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A classification of water erosion
models according to their geospatial
Christos G. Karydas
, Panos Panagos
& Ioannis Z. Gitas
School of Forestry and Natural Environment, Aristotle University
of Thessaloniki, Thessaloniki, Greece
Joint Research Centre of the European Commission, Institute for
Environment and Sustainability, Ispra, Italy
Available online: 02 Apr 2012
To cite this article: Christos G. Karydas, Panos Panagos & Ioannis Z. Gitas (2012): A classification of
water erosion models according to their geospatial characteristics, International Journal of Digital
Earth, DOI:10.1080/17538947.2012.671380
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A classification of water erosion models according to their geospatial
Christos G.Karydas
*,Panos Panagos
and Ioannis Z.Gitas
School of Forestry and Natural Environment,Aristotle University of Thessaloniki,Thessaloniki,
Joint Research Centre of the European Commission,Institute for Environment and
(Received 14 September 2011;final version received 27 February 2012)
In this article,an extensive inventory in the literature of water erosion modelling
from a geospatial point of view is conducted.Concepts of scale,spatiality and
complexity are explored and clarified in a theoretical background.Use of
Geographic Information Systems (GIS) is pointed out as facilitating data mixing
and model rescaling and thus increasing complexity in data-method relations.
Spatial scale,temporal scale and spatial methodologies are addressed as the most
determining geospatial properties underlying water erosion modelling.Setting
these properties as classification criteria,82 water erosion models are identified
and classified into eight categories.As a result,a complete overview of water
erosion models becomes available in a single table.The biggest share of the
models is found in the category of the mechanistic pathway-type event-based
models for watershed to landscape scales.In parallel,geospatial innovations that
could be considered as milestones in water erosion modelling are highlighted and
discussed.An alphabetical list of all models is also listed in the Appendix.For
manipulating scale efficiently,two promising spatial theories are suggested for
further exploitation in the future such as hierarchy theory and fractals theory.
Regarding erosion applications,uncertainty analysis within GIS is considered to
be necessary for further improving performance of erosion models.
Keywords:erosion;geospatial;model;classification;digital earth
Water erosion is a dynamic soil threat with physical and socioeconomic attributes.
Effective modelling of water erosion can provide crucial information about erosion
patterns and trends and moreover allow scenario analysis in relation to current or
potential land uses (Millington 1986).However,assessing water erosion is a difficult
undertaking as is the result of many processes influencing each other in complex
interactions and proceeds at rates that vary with space and time (Driesen 1986,
Kinnel 2005).Since the 1930s,soil scientists and decision-makers have been
developing and using models extensively in order to calculate soil loss from a field,
a hillslope or a watershed (Wischmeier and Smith 1978).Every model has to make
particular options with regard to several erosion parameters,such as extent and
duration of implementation,influencing factors,processes taken into account,
International Journal of Digital Earth,
2012,1￿22,iFirst article
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features to be assessed,forms of hazard,type of algorithm and type of assessment
(Table 1).
Rise and significant improvements in Geographic Information Systems (GIS)
and Remote Sensing,as well as the advances made in computing power have assisted
in the orientation of modelling efforts towards the spatial attributes of erosion
processes and features (De Jong 1994).GIS is defined as a computerised systemused
for collecting,storing,transforming and displaying spatial data with aviewto solving
geospatial problems (Longley et al.2004).As a result,the most prominent
contribution of GIS in erosion modelling was expected to be a more realistic
simulation of the phenomenon.Although this was accomplished in a degree,
important problems associated with erosion modelling still exist in the GIS era,or
even have been stretched (Boardman 2006).Therefore,there is a need to further
examine the role of GIS in water erosion modelling and assess the potential of
The geospatial concepts underlying water erosion modelling have been addressed
by several reviews through time (King and Delpont 1993,Zhang et al.1996,Jetten
et al.2003,Merritt et al.2003,de Vente and Poesen 2005,Vrieling 2006).
Incorporating the findings from these reviews,we aimed at exploring the geospatial
characteristics of water erosion models in a more systematic way,with a view to
answer to the following questions:
What are the most determining geospatial properties in water erosion
How GIS has influenced data-method relations,rescaling potential,model
calibration and model-user interfaces?
Are there any limitations of modern GIS for water erosion modelling?
What is the potential of using GIS in erosion studies and decision-making?
Our inventory in the literature was accomplished through a classification of the
discovered water erosion models using the most determining geospatial properties as
classification criteria.The need to classify erosion models according to their scale of
application has been stretched by Garen et al.(1999).As a result of our classification,
a complete list of 82 water erosion models (including different model versions) has
become available in a single table.Many of them are currently in use,whereas others
have paled out or have been evolved to a different model.In addition to the
Table 1.Main water erosion modelling parameters and relevant options.
Modelling parameters Modelling options
Extent Field/hillslope/watershed/landscape
Duration Event-based/averaged
Factors Climate/topography/soil/vegetation
Processes Splash detachment/runoff transfer/runoff detachment
Features Soil loss/deposition/sediment yield
Forms Sheet/rill/gully/bank
Algorithms Empirical/mechanistic
Assessment Qualitative/quantitative
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classification table,a complete alphabetical list of all models has been created and
listed in Appendix 1.We consider this review as a serious contribution to the Digital
Earth vision for a multi-dimensional,multi-scale,multi-temporal and multi-layer
information facility towards monitoring,measuring and forecasting natural and
human activity on the planet.
