputs as illustrated using GIS provedto be effective in analysing the physics of the rainfall-runoff process in detail. Such illustration of spatial andtemporal distribution of model outputs has also proved tobe very useful in understanding the draining characteris-tics of the whole watershed. Also, it is worth mentioninghere, that to the best of our knowledge this is the firsttime that any distributed hydrological model is evaluatedboth at watershed outlet as well as at an internal gaug-ing station for such a medium-sized Indian watershed. Insome way, it can be said that this study demonstrates asort of blind validation for the internal responses of thestudy watershed, i.e. the proposed model has not been cal-ibrated against the measured values at the internal gaugestation before performing the validation. However, it hasbeen calibrated for the outlet response. In conclusion,it can also be stated that the information obtained viathe spatially distributed output maps can serve as a firstestimate about the existing hydrological characteristicswithin the watershed, which can subsequently be usedfor planning watershed management activities.

Considering the complex nature of the runoff processand the inbuilt errors in the numerous hydrologic interre-lationships used in the simulation of runoff under naturalconditions, the deviation of 21% may not be consid-ered high. One of the limitations of this study is thatowing to the dearth of measurement of soil and lan-duse input parameters, we could not ascertain whether thefield measured soil and landuse input parameters supportgood simulations or not without any calibration. Like-wise, though the model has the capability to be used in apredictive way, we could not demonstrate it due to lackof real-time observations on initial soil moisture status.Hence, one can say that the developed model stands val-idated yet under simplified conditions. It is encouragingto be able to say that this study did indicate that thedeveloped model can work under certain conditions inthe Pathri Rao watershed. Many more validation studiesneed to be carried out for many sites under various sce-narios to establish the model performance trends and itsconsistency.

ACKNOWLEDGEMENTS

The first author wishes to thank the All India Council forTechnical Education (AICTE), New Delhi, and DeutscherAkademischer Austausch Dienst (German AcademicExchange Service, DAAD), Bonn, for providing finan-cial aid through National Doctoral Fellowship (NDF) andthrough DAAD sandwich model scheme, respectively, tocarry out this work reported herein. The authors are alsoindebted to two anonymous peer reviewers for the qualityand exhaustivity of their recommendations.

REFERENCES

Abbott MB, Bathurst JC, Cunge JA, OConnell PE, Rasmussen J. 1986a.An introduction to the European Hydrological SystemSyste`me

Hydrologique Europeen, SHE, 1: history and philosophy of aphysically-based, distributed modelling system. Journal of Hydrology87: 4559.

Abbott MB, Bathurst JC, Cunge JA, OConnell PE, Rasmussen J. 1986b.An introduction to the European Hydrological SystemSyste`meHydrologique Europeen, SHE, 2: structure of a physically-based,distributed modelling system. Journal of Hydrology 87: 6177.

Al-Qurashi A, McIntyre N, Wheather H, Unkirch C. 2008. Applica-tion of the Kineros2 rainfall-runoff model to an arid catch-ment in Oman. Journal of Hydrology 355: 91105. DOI:10.1016/j.hydrol.2008.03.022.

Ambroise B, Perrin JL, Reutenauer D. 1995. Multicriterion validation ofa semidistributed conceptual model of the water cycle in the Fechtcatchment (Vosges Massif, France). Water Resources Research 31:14671481.

Anderton S, Latron J, Gallart F. 2002a. Sensitivity analysis and multi-response, multi-criteria evaluation of a physically based distributedmodel. Hydrological Processes 16: 333353.

Anderton SP, Latron J, White SM, Llorens P, Gallart F, Salvany C,OConnell PE. 2002b. Internal evaluation of a physically-baseddistributed model using data from a Mediterranean mountaincatchment. Hydrology and Earth System Sciences 6: 6783.

Arcement Jr, GJ, Schneider VR. 1992. Guide for Selecting ManningsRoughness Coefficients for Natural Channels and Flood Plains . USGSWater Supply Paper, vol. 2339, 38.

Arnold JG, Srinivasan R, Muttiah RS, Williams JR. 1998. Large areahydrologic modeling and assessment. Part I: Model development.Journal of American Water Resource Association 34: 7389.

Bathurst JC. 1986. Physically-based distributed modelling of an uplandcatchment using the Syste`me Hydrologique Europeen. Journal ofHydrology 105: 157172.

Bathurst JC, Ewen J, Parkin G, OConnell PE, Cooper JD. 2004.Validation of catchment models for predicting land-use and climatechange impacts. 3. Blind validation for internal and outlet responses.Journal of Hydrology 287: 7494.

Bathurst JC, Kilsby C, White S. 1996. Modelling the impacts of climateand land use change on basin hydrology and soil erosion inMediterranean Europe. In Mediterranean Desertification and LandUse. Brandt CJ, Thornes JB (eds). J. Wiley & Sons: Chichester, UK;355387.

Bathurst JC, Wicks JM, OConnell PE. 1995. The SHE/SHESED basinscale water flow and sediment transport modeling system. In ComputerModels of Watershed Hydrology , Singh VP (ed). Water ResourcesPublications: Littleton, CO; 563594.

