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, Turkey b 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/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.catena.2005.08.008 * Corresponding author. Fax: +90 212 2856587. E-mail address: [email protected] (H. Aksoy). Catena 64 (2005) 247 – 271 www.elsevier.com/locate/catena
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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.
H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271254
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
H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 259
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
H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271260
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
H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 261
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
H. Aksoy, M.L. Kavvas / Catena 64 (2005) 247–271 265
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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