2.1.Model scale
There has been long evidence that most erosion parameters are scale-dependent in
one degree or another.Ciesiolka and Rose (1998) observed that studies conducted on
a smaller geographical scale (extent) tend to emphasise on-site impacts of erosion,
while studies conducted on a larger geographical scale concentrate on the off-site
impacts.Also,it has been recognised that temporal and spatial scales are closely
related in water erosion,especially with regard to sedimentation processes (de Vente
and Poesen 2005).In order to gain an overviewof the water erosion phenomena with
regard to their spatial and temporal scales,erosion processes,forms and features may
be viewed together in a spatio-temporal continuum.However,there are no crisp
thresholds to discriminate erosion parameters and most of themoverlap in space and
time (Figure 1).
The possibility of GIS to mix up large data-sets from many different sources has
facilitated model rescaling significantly.This was accomplished either by modifying
erosion model structures or by inheriting various modules from pre-existing erosion
models.Some models were evolved into completely new models with a view to
improving some specific characteristics of the original models.Inheriting their basic
Figure 1.Erosion processes (continuous blue line),forms (dashed red line) and features
(dotted brown line) placed indicatively in a spatio-temporal continuum (extent vs.duration).
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mechanisms from USLE model,which functions at a field- to hillslope-scale (Meyer
and Wischmeier 1969),EHU and CORINE models emphasised land management
and climate properties respectively,thus moving their functional scale towards
landscape (Giordano et al.1991,de Vente and Poesen 2005).
In several cases,spatial scale modifications were followed by temporal integra-
tions.An example of spatio-temporal scale adaptation is EUROSEMmodel,which
was developed originally as a field-scale event-based model (Morgan et al.1998).
Without changing name,the model was modified to function as an annual erosion
model at a watershed-scale,provided that a data-series of rainfall events would be
integrated over a year and network analysis of a set of elements and channels would
be implemented in a vector GIS environment.
Rescaling,however,has several consequences.Data are usually collected through
field measurements in experimental plots.Given,therefore,that most erosion
parameters are scale-dependent,data collected on a plot scale are not always
appropriate for developing,calibrating or validating models on a watershed scale
(Boardman 2006,Verheijen et al.2009).Scaling up models through data aggrega-
tions may cause biases,generally known in spatial statistics as the Modifiable Areal
Unit Problem (MAUP).For a partial overcoming of difficulties in scaling up,King
et al.(1998) have suggested defining erosion risk in terms of hazard severity categories
rather than absolute erosion rates.However,it is questionable if this approach could
resolve scaling problems in an understandable way or simply hide them by averaging
errors.For modelling erosion in a watershed,where processes on many scales are
involved,Merritt et al.(2003) have suggested the choice of both a module for soil loss
and a spatial disaggregation criterion for the sediment delivery process.
An inverted type of biases,those caused by inferring relations at the individual
level from groups (i.e.when a model is scaled down) are known as ecologic fallacy.
The need for scaling down erosion models has been mostly associated with a
decision-making perspective,for example allocation of erosion hot-spots in large
areas (Kirkby 1998).Through the concept of spatial autocorrelation,ecologic fallacy
and the MAUP are understood to be interrelated spatial problems (King et al.1998,
Longley et al.2004).
2.2.Model spatiality
The predominant discrimination of the literature with regard to the degree to which
spatial parameters affect erosion modelling (which fromnowon will be called ‘model
spatiality’) is between ‘lumped’ and ‘spatially distributed’ erosion models.Zhang
et al.(1996) identified spatially distributed models as those reflecting spatial
variability of processes and outputs.Merritt et al.(2003) considered an erosion
model as spatially distributed only if modules for describing sedimentation at the
watershed scale are explicitly addressed in the model structure.Jetten et al.(2003)
stretched that allocation of source and sink areas of water,sediment and associated
chemicals within a watershed,is a critical issue in erosion modelling.Furthermore,de
Vente and Poesen (2005) conclude that there is always a geospatial link of erosion
forms with erosion impacts,and more specifically sheet/rill forms with on-site
impacts and gully/bank forms with off-site impacts of erosion.Especially for
mechanistic models,Aksoy and Kavvas (2005) argue that lumped models are those
expressed by ordinary differential equations (with time being the independent
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variable),whereas distributed models are those constructed by partial differential
As it can be conceived from the above,some authors consider model structure as
the only field where a model is judged for its spatiality;whereas others take into
account both structure and data.But still,in many applications the term ‘spatially
distributed’ is related to the mere use of spatial data alone.As a result,over the years
there has been some confusion in using the terms ‘spatially distributed’ and ‘lumped’
for characterising erosion models.In order to raise this confusion,we recommend
adopting the term ‘spatially distributed’ for any case of using spatial data,no matter
if the model structure can be considered spatial or not.Therefore,we can redefine
‘spatially distributed’ and ‘lumped’ models as follows:
Spatially distributed models are those capable to produce erosion patterns in a
single run.
