finite element method and gis based distributed model for soil erosion and sediment yield in a...

Water Resour Manage (2009) 23:553–579DOI 10.1007/s11269-008-9288-y

Finite Element Method and GIS BasedDistributed Model for Soil Erosionand Sediment Yield in a Watershed

M. Gopal Naik · E. P. Rao · T. I. Eldho

Received: 24 April 2007 / Accepted: 23 May 2008 /Published online: 10 July 2008© Springer Science + Business Media B.V. 2008

Abstract The objective of this study is to develop a soil erosion and sedimentyield model based on the kinematic wave approximation using the finite elementmethod, remote sensing and geographical information system (GIS) for calculatingthe soil erosion and sediment yield in a watershed. Detachment of soil particles byoverland flow occurs when the shear stress at the surface overcomes the gravitationalforces and cohesive forces on the particles. Deposition occurs when the sedimentload is greater than the transport capacity. Beasley et al.’s (Trans ASAE 23:938–944, 1980) transport equations for laminar and turbulent flow conditions areused to calculate the transport capacity. The model is capable of handling distributedinformation about land use, slope, soil and Manning’s roughness. The model isapplied to the Catsop watershed in the Netherlands and the Harsul watershed inIndia. Remotely sensed data has been used to extract land use/land cover map ofthe Harsul watershed, and other thematic maps are generated using the GIS. Thesimulated results for both calibration and validation events are compared with theobserved data for the watersheds and found to be reasonable. Statistical evaluation ofmodel performance has been carried out. Further, a sensitivity analysis has also beencarried out to study the effect of variation in model parameter values on computedvolume of sediment, peak sediment and the time to peak sediment. Sensitivityanalysis has also been carried out for grid size variation and time step variation ofthe Catsop watershed. The proposed model is useful in predicting the hydrographsand sedigraphs in the agricultural watersheds.

Keywords Kinematic wave approximation · Finite element method · Erosion ·Sediment yield · Geographical information system · Remote sensing

M. Gopal Naik · E. P. Rao (B) · T. I. EldhoDepartment of Civil Engineering,Indian Institute of Technology Bombay, Mumbai, Indiae-mail: [email protected]

554 M. Gopal Naik et al.

1 Introduction

Soil erosion is caused by detachment and removal of soil particles from the landsurface. Soil erosion depends on whether local transport capacity is greater thanor less than the sediment available for transport (Meyer and Wischmeier 1969).Numerous studies have addressed the modeling of soil erosion by rainfall-runofffrom upland and low land areas. A survey of the pertinent literature indicatesdifferent approaches to modeling soil erosion from upland watersheds. One ofthe approaches has been to utilize, empirical equations like Universal Soil LossEquations or Revised Universal Soil Loss Equations (Jain and Kothyari 2000; DiStefano et al. 2000; Bhattarai and Dutta 2007, etc.). Another approach has beento utilise the kinematic/diffusion wave theory to develop mathematical models. Themodels have been solved by analytical method or by numerical techniques like FiniteDifference or Finite Element Method (Ariathurai and Krone 1976; Singh and Regl1983; Beven 1993; Sharda and Singh 1994; Heppner et al. 2006; Rai and Mathur 2007,etc.). Many process based models have been developed in the past for rainfall-runoff-erosion modeling like, ANSWERS (Beasley et al. 1980), WEPP (Nearing et al. 1989),EUROSEM (Morgan 1995), and SHESED (Wicks and Bathurst 1996) etc.

Sharda and Singh (1994) have developed a finite element model to simulate runoffand soil erosion from agricultural lands. The computational efficiency and stabilityof various numerical schemes used for the time integration has been described. Afinite element solution of the one-dimensional Richards equation has been used tosimulate infiltration and soil moisture balance in cropped fields. A finite elementsolution of the sediment continuity equation in conjunction with a fully implicitscheme for time integration and Yalin’s equation for sediment transport capacity hasbeen developed to simulate the soil erosion. Kothyari et al. (1997) have developedkinematic wave based sediment yield model for overland flow using time–areasegment concept. Folly et al. (1999) have used EUROSEM model which computesrunoff based on kinematic wave approximation and sediment yield based on dy-namic mass-balance equation. Jain et al. (2005) have developed finite volume baseddistributed rainfall-runoff-soil erosion model and applied to different watersheds.The model operates on a cell based concept and surface runoff and sediment flowrouted through each cell, based on cell slopes. The sediment contribution by overlandflow and stream flow could not be accounted separately in this model. Rai andMathur (2007) have developed an event based soil erosion model to estimate thesediment yields and sedimentographs of small watersheds. This model is based on thesimultaneous solution of flow dynamics followed by dynamic erosions. The governingequation of the kinematic wave model developed for overland flow and channelizedflow are solved by adopting the two first order explicit numerical schemes using theCourant Number as the stability criteria.

The aim of the present study is to develop a soil erosion and sediment yieldmodel based on the kinematic wave approximation using the finite element method(FEM), remote sensing and geographical information system (GIS). The modeluses sediment continuity equation for predicting soil erosion and sediment yield.Detachment of soil particles by overland flow occurs when the shear stress at thesurface overcomes the gravitational and cohesive forces on the particles. In themodel, net detachment by overland flow occurs when the sediment load is less thanthe sediment transport capacity and deposition takes place when sediment load is

Finite element method and GIS based distributed model 555

greater than the transport capacity. Beasley’s transport equations for laminar andturbulent flow conditions are used to calculate the transport capacity in overlandand channel processes. The FEM technique has been applied to solve the partialdifferential equation of conservation of mass and conservation of linear momentumgoverning the hydrologic and erosion processes. The developed model has beenused to simulate soil erosion and sediment yield for two watersheds, one in TheNetherlands and the other in India.

