Catena 64 (2005) 247–271

www.elsevier.com/locate/catena

A review of hillslope and watershed scale erosion

and sediment transport models

Hafzullah Aksoy a,*, M. Levent Kavvas b

a Istanbul Technical University, Department of Civil Engineering, Hydraulics Division 34469 Maslak, Istanbul, Turkeyb University of California, Department of Civil and Environmental Engineering, Davis, CA 95616, USA

Abstract

This study reviews the existing erosion and sediment transport models developed at hillslope and

watershed scales. The method followed in this review is to summarize the models with a focus on the

physically based modeling technique as well as with a brief discussion about empirical and

conceptual models. Approaches for determining the sediment transport capacity of flow are

explained. The extension of a sediment transport model to a nutrient transport model is then

discussed. Finally, the future of erosion and sediment transport models are projected to include the

probabilistic description of hydrology, the physical characteristics of the watershed, and the

stochastic structure of soil properties. The review is expected to be of interest to researchers,

watershed managers and decision-makers while searching for models to study erosion and sediment

transport phenomena and related processes such as pollutant and nutrient transport.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Conceptual models; Empirical models; Erosion; Physically based models; Sediment transport; Upland

erosion

1. Definitions and basic concepts

Defined by ASCE Task Committee (1970) as the loosening or dissolving and removal

of earthy or rock materials from any part of the earth’s surface, erosion is a process of

detachment and transportation of soil materials by erosive agents (Foster and Meyer,

0341-8162/$ -

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* Correspon

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ding author. Fax: +90 212 2856587.

ress: haksoy@itu.edu.tr (H. Aksoy).

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271248

1972). Erosion can be caused by wind (wind erosion), by rainfall (rainfall erosion), or by

runoff (runoff erosion). Runoff erosion can happen in unconcentrated flow (sheet erosion),

in rills (rill erosion), or gullies (gully erosion). Rills are such small concentrations of

running water that they can be completely removed by normal cultivation methods,

whereas gullies cannot be. Erosion in the channel is called channel erosion.

Soil eroded from a given area is defined in terms of rate of erosion. Total sediment

outflow from a watershed per unit time is called sediment yield. It is obtained by

multiplying the sediment loss by a delivery ratio (Novotny and Chesters, 1989). The

transported portion of the eroded sediment (ratio of yield to the total eroded material) is

called sediment delivery or sediment delivery ratio. Sediment delivery decreases with

increasing basin size as large basins have more sediment storage sites where eroded

sediment is kept. Sediment delivery can be limited by reducing either the detachment rate

or the transport capacity depending on which has a lower value.

Sediment particles are detached from their current places if the sediment load in the

flow is smaller than the sediment transport capacity of flow. For this, the shear stress

exerted by flow should be greater than the critical shear stress that is required for sediment

particles to be removed from their current locations. Otherwise deposition is observed

whenever the flow has a sediment load exceeding its transport capacity. This is illustrated

in Table 1 where three movement modes of sediment are given. Entrainment is the actual

rate of mass temporarily leaving the overland surface, which may or may not be

transported. Deposition is the actual rate of mass temporarily reaching the overland

surface. If deposition exceeds entrainment, then net deposition takes place; if entrainment

exceeds deposition, then net erosion takes place. When deposition is equal to entrainment,

then the sedimentation process is said to be in equilibrium (Croley, 1982).

Annual amount of sediment eroded from a watershed is called annual gross erosion.

A small portion (less than one-fourth) of the eroded sediment is delivered to the

receiving bodies (e.g. sea, inland lakes, streams, etc.) while the remaining is deposited in

their way. The major part of the annual sediment discharge is transported in a short

period of time by a few storms during which the discharge of the stream is continuously

changing. Therefore temporal variation of the stream discharge is very important

(Bennett, 1974).

Sediment concentration is higher at higher rainfall intensity due to its higher

detachability capacity. With increasing flow discharge sediment concentration decreases.

Sediment concentration is the highest at the beginning of the rainfall and decreases until

the steady state is reached. Detachability or re-detachability, hence soil loss, is expected to

decrease as the water depth in the flow increases (Proffitt et al., 1991). The decrease in soil

loss at the greater water depth can be attributed to the increased protection of the soil

Table 1

Movement mode of sediment for different cases of transport capacity (Tc) of flow and sediment load (Qs) in the

flow

Case Deposition Transport Erosion

I TcbQs � �II Tc=Qs �III TcNQs � �

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 249

surface from the raindrop impact as the mean water depth of surface water increases

(Singh and Prasad, 1982).

Factors affecting water erosion are climate, topography, soil, vegetation and

antropogenic activities such as tillage systems and soil conservation measures (Kuznetsov

et al., 1998). Natural vegetative cover is sparse in arid regions and, therefore, runoff events

cause entraining very high concentrations of sediment resulting in a limitless sediment

supply. However, in the more humid regions, the vegetation usually prevents runoff from

entraining soil. Therefore, the antecedent soil conditions become important although they

are region dependent. Winter storms result in less sediment transport than summer storms.

However, large amounts of precipitation and runoff occurring during winter could cause

high erosion rates if the soil cover is minimal (ASCE Task Committee, 1970). This fact

was observed by Emmett (1970) who concluded, based on nearly 10-year experimental

data, that sediment concentration in overland flow is negatively correlated with vegetation

cover of the region.

Sediment transport is sensitive to the flow hydraulics. Therefore, when applying

physically based models, detailed and accurate simulation of the velocity and depth of

flow is more important than an accurate calibration of rainfall erosion and runoff erosion

parameters although, in some cases, erosion can be sensitive to those parameters (Smith et

al., 1999).

An bupland areaQ in a watershed is where surface runoff can be considered as

overland flow in hydrological analysis. Upland erosion is affected by hydrology,

topography, soil erodibility and transportability, vegetation cover, land use, subsurface

effects, tillage roughness and tillage marks (Foster, 1982). Sediment discharge becomes a

function of hydraulic properties of flow, physical properties of soil, and surface

characteristics. On the upland area, four different processes accomplish sediment removal

and transport: detachment by raindrop impact, detachment by runoff, transport by

raindrop splash, and transport by runoff. Flow and raindrop detachment rates are not

simple, and they are, therefore, given by empirical formulas (Bennett, 1974). The

inception of sediment motion on a slope was found to be dependent upon the slope plus

the Reynolds number of the flow over the slope (Lau and Engel, 1999). Increasing bed

slope reduces the critical shear stress that should be exceeded for a sediment particle to

start its motion.