Lumped models are those capable to produce only a single erosion value (no
patterns) in a single run.
After this clarification,spatially distributed models can be further discriminated
according to the type of spatial method followed,into two categories:
Those using a spatial coexistence (SC) type method,in which position is the
only spatial property of erosion parameters taken into account by the model.
Most commonly,SC methods are employed to estimate soil loss at a specific
location without contribution from,or attribution to,any other neighbouring
or remote spatial entities.When raster data-sets are used,outputs can be
calculated using map algebra,while for vector data-sets an overlay set of
functions would be appropriate.
Those using a pathway (PW) type method,in which a well-defined soil
sediment transport process between sources and receptors is established.In
this case,several topological relations (e.g.association,neighbourhood,or
proximity) may be employed by the model and thus these relations constitute
parts of the model.Outputs are calculated by stepwise techniques (
analysis,flow accumulation) using either vector or raster data-sets.‘Con-
ceptual models’ as defined by Merritt et al.(2003) should be included in this
category (Figure 2).
There are several possibilities of GIS manipulating spatially distributed water erosion
models with regard to their type of methodology (SC vs.PW) and data format
(vector vs.raster) (Figure 3):
When SC methodologies are implemented with vector data-sets,there is no
possibility for interaction between spatial units (i.e.points,lines or polygons).
The role of vector features is exhausted in dividing the study area into smaller
units ( using overlay operations between GIS layers) and implementing
non-spatial algorithms on them.
When SC methodologies are implemented with raster data-sets,again there is
no interaction between spatial units (cells),but only between cells of the same
position ( using raster algebra between GIS layers).
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When PW methodologies are implemented with vector data-sets,erosion
features and parameters and their properties can be manipulated as input/
output data by explicit propagation mechanisms ( using network
analysis within GIS layers).
When PW methodologies are implemented with raster data-sets,erosion
parameters can be manipulated as input/output data by explicit propagation
mechanisms ( using neighbourhood operations within GIS layers).
Without spatial data available,there is no possibility for spatially distributed
modelling,as model implementation is eliminated into a single homogeneous area
(lumped models).
2.3.Model complexity
A large part of the applications in water erosion modelling is dedicated to the
preparation of the input data-sets.Given that data-sets are never perfect,preparation
means to bring the data-set as closely as possible to model specifications or to adapt
Figure 2.Examples of the two modelling method types:(A) implementation of a co-existence
method with rainfall raster data (coloured cells) and land use vector data (labelled black
polygons);(B) implementation of a pathway method by using vector format for both the
stream network (blue lines) and the watershed network (pink/red polygons).
Figure 3.Association of data formats with methodology types of spatially distributed models.
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a model to the properties of the data-set.In this sense,the process of matching data
with erosion model requirements can be considered as hidden calibration of the
model (Jetten et al.1999,Longley et al.2004).
The broad availability of spatial data in the last two decades has increased
complexity of data-method relations due to the following reasons:
(1) Extra dimensions were added in the input data-set,i.e.the spatial variables x,
y,z.This type of complexity can be expressed in a twofold way:
As inherent spatial heterogeneity of the data-set (thus creating within-layer
As lack of coherence between the various input data-sets (thus creating
between-layer uncertainty).
(2) Spatial relationships between erosion processes and features were introduced
in the model structure.
Spatial heterogeneity affects spatial dependency relations and,therefore,spatial
processes.Simulated experiments by Moglen and Bras (1995) have provided
analytical evidence of the influence of spatial heterogeneity of soil erodibility on
the drainage pattern of a watershed.According to their study,high heterogeneity
degrees would add small scale roughness to the topography and thus would force a
more irregular channel network.
Lack of data coherence is associated with different data sources and different
geospatial processing strategies.Indicative data sources include agricultural statistics,
census data,soil maps,remotely sensed data,expert judgments and experimental
plots.Indicative geospatial processing strategies include geostatistical operations,
neighbourhood operations,image transformations,etc.In addition to the above,
almost every operation can follow different protocols of conversion,reprojection,
aggregation,resampling and reclassification (Van Rompaey and Govers 2002).For
example,rainfall erosivity surfaces can be calculated from data recorded at weather
stations,using spatial interpolation,regression with topographic parameters,
stratification according to hydrological units or calibration according to several
geographic attributes (Grimm et al.2003).Each of these techniques may create
significantly different erosivity patterns,which are rarely validated;or are validated
based only on hydrographs and sedigraphs measured at watersheds outlets (
points),an approach which renders to become a common practice (Merritt et al.
2003,Boardman 2006).Even when spatial data-sets are available,they do not always
provide the necessary detail to evaluate erosion model performance accurately,
especially when the goal is to describe spatial heterogeneity of soil loss (Brazier et al.