2 Methodology and Governing Equations

In a watershed, surface runoff with sediment can be divided into overland flow andstream flow components. In this study, one dimensional kinematic wave approxi-mation of the St. Venant equations form the mathematical basis for modeling bothcomponents. Interception has been estimated using an exponential model based onLeaf Area Index (LAI). Infiltration has been estimated using Green-Ampt model.In this model, sediment transport by overland flow and stream flow are estimatedseparately. Soil erosion and sediment transport is modeled by the sediment conti-nuity equation. Auxiliary equations for sediment detachment by raindrop impactand shear force of flowing water are used in conjunction with sediment continuityequations. In the present investigation, the whole watershed is divided into overlandflow strips on either side of the main stream. Each overland flow strip is discretizedinto overland flow elements. The main stream has been divided into stream flowelements which are equal to the number of strips. The present model needs inputdata of slope and Manning’s roughness, cover management factor and erodibilityfactor at the nodal level. It is obtained by taking average of adjacent element values.Finally, the two sediment flow models are coupled and routed to get the sedimentyield at the watershed outlet.

In the present model, the interception is estimated based on the LImburg SoilErosion Model of Jetten (2002). In this model, canopy of crops and vegetation areregarded as simple storage. The cumulative interception during an event is given as(Aston 1979):

Ic = cp.Scmax

[1 − e−cvd. Pcum

Sc max

](1)

where Ic is cumulative interception (mm), cp is fraction of vegetation cover, cvd iscorrection factor for vegetation density and is given as cvd = 0.046 × LAI, Pcum iscumulative rainfall (mm), Scmax is canopy storage capacity (mm) and LAI is LeafArea Index. Canopy storage capacity Scmax is calculated by the equation developedby Von Hoyningen–Huene (Jetten 2002) and is given as follows:

Scmax = 0.935 + 0.498 × LAI − 0.00575 × LAI2 (2)

The interception loss (I) for every time step is calculated as follows:

I = (Ic)t+�t − (Ic)t (3)

where t is time and �t is time step. Interception rate from the interception loss hasbeen calculated and is deducted from rainfall intensity to get the effective rainfallintensity which is used to calculate infiltration and subsequent runoff.


Green Ampt model (Chu 1978) has been used to estimate the infiltration. GreenAmpt model is a simplified representation of the infiltration process in the field(Chu 1978). It assumes a homogeneous soil profile and a uniform distribution ofantecedent soil moisture. The movement of water in the soil is assumed to be inthe form of an advancing wetting front. The equation for infiltration rate given byGreen-Ampt in 1911 (Mein and Larson 1973) is as follows:

fp = Ks

[1 + sc M

F

](4)

where fp is infiltration capacity (cm h−1), Ks is saturated hydraulic conductivity(cm h−1), sc is capillary suction at the wetting front (cm), F is cumulative infiltration(cm) and M is initial soil moisture deficit (cm3 cm−3). The modified version of theinfiltration process under a ponded surface during the rainfall event is given as(Chu 1978):

Fp

sav M− ln

[1 + Fp

sav M

]= Ks

(t − tp + ts

)

sav M(5)

where sav is average capillary suction at the wetting front (cm), Fp is cumulativeinfiltration after time of ponding (cm). The ponding time (tp) is the elapsed timebetween the time rainfall begins and the time water begins to pond on the soil surface,ts can be interpreted as shift of time scale due to the effect of cumulative infiltrationat the ponding time. The excess rainfall after interception and infiltration is routedto the outlet of the watershed using the kinematic wave model.

2.1 Sediment Continuity Equation for Overland Flow

Soil erosion rate and sediment yield are estimated using the kinematic wave basedsediment continuity equation. The basic one-dimensional governing equation, de-scribing erosion by overland flow is the equation of continuity of sediment mass(Bennett 1974; Foster 1982) and is given as:

∂qs

∂x+ ρs

∂ (csh)

∂t= DR + DF (6)

where qs is the sediment load (kg m−1 s−1), ρs is the mass density of the sedimentparticles (kg m−3), cs is the concentration of sediment in the flow (m3 m−3), h is theflow depth (m), x, t are spatial and temporal coordinates, DR is the rainfall impactdetachment rate (kg m−2 s−1) and DF is the flow detachment rate (kg m−2 s−1).Under unsteady conditions, substituting qs = ρs · cs · q and q = v · h; qs

/v = As and

As = ρscsh results in:

∂qs

∂x+ ∂ As

∂t= DL (7)

where q is the discharge per unit width (m3 s−1 m−1), v is the velocity of flow (m s−1),and As is the mass sediment under the movement per unit area (kg m−2). ∂qs/∂xis the build-up or loss of sediment load with distance, ∂As/∂t is the storage rate of


sediment within the flow depth. DL is the lateral inflow rate of the sediment per unitlength per unit width of flow regime (kg m−2 s−1) and is given as DR + DF . Flowdepth and discharge per unit width are calculated using the kinematic wave model(Reddy et al. 2007).

2.1.1 Soil Detachment Due to Raindrop Impact

Soil detachment by raindrop impact is a function of the rainfall intensity and theerodibility of the soil particles. Raindrop impact breaks the cohesive bond betweensoil particles, thereby detaching particles from the soil mass and making themavailable for transport by flowing water. The detachment by raindrop impact (DR) iscomputed using the following equation of Park et al. and used by Wicks and Bathurst(1996):

DR = ω.Fw.CF .KF .I2.(2.96 S0.79

0 + 0.56)

(8)

where ω is the calibration coefficient, Fw is the water depth correction factor, I isthe rainfall intensity (mm h−1), S0 is the bed slope and CF and KF are the covermanagement factor and soil erodibility factor (kg h N−1 m−2) respectively of theUniversal Soil Loss Equation (USLE). Surface water depths greater than a thresholddepth protect the soil from raindrop impact erosion. The effect is accounted in themodel by the following expression:

Fw = exp

(1 − h

Dm

)i f h > Dm (9)

Fw = 1 i f h ≤ Dm (10)

where Dm is the median raindrop diameter (m) and may be given as:

Dm = 0.00124I0.182 (11)

2.1.2 Soil Detachment by Overland Flow

The flow detachment rate has been computed by using the following equation(Foster 1982):

DF = η.CF .KF .τ 1.5 (12)

where η is the calibration coefficient, τ is the shear stress (Nm−2).