The upland area is usually considered to have both interrill areas and rills.

Consequently, erosion in such areas is divided into rill erosion and interrill erosion. The

upland sediment load is given by the detachment (or deposition) rate in rills plus delivery

rate of particles detached by interrill erosion to rill flow (Foster and Meyer, 1975). Interrill

erosion process is rainfall dominated, whereas rill erosion is mostly defined by runoff.

It is important to note that rainfall erosion controls the rising limb of the sediment graph

while runoff (flow) erosion rates are closely related to the recession (Park et al., 1982).

Erosion in rills is due mainly to flow detachment. An equation such as that of Yalin (1963),

developed for streamflow, seems to be applicable for determining the transport capacity of

flow in the rill.

Gully erosion is, in general, similar to rill erosion. Gully erosion and rill erosion differ

from rainfall erosion in that raindrop impact is not important (Foster and Meyer, 1975).

The initiation and development of gully erosion is a response to widespread clearing and

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271250

intensive land use. Landslides are other kinds of erosion that can occur in a basin.

Different kinds of assessment techniques are available. Montgomery and Dietrich (1994)

proposed a slope stability model for predicting the location of shallow landsliding.

Increasing rainfall rate makes the catchment unstable. Steep channels in the basin

headwaters transport huge debris flow, while the lower-gradient channels in the major

valleys are within the depositional zone.

Lowland streams in which the flow is usually perennial carry coarser bed material. It is

usually assumed that the bed material transport velocity is the same as the mean stream

velocity and that the longitudinal dispersion is negligible (Bennett, 1974). Lowland

(channel) erosion consists of streambed and stream bank erosions. A simple way to predict

erosion in the channel is to use the formula

QS~Gsds ð1Þ

in which Q is stream discharge, S slope of stream channel, Gs bed load sediment discharge

and ds particle diameter of bed load sediment (ASCE Task Committee, 1970). Flow

velocity near the banks of the channel is much smaller than that in the center. This results

in relatively coarse materials being moved down while fine material being deposited near

the banks, and suggests the use of two-dimensional models for stream channel processes.

However, practical considerations force one to use one-dimensional models. This effect

can, for instance, be considered by subdividing the cross-sectional area of the channel into

mid-channel and side-channel subsections. Alternatively, an effective depth can be defined

in order to take the variability along the channel cross-section into account (Johanson and

Leytham, 1977).

The following section summarises the existing watershed and hillslope scale erosion

and sediment transport models with a focus on those that are physically based. It is

then explained how the transport capacity of flow is determined. Data requirements of

the models are discussed. Extension of a sediment transport model to a nutrient

transport model is given in a later section together with some existing nutrient

transport models. Finally the review is summarised and projections for the future are

drawn.

2. Existing erosion and sediment transport models

A review of watershed hydrology models was recently given by Singh and Woolhiser

(2002). Three review papers were observed in literature for erosion and sediment transport

models developed at hillslope and watershed scales. Bryan (2000) performed a review on

the water erosion on hillslopes while Zhang et al. (1996a) reviewed modelling approaches

used for the prediction of soil erosion in catchments. Models mentioned in that review

were limited to a number of very well known models only. The third one (Merritt et al.,

2003) gave the most recent review that analyzes specific models based on model input–

output, model structure, runoff, erosion/transport and water quality modeling, and

accuracy and limitation of the model.

Some models are similar, because they are based on the same assumptions and some are

distinctly different. Models so far developed can be categorized according to different

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 251

criteria that may encompass process description, scale, and technique of solution (Singh,

1995).

A model may be based on a conceptual or an empirical framework. Such models are

called conceptual and empirical models, respectively. In conceptual models, a watershed

is represented by storage systems. Empirical models are limited to conditions for which

they have been developed. If a model is constructed by using mass conservation

equation of sediment, it is called a physically based erosion and sediment transport

model. For instance, the USLE (Wischmeier and Smith, 1978) is an empirical model

which is based on a large amount of data from the United States. AGNPS (Young et al.,

1989) uses a modified form of USLE. The hydrological part of ANSWERS (Beasley et

al., 1980) is a conceptual process. KINEROS (Smith, 1981), WESP (Lopes, 1987),

SEM (Storm et al., 1987), SHESED (Wicks, 1988) and EUROSEM (Morgan et al.,

1998) are some examples for the physically based erosion and sediment transport

models.

Table 2 categorises the erosion and sediment transport models depending upon the

process description used in their formulation. These models will be discussed into detail in

the following sections. Most of the models in Table 2 are physically based although the

first attempts in the modeling of erosion and sediment transport started with empirically

based approaches of the USLE. Also some conceptual models such as LASCAM (Viney

and Sivapalan, 1999) were developed.

2.1. Empirical and conceptual models

Given below are summaries of the empirical and conceptual erosion and sediment

transport models listed in Table 2.

Table 2

Erosion and sediment transport models

Model Empirical Conceptual Physically based

USLE �MUSLE �RUSLE �SEDD �AGNPS �LASCAM �ANSWERS �LISEM �CREAMS �WEPP �EUROSEM �KINEROS �KINEROS2 �RUNOFF �WESP �CASC2D-SED �SEM �SHESED �

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271252

2.1.1. USLE

The Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1978) is given by

E ¼ RKSLCP ð2Þ

where E is average annual soil loss in tons/acres, R rainfall erosivity index, K soil

erodibility index, S slope, L length of the slope, C cropping management factor and P

supporting conservation practice factor. The equation is based on a huge amount of data

from the United States. The USLE computes annual soil loss. Its modified version

(MUSLE) has been an attempt to compute soil loss for a single storm event. The USLE was

revised (RUSLE) (Renard et al., 1991) and revisited (Renard et al., 1994) for improvement.

2.1.2. SEDD

The SEdiment Delivery Distributed (SEDD) model, which is based on the empirical

USLE model was proposed by Ferro and Porto (2000). A Monte Carlo technique was used

to test the effect of uncertainty in the model parameters on sediment yield computations,

similar to the study by Biesemans et al. (2000) on the RUSLE.

