Dealing with Uncertainty in Erosion Model Predictions - Erosion Modelling - page 60

(2) Although some effort was made by Wei et al .
(2007) to relate the model sensitivity to observed
soil loss, this was not done in a structured sense,
so that there is no indication of how well the
model performs against the real world data (eval-
uation), just a suggestion that there is more model
sensitivity in the predictions made of low soil
loss. Further progress is made with analysis of the
RHEM in Wei et al . (2008) (see below).
Finally, an example of a recent sensitivity
analysis was conducted by Morgan and Duzant
(2008) on the Morgan-Morgan-Finney (MMF)
model. Improvements to the original MMF model
were made in order to account for the effects of
vegetation cover on soil erosion predictions. The
approach was similar to that of Nearing et al .
(1990) - as described above - which holds all
parameters at a set value whilst varying one at a
time to study the effects upon model output.
Results were ranked in terms of relative influ-
ence on model output and were deemed to be
acceptable as they conformed to previous analy-
sis of the MMF model (Morgan et al ., 1984). The
main criticism here (in addition to those described
in the previous paragraph) is that unlike the
recent modifications to the model that Morgan
and Duzant (2008) provide, the approach used to
assess the model performance is more than 20
years old and has been superseded by a range of
methods described below that provide a far more
informative perspective on model uncertainty.
As has been demonstrated, sensitivity analy-
ses may serve as a useful initial exploration of the
importance of each parameter within a model
structure, as many of the above-mentioned mod-
els contain dozens of parameters, not all of which
can be well estimated. Model complexity, how-
ever, is not easily explored simply by varying sin-
gle parameters, and indeed it has been argued that
a meaningful exploration of the multidimen-
sional parameter space that these models occupy
demands the variation of multiple parameters in
parallel with each other (Saltelli et al ., 2004;
Pappenberger et al ., 2006, 2008; Beven, 2009).
Univariate approaches provide no assessment of
the interaction of parameters or the levels of
autocorrelation between parameters, which may

exert more (or a different) control on model out-
put than the variation of a single parameter in
isolation. In addition, many sensitivity analyses
are carried out without recourse to observed data
as forward error or uncertainty analyses. Such
exercises can be conducted as useful numerical
experiments to underpin more robust evaluation
or even calibration of less certain parts of the
erosion model. For example, Wainwright et al .
(2008a,b,c) calibrated sensitive hydrological
parameters to test performance of different sedi-
ment models for the correct hydrological reasons.
However, ideally, sensitivity of a model to varia-
tions in parameter values should be assessed via
comparison of model output with observed data,
in order to relate model predictions to the real
world (Brazier et al ., 2000). Therefore, the types
of sensitivity analyses described above are per-
haps best used as the starting point of model eval-
uation, as just one of the tools that an erosion
modeller may employ to explore model capabil-
ity and test model performance.

4.5.2 Forward error analysis

of erosion models

Numerous papers describe the 'error' associated
with model predictions with respect to some
objective function of model performance when
compared with observed data. Examples of such
an approach to understanding 'error' in the USLE
and derivatives are illustrated in Risse et al .
(1993), Spaeth et al . (2003) and Tiwari et al . (2000).
Very few authors, however, try to analyse the
sources of this error within the model parame-
ters, structure or observed data. It is this analysis
of error that the following section is concerned
with - as an attempt to understand where a model
might be in error and why that model makes erro-
neous predictions, in order to improve model pre-
dictions through reduction of that error.
Examples of the error analysis of erosion mod-
els in the literature are rare despite the tools
available to model error, particularly in GIS-based
models (Heuvelink, 1998; Forier & Canters,
1996). Wang et al . (2000a,b, 2002) attempted to
quantify the spatial error of the topographic factor