2.1.3 Transport Capacity of Overland Flow

The balance between transport capacity and sediment supply determines whethernet erosion or deposition will occur. The sediment load at the watershed outlet iscontrolled by the amount of sediment made available for transport by the detach-ment processes and by the transport capacity of the flow (Meyer and Wischmeier1969). Although, the use of transport capacity has been questioned by some authors(Hairsine and Rose 1992; Polyakov and Nearing 2003; Sander et al. 2007), Beasleyet al. (1980) transport capacity equations have been used by many other researchers(Kothyari et al. 1997; Jain et al. 2005; Rai and Mathur 2007, etc.).


Beasley et al. (1980) compared different relationships for transport capacity,and suggested equations for the transport capacity as a function of discharge perunit width and bed slope for laminar and turbulent flow conditions as given below(Kothyari et al. 1997):

TF = ξ1.KF .S0.q1/2 f or q < 0.046 (13)

TF = ξ2.KF .S0.q2 f or q > 0.046 (14)

where TF is the transport capacity of flow (kg m−1 min−1), ξ 1 and ξ 2 are calibrationcoefficients and q is overland flow (m2 min−1).

2.2 Sediment Continuity Equation for Stream Flow

The sediment continuity equation for one dimensional sediment transport in a streammay be given as (Bennett 1974):

∂ Qsc

∂x+ ∂ Asc

∂t= qs (15)

where Qsc (ρscsAV) is the sediment load (kg s−1), V is the flow velocity (m s−1), A isthe cross-sectional flow area (m2), Asc (ρscs A) is the mass of sediment moving downthe stream per unit length (kg m−1), ∂Qsc/∂x is the erosion or deposition rate per unitlength, and ∂Asc/∂t is the storage rate of sediment within the stream flow. The streamflow parameters are calculated by the kinematic wave model (Reddy et al. 2007).

2.2.1 Transport Capacity of Stream Flow

Selecting a reliable sediment transport capacity equation is the most critical com-ponent for predicting sediment yield in agricultural watersheds. The sediment loadcoming out of the grid and finally reaching the outlet of the watershed is controlledby the amount of sediment made available for transport by the detachment processor by the transport capacity of the flow (Rai and Mathur 2007). In general, streamflow is turbulent and hence an equation for transport capacity of sediment flow ismodified and proposed by incorporating the KF parameter of the USLE, to accountfor the effect of changing soil grain size characteristics that cause resistance to flow.Thus, the proposed modified transport capacity relationship is as follows:

TFC = . KF .S0.Q2 (16)

where TFC is the transport capacity of flow in stream (kg min−1), and is thecalibration coefficient.

3 FEM Formulation

The FEM was selected for the model formulation because of its relative flexibilityfor discretizing a prototype system and representing boundaries accurately. TheEq. 7 was solved by using a Galerkin-based finite element method in the spacedomain and an implicit finite difference method in the time domain. In Galerkin’sformulation, the product of the weighting function and the residual should be zero


when integrated over the entire problem domain (Sharda and Singh 1994; Vieuxet al. 1990).

3.1 Overland Sediment Flow

The Galerkin formulation for one-dimensional conservation of sediment load forEq. 7 can be written as (Segerlind 1984):

L∫

0

NT[

∂qs

∂x+ ∂ As

∂t− DL

]dx = 0 (17)

where NT is transpose of shape function. Equation 17 can be written as:

L∫

0

NT ∂qs

∂xdx +

L∫

0

NT ∂ As

∂tdx −

L∫

0

NT DL dx = 0 (18)

By substituting qs as [N]{qs} and As as [N]{As} in Eq. 18 gives the following:

L∫

0

NT ∂ N∂x

{qs} dx +L∫

0

NT N{

∂ As

∂t

}dx −

L∫

0

NT {DL} dx = 0 (19)

The above Eq. 19 can be written in matrix form as follows:

[B] {qs} + [C

] {∂ As

∂t

}− { f } {DL} = 0 (20)

where B =L∫0

NT ∂ N∂x dx; C =

L∫0

NT Ndx and { f } =L∫0

NTdx. By applying the finite

difference in time domain to the Eq. 20, will give the following:

[B]{(1 − ) {qs}t + {qs}t+�t

} + [C

] { {As}t+�t − {As}t

�t

}

−{ f } {(1 − ) {DL}t + {DL}t+�t

} = 0 (21)

The subscripts t and t + �t indicate the variables at the current time and after onetime step. The weighting factor is used for the time derivative to determine thetypes of finite difference scheme involved. In the present study, the Crank–Nicolsonimplicit scheme with = 0.5 is used. By rearranging the terms in Eq. 21, the finalform of aforementioned equation is as follows:

[C

] {As}t+�t = [C

] {As}t − �t [B]{(1 − ) {qs}t + {qs}t+�t

}

+�t { f } {(1 − ) {DL}t + {DL}t+�t

}(22)

where [C], [B] and { f } are the global matrices and can be constructed using theelement matrices based on the discretization of the spatial domain. Here, linear lineelements are used in the developed model. The element matrices for line element aregiven as follows (Segerlind 1984):

[B](e) = 1

2

[−1 1−1 1

]; [

C](e) = L

6

[2 11 2

]and { f }(e) = L

2

[11

];


where [C](e), [B](e) and { f }(e) are element matrices and L is the length of linear lineelements. The above Eq. 22 is applied to all elements in the domain and assembledto form a system of equations. The system of equations is solved using Choleskyscheme after applying the boundary conditions for the unknown values of As. Thesolution of As requires iteration due to non-linearity of the Eq. 22 resulting fromthe relationship between qs and As based on the kinematic wave approximation.Iteration is continued until the convergence is reached to a specified tolerance value.After convergence on As, the time step is incremented and the solution proceeds inthe same manner by updating the time matrices and evaluating the new As values.