2.1.3. AGNPS

An event-based model, AGNPS (AGricultural NonPoint Source) simulates runoff,

sediment and nutrient transport from agricultural watersheds. The model divides the

watershed into square cells uniformly distributed over the watershed. The erosion and

sediment transport component is based on estimating the upland erosion by the USLE and

routing it by the steady-state continuity equation of sediment. Eroded soil is subdivided

into five size classes: Clay, silt, small aggregates, large aggregates and sand. The model

produced favourably comparable results for runoff and sediment (Young et al., 1989).

AGNPS was applied to two medium size (80–130 km2) watersheds in Central Europe

(Rode and Fredo, 1999; Pekarova et al., 1999). Although total runoff volume was

simulated with small deviations from observations in both watersheds, sediment was

computed satisfactorily for only one of the two watersheds.

2.1.4. LASCAM

A continuous (daily time interval), conceptual sediment generation and transport

algorithm was coupled to an existing water and salt balance model, LASCAM (Viney and

Sivapalan, 1999). LASCAM was originally developed to predict the effect of land use and

climate change on the daily trends of water yield and quality in forested catchments in

Western Australia. The developed sediment transport algorithm does not discriminate

between sediment size classes. It was found that the amount of runoff and sediment

produced by the model was matched well in monthly and daily time intervals. Viney et al.

(2000) later coupled a conceptual model of nutrient mobilisation and transport to the

LASCAM.

2.2. Physically based models

Table 3 focuses on watershed scale physically based erosion and sediment transport

models for which detailed information is provided below.

Table 3

Physically based erosion and sediment transport models

Model Lumped Distributed Stochastic Deterministic 1-D 2-D Steady

state

Unsteady

state

Event-base Continuous Rilled

structure

No rilled

structure

Single-size Multi-size

ANSWERS � � � � � � �LISEM � � � � � � �CREAMS � � � � � � �WEPP � � � � � � �EUROSEM � � � � � � �KINEROS � � � � � � �KINEROS2 � � � � � � �RUNOFF � � � � � � �WESP � � � � � � �CASC2D-SED � � � � � � �SEM � � � � � � �SHESED � � � � � � �

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Process based classification divides this type of models into lumped and distributed. A

lumped model uses single values of input parameters with no spatial variability and results

in single outputs. A distributed model, however, uses spatially distributed parameters and

provides spatially distributed outputs by taking explicit account of spatial variability of the

process. A model can be considered deterministic or stochastic depending upon the way

the process is described. In physically based models, the model is called one- or two-

dimensional depending upon the number of dimensions of the mass conservation equation

used in the model. Erosion and sediment transport models generally take the non-

stationarity in the erosion process into account although a number of them are interested

only in the steady state case. A model is called an event-based model if it is used for the

simulation of sediment produced by one single rainfall–runoff event. A continuous model

is used for the simulation of sediment due to many consecutive rainfall–runoff events

occurring during a season or longer time period. Single-size erosion and sediment transport

models can only predict sediment transport for a mean grain size and can give the total

sediment mass leaving the catchment. The sediment size distribution is very important in

sediment quality since pollutants are usually sorbed to finest particles. This is achieved in

multi-size models. In a similar manner, models with rilled structure perform better in the

simulation of the natural topography in the watershed.

2.2.1. ANSWERS

The ANSWERS (Areal Nonpoint Source Watershed Response Simulation) model

(Beasley et al., 1980) includes a conceptual hydrological process and a physically based

erosion process. The erosion process assumes that sediment can be detached by both

rainfall and runoff but can only be transported by runoff. ANSWERS model divides a

watershed into small, independent elements. Within each element the runoff and erosion

processes are treated as independent functions of the hydrological and erosion parameters

of that element. In the model, surface conditions and overland flow depth in each element

are considered uniform. No rilling is considered. The effect of rills is assumed to be

described by the roughness coefficient of the Manning equation used in the model.

According to ANSWERS subsurface return flow and tile drainage are assumed to produce

no sediment. A detached sediment particle is reattached to the soil, if it deposits.

Detachment of such a particle requires the same amount of energy as required for the

original detachment. Channel erosion is negligible. In the erosion part, the differential

equation given by Foster and Meyer (1972) is used. Preparing input data file for

ANSWERS is rather complex (Norman, 1989) as it is the case for many physically based

hydrology and erosion and sediment transport models. The model can be considered a tool

for comparative results for various treatment and management strategies (Beasley et al.,

1980). Park et al. (1982) added a sediment transport component to the previously

developed ANSWERS hydrological model. In this new form ANSWERS is a single event

model, and it uses distributed parameters. Also a channel erosion component is included in

the new version.

2.2.2. LISEM

Because of spatial and temporal variation in runoff and soil erosion processes, GIS has

been a very useful tool to use in hydrological applications. The LImburg Soil Erosion

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 255

Model (LISEM) (De Roo et al., 1996) is one of the first models that use GIS. Although it

is physically based, LISEM mostly uses empirically derived equations. The model, in the

soil erosion part, accounts also for roads, wheel tracks and channels. There are some

indices used for prediction of the soil erosion (De Roo, 1998). For example, wetness index,

defined as the natural logarithm of As /S where As=contributing area and S=slope

gradient, can be used to identify possible stream paths. Wetness index can also be used for

indicating wet and dry areas, and thus possible source areas for saturation overland flow,

which is one of the main causes of erosion. The wetness index originally comes from the

TOPMODEL of Beven and Kirkby (1979). Flow detachment risk is related to the stream

power index, which is the product of the unit contributing area and slope gradient. There is

also a sediment transporting capacity index, which is again a function of contributing unit

area and slope. The above given indices are used to give the soil erosion hazard index.

GIS can be used in obtaining the index maps of the basin. CATSOP experimental

watershed located in the Limburg area in the Netherlands was used for calibration and

validation of the LISEM model parameters. EROSION 2D/3D (Schmidt et al., 1999) is

another model, with similar structure to LISEM, for which an application based on the

same data set from the CATSOP watershed was performed.

2.2.3. CREAMS

The sediment transport component of CREAMS (Chemicals, Runoff, and Erosion from

Agricultural Management Systems) analyzes the interrill area and rill separately.

Detachment on both rill and interrill area is determined by the modified USLE. The

procedure allows parameters to change along the overland flow profile and along

waterways to describe spatial variability (Foster et al., 1981).