Introduction of spatial relationships in model structure increased modelling
uncertainty further.A model may contain conceptual,logical,parameter and
solution uncertainties (Brown and Heuvelink 2005).‘Small slope lengths’ and
‘homogeneous hillslopes’ as required by the USLE model are examples of conceptual
uncertainty;the condition for steady state flow by most mechanistic models is an
example of logical uncertainty;while,user-defined empirical factors in the Slope
Length and Steepness (LS) formula (developed by USLE) is an example of
parameter uncertainty.Model solution uncertainties are described by the error
propagation theory (Refsgaard et al.2007).
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Furthermore,conditions and assumptions of erosion models are not taken
always strictly into account by the users.For example,Digital Elevation Models
(DEMs) of 30 m cell-size are widely used in applications with USLE-family models
although they cannot be considered quite appropriate for it (Smets et al.2008).
Uncertainties can be stretched even more by the fact that complexity of erosion
processes increase with rain intensity and slope,as it has been showed recently by
Yang et al.(2011).
Modelling uncertainties,however,do not always affect erosion outputs in a
straightforward way,but instead are associated with the complexity degree of the
model in use (Van Rompaey and Govers 2002).For example,soil erodibility values
could be found unrealistic if estimated from a soil map in plot experiments with
USLE (straightforward procedure),whereas use of physiographic maps from which
to imply soil erodibility levels could be proved a more effective approach (Perez-
Rodriguez et al.(2007).
2.4.Model-user interface
Model-user interfaces of water erosion models have employed GIS in two different
ways (De Roo 1998):
Loose coupling of the model with GIS.In this case,the erosion model is
described by programming scripts in the analytical engine of existing GIS
software.For example,MUSLE has been integrated within ArcGIS#as an
extension called ArcMUSLE#(Zhang et al.2009).An interface to ArcGIS#
software has been developed also in the context of MIKE-SHE model.
AGNPS model has been linked to several GIS interfaces,such as Arc/Info#,
GRASS#and IDRISI#(Lenzi and Di Luizio 1997).Finally,routines of
several other models,such as TOPMODEL,ANSWERS,SWAT,or ME-
DRUSH,have been written in the GRASS GIS#software.
Embedded coupling of the model with GIS.In this case,a new GIS interface is
added to the erosion modelling system.For example,the LISEMwebsite offers
for free PCRaster#,a piece of raster-based GIS software in which the model is
fully integrated.Using IDRISI#software,WATEM (or SEDEM) has
developed its own GIS interface,which can be downloaded from the Internet.
During the 1990s and 2000s,several erosion models have become publicly
available through the Internet,either in combination or not with relevant spatial
databases.Some of these models work online,while others offer downloadable-
executable files for decision support.
3.1.Definition of classes
According to the exploration in the ‘Background’ section,three geospatial properties
can be indicated as the most determining for modelling water erosion:spatial scale,
temporal scale and spatial methodology.Note that temporal scale may well be
considered a geospatial property in a GIS framework considering its strong and
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inherent relation with spatial scale.Taking these geospatial properties as classifica-
tion criteria and following a library classification system(where each model can only
be placed in one class),an 8-class nomenclature of models was formulated from the
combination of two options per criterion.More specifically:
(1) Two classes were introduced according to models’ spatial scale (as corre-
sponding to the extent of application):
The field- to hillslope-scale models,including also the models developed
for ‘hillslopes up to small homogeneous catchments’,as is denoted quite
The watershed- to landscape-scale models;‘landscape’ in erosion model-
ling should be considered as an area far larger than a hillslope and not
fitting necessarily to a watershed.
(2) Two classes were introduced according to models’ temporal scale of
application (as corresponding primarily to the time integration method and
secondarily to the duration of the application):
The event-based models,that is,those assessing single- or multiple-events;
multi-event models can be found also as ‘continuous models’ in the
literature (Merritt et al.2003).
The averaged-based models,that is,those assessing erosion on an hourly,
daily,monthly,annual,or any other pre-defined period of time based on
long-term rainfall statistics.
(3) Two classes were introduced according to the spatial methodology type
adopted by the model structure:
The SC type models.
The PW type models.
The classes of spatial scale and spatial method have been arranged hierarchically;
thus,each of the spatial scale classes have been further divided into SC- and PW-type
classes.Models are listed in a chronological order within every class.Data format
(raster/vector) or any other data property was not considered as a determining
classification criterion.In data-method relations,methodology is considered to be
predominant over any data properties by default,as GIS offers numerous data
conversion possibilities.Different versions of the same model have been classified as
different models,because these models can have different geospatial characteristics.
The year of development is provided in brackets for every model (year of first version
if more versions have been developed),while the type of algorithm (mechanistic or
empirical) is also provided in square brackets (Table 2).
Because many models in practice comprise a mixture of mechanistic and
empirical modules,mechanistic models are considered here those having at least
one mechanistic module in their structure.Models originally developed as
coexistence-type,but later converted into PW-type ones keeping the same name,
have been classified in the group of ‘Pathway’ indicated with an asterisk.Also,a
model using a PW method for the assessment of at least one erosion factor will be
assigned to the PWmodels,irrespectively if all the rest factors are calculated with a
coexistence approach.A model adapted both to events or averaged assessments over
time will be classified in event-based models.In general,procedures of a higher
complexity degree predominate in the current model characterisation.
