Geology Reference
In-Depth Information
18
Applications of Long-Term
Erosion and Landscape
Evolution Models
G.R. WILLGOOSE
1
AND G.R. HANCOCK
2
1
School of Engineering, Faculty of Engineering and the Built Environment,
The University of Newcastle, Callaghan, New South Wales, Australia
2
School of Environment and Life Sciences, Faculty of Science, The University of Newcastle,
Callaghan, New South Wales, Australia
18.1
A Short History of Landform
Evolution Modelling
pendent of distance downslope, resulted in slopes
with convex profiles (hereafter a convex slope is
one that has a downward curvature in its eleva-
tions in the direction of flow, while a concave
slope has an upward curvature). Kirkby (1971)
was the first to quantify the process interaction
between distance down a hillslope and slope,
defining the hillslope profile and its concavity in
terms of causal processes. Kirkby did this by solv-
ing a differential equation for hillslope elevations
and erosion processes, constructing in the proc-
ess a simple landform evolution model.
In Kirkby's work, hillslopes were assumed to
have parallel flow lines with a fixed downstream
boundary condition (determined by the river bed
elevation) so that neither flow convergence and
divergence nor interaction with a dynamic river
were considered in his solutions. Ahnert (1976)
constructed the first landform evolution model
where flow convergence was allowed, and applied
it to understanding the evolution of mountain
ranges (e.g. Ahnert, 1984).
The modern generation of landform evolu-
tion models is generally considered to have
started with those presented by Willgoose
et al
.
(1991a) and Howard (1994). These models simu-
lated entire catchments rather than a single
hillslope, the simultaneous evolution of the
hillslopes and channels by different processes
(and channel extension and retreat), and allowed
for flow convergence on slopes. Moglen and Bras
(1994) built on the work of Willgoose to allow
Landform evolution models were initially devel-
oped as a means of understanding the links
between environmental processes acting on a
landform (primarily runoff and erosion) and the
form of the landscape resulting from the long-
term action of those processes (i.e. the geomor-
phology). With their use we are able to (1) identify
the geomorphological fingerprint of an individual
process, so that aspects of the natural process act-
ing on that landform can be identified and/or cali-
brated (or at least constrained) from the landform
statistics, and (2) relate geomorphological scaling
and organization principles to process, allowing
simplified, but still physically-based, representa-
tions of catchment-scale processes. More recent
developments have seen these models used for
practical erosion modelling applications. It is
these recent developments that will be the focus
of this chapter. We first provide some context for
the original models because their capabilities are
underpinned by the science agenda justifying
their original and continued development.
Gilbert (1909) was the first to note that hill-
slopes subjected to an erosion process with a rate
that increased with slope, but which was inde-