2.2.4. WEPP

WEPP (Water Erosion Prediction Project) (Nearing et al., 1989) is a model to predict

soil erosion and sediment delivery from fields, farms, forests, rangelands, construction

sites and urban areas (Laflen et al., 1997). It is a daily continuous model. WEPP divides

runoff between rills and interrill areas. Consequently, it calculates erosion in the rills and

interrill areas separately. The steady-state sediment continuity equation is used to predict

rill and interrill processes (Nearing et al., 1989). Rill erosion occurs if the shear stress

exerted by flow exceeds the critical shear stress while sediment load in the flow is smaller

than the transport capacity of flow. Interrill erosion is considered to be proportional to the

square of the rainfall intensity. Interrill area delivers sediment to rills. The model solves the

non-dimensional (normalized) detachment and deposition equations. The normalized load

is calculated and then is converted to the actual load. It was found by Zhang et al. (1996b)

that the model was reliable in predicting long term averages of soil loss under cropped

conditions.

2.2.5. EUROSEM

The EUROpean Soil Erosion Model, EUROSEM, (Morgan et al., 1998) is a model for

predicting soil erosion by water from fields and small catchments. The model was

designed as an event-based model, since it was thought that erosion was dominated by

only a few events per year. Moreover, continuous models require substantial amount of

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271256

data, as many of them are not physically measurable at field or in the laboratory.

EUROSEM is a dynamic erosion model and is able to simulate sediment transport,

erosion and deposition by rill and interrill processes over the hillslope. The model

provides total runoff, total soil loss, storm hydrograph and storm sediment graph. In

EUROSEM, soil detachment by raindrop impact is the sum of the direct throughfall and

leaf drainage and it depends on the kinetic energy of the rainfall. Splash erosion takes

place before runoff begins. Therefore, initial sediment concentration should be taken as a

non-zero value. Three cases were considered for hillslope erosion: hillslopes without rills,

hillslopes with rills and interrill areas, and hillslopes with very dense rill structure. The

channel erosion process is treated similar to the rill erosion with the exception that the

raindrop impact is neglected and lateral inflow of sediment to the channel from the

hillslope becomes important. Bank collapse is not simulated (Morgan et al., 1998, 1999;

Kinnell, 1999). EUROSEM was applied to the CATSOP experimental watershed in the

Netherlands. This is a watershed on which LISEM (De Roo et al., 1996) and EROSION

2D/3D (Schmidt et al., 1999) were also applied. The model was found to be useful for

the short duration storms, which were characterized by a single pulse of rainfall (Folly et

al., 1999). Veihe and Quinton (2000) and Veihe et al. (2000) used Monte Carlo

simulations for the sensitivity analysis of hydrological, soil and vegetation parameters of

EUROSEM as well as the effect of rills and rock fragments. Hydrological parameters

were found to be the most important parameters. Detachability and cohesion of the soil

were also found to be important but vegetation parameters were found to have

insignificant effect.

2.2.6. KINEROS

KINEROS (KINematic EROsion Simulation) (Smith, 1981; Woolhiser et al., 1990) is

composed of elements of a network, such as planes, channels or conduits, and ponds or

detention storages, connected to each other. KINEROS is an extension of KINGEN, a

model developed by Rovey et al. (1977), with incorporation of erosion and sediment

transport components. The sediment component of the model is based upon the one-

dimensional unsteady state continuity equation. Erosion/deposition rate is the combination

of raindrop splash erosion and hydraulic erosion/deposition rates. Splash erosion rate is

given by an empirical equation in which the rate is proportional to the second power of the

rainfall. Hydraulic (runoff) erosion rate is estimated to be proportional to the transport

capacity deficit, which is the difference between the current sediment concentration in the

flow and steady state maximum concentration. Hydraulic erosion may be positive or

negative depending upon the local transport capacity. A modified form of the equation of

Engelund and Hansen (1967) was used for determining the steady state flow

concentration. A single-mean sediment particle size was used in the formulation.

KINEROS does not explicitly separate rill and interrill erosion. Channel erosion is taken

the same as the upland erosion except for the omission of the splash erosion as it is no

longer effective on erosion in the channel phase. Soil and sediment are characterised by a

distribution of up to five size class intervals in the new version of the model, KINEROS2

(Smith et al., 1995a,b). Smith et al. (1999) applied the model to a catchment in the

Netherlands. It was also applied to a catchment in Northern Thailand to see its

applicability for unpaved mountain roads (Ziegler et al., 2001).

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 257

2.2.7. RUNOFF

The sediment transport component of RUNOFF (Borah, 1989) computes soil erosion

and routes the sediment to the downstream end of the slope on which flow occurs. The

model has two parameters: flow detachment coefficient that should be calibrated by the

observed data, and the raindrop detachment coefficient that is fixed. Although the model

simulated the sediment discharge reasonably, there are, however, some discrepancies due

to parameters fixed in time.

2.2.8. WESP

Using the one-dimensional continuity equation for sediment transport Lopes (1987) and

Lopes and Lane (1988) developed a physically based, event-oriented mathematical model

for sedimentation in small watersheds. The sediment-flux term of the model for overland

flow area is an outcome of the sediment entrainment by overland flow shear stress, the rate

of sediment entrainment by rainfall impact and the rate of sediment deposition. In the

model, it is assumed that both erosion and deposition occur simultaneously. Erosion by

overland flow shear stress is proportional to a power of the average shear stress acting on

the soil surface.

ER ¼ KR sð Þk : ð3Þ

In Eq. (3), KR is soil detachability factor, s average effective shear stress, and k an

exponent equal to 1.5 in Lopes (1987). Note that in this formulation there is no critical

shear stress that should be exceeded for the initiation of sediment particles. WESP assumes

there are always fine particles of sediment, detached by the action of wind or other

elements between storm events which will be available for transport by sheet flow as soon

as rainfall exceeds infiltration rate, without any resistance to removal (Lopes, 1987).

Sediment deposition rate, simultaneously occurring together with erosion, is given by

d ¼ aVsCs ð4Þ

where a is dimensionless coefficient depending upon the soil and fluid properties, Vs

particle fall velocity, and Cs sediment concentration. In the case of uniform rainfall

intensity (r), detachment by raindrop impact (EI) is given as

EI ¼ ar2 ð5Þwhere a is a coefficient to be calibrated. The channel erosion part of the model uses a

standard continuity equation with a source term composed of the rate of entrainment by

channel flow, rate of sediment deposition and lateral sediment inflow from surrounding

overland flow areas. A critical shear stress needs to be exceeded for initiation of sediment

in the channel bed. There will be no sediment as long as the flow shear stress is smaller

than the critical shear stress. The model was applied to rainfall simulator and natural data

sets. Hydrographs were simulated well, whereas sedigraphs were not. However, the total

sediment load was reproduced quite well.