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3.2.Classification results
Eighty-two water erosion models were classified according to the geospatial criteria
selected and the rules described earlier (Table 2).It should be noted that only
complete procedural schemes resulting in the assessment of one or more of the three
erosion features (i.e.soil loss,deposition and sediment yield) were identified as water
erosion models.Parts of erosion procedures (usually called modules or components
of an erosion model),or integrations of erosion models with other land or water
assessment tools,have not undergone the classification,as they cannot be considered
independent erosion models.Example of an erosion module is the Hydro-
geomorphic Universal Soil Loss Equation (HUSLE),an algorithm used by
AnnAGNPS for assessing sediment delivery ratio (Bingner and Theurer 2001);
whereas,example of a multi-modelling scheme is the Sediment Phosphorus Nitrogen
Model (SPNM),an integration of MUSLE (employed for sediment yield assessment)
with models for nutrient load assessments within a FORTRAN programming
environment (Williams 1980).
In addition to the literature cited elsewhere in this study,the following titles were
also studied for evaluating the character of various erosion models populating Table
2:Frere et al.(1980),Knisel (1980),Arnold and Williams (1987),Leonard et al.
(1987),Young et al.(1987),Gavrilovic (1988),Beven et al.(1995),Smithers and
Schulze (1995),Gerlinger and Scherer (1998),De Jong et al.(1999),Kirkby and
McMahon (1999),Viney et al.(2000),Dostal et al.(2000),Van Oost et al.(2001),
Van Rompaey et al.(2001),Di Luzio et al.(2004),Capra et al.(2005),Sadeghi et al.
(2007),Le Gouee et al.(2008),Bonilla et al.(2008),Morgan and Duzant (2008),
Evrard et al.(2009),Sonneveld and Dent (2009).
4.1.Generic notifications
The first output that can be derived from the conducted classification is a
quantification of erosion models’ characteristics.More specifically,when the spatial
scale is concerned in the classification,27 models are classified as field to hillslope;
whereas 55 are classified as watershed to landscape (i.e.33% vs.67%).In terms of
temporal scale,56 models are classified as event based;whereas 26 are classified as
averaged (i.e.68% vs.32%).In terms of spatial method,23 models are classified as
SC type;whereas 59 are classified as PW type (i.e.28% vs.72%) (Figure 4).
If the discrimination of empirical vs.mechanistic models (E/Mcodes in Table 2)
is taken into account in addition to the above 8-class classification,a new 16-class
nomenclature can be proposed.In this newclassification,the name of every class can
be denoted by a code of 4 digits and more specifically by a combination of the upper-
case letters F or Wfor the spatial scale (Field/hillslope vs.Watershed/landscape),C
or P for the spatial method (Coexistence type vs.Pathway type),E or A for the
temporal scale (Event based vs.Averaged) and Mor E for the algorithmic type of the
models (Empirical vs.Mechanistic).For example,the class of field to hillslope,
coexistence type and event based,mechanistic models could be addressed as ‘FCEM’
and a model belonging to this class (e.g.MUSLE,GUEST,RHEM,etc) as a FCEM
model.The class ‘WPEM’ was found to be the most populated in the classification
table as it contains 28 models (about 1/3 of all the classified models).
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The second output that can be observed is the degree in which different model
characteristics are interrelated.The type of algorithmof the models (i.e.empirical vs.
mechanistic) was found to be related to the geospatial classification parameters in
different ways.In general,25 models were found to be empirical against 57
mechanistic (i.e.30% vs.70%).With regard to the spatial method type (i.e.SC vs.
PW),the share of SC-type is disproportionally large for the empirical models in
comparison to the generic trend (12 out of 25 or 48% of the coexistence-type class,
instead of 28% of the generic);a similar trend can be observed for the share of PW
type for the mechanistic models.However,a strong connection between type of
algorithm and spatial scale cannot be implied from the results of the classification.
Empirical models are slightly more related to the watershed to landscape scale,
whereas the mechanistic to the field to hillslope scale.
With regard to temporal scale,the vast majority of the event-based models were
found into the mechanistic class (only 7 out of 56 event-based models were
empirical).However,the majority of averaged models were found to be empirical
(8 out of 26 averaged models were mechanistic).The latter is especially true for the
coexistence-type watershed-scale models,as all of them belong to the ‘semi-
quantitative’ category according to de Vente and Poesen (2005).Therefore,it can
be argued that there is a strong link between temporal scale and type of algorithmof
the erosion models.This can be attributed possibly to the fact that mechanistic (or
physical) formulas have been used in order to describe erosion processes generated by
storm events (thus giving birth to single- or multiple-event models);whereas,similar
equations for long-termperiods statistically assessed are not yet available or have not
been exploited accordingly.
Finally,through model classification,several spatial methodological innovations
have been indicated and associated with some pioneering models.Most of these
innovations are linked to the development of PW-type models and one with the
gradual evolution of the USLE-family models.Froma geospatial point of view,these
innovations could be considered as milestones in water erosion modelling (Figure 5).
Figure 4.The number of models with similar spatio-temporal identity (see also Table 2).