3.2 Stream Sediment Flow

Applying Galerkin’s criterion to stream sediment flow Eq. 15, results in the followingexpression:

L∫

0

NT[

∂ Qsc

∂x+ ∂ Asc

∂t− qs

]dx = 0 (23)

The final form of the above equation can be written as:

[C

] {Asc}t+�t = [C

] {Asc}t − �t [B]{(1 − ) {Qsc}t + {Qsc}t+�t

}

+�t { f } {(1 − ) {qs}t + {qs}t+�t

}(24)

where [C], [B] and { f } are the global matrices. Global matrices for stream flow canbe formed as explained in the overland flow model.

4 Model Development and Statistical Evaluation

The overland flow and stream flow sediment transport models were developed basedon the above formulation. The model code was written in C-language. The flow chartof the model developed is given in Fig. 1. The various steps of the model developmentare as follows:

• Mathematical formulation of the kinematic wave model for sediment transportby overland flow and stream flow.

• Data processing for the selected watershed: data includes physiography, rainfall,stream and sediment load.

• Preparation of the required thematic maps of the watershed from remotelysensed data and topographical maps using ERDAS IMAGINE software andArcGIS software.

• Preparation of the finite element grid and input data required for the model usingArcGIS.


Start

Input data of rainfall, time step, elements details and watershedparameters etc., Calculation of Interception and Infiltration loss

Generation of global matrix by assembling element matrices and applying boundary conditions for flow

Solve the system for overland sediment flow

Solve the system for stream sediment flow

Stop

No

No

Yes

Yes

No

Yes

[ ][ ]

1

1

t tk

t ts k

h [ ]h

A [ ]sA

Δ

Δ

+ t tk

Δ++

+ t tk

Δ++

=

=[ ][ ]

1t tk k

s s

if

h [ ]h

A [ ]sA

Δ ε

ε

+ t tΔ++ −

1t tk

Δ++

t tk

Δ+−

<

<

[ ] [ ][ ] ][[ ] [[ ]

t t t

t

ts

tS C

h h

A A

A ]sA

A [ ]S CA

t t t

Δ

Δ

+

t tΔ+

t tΔ+

t tΔ+

=

=

=

== +

[ ] [ ][ ]

1

1

t tk

t tSC k

A A

A [ ]SCA

Δ

Δ

+ tk

Δ++

+ t tk

Δ++

=

=

[ ] [[ ]

1

1

t tk

t tSC k s

if

A ]A

A [ ]SCA

Δ

Δ

ε

ε

+ t tk

Δ++

+ t tk

Δ++

− <

− <

: am xi f t t tΔ+ ≤

Fig. 1 Flow chart for overland and stream sediment flow

• Calculation of various flow parameters using kinematic wave model.• Calibration and validation of the model for various rainfall events.

4.1 Statistical Evaluation

The statistical evaluation criteria used in this study are root mean square error(RMSE) and coefficient of determination (R2).

Root mean square errorIt is an index of the variance between computed and observed values and is

expressed as:

RMSE =√√√√ 1

nr

nr∑i=1

(Yi − Yi

)2(25)

where Yi is observed value, Yi is predicted value and nr is sample size. Higher RMSEvalue indicates poor performance of the model and vice-versa.


Coefficient of determinationCorrelation coefficient (R) is one of the widely used statistical parameter in model

performance evaluation. Its value varies from +1 to -1. It is defined as follows(McCuen 1989):

R =nr

nr∑i=1

YiY −nr∑

i=1Yi

nr∑i=1

Y√√√√

[nr

nr∑i=1

Y2i −

(nr∑

i=1Yi

)2][

nr

nr∑i=1

Y2i −

(nr∑

i=1Y

)2] (26)

Square of the correlation coefficient is called coefficient of determination (R2). Itis equal to the percentage of variance in the criterion variable that is explained byvariance of the predictor variable. Because of this physical interpretation, R2 is ameaningful indicator of the accuracy of predictions (McCuen 1989). The value of R2

varies from 0.0 to 1.0. Values closer to 1.0, indicate better performance of the model.

5 Study Areas and Hydrological Database Preparation

5.1 The Catsop Watershed

The data from Catsop watershed located in South-Limburg, the Netherlands andis monitored by the Utrecht University (Jetten 2003) is used in this study. Thewatershed has an area of 41.56 ha, and has a gentle to moderately sloping topographywith altitudes from 80 to 110 m above the mean sea level. About 86% of the slopeshave a gradient of less than 10%, and 3.5% of the slopes are steeper than 15%. Thedominant flow direction of surface runoff is to the west. The parent soil material isloess. The loess deposits lie on top of Tertiary sand deposits and Quaternary depositsof the ‘West-Maas’ river. Both deposits locally appear close to the soil surface. Thesoils in the watershed are mainly silty loams. Mean annual precipitation for thewatershed is estimated as 675 mm. The drainage system and finite element grid areshown in Fig. 2. Land use in the watershed is dominated by crops of winter wheat,sugar beet and potatoes. A Digital Elevation Model (DEM) and maps of slope, soiltype and land use (for each storm event) were obtained in ASCII format with a 10 mgrid resolution (Vector Jetten, personal communication).

The Manning’s roughness values range from 0.08 to 0.264, depending on land use(Folly et al. 1999; Jain et al. 2005; Reddy et al. 2007). Based on these values, land usemaps were reclassified as Manning’s roughness maps by using the reclassify tool inthe Spatial Analyst extension of ArcMap. The cover management factor values forthis watershed range from 0.013 to 0.640, depending on land use and the value of soilerodibility factor is taken as 0.40 (Jain et al. 2005).