Beasley DB, Huggins LF, Monk EJ. 1980. ANSWERS: A model forwatershed planning. Transactions of American Society of AgriculturalEngineers 23: 938944.

Bhardwaj AB, Kaushal MP. 2009. Two-dimensional physically basedfinite element runoff model for small agricultural watersheds: I.Model development. Hydrological Processes 23: 397407. DOI:10.1002/hyp.7150.

Bingner RL, Murphree CE, Mutchler CK. 1989. Comparison of sedimentyield models on watersheds in Mississippi. Transactions of AmericanSociety of Agricultural Engineers 32: 529534.

Chow VT, Maidment DR, Mays LW. 1988. Applied Hydrology .McGraw-Hill Inc.: New York.

Chung SW, Gassman PW, Kramer LA, Williams JR, Gu R. 1999.Validation of EPIC for two watersheds in southwest Iowa. Journalof Environmental Quality 28: 971979.

Chung SW, Gassman PW, Gu R, Kanwar RS. 2002. Evaluation ofEPIC for assessing the tile flow and nitrogen losses for alternativeagricultural management systems. Transactions of the American Societyof Agricultural Engineers 45: 11351146.

De Roo APJ, Wesseling CG, Ritsema CJ. 1996. LISEM: a single-eventphysically based hydrological and soil erosion model for drainagebasins: I. Theory, input and output. Hydrological Processes 10:11071117.

Desconnets JC, Vieux BE, Cappelaere B, Delclaux F. 1996. A GIS forhydrological modelling in semi arid, HAPEX-Sahel experimental areaof Nigeria, Africa. Transactions of GIS 1: 8294.

Douglas DH. 1986. Experiments to locate ridges and channels to createa new type of digital elevation models. Cartographica 23: 2961.

Du J, Xie S, Xu Y, Xu C, Singh VP. 2007. Development and testing ofa simple physically-based distributed rainfall-runoff model for stormrunoff simulation in humid forested basins. Journal of Hydrology 336:334346.

Dunne T. 1983. Relation of field studies and modelling in the predictionof storm runoff. Journal of Hydrology 65: 2548.



Engman ET. 1986. Roughness coefficients for routing surface runoff.Journal of Irrigation Drainage, ASCE 112: 3953.

Ewen J, Parkin G, OConnell PE. 2000. SHETRAN: a coupledsurface/subsurface modelling system for 3D water flow and sedimentand solute transport in river basins. Journal of Hydrologic EngineeringASCE 5: 250258.

Fairfield J, Leymarie P. 1991. Drainage networks from grid digitalelevation models. Water Resources Research 30: 16811692.

Figueiredo EE de, Bathurst JC. 2002. Sediment yield modelling atvarious basin scales in a semiarid region of Brazil using SHETRAN .Hydroinformatics 2002: Proc. 5th Intl. Conf. on Hydroinformatics, 15July, Cardiff, 316321.

Flanagan DC, Gilley JE, Franti TG. 2007. Water Erosion PredictionProject (WEPP): Development history, model capabilities, and futureenhancements. Transactions of the ASABE 50: 16031612.

Foglia L, Hill MC, Mehl SW, Burlando P. 2009. Sensitivity analysis,calibration, and testing of a distributed hydrological model using error-based weighting and one objective function. Water Resources Research45: W06427.

Folly A, Quinton JN, Smith RE. 1999. Evaluation of EUROSEM modelusing data from Catsop watershed, The Netherlands. Catena 37:507519.

Franks SW, Gineste P, Beven KJ, Merot P. 1998. On constraining thepredictions of a distributed model: The incorporation of fuzzy estimatesof saturated areas into the calibration process. Water ResourcesResearch 34: 787797.

Fread DL. 1974. Numerical properties of implicit four point finitedifference equations of unsteady flow, NOAA technical memorandumNWS HYDRO-18 . National Weather service, NOAA, US Departmentof Commerce: Silver Spring, MD.

Garbrecht J, Martz LW. 1999. An automated digital landscape analysistool for topographic evaluation, drainage identification, watershedsegmentation, and subcatchment parameterization. Rep.# GRL 99-1, Grazinglands Research Laboratory, USDA, Agricultural ResearchService, El Reno, OK.

Grayson RB, Moore ID, McMahon TA. 1992. Physically based hydro-logic modeling 2. Is the concept realistic? Water Resources Research26: 26592666.

Gupta SR, Solomon SI. 1977. Distributed numerical model for estimatingrunoff and sediment discharge of ungauged rivers. Water ResourcesResearch 13: 613635.

Hadley RF, Lal R, Onstad CA, Walling DE, Yair, 1985. Recentdevelopments in erosion and sediment yield studies . UNESCO, (IHP)Publication: Paris; 127.

Henderson FM. 1966. Open Channel Flow . The MacMillan Company:New York.

Hirshi MC, Barfield BJ, 1988. KYER

geospatially based distributed rainfall-runoff modelling for simulation of internal and outlet...

Documents