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4.2.The PW-type models
PW-type models are of particular interest for geospatial analysis,because they have
the potential to exploit a variety of spatial relationships and not merely use spatial
data-sets.The first models following a PW-type were the event-based mechanistic
models.This could be attributed to the following facts:
Spatial dimensions (x,y,z) can be contained in the set of independent variables
of the partial differential equations employed by the mechanistic models
(Aksoy and Kavvas 2005).In other words,the mathematical basis of the
mechanistic models offered a fertile ground for employing spatial relationships.
Physical equations usually depend on time,a fundamental parameter in event-
based models.
Given that empirical models are based on experimentation,their adaptation to
local conditions,that is,their site-specificity,can be achieved through their
global or local calibration.Therefore,the necessity for a PWapproach was not
Several raster algorithms have been invented in order to implement PW-
methodologies,such as the slope length,the wetness index or the stream power
index,all based on spatial arrangements of cell values in topographic grids,following
the original invention of the topographic index by TOPMODEL (De Roo 1998).
Grid format was also used to divide a watershed into sub-areas,while sediment flows
would be dynamically propagated within the sub-areas.In this way,simulation of
deposition was made possible (ANSWERS model) (Beasley et al.1980).Dirichlet
tessellation (a method based on a cell-based segmentation) has been used in order to
represent upland and channel conditions.Routing from cell-to-cell was estimated by
the steady-state continuity equation of sediment (AGNPS model) (Aksoy and
Kavvas 2005).Self-organising dynamic systems were used to describe iterative
interaction between micro-topography,runoff routing and soil loss,for rill mapping.
Extraction of micro-topography patterns have been derived from photogrammetric
DEMs (RillGrow and EGEM models) (Favis-Mortlock et al.1998).
Vector features have been employed by several models to represent watershed
elements,such as planes,channels and ponds,as a set of related elements through
Figure 5.Milestones in the development or adoption of innovative techniques by some
pioneering erosion models.
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network analysis (WEPP and KINEROS models) (Nearing et al.1989,Smith et al.
1995).Hierarchical approaches have been used by MEDRUSHmodel (Kirkby 1998,
Verheijen et al.2009) to simulate erosion and runoff processes operating on a plot
scale.The results were nested within flow strips oriented up and down the slope.
Water and sediment generated at this scale was then routed via computed linear
transfer functions into the sub-catchment entities.Finally,the outputs of this scale
fed the main channel network,corresponding to the watershed scale.MEDRUSH
was a very data-demanding model,not in use any more (M.Kirkby,personal
communication,24 May 2011).
In contrast to most PW mechanistic models,PESERA and SHETRAN have
been developed for averaged assessments.Both use grid input data-sets,with
PESERAfocusing on soil loss and SHETRANfocusing on sedimentation.PESERA
has adopted simplified physical formulas for generating inputs at three stages:daily
runoff estimation,daily erosion at the hillslope base,and long-term estimation by
integrating daily outputs over time.Runoff is accumulated downslope through a
networking procedure incorporated in the model structure.Sediment erosion and
transport in SHETRANare modelled based on partial differential equations of mass
and energy conservation or by empirical equations derived from independent
experimental research (Lukey et al.2000).
A particular case of PW mechanistic models is WEHY model,which describes
hydrologic processes within a watershed,based on up scaled hydrologic conservation
equations through their ensemble-averaged forms (Kavvas et al.2004).Different
geological formations are taken into account for defining regional groundwater flow,
a characteristic facilitating erosion assessments in basins where sedimentary rock
formations underlie a watershed.The model has been implemented in the case of
Central Valley in California (Kavvas et al.2006).
4.3.The USLE-family of models
Universal Soil Loss Equation (USLE) is the most widely used empirical model,
converted from SC- into PW-type.This was achieved through the modification of its
topographic influence factor (also known as LS).The original version of USLE
model did not consider the existence of convergent and divergent slopes in water
movement,but instead it assumed the topographic slope of a study site as
homogeneous.The PW condition was satisfied through the invention of two
alternative algorithms for topographic influence estimation,both based on the
concept of ‘unit contributing area’ (measured in m
/m) instead of using slope length
and gradient.The first algorithm,developed by Moore and Burch (1986) and
proposed by Desmet and Govers (1996),was adopted also by MUSLE,RUSLE,
EPIC and G2 models;whereas,the second was associated with the development of
USPED model by Mitasova et al.(1996).
Universal Soil Loss Equation (USLE)-family models can be found in different
categories of the classification proposed in this review.USLE,RUSLE1 (identical to
RUSLE),RUSLE2 and USPED are all PW-type models (after the topographic
factor modifications) for field- to hillslope-scale,temporally averaged assessments of
soil loss.Beyond the expansion of their experimental basis,however,a geospatial
advancement of RUSLE versions (in comparison to USLE) is the fact that they
contain an extra component for assessing deposition;a feature further strengthening
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the PW character of these models.The deposition component of RUSLEs is based
on physical equations,a fact that renders them mechanistic,although they conserve
all the empirical background inherited from the original USLE (Renard et al.1991).