Using the same method as in WESP, Santos et al. (1998) found that the initial moisture

content of the soil influenced the runoff hydrograph and hence the sedigraph. Hydrograph

and sedigraph of a rainfall event, occurring very shortly after the previous one, were

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271258

simulated well. WESP was modified by Santos et al. (2000) for large watersheds. Instead

of using the simultaneous erosion and deposition concept of the original WESP model,

flux of sediment transport by overland flow was calculated as the difference between the

erosion and deposition.

2.2.9. CASC2D-SED

The upland erosion routine of the physically based hydrological model CASC2D was

introduced by Johnson et al. (2000). The hydrological model uses two-dimensional

continuity and momentum equations for runoff and adopts the diffusion wave

approximation. In the upland erosion part of the model, transport capacity of flow is

determined by a modified version of the regression equation given by Kilinc and

Richardson (1973). Although runoff hydrographs were computed reasonably well,

sedigraphs could not be simulated adequately. The sediment yield was found within a

range of 50% to 200%.

2.2.10. SEM

A distributed soil erosion and sediment transport model (SEM) (Storm et al., 1987) was

incorporated into the SHE hydrological modeling system (Abbott et al., 1986a,b). SEM

simulates the spatial and temporal variation of soil erosion in catchments. The splash-

detached soil particles are transported by overland flow. Overland flow itself has a

detachment potential, which was called flow entrainment, and was taken equal to the

transport capacity of flow. The net erosion or deposition is calculated as the difference

between the sediment load entering and leaving each grid in the catchment. The model has

two parameters to be calibrated from the available data that are related to the soil

erodibility and flow entrainment.

2.2.11. SHESED

SHESED (Wicks, 1988) is the sediment transport component of the SHE hydrological

model (Abbott et al., 1986a,b). SHESED considers erosion as the sum of erosion by

raindrop and leaf drip impacts and that by overland flow. Erosion takes place in the

channel bed too. The eroded sediment is transported by overland flow to channels. Once

the eroded sediment gets to the channel, it is further transported downstream. Soil erosion

by raindrop and leaf drip impacts is given by an equation based on the theoretical work of

Storm et al. (1987). The overland flow soil detachment is given by an equation accounting

for interrill areas and rills together. Therefore rills are not accounted for explicitly in the

model. Ground cover, given in the raindrop detachment equation, is low-lying cover,

which shields the soil from raindrop impact erosion. Canopy cover refers to taller

vegetation, which shields the soil from the direct impact of the raindrops but allows the

rainwater to coalesce on its surface and fall to the ground as large leaf drips (Wicks and

Bathurst, 1996). In SHESED, overland flow and sediment transport are based upon the

two-dimensional mass conservation equations. Either the Ackers and White (1973)

equation or the Engelund and Hansen (1967) equation is used in determining the transport

capacity of flow. Selection of the transport capacity equation in SHESED is based upon a

trial and error technique, and is chosen in the calibration stage of the model. Also the

raindrop and overland flow erodibility coefficients are calibrated. The sediment yield

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simulations showed sensitivity to the erodibility coefficient. Therefore, accurate

calibration is needed (Wicks et al., 1992). Particle size distribution is not considered.

The equation is solved by an explicit finite difference method (Bathurst et al., 1995).

Channel erosion in SHESED includes local bed erosion (bed load plus suspended load)

in the channel, sediment inflow from upstream, and sediment flow from overland flow. A

one-dimensional transport equation is used. Inputs of the channel component are overland

flow and rainfall conditions, supplied by either SHE or taken directly from measurements.

Gullying, mass movement, channel bank erosion, or erosion of frozen soil are not

considered in the SHESED. It does not feedback to SHE, meaning that change at the

channel bed elevation due to erosion is not given as input to SHE, as the change is very

small.

2.3. Hillslope scale erosion and sediment transport models

Detachment of sediment by rainfall and entrainment of sediment by overland flow on a

plane slope without rills were studied by Rose et al. (1983a). Rainfall detachment was

taken proportional to a power of rainfall rate, whereas sediment entrainment by overland

flow was given by an equation based on the stream power concept for bed-load sediment

(Bagnold, 1977). Deposition rate was considered to depend on the settling velocity of

sediment particles. The analysis resulted in an ordinary differential equation (ODE)

expressing the conservation of mass of sediment. Application of the theory to data from a

plane slope in an arid region in Arizona (Rose et al., 1983b) showed good agreement

between measured and calculated sediment concentrations and fluxes over time. Hairsine

and Rose (1991) developed a formula describing rainfall detachment in the absence of

overland flow driven erosion. Rate of rainfall detachment per unit area of soil (EI) was

assumed to be dependent upon rainfall rate (r) as

EI ¼ arb ð6Þ

where a is detachability coefficient of the original soil, b an exponent that can be equated

to unity (Proffitt et al., 1991). Detachment of the original soil and re-detachment of the

deposited sediment were considered separately. Sediment was classified based upon the

particle settling velocity. In the study by Hairsine and Rose (1992a), a new model for

erosion on a plane surface was developed using physical principles. The model uses the

stream power approach (Bagnold, 1966) and considers the raindrop impact and overland

flow removal. The model also contains the deposition and re-entrainment of the deposited

sediment. By considering the rill formations (Hairsine and Rose, 1992b) the model was

further developed. In the stochastic model of Lisle et al. (1998), trajectories of sediment

particles were represented by alternating periods of rest (stationary phase) and motion

(mobile phase). A sediment particle was supposed to have only two velocity states: resting

on the bed (zero velocity), and moving in the water at the water velocity u. Parlange et al.

(1999) gave an analytical approximation with similar mathematical structure of studies

mentioned above, for rainfall induced erosion on a hillslope. Sediment sorting was

investigated by Hairsine et al. (1999), and theoretical results were compared to

experimental results provided by Proffitt et al. (1991). A simple experimental set-up

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was developed for rainfall induced erosion on hillslope (Heilig et al., 2001). Another study

performed by Siepel et al. (2002) took the effect of vegetation elements on rainfall induced

erosion at hillslope scale.