The finite element grid was prepared in the ArcMap with overland flow strips asshown in Fig. 2. The length of each overland flow element is 50 m and width variesfrom 50 to 100 m. The finite element grid for the Catsop watershed was overlaid onthe slope, Manning’s roughness and cover management factor and soil erodibilitylayers in ArcMap, and the mean value of these parameters were calculated foreach grid element using the Zonal Statistics tool in Spatial Analyst. The attribute


Wat

ersh

ed o

utle

t

Mai

n ch

anne

l

Streams

Ove

rland

flow

strip

s

Fig. 2 Finite element grid and drainage map of Catsop watershed

table of the grid containing the element number and mean value of the parameterswas exported as a data base file. The model needs input data of slope, Manning’sroughness, cover management factor and soil erodibility factor at the overland andstream flow element nodes. These are obtained by taking the average of the valuesin the adjacent grid elements. For the stream, a constant width of 4.4 m, a slopeof 0.022 and a Manning’s roughness of 0.23, were used for the simulation (Vector


Jetten, personal communication; Smith et al. 1999). A time step of 30 s is used in themodel run.

5.2 The Harsul Watershed

The Harsul watershed is situated between the longitudes 73˚ 25′ E and 73˚ 29′ E andthe latitudes 20˚ 04′ N and 20˚ 08′ N. The watershed has a drainage area of 10.929 km2

The highest peak in the area has an elevation 730 m above mean sea level, whereasthe lowest point where the main stream drains has an elevation of 368 m above meansea level, leading to an average slope of 6.6% along the main stream of the Harsulwatershed. The soils in the watershed are mainly sandy silty loam.

The watershed is mostly hilly and have undulating to rolling topography. Thescattered and the sharp hills are intersected by numerous streams and gullies. Thehills and the hill terraces of this area are mostly steep and rugged. The area can bedivided into the following land forms (1) hill terraces and plateau (2) hill slope andescarpment (3) subdued hills (4) valley and (5) recent alluvium. The principal rockformation in the area is western ghat of Deccan plateau consisting of basaltic trapand amygdaloids and conglomerates underlying hills and terraces. The climate of thearea in general is tropical humid with three distinct seasons namely, monsoon, winterand summer. Mean annual precipitation is 2,275 mm and mean annual temperatureis 26.5˚C, minimum being 14˚C in winter season and maximum being 36˚C in summerseason (Wankhede et al. 1984).

The hydrological data of the watershed has been obtained (Guy Honore, per-sonal communication) and analyzed. The watershed data were collected as partof the “Indo German Bilateral Project-Watershed Management”, of the Ministry ofAgriculture, Government of India, and the Deutsche Gesellschaft fur TechnischeZusammenarabeit. Survey of India 1:25,000 topographical maps were scanned andregistered in ERDAS IMAGINE to prepare the thematic maps of the watershed.The drainage divides and drainage network were digitized in ArcMap. Contour lineswith a 10 m interval were digitized in ArcMap from the toposheets, and DEM witha 100 m cell size was generated using TOPOGRID tool in ArcInfo. The watersheddrainage along with finite element grid is shown in Fig. 3. The slope map was derivedfrom the DEM by using the slope tool and the Raster calculator in Spatial Analyst.The slope of the elements ranges from 0.005% to 0.42%

Remote sensing data from IRS-1D LISS-III imagery of January 13, 1998, withresolution of 23.5 m was used to extract the land use (LU)/land cover (LC) mapof the watershed. The LU/LC map was derived by supervised classification usingERDAS IMAGINE software and is presented in Fig. 4. The LU/LC classes of thiswatershed are cultivated land, forest land and waste land. Manning’s roughnessvalues for overland flow were assigned for cultivated land, forest land and waste landas 0.035, 0.1 and 0.015 respectively (Vieux 2001). The LU/LC map was reclassifiedas a Manning’s roughness map using the Reclassify tool option of Spatial Analyst.The cover management factors for this watershed are taken as 0.315, 0.01 and 0.1 forcultivated land, forest land and waste land respectively (Challa et al. 2004). The valueof soil erodibility factor was calculated as 0.020 using nomogram, based on grain sizeanalysis. The finite element grid was prepared in ArcMap with overland flow stripsas shown in Fig. 3. The length of each overland flow element is 250 m and the averagewidth of the elements ranges 250 to 750 m. For stream nodes, a Manning’s roughness


0.6 0 0.6 1.20.3Kilometers

Drainage

Boundary

FEM Grid

FEM Grid

Fig. 3 Finite element grid and drainage map of Harsul watershed


0.6 0.3 0 0.6 1.2Kilometers

Land use/Land cover

Cultivated land

Waste land

Forest land

Fig. 4 Land use/land cover map of Harsul watershed

value ranging from 0.035 to 0.045 was assigned based on the stream condition (Chow1959; Jain et al. 2005) and ground truth information. The watershed streams aremountain streams with no vegetation in channel with steep banks. The bed materialconsists of gravels, Cobbles and few boulders. For the stream, a constant width of


18 m was used whereas slope varied from 0.008 to 0.360. A time step of 30 s was usedfor the model runs.

6 Results and Discussion

For model application, storm events were divided into two groups. The first group ofevents indicated as calibration storms were used for model calibration. In the presentstudy, the model calibration is performed by systematically varying the values ofcalibration coefficients. The model calibration has been carried out by trial and errorbased on the best visual fit of the hydrographs and sedigraphs. Two storms were usedfor the calibration and four storms were used for validation of Catsop watershed.Three storms were used for the calibration and three storms were used for validationof Harsul watershed. Through the calibration exercise, it was possible to identify atrend in the values of the parameters which could be used to parameterise the stormevents, though this depended on the storm characteristics. The best calibrations havebeen achieved by decreasing the coefficient for the raindrop impact detachment rateand increasing the coefficient for the transport capacity of overland flow.