In cases,however,where RUSLEs are implemented for soil loss assessments only
(and not for deposition),they should not be considered as mechanistic.
The MUSLE model was evolved from USLE in order to assess single storm
events rather than long-term erosion assessments ( was modified in terms of
temporal scale only).MUSLE has not incorporated any topographic modifications,
thus keeping a coexistence-type character (Zhang et al.2009).
Ferri and Minacapilli (1995) and Ferro and Porto (2000) extended USLE with a
sediment delivery term,so as to allow it predicting sediment outputs from
watersheds.This work should be considered as multi-scale modelling,as it links
small homogeneous geomorphological units where soil loss is assessed using USLE,
with sediment yield through the drainage network of the watershed.The approach
was based on the work of Walling (1983) and had as an output the SEDD model.
The most recent G2 model takes input from month-step biophysical parameters
derived from remotely sensed data-sets on a landscape scale,thus emphasising
seasonality of soil loss assessments in the framework of a pan-European operational
service (Panagos et al.2011).
Spatial scale,temporal scale and spatial methodologies were addressed by this review
as the most determining geospatial parameters in water erosion modelling.It was
also indicated that use of GIS for water erosion modelling had the following
It facilitated multiple-source data mixing.
It created a computing environment for potential model rescaling.
It increased complexity in data-method relations.
Therefore,those spatial methodologies that are capable to handle complexity
efficiently,to serve multiple scales and to be integrated unconditionally into GIS
should be considered as privileged for simulating water erosion effectively.In
parallel,there are no signs of technological limitations that GIS could arise to such
Several spatial methodologies have been proposed for manipulating scale flexibly
and efficiently,with hierarchy theory and fractals theory being two of the most
promising cases.Hierarchy theory is a dialect of the general systems theory,focusing
on levels of organization and issues of scale.A hierarchical structure is called nested
when it involves levels which consist of,and contain,lower levels.Natural landscapes
are considered to be inherently hierarchical (O’Neill et al.1986).A description of
hierarchy principles linked to erosion processes and features is provided by Okoth
(2002).Use of hierarchy theory has already been adopted by some erosion models,
such as the MEDRUSH and RDI models (Kirkby 1998).
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Fractals theory attempts to model complex processes by searching for the simple
processes underneath.Afractal is a rough or fragmented geometric shape that can be
split into parts,each of which is a reduced-size copy of the whole,a property called
self-similarity (Mandelbrot 1982).Fractal geometry is considered to be especially
powerful for characterizing the Earth’s surface.Takayasu and Inaoka (1992)
modelled the erosion process on a two-dimensional triangular lattice using fractal
geometry.The model was graphically demonstrated through an evolution of river
and contour patterns.
5.2.Decision making
When erosion modelling is serving primarily decision-making support,the degree of
the outputs’ uncertainty becomes a critical parameter.If the sources of uncertainty
become known to the modellers (i.e.the uncertainty can be explained),the outputs
can either be improved or be accepted within a specific decision-making framework.
In order to estimate uncertainty degree and causes,the analysis should be conducted
in advance of model development or implementation, parallel with problem
definition,identification of modelling objectives,and throughout the whole
modelling process (Refsgaard et al.2007).
Among other approaches,an extended peer review of the quality assurance of
modelling process by stakeholders is an accepted method of uncertainty analysis in
environmental modelling.Although stakeholders reasoning,observation and judge-
ment are not always bounded by scientific rationality,this method can be proved
beneficial when tackling ill-structured,complex environmental problems such as
erosion (Refsgaard et al.2007).Broadman (2006) argued that the involvement
of decision makers specifically at the field level would be a challenge towards a
dynamic modelling environment.This consideration agrees particularly with the
purpose of many modelling approaches, allocate and map hot spots of erosion
instead of detailed erosion outputs.This approach was followed by Adinarayanaa et
al.(1999),who combined data resources and expert information in a rule-based
approach in order to map spatial patterns in terms of erosion severity using the
USLE model.
New policy developments,such as the INSPIRE Directive (2007),are expected to
have a positive influence to national and local authorities in Europe towards sharing
their data-sets,thus promoting accessibility to reliable and updated spatial data-sets.
In addition,recent advances in service-oriented architectures allow users to migrate
from dedicated desktop solutions to online,loosely coupled and standards-based
services (Panagos et al.2008,Granell et al.2010).
The big number of erosion models reflects the high complexity of the problem
and the different management needs ought to serve.Specific models can be very
successful for particular spatial and temporal scales and consequently for particular
management needs.The conducted classification in this review creates a basis for
model comparison and could support decision makers in selecting appropriate
models for their purposes.However,model selection should be followed by
uncertainty analysis within GIS,an alternative in exploring data-method relations,
given that model validation is a very tough task at the decision-making level.