Govindaraju and Kavvas (1991) coupled analytical solutions developed by Govindaraju

et al. (1990) for overland flow to the erosion model of Foster and Meyer (1972). The

overland flow component used the diffusion wave approximation. The overland flow

depth was approximated by a sinusoidal expression. Analytical solutions, obtained after

coupling, were compared to the experimental results of Kilinc and Richardson (1973) and

Singer and Walker (1983).

The influence of micro-topography on overland flow and erosion and sediment

transport is of great importance. Flow discharge and sediment discharge in rills are greater

than those on interrill areas. Knowing the importance of the micro topography Kavvas and

Govindaraju (1992) and Govindaraju and Kavvas (1992) modeled the rill structure of a

hillslope. A non-dimensional erosion formulation was developed by Govindaraju (1995)

who reduced the number of calibration parameters, to be used in the formulation, to only

two. The first gave the erodibility characteristics of the soil, whereas the second defined

the stage of the erosion process. Soil erosion is sensitive to both the critical shear stress

and the soil erodibility. Govindaraju (1998) explained the stochastic structure of these two

factors by taking the flow dynamics into account. The critical shear stress, assumed to be

exponentially distributed along the slope length, and soil erodibility were treated as

homogeneous uncorrelated random variables.

Laguna and Giraldez (1993) aimed to explore the fit of kinematic wave simplification

to the sediment transport processes. A sensitivity analysis was performed. The analysis

showed the sensitivity to interrill erosion parameters to be high at the rising stage during

which erosion processes are controlled by the rainfall impact detachment. Erosion was,

however, found to be sensitive to the rill erosion component of the model at the recession

stage during which soil loss is primarily due to rill erosion. This means, as stated before,

that erosion on the interrill area controls the rising stage of erosion while the rill erosion

controls the recession stage. From the study, it was also seen that there was no clear

relationship between sediment yield and peak runoff rate. However, important relations

between sediment yield and runoff volume and rainfall rate were found. The kinematic

wave approximation was found to be an applicable approach for modelling sediment

transport. Tayfur (2001) used the two-dimensional flow and sediment continuity equations

with the kinematic wave approximation. The erosion term in the sediment mass

conservation equation was considered as the sum of raindrop induced (rainfall) erosion

and sheet flow generated (runoff) erosion. Soil detachment due to raindrop was related to

the rainfall intensity and overland flow depth. Erosion by overland flow is a linear function

of the difference between the transport capacity of the flow and the sediment load in the

flow. Based upon the analysis in the study, the most sensitive parameters were found to be

the soil erodibility coefficient (g) and the exponent (k) in

Tc ¼ g s � scð Þk ð7Þ

where Tc is transport capacity of flow, s and sc flow shear stress and its critical value,

respectively. A recent study was performed by Aksoy and Kavvas (2001) for erosion and

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sediment transport at hillslope scale. Rill and interrill interaction over the hillslope, which

was not taken into account in many of the existing models, was considered. Formulation

for the interrill area used the two-dimensional continuity equation plus momentum

equation simplified with kinematic wave approximation. Erosion was divided into rainfall

erosion for which a simple formula depending upon the rainfall intensity was used, and

runoff erosion for which the transport capacity was determined by Yalin (1963) equation.

Non-physical erosion parameters included in the rainfall and runoff erosion equations were

calibrated by using a field experimental data set. Aksoy and Kavvas (2001), in order to

simplify the modelling technique, reduced the two-dimensional partial differential

equation (PDE) governing the erosion and sediment transport process over interrill area

into a one-dimensional form. The original PDE was even reduced to an ODE at hillslope

scale by means of areal averaging of the original conservation equation.

2.4. Transport capacity of overland flow

Sediment transport capacity of overland flow is the maximum flux of sediment that

flow is capable to transport. All physically based soil erosion models contain a sediment

transport equation. Many of the existing models use either a bed load or a total load

formula originally developed for rivers. Other soil erosion models use simple empirical

formulas. Sediment transport capacity can be formulated by either sediment concentration

or sediment load. Concentration is a more fundamental variable than the sediment load.

Early approaches to the sediment transport capacity have used the shear stress (Yalin,

1963), stream power (Bagnold, 1966), or unit stream power (Yang, 1972). Alonso et al.

(1981), after comparison of nine sediment transport formulas, suggested the use of Yalin’s

(1963) equation in computing the sediment transport capacity for overland flow. Nearing

et al. (1989) used a simplified function of the hydraulic shear stress acting on the soil for

calculating the sediment transport capacity of flow. Tayfur (2002) analysed those

approaches and concluded that the unit stream power could be selected for the simulation

of unsteady state erosion and sediment transport from very mild bare slopes and, under

low rainfall intensities, it could also be employed to simulate loads from mild and steep

slopes. For the very steep slopes, the shear stress and stream power models could be used.

The stream power and the shear stress models could also be employed in order to simulate

sediment load from mild and steep slopes under high rainfall intensity.

Based upon data of nearly 10 years in a semi-arid area of New Mexico, USA, Emmett

(1970) concluded that sediment and organic content in overland flow was positively

correlated with ground slope and negatively correlated with vegetation. A general

relationship between variables that affect the sediment transport capacity was developed

by Julien and Simons (1985) as

qs ¼ aSbqcrd 1� scs

�e�ð8Þ

where qs is sediment discharge, S slope, q discharge, r rainfall intensity, sc critical shearstress, s actual shear stress, a a coefficient and b, c, d, e exponents to be determined from

laboratory or field experiments. When sc remains very small compared to s and when it is

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271262

considered that the sediment transport capacity of turbulent flow in deep channels is not a

function of rainfall then Eq. (8) reduces to

qs ¼ aSbqc: ð9Þ

Prosser and Rustomji (2000) addressed the same equation for the sediment transport

capacity. As q is a function of the upslope contributing area, sediment discharge is

evaluated completely by topographic factors. From examination of many studies based

upon flumes, laboratory and field plots and rivers, b and c, exponents of S and q in Eq.

(9), were found to be bounded by 0.5 and 2.0, as lower and upper limits, respectively.

