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structure imposes constraints upon how well soil
erosion models can perform. The review is
restricted to first-order variance or univariate
techniques as, despite the shortcomings of these
approaches (Summers et al ., 1993; Saltelli et al .,
2004; Pappenberger et al ., 2006, 2008; Beven,
2009), they are the most common methods used
to assess the performance of soil erosion models.
Despite the many hundreds of scientific papers
written about the Universal Soil Loss Equation
(USLE), very little research has been performed
which provides a robust evaluation of model per-
formance against observed data, whilst consider-
ing model uncertainty. Indeed, Risse et al . (1993)
stated: “Although nearly three decades of wide-
spread use have confirmed the reliability of the
Universal Soil Loss Equation, very little work has
been done to assess the error associated with it”.
Such a statement might be considered to be some-
what paradoxical if we propose that a reliable pre-
diction should be one where error is both explicit
and ideally minimal. Nonetheless, Risse et al .
(1993) demonstrated that the USLE performs rea-
sonably well when predicting soil loss from the
plots that it was originally formulated on - Nash-
Sutcliffe efficiencies of 0.58 when comparing
annual soil loss predictions with observations,
improving to 0.75 when average annual data are
considered. The model predictions were most
sensitive to the topographic factor ( LS ) and the
cover and management factor ( C ), largely due to
the multiplicative nature of the model structure
which ensures that any error associated with
parameterisation is multiplied through to the
model output. Sonneveld and Nearing (2003)
developed this point further, by illustrating that
the “… modest correlation between observed soil
losses and model calculations, even with the
same data that was used for its calibration …
raises questions about its mathematical model
structure and the robustness of the assumed
parameter values that are implicitly assigned to
the model”. To address these points, Sonneveld
and Nearing (2003) conducted a validation of the
model which tested the sensitivity of the param-
eters and demonstrated that the “USLE model is
not very robust”, which undermines the wide-
spread use of such a tool within erosion model-
ling, despite (and perhaps because of) its desirably
simple model structure. Such a conclusion is fur-
ther underlined by the work of Boomer et al .
(2008) who found that the USLE and its successor,
the R (Revised) USLE2, failed to predict sediment
yields adequately in 101 catchments in the
Chesapeake Bay area, indicating the need to eval-
uate such models with appropriate observed data
before they are useful as land management tools.
In response to the conceptually simple struc-
ture of the USLE and the vast improvements in
computational speed and processing capability
that have evolved since the late 1980s, physically-
based erosion models such as the Water Erosion
Prediction Project (WEPP), hailed as the “new
generation of erosion prediction technology”
(Laflen et al ., 1991), have been developed. With
such models came an increase in both the number
of parameters that were being used to model soil
erosion and the consequent uncertainty that was
associated with their output. Early efforts to eval-
uate model performance generally took the form
of univariate sensitivity analyses, where parame-
ters were varied one at a time, around their
'estimated' values (see Nearing et al ., 1990;
Tiscareno-Lopez et al ., 1995), in an effort to iden-
tify which parameters the model output was most
sensitive to. The goal of univariate sensitivity
analyses in this context is to understand which
parameters need to be estimated most carefully
and which parameters are more redundant within
the model structure, and therefore require less
attention. Invariably, parameters controlling the
hydraulic conductivity and the erodibility of soils
tend to exert the strongest influence on model
output, although parameters describing rainfall
characteristics, particularly rainfall intensity, are
also often found to exhibit sensitivity. Similar
findings, describing the influence of the saturated
hydraulic conductivity parameter, were also pre-
sented after sensitivity analysis of the Limburg
Soil Erosion Model, LISEM (De Roo et al ., 1996),
highlighting the importance of predicting hydrol-
ogy correctly in erosion models.
The Chemicals, Runoff, and Erosion from
Agricultural Management Systems (CREAMS)
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