For the Catsop watershed, the initial values of the calibration coefficients weretaken from the literature (Jain et al. 2005). The values of ω, ξ 1 and ξ 2 were calibratedas 0.008, 4,500, and 7,500 respectively. The value of η was calibrated as 1.0 for all thestorm events. The coefficient was calibrated as 8 for the rainstorm event of August18, 1987 and as 18 for the event of June 26, 1987. Validation of four rainfall events iscarried out with the above calibrated parameters of the storm of June 26, 1997. Thecalibrated values of the storm of August 18, 1987 have not been used, because of itsdifferent behaviour in calibration (Folly et al. 1999). The volume of total sediment,peak sediment yield and time to peak sediment yield for calibrated and validatedrainfall events are given in Table 1, together with simulated results available in theliterature. The observed and simulated hydrographs and sedigraphs are shown inFig. 5. The present model results are also compared with the finite volume basedmodel results (Jain et al. 2005) and EUROSEM model results (Folly et al. 1999).

Table 1 shows that the volume of total sediment yield has been simulated to withina difference of 19% to 41%, peak sediment yield has been simulated to within adifference of −12% to 16%, and time to peak sediment yield has been simulatedto within a difference of −19% to 2% for the calibrated events. The results of thepresent model are in fair agreement with the results of EUROSEM model by Follyet al. (1999) and finite volume model by Jain et al. (2005). The results for validatedevents show a mixed performance of the model. The volume of total sediment yieldhas been simulated to within a difference of −34% to −91%, peak sediment yield hasbeen simulated to within a difference of −81% to −95% and time to peak sedimentyield has been simulated to within a difference of 6% to 36%. However, for twoevents, the error in time to peak sediment yield is above 100%. Large differencebetween observed and simulated values for validated events may be attributed tothe differences in characteristics between the calibration storms and those in thevalidation data set (Folly et al. 1999).

It is also seen from Table 1 that, the range of deviations obtained by usingEUROSEM model (Folly et al. 1999) for the total sediment yield has been simulatedwithin a difference of 91% to 96% for calibration events and 0% to 616% for


Tab

le1

Mod

elre

sult

sof

calib

rate

dan

dva

lidat

edev

ents

ofC

atso

pw

ater

shed

Rai

nfal

leve

nts

Vol

ume

ofto

tals

edim

enty

ield

(N)

Pea

kse

dim

enty

ield

(Ns−

1)

Tim

eto

peak

sedi

men

tyie

ld(m

in)

Obs

erve

dSi

mul

ated

Diff

.(%

)O

bser

ved

Sim

ulat

edD

iff.(

%)

Obs

erve

dSi

mul

ated

Diff

.(%

)

Cal

ibra

ted

even

tsJu

ne26

,198

722

,563

31,8

00(4

4,14

5a ,24,

623b

)40

.94

14.6

512

.92

(14.

20b)

−11.

8562

50(4

4b)

−19.

3A

ugus

t18,

1987

8,24

09,

780

(15,

696a ,1

3,53

7.8b

)18

.68

3.94

4.55

5(6

.05b

)15

.54

6061

(54b

)1.

67V

alid

ated

even

tsM

ay13

,198

79,

810

859

(9,8

10a ,1

6,48

0.8b

)−9

1.2

3.07

0.23

6(2

.32b

)−9

2.31

344

366

(358

b)

6.39

Janu

ary

22,1

993

30,4

114,

750

(217

,782

a ,28,

939.

5b)

−84.

427

.71.

492

(12.

11b)

−94.

6133

78(5

8b)

136.

3M

ay30

,199

330

0,18

691

,580

(73,

575a ,4

3,45

8.3b

)−6

9.5

433.

939

.346

(15.

34b)

−90.

929

39.5

(34b

)36

.2O

ctob

er14

,199

310

1,04

366

,787

(250

,155

a ,134

,397

b)

−33.

975

.67

14.4

4(3

1.22

b)

−80.

947

495

3.5

(489

b)

101.

2

diff

.Diff

eren

cea T

heva

lues

obta

ined

byF

olly

etal

.(19

99)

bT

heva

lues

obta

ined

byJa

inet

al.(

2005

)


a b

c d

e f

Fig. 5 Observed and simulated hydrographs and sedigraphs of Catsop watershed. a Calibrated event,June 26, 1987. b Calibration event, August 18, 1987. c Validated event, January 22, 1993. d Validatedevent, May 30, 1993. e Validation event, May 13, 1987. f Validated event, October 14, 1993

validation events of Catsop watershed. The ranges of deviations obtained by finitevolume method (Jain et al. 2005) for the same watershed are: total sediment yieldhas been simulated within a difference of 9% to 64%, peak sediment yield has beensimulated within a difference of −3% to 54%, and time to peak sediment yield hasbeen simulated within a difference of −10% to −29% for the calibration events. Forvalidation events, the total sediment yield has been simulated within a difference of−85% to 68%, peak sediment yield has been simulated within a difference of −96%to 33% and time to peak sediment yield has been simulated within a difference of3% to 76%.

For the Harsul watershed, the values of ω, ξ 1 and ξ 2 were calibrated as 0.008, 4,500,and 7,500 respectively. The value of η was calibrated as 1.0 for all the storm events.


Tab

le2

Mod

elre

sult

sof

calib

rate

dan

dva

lidat

edev

ents

ofH

arsu

lwat

ersh

ed

Rai

nfal

leve

nts

Vol

ume

ofto

tals

edim

enty

ield

(N)

Pea

kse

dim

enty

ield

(Ns−

1)

Tim

eto

peak

sedi

men

tyie

ld(m

in)

Obs

erve

dSi

mul

ated

Diff

.(%

)O

bser

ved

Sim

ulat

edD

iff.(

%)

Obs

erve

dSi

mul

ated

Diff

.(%

)

Cal

ibra

ted

even

tsJu

ly27

,199

719

1,65

159

,455

−68.

9723

.126

22.3

38−3

.40

240

268.

511

.87

Aug

.4,1

997

83,0

0150

,970

−38.