When one single combination is desired, a median value of 1.4 can be used for both

exponents. The sediment transport capacity (Tc) of overland flow was also found to be

proportional to the overland flow discharge ( q) only, as Tc~qc, where c ranged between

1.2 and 1.5. Then the sediment concentration (Cs) in the runoff becomes Cs~qc�1

(Novotny and Chesters, 1989). Abrahams et al. (1998) obtained a regression equation for

the transport capacity of overland flow by combining results of laboratory experiments.

2.5. Data requirement

The data requirements of any model dramatically increase with the complexity included

in the model. Distributed models, in particular, need more data than other models. Erosion

and sediment transport models contain non-physical parameters in formulating the rainfall

and runoff erosion. This requires data for calibrating and then validating those parameters.

However, it is known that it is a difficult task to collect erosion and sediment data from a

watershed or from a specific hillslope in a watershed. Data collection is much harder for

detailed models. For example, collecting data for a model with no rill and interrill area

distinction will be much easier than doing it for a model with this distinction.

Input data for erosion and sediment transport models include outputs from hydrological

models. Therefore, in order to be able to run any erosion model it is first required to run a

hydrological model so that the hydrological outputs can be supplied as input for the

erosion model. An erosion modeller should either run the hydrological part of the model or

the modeller should be supplied with the hydrological inputs. GIS has been a very

important tool in developing data files required for the models. It helps modellers to use

more complicated models, as preparing data with GIS is easier than doing it by traditional

ways. By using GIS, a parameter can be distributed not only in time but also in space.

3. Extension of a sediment transport model to a sediment-bound pollutant transport

model

Pollutant or nutrient yield can be simply calculated by multiplying the sediment yield

by a potency factor, which is pollutant content of the sediment. This content is usually

given in grams of pollutant in grams of soil. Non-point pollution is caused by humankind’s

activities on the land and differs from the natural erosion and sediment movement. For

example; erosion and sediment transport caused by cutting a forest down is considered

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 263

pollution, while a mudslide, caused by an earthquake, is not. Sediment concentrations two

orders of magnitude lower than the natural erosion are not tolerable if they are caused by

non-point pollution. Use of lumped models is avoided in water quality studies as the

delivery process and related parameters represent a hydrologic stochastic process. It is

therefore suggested to take the stochastic structure of the nonpoint pollution processes into

account and also to establish the statistical characteristics of the processes (Novotny and

Chesters, 1989).

Sediment yield of a stream is strongly related to the flow. Flow is monitored in streams

more frequently than the sediment concentration or phosphorus loads. Therefore, relations

between flow and sediment or phosphorus are usually based on some regression equations.

For example, sediment–turbidity relationship is used to convert a time-series of turbidity to

suspended sediment concentration. If turbidity is missing for a period but flow has been

measured at that period, the suspended sediment–flow relationship can be used to fill the

gaps in the data (Green et al., 1999).

Phosphorus transported by the flow is much more than that associated with the soil

since phosphorus is mainly associated with finer particles (Quinton, 1999). It is known that

phosphorus mainly moves with sediment by being attached to the surface of sediment

particles. Therefore, it is reasonable to assume the sediment transport process as an

indicator of phosphorus transport. Chemical properties are other factors that should be

taken into account in the soil detachment processes, yet none of the existing models do so.

Akan (1987) studied pollutant washoff by overland flow on impervious surfaces.

Ashraf and Borah (1992) worked on the modeling of pollutant transport in runoff and

sediment. Yan and Kahawita (1997, 2000) and Wallach et al. (2001) studied modeling

pollutants in the overland flow at the hillslope scale.

A model called SPNM (Sediment–Phosphorus–Nitrogen Model) was developed by

Williams (1980) for simulating contribution of agriculture to water pollution. SPNM was

designed to predict sediment, P, and N yields for individual storms and to route these

yields through streams. The model computes the total sediment yield predicted by the

Modified Universal Soil Loss Equation (MUSLE). The P model predicts average annual P

yields. The N model simulates both organic and inorganic N yields associated with the

sediment and runoff. The organic N model has the same structure as the P model because

both N and P are transported with sediment. The organic N tends to associate with fine

clay, whereas P tends to associate with coarse clay and silt as well as fine clay. The nitrate

concentration in surface and subsurface flow are modeled separately. SPNM gave good

results for sediment yield. Results for nutrients were found realistic.

AGNPS (Young et al., 1989) has a subcomponent for estimating P, N and COD

(chemical oxygen demand). Chemical transport calculations are divided into soluble and

sediment adsorbed phases. Nutrient yield in the sediment-adsorbed phase is obtained by

multiplying the total sediment yield in a cell by the nutrient content in the field soil and the

enrichment ratio, which is a function of sediment yield. Soluble nutrient yield is estimated

by multiplying total runoff by the mean concentration of the nutrient at the soil surface

during runoff and an extraction coefficient of nutrient for movement into runoff.

SHETRAN (Ewen et al., 2000) is a reactive solute transport model. Three main

components in SHETRAN are water flow, sediment transport and solute transport. Flow is

assumed not to be affected by sediment transport and sediment transport not to be affected

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271264

by solute transport. Therefore, the three components are independent of each other.

SHETRAN models a single complete river basin. It has a stream link and column

structure. River network is modeled as stream links and the rest of the basin is modeled as

a set of columns. Transport along the links and vertical transport in the columns are the

two main movements. There is also lateral movement between cells in neighboring

columns. Later, Birkinshaw and Ewen (2000) developed a nitrogen transformation

component and integrated it into the SHETRAN.

4. Summary of review and projections for the future

Erosion is a very important natural phenomenon ending with soil loss. It causes also

loss of storage volume in river reservoirs where eroded sediment deposits. The USLE was

designed as a tool to be used in the management practices of agricultural lands. It is the

first attempt in computing the sediment yield of a catchment. Although its development is

based on data from the United States, it has been used widely all over the world. The

USLE with some modifications and revisions is still a useful tool in watershed

management. A large number of the existing erosion and sediment transport models are

based on the USLE. Their applications are, however, limited to the environmental

circumstances from which the USLE was generated.

Limitations of the USLE and its modified or revised versions (MUSLE and RUSLE)

forced modelers to use distinctly different alternatives. WEPP in the United States and

SHESED and EUROSEM in Europe were derived based on physical description of the

erosion and sediment transport processes. Although preparation of data for physically

based models is a hard task, they have been used extensively. It is obvious that a

physically based model has much more detail than USLE or its derivatives have.

