Geology Reference
In-Depth Information
assumed homogeneous over a cell, which is con-
trary to evidence for hillslopes that exhibit patchy
flow concentration in few threads (i.e. some con-
centrated flow within broader unconcentrated
flows). Given that the relationship between sedi-
ment transport models and flow properties is
likely to be strong, this approximation is likely to
have a non-linear effect on erosion prediction. For
example, Abrahams
et al
. (1989) looked at the
impact of using mean flow depths as compared to
distributions of flow depths across a slope in
predicting erosion. They found that mean depths
led to significant underpredictions of erosion.
Subsequently, Parsons and Wainwright (2006)
have argued that the occurrence of distributions
of depths and the form of those distributions are
critical in the estimation of the onset of concen-
trated overland flows.
Temporal lumping is a related issue. For
process-based erosion models, the most common
case where this occurs is in the assumption,
largely for consideration of simplicity or numeri-
cal stability, that topography is invariant through
time, despite the fact that erosion and sedimen-
tation must cause changes. Attempts have been
made to update topography in erosion models
such as RillGrow (Favis-Mortlock
et al
., 2000)
which consider the evolution of topography explic-
itly and operate on a very high resolution to allow
rills to self-organize. In practice, such updating of
feedbacks between erosion process and hillslope
form often proves difficult, both to simulate and
to evaluate, but if the goal of the erosion modeller
is to simulate hillslope evolution on temporal
scales that are longer than single events, some
updating of topographic evolution will be neces-
sary (see also Section 2.5). In addition, temporal
lumping of parameters also occurs in terms of soil
conditions, such as antecedent soil moisture sta-
tus and vegetation cover, both of which may
change within or between rainfall events, leading
to further misrepresentation of the temporal scale
at which key processes operate.
Soil-erosion models are typically driven by
some representation of the hydrological system.
Process-based erosion models have a further layer
of problems in evaluating the complexity of scal-
ing, in that they are by necessity coupled with
hydrological models, which themselves may
reproduce the flow hydraulics that fundamentally
control erosion processes to a greater or lesser
extent (Merritt
et al
., 2003; Wainwright
et al
.,
2008a). For example, Wainwright and Parsons
(1998) demonstrated that different forms of ero-
sion model were sensitive in different ways to
flow hydraulics, and thus to different hydrology
submodels. Because erosion predictions depend
non-linearly on the hydraulics predictions, the
erosion models in these contexts are ill-
conditioned, leading to significant amounts of
error propagation (see Chapter 4). Therefore, error
propagation in erosion models is
always
worse
than that in the underlying hydrological models
because of model coupling, and hydrology models
often produce poor estimates of even basic runoff
properties (Beven, 2004).
As flow parameters are derived from hydro-
logical routing, on all but the simplest topogra-
phies, increasing the extent of a study will lead to
errors which are not only quantitative but also
qualitative, inasmuch as DEM resolution affects
aspect changes and thus patterns of flow accumu-
lation (e.g. Zhang & Montgomery, 1994; Holmes
et al
., 2000). At larger scales, flow routing is often
used directly to drive erosion, typically by assum-
ing a relation between discharge and local slope
and upslope contributing area (e.g. Peeters
et al
.,
2008). Therefore, the approach taken and the
scale over which fundamental equations are
applied needs to be taken into consideration for
the environment of interest. For example, the
assumption that flow may be parameterized as a
function of upslope contributing area is inappro-
priate in semi-arid environments, where localized
storms are mismatched with the area of the catch-
ment. In addition, the assumption that erosion is
driven by a single, representative discharge is
flawed; numerous studies have demonstrated
that assumptions of a single discharge produce
different results compared with a range of dis-
charges (Wainwright & Parsons, 1998; Zhang
et al
., 2002; Huang & Niemann, 2006).
Finally, the error in representing spatial varia-
bility in erosion predictions (often with lumped