5915

.19

12.2

8−1

9.16

540

533

−1.2

9A

ug.2

2,19

9745

2,85

840

9,20

7−9

.64

50.2

267

.901

35.2

042

038

4−8

.57

Val

idat

edev

ents

July

26,1

997

671,

912

153,

948

−77.

0844

.897

29.5

79−3

4.11

300

291.

5−2

.83

Aug

.21,

1997

37,9

978,

500

−77.

635.

882

1.17

3−8

0.05

600

446

−25.

67A

ug.2

3,19

971,

638,

300

1,44

9,17

1−1

1.54

140.

732

163.

2415

.99

900

839.

5−6

.72

diff

.Diff

eren

ce; (

%)=

( sim

ulat

ed−o

bser

ved

obse

rved

) ×100


The coefficient was calibrated as 0.8 for all the rainstorm events. The volumeof total sediment yield, peak sediment yield and time to peak sediment yield forthe calibrated and validated rainfall events are given in Table 2. The observed andsimulated hydrographs and sedigraphs are shown in Fig. 6. Table 2 shows that thevolume of total sediment yield has been simulated to within a difference of −10%to −69%, peak sediment yield has been simulated to within a difference of −3%to 35%, and time to peak sediment yield has been simulated to within a differenceof −1% to 12% for the calibrated events. The results of validated events show afair performance of the model, the volume of total sediment yield was simulated to

a b

c d

e f

Fig. 6 Observed and simulated hydrographs and sedigraphs of Harsul watershed. a Calibrated event,July 27, 1997. b Calibrated event, August 4, 1997. c Calibrated event, August 22, 1997. d Validatedevent, July 26, 1997. e Validated event, August 21, 1997. f Validated event, August 23, 1997


within a difference of −12% to −77%, peak sediment yield was simulated to within adifference of −80% to 16%, and time to peak sediment yield was simulated to withina difference of −3% to −26%.

The statistical evaluation criteria used in this study are RMSE and coefficient ofdetermination (R2). From the model results of Catsop watershed, it is seen that, thevalues of RMSE, for total sediment yield, peak sediment yield and time to peaksediment yield are calculated as 87.09, 163.36 and 196.92 respectively. The valuesof R2 statistic for the total sediment yield, peak sediment yield and time to peaksediment yield are calculated as 0.736, 0.804 and 0.886 respectively. The same isshown as scatter plots for the observed and simulated results of all the events ofCatsop watershed in Fig. 7. From the model results of Harsul watershed, it is seen

Fig. 7 Scatter plots ofobserved vs. simulated valuesfor all rainfall events of Catsopwatershed. a Total sedimentyield. b Peak sediment yield.c Time to peak sediment yield


that, the values of RMSE, for total sediment yield, peak sediment yield and time topeak sediment yield are 232.78, 13.44 and 70.24 respectively. The values of R2 statisticfor the total sediment yield, peak sediment yield and time to peak sediment yieldare calculated as 0.884, 0.963 and 0.932 respectively. The same is shown as scatterplots for the observed and simulated results of all the events of Harsul watershed inFig. 8. As discussed above, the statistical evaluation describes the effectiveness of theproposed model in soil erosion and sediment yield estimation.

Fig. 8 Scatter plots ofobserved vs. simulated valuesfor all rainfall events of Harsulwatershed. a Total sedimentyield. b Peak sediment yield.c Time to peak sediment yield


6.1 Model Advantages and Limitations

The developed model has the following advantages: The proposed model can beapplied to small to medium watersheds for the event based soil erosion and sedimentyield simulation. It is integrated with GIS and remote sensing so that the advantageof GIS and remote sensing can be utilised. For the given rainfall, the sediment yieldcan be predicted at any location of the stream with respect to time.

Following are some of the limitations of the developed model: As the presentmodel is a distributed model, large quantity of data and field measurements arerequired for the soil erosion and sediment yield simulation. The model is sensitiveto various calibration parameters and watershed parameters. The accuracy of pre-diction also depends on the accuracy of field parameters. Present model will notbe applicable to watersheds, where the water retention structures are built acrossstreams of the watershed, because of internal boundary conditions. However, themodel can be modified to take care of these structures.

7 Sensitivity Analysis

Sensitivity analysis is the process of varying model input parameters over a reason-able range and observing the relative changes in model response with the purposeof demonstrating the sensitivity of the model outcome to uncertainties in the inputdata. A sensitivity analysis of the model was carried out by altering the calibrationcoefficients and watershed parameters i.e., ω, η, , ξ 1 and ξ 2, CF and KF by ±10%for all rainfall events of Catsop watershed. The effects of the change in calibrationcoefficients and watershed parameters on the computed volume of total sedimentyield and peak sediment yield are shown in Fig. 9a, b respectively, for two rainfallevents of the watershed. Figure 9a, b shows that the simulated volume of totalsediment yield and peak sediment yield are sensitive to coefficient of transportcapacity in channel (). For ±10% variation in , the volume of total sediment yieldvaried by 9% to 10% and the peak sediment changed by 9% to 10%. For ±10%variation in ξ 1 and ξ 2, the volume of total sediment yield and peak sediment yieldvaried by less than 1%. Other parameters like η, ω, CF and KF are less sensitive thanthe aforementioned parameters.

Sensitivity analysis for model parameters is also carried out for Harsul watershedby altering the calibration coefficients and watershed parameters i.e., ω, η, , ξ 1

and ξ 2, KF and CF by ±10% for all rainfall events. The effects of the change inthe calibration coefficients and watershed parameters on the simulated volume oftotal sediment yield and peak sediment yield are shown in Fig. 9c, d respectively, fortwo rainfall events of the watershed. From Fig. 9c, d, it seen that model coefficientof transport capacity in stream is most sensitive followed by coefficient of transportcapacity for overland flow, soil erodibility factor and cover management factor. For±10% variation in , the volume of total sediment yield varied by 7% to 10% andthe peak sediment changed by 4% to 10%. For ±10% variation in ξ 1, the volumeof total sediment yield varied by 1% to 2% and peak sediment yield varied by 3%to 4%. Similarly, for ±10% variation in ξ 2, the volume of total sediment yield andpeak sediment yield varied by less than 1%. For ±10% variation in KF , the volume


Fig. 9 Results of sensitivity analysis for Catsop and Harsul watersheds. a Percent change in totalsediment volume (Catsop). b Percent change in peak sediment yield (Catsop). c Percent change intotal sediment volume (Harsul). d Percent change in peak sediment yield (Harsul)

of total sediment yield varied by 2% to 3% and peak sediment yield varied by 4% to5%. Other parameters like η, ω and CF are less sensitive than the above parameters.