Therefore, there has been a big effort in developing physically based erosion and sediment

transport models.

A physically based model may use lumped or distributed inputs to generate lumped or

distributed outputs. A distributed model is constructed by using partial differential

equations, whereas a lumped model is expressed by ordinary differential equations (Singh,

1995). A physically based model may be a semi-distributed model as well. This means that

not all model parameters need to be of distributed type. Some parameters, especially those

that cannot be collected easily in the field, can be used as lumped. It may also be noted that

some physically based models may include non-physical descriptions in their formulation.

For example, LISEM contains many empirically derived equations although it is presented

as a physically based model.

A differential equation, used for constructing a physically based model, may be

deterministic or stochastic. All the existing models are deterministic models where the

erosion and sediment transport processes are formulated by deterministic differential

equations. None of the models can yet consider the stochasticity included in the erosion

and sediment transport processes. Thus, models in Table 3 are categorised as distributed

type deterministic physically based erosion and sediment transport models.

Physically based models use different approximations by which they simplify the

system (nature) in formulating the erosion and sediment transport processes. One

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simplification used is to reduce the number of dimensions of the governing equations. For

example, the three dimensional topographical terrain is reduced into a two-dimensional

form. SHESED is one of those models that use erosion and sediment transport in the two-

dimensional form. Increasing number of dimensions results in more intensive computa-

tions by a model. A hillslope can be thought of as a sheet where processes take place in

one dimension. Even in two-dimensional models, the number of dimensions may be

reduced to one by performing local scale averaging. However, in such a simplification the

effect of the second dimension is not neglected but indirectly incorporated into the model.

The partial differential equation governing the process may even be reduced to an ordinary

partial differential equation (Aksoy and Kavvas, 2001).

Some physically based models do not consider the time derivative term. WEPP is such

a model. Also Foster and Meyer (1972) used the steady state continuity equation of mass

transport, which is the basis for the ANSWERS model. The case for most of the existing

physically based erosion and sediment transport models is the unsteady state where the

time derivative of sediment concentration is taken into consideration.

Initial and boundary conditions become very important in cases where the model

simulates erosion and sediment transport continuously. Continuous simulation models

require large quantities of data for weather and land use. They generate a large number of

small events that may not cause significant runoff or soil loss. Some physically based

models were, therefore, designed as event based models that can be run for each specific

event. This indicates that erosion is dominated by only a few events per year. EUROSEM

is such a model. Only SEM, SHESED and WEPP can simulate the erosion and sediment

transport continuously.

Smoothing irregularities (rills and interrill areas) over a hillslope is another

simplification although it has been shown experimentally by Govindaraju et al. (1992)

that, erosion in rills is, at least, one order of magnitude greater than erosion on interrill

areas. Therefore, modellers should be aware of the rill–interrill interaction on a hillslope

although it is not easy to incorporate it into a model. Some models are capable of

distinguishing among the sediment sizes.

Modellers aimed to construct models that are less complex than the physically based

models but that yield simulations more precise than those obtained by the USLE or its

derivatives. This directed modellers to build conceptual models where the erosion process

is conceptualised. In such a model there is a non-physical but conceptually meaningful

relation between the elements of the process.

Geographical Information Systems (GIS) have been a very useful tool for hydrologists,

in particular for physically based modellers in providing the spatially distributed data. GIS

can also supply the time distribution of the hydrological data. GIS uses the digital

elevation model (DEM) that can provide information on elevation, slope and aspect of the

catchment. By using the 10-m DEM, one can delineate the rill and gully structure of the

watershed. GIS seems, at least for now, as the only way for supplying the necessary data

for the physically based models. It is possible to incorporate the physical heterogeneity in

a catchment by using GIS. Heterogeneity in hydrological variables can, however, be

obtained by performing hydrological data measurements not only at the outlet of a

catchment but also at least at the outlet of each subcatchment. The measurements help in

assessing the hydrological behaviour of each subcatchment.

H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271266

Erosion and sediment transport models are extensions of hydrological models.

Therefore, erosion and sediment transport equations are coupled to existing hydrological

algorithms. In such a coupling, output of the hydrological model becomes input for the

erosion part of the model. In the same sense, an erosion and sediment transport model can

be extended easily to a nutrient transport model, as it is known that nutrients are mainly

transported by sediment particles. It is much easier to extend a multi-size erosion and

sediment transport model to a nutrient transport model since nutrient transport is a size

selective process.

Current physically based models are deterministic where rainfall–runoff, erosion and

sediment transport are thought of as deterministic processes. Probability based stochastic

modelling techniques can be derived in the future for the erosion and sediment transport

modelling. Such a technique should include the probability distribution of rainfall. Spatial

and temporal distribution of rainfall as a random input to the rainfall–runoff part of the

model will result in randomly simulated runoff. In such a modelling technique

heterogeneity in the physical structure of watershed (Kavvas, 1999) can be given by

probability distribution functions. Rill occurrence probability over an interrill area

(Govindaraju and Kavvas, 1992) is an example of this. Also non-physical erosion

parameters have probability distributions (Govindaraju, 1998). This is because of the

critical soil properties, such as aggregation or soil resistance to erosion, which are random

processes due to heterogeneity of soils.

Acknowledgements

The first author (H. Aksoy) was a post-doctoral researcher with the second author (M.L.

Kavvas) when this study was performed at the Hydrologic Research Laboratory,

Department of Civil and Environmental Engineering of University of California at Davis

(UCDavis). This stay was supported by Istanbul Technical University (ITU) through a

postdoctoral research scholarship, by Scientific and Technical Research Council of Turkey

(TUBITAK) through NATO B-1 postdoctoral scholarship, and by UCDavis through CA

State EPA 205J Grant. The second author’s work was supported partially by US EPA

Center for Ecological Health Research (Grant No. R819658) at University of California,

Davis, and partially by US EPA Grant No. R826282010. However, the views expressed in

this paper do not necessarily reflect those of the funding agencies, and no official

endorsement should be inferred. The authors also would like to acknowledge constructive

comments by two anonymous reviewers, guest editors (Dr. W. Cornelis and Dr. D.

Gabriels of Ghent University, Belgium), and editor-in-chief at CATENA at different stages

of this manuscript.

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