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This study was supported by the Research Committee of the Aristotle University of
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Appendix 1:Alphabetical list of the inventoried water erosion models
ACTMO:Agricultural Chemical Transfer MOdel
ACRU:Agricultural Catchments Research Unit
AGNPS:Agricultural Non-Point Source pollution
AnnAGNPS:Annualized AGNPS
ANSWERS:Areal Nonpoint Source Watershed Environmental Response Simulation
ARM:Agricultural Runoff Management
BTOPMC:Block-wise use of TOPMODEL with Muskingum-Cunge flow routing method
CASC2D-SED:CASCade 2-Dimensional SEDimentation
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CORINE:COoRdinate INformation on the Environment
CREAMS:Chemicals,Runoff and Erosion from Agricultural Management Systems
CSEP:Climatic index for Soil Erosion Potential
CSSM:Coleman and Scatena Scoring Model (named partially after the authors Coleman and
DWSM:Dynamic Watershed Simulation Model
EGEM:Ephemeral Gully Erosion Model
EHU:Erosion Hazard Units
EPIC:Erosion Productivity Index Calculator (original name) or Environmental Policy
Integrated Climate (current name)
EPM:Erosion Potential Method (identical to Gavrilovic model)
EROSION 2D/3D:EROSION 2-Dimensional/3-Dimensional
EUROSEM:EUROpean Soil Erosion Model
EUROWISE:EUROpe WIthin Storm Erosion (named partially after the project ‘Modelling
Within Storm Erosion Dynamics’)
FKSM:Fleming and Kadhimi Scoring Model (named partially after the authors Fleming and
FSM:Factorial Scoring Model
G2:Geoland2 (named after the project ‘geoland2’)
Gavrilovic/EPM:(named after the main author)/Erosion Potential Model
GLEAMS:Groundwater Loading Effects of Agricultural Management Systems
GUEST:Griffith University Erosion System Template (named partially after the university-
HSPF:Hydrologic Simulation Program ￿ FORTRAN
IHACRES-WQ:Identification of unit Hydrographs And Components flows from Rainfall,
Evaporation and Streamflow data ￿ Water Quality
IQQM:Integrated Quantity and Quality Model
KINEROS:KINematic EROsion Simulation
LASCAM:LArge Scale CAtchment Model
LEAP:Land Erosion Analysis Programs
LISEM:LImburg Soil Erosion Model (named partially after the university-developer)
MEDALUS:MEditerranean Desertification And Land USe impacts
MEDRUSH:MEdalus Desertification Response Unit SHe (see below)
MEFIDIS:Modelo de Erosao FIsico e DIStribuido (Portuguese acronym for ‘Physically
Based Distributed Erosion Model’)
MESALES:Mode`le d’Evaluation Spatiale de l’ALe´a Erosion des Sols (French acronym for
‘Spatial Model Evaluation of Soil Erosion Hazard’) (identical to PESERA model)
MIKE/SHE:MIKE (named partially after the author Michael (Mike) Abbott) ￿ SHE (see
MMF:Morgan-Morgan-Finney (named after the initials of the authors Morgan,Morgan,
and Finney)
MULTSED:MULTiple-watershed SEDiment-routing
MUSLE:Modified USLE (see below)
OPUS (not an acronym)
PALMS:Precision Agricultural-Landscape Modeling System
PEPP:Process-orientated Erosion Prediction Program
PESERA:Pan European Soil Erosion Risk Assessment
PRMS:Precipitation-Runoff Modeling System
PSIAC:Pacific Southwest Inter-Agency Committee
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RDI:Regional Degradation Index
RHEM:Rangeland Hydrology and Erosion Model
RillGrow (not an acronym)
RillGrow2 (not an acronym)
Rose:(named after the main author)
RUNOFF (not an acronym)
RUSLE:Revised USLE (see below)
SCALES:Spatialisation d’e´Chelle fi ne de l’ALe´a Erosion des Sols (French acronym for
‘Large-Scale Assessment and Mapping Model of Soil Erosion Hazard’)
SEDD:SEdiment Delivery Distributed
SEDEM:SEdiment DElivery Model (identical to WATEM)
SedNet:SEDiment river NETwork
SEM:Soil Erosion Model
SEMMED:Soil Erosion Model for MEDiterranean areas
SHE:Syste`me Hydrologique Europe´en (French acronym for ‘European Hydrologic System’)
SHE-SED:SHE ￿ SEDimentation
SHETRAN:SHE sediment and solute TRANsport
SIMWE:SIMulation of Water Erosion
SLEMSA:Soil Loss Estimation Model for Southern Africa
SMODERP:Simulation Model of OverlanD flow and ERosion Processes
STREAM:Sealing,Transfer,Runoff,Erosion,Agricultural Modification
SWAT:Soil and Water Assessment Tool
SWIM:Soil and Water Integrated Model
SWRRB:Simulator for Water Resources in Rural Basins
TREX:Two-dimensional Runoff,Erosion,and eXport
USLE:Universal Soil Loss Equation
USPED:Unit Stream Power based Erosion Deposition
VSD:Vegetation Surface material Drainage density
WATEM:WAter and Tillage Erosion Model
WEHY:Watershed Environmental HYdrologic
WEPP:Water Erosion Prediction Process
WESP:Watershed Erosion Simulation Program
WSM:Wallingford Scoring Model (named partially after the company-developer)
Notes:The word ‘model’ has been included in the full name only if it is a part of the acronym.
22 C.G.Karydas et al.
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