Sensitivity analysis of the grid size variation has also been carried out to study theeffect of grid size variation in the model results. Two grid maps for Catsop watershedhave been prepared in ArcMap, with element of length 75 and 50 m for the overlandflow. Time step used in this study is 30 s. Simulated values with 75 and 50 m gridagainst observed data for Catsop watershed are given in Table 3. From Table 3, it isobserved that for 75 m grid size variation, the volume of total sediment yield varied inthe range of 4% to 16%, peak sediment yield varied in the range of 24% to 37% andtime to peak varied in the range of 6% to 15% for calibrated events. For validationevents, the volume of total sediment yield varied in the range of 48% to 94%, peak


Tab

le3

Sens

itiv

ity

anal

ysis

ofgr

idsi

zeva

riat

ion

ofC

atso

pw

ater

shed

Rai

nfal

leve

ntV

olum

eof

tota

lsed

imen

tyie

ld(N

)P

eak

sedi

men

tyie

ld(N

s−1)

Tim

eto

peak

sedi

men

tyie

ld(m

in)

Obs

erve

d75

m50

mO

bser

ved

75m

50m

Obs

erve

d75

m50

m

June

26,1

987

22,5

6323

,440

31,8

0014

.65

9.25

12.9

162

52.5

50A

ugus

t18,

1987

8,24

0.4

6,92

99,

780

3.94

3.0

4.55

6064

61Ja

nuar

y22

,199

330

,411

3,25

84,

750

27.7

1.01

41.

4933

8178

May

30,1

993

300,

186

61,9

0591

,580

433.

926

.67

39.3

429

4439

.5M

ay13

,198

79,

810

558

859

3.07

0.13

70.

2434

436

7.5

366

Oct

ober

14,1

993

101,

043

52,0

3366

,787

75.6

710

.37

14.4

447

495

195

3.5


Table 4 Sensitivity analysis of time step variation of Catsop watershed

Rainfall Volume of total Peak sediment Time to peakevent sediment yield (N) yield (N s−1) sediment yield (min)

60 s 30 s 15 s 60 s 30 s 15 s 60 s 30 s 15 s

June 26, 1987 34,459 31,800 30,057 13.94 12.91 12.25 50 50 50August 18, 1987 10,878 9,780 9,112 5.07 4.55 4.23 61 61 61.5

sediment yield varied in the range of 86% to 96%and time to peak sediment yieldvaried in the range of 6% to 51%. However, for two events, the variation in timeto peak sediment yield is above 100%. Similarly, for 50 m grid size variation, thevolume of total sediment yield varied in the range of 18% to 41%, peak sedimentyield varied in the range of 11% to 15% where as time to peak sediment yield variedin the range of 2% to 19% for calibrated events. For validation events, the volume oftotal sediment yield varied in the range of 34% to 91%, peak sediment yield varied inthe range of 80% to 94%and time to peak sediment yield varied in the range of 6%to 36%. It is also seen that with decrease in grid size, the volume of total sedimentyield and the peak sediment yield increased and the time to peak sediment yielddecreased.

Sensitivity analysis has also been carried out to study the effect of time stepvariation in the model results. The time steps of 60 and 15 s in addition to 30 s ongrid element length of 50 m for calibrated events and the results are given in Table 4.It is seen from the results that the volume of total sediment yield varied in the rangeof 8% to 11%, peak sediment yield varied in the range of 8% to 11% where astime to peak sediment yield has remained constant for 60 s time step compared with30 s time step. Similarly, From Table 4, it is also observed that the volume of totalsediment yield and peak sediment yield varied in the range of 5% to 6% and 5%to 7% respectively, where as time to peak sediment yield has remained constant for15 s time step compared with 30 s time step. It is observed from the results that withincrease in time step, the volume of total sediment yield and peak sediment yieldincreased where as the time to peak sediment yield remained constant.

8 Conclusions

In this study, a soil erosion and sediment yield model based on the kinematic wavemodel using the finite element method has been developed and integrated with GIS.The model was applied to two watersheds having different climates such as Catsopand Harsul watersheds. The input data for the model were processed using GIS andremote sensing. The model was found to produce reasonable results for the temporaland spatial variation of sediment yield for both watersheds, showing the generalityof modeling approach. The simulated and observed hydrographs and sedigraphsshowed a reasonable match. Values of RMSE and R2 statistic have been calculatedfor both the watersheds for total sediment yield, peak sediment yield and time topeak sediment yield. These values indicate good correlation between simulated andobserved data.


A sensitivity analysis of the model was carried out by altering the calibrationcoefficients and watershed parameters of ω, η, , ξ 1 and ξ 2 by ±10% for bothwatersheds. The results showed that the volume of total sediment yield, peaksediment yield and time to peak sediment yield are more sensitive to the coefficientof transport capacity in stream . A sensitivity analysis of the grid size and timestep variation has also been carried out. The results of the model application tothe watershed indicate that the physically based distributed model developed in thepresent study is useful for generating the hydrographs and sedigraphs for overlandand stream flow in agricultural watersheds.

Acknowledgements Authors are thankful to the Prof. Victor Jetten, Utrecht University, TheNetherlands for providing the Catsop data base. Authors are also thankful to Mr. Guy Honore,the coordinator of the Indo German Bilateral Project-Watershed Management, for providing thehydrological data of the Harsul watershed.

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