Geology Reference
In-Depth Information
the modelling of flow divergence. The main dif-
ference in the approaches of Willgoose and
Howard was in the dominant erosion process
modelled. Willgoose used a transport-limited
erosion process where the driver of erosion and
deposition was whether the amount of sediment
carried by the flow was above or below the trans-
port capacity of the flow. Howard modelled a
detachment-limited erosion process where the
erosion rate was determined by the ability of the
flow to detach particles from the land surface.
Willgoose assumed that there was no limitation
on the detachment rate. Howard implicitly
assumed that sediment transport was always
below the transport capacity, so his model
was unable to model sediment deposition.
Subsequent developments of both models have
seen a convergence of their capabilities, with
both now capable of modelling both transport-
and detachment-limited erosion.
Subsequent developments in landform evolu-
tion models (there are now many tens of models
worldwide) are detailed in Willgoose (2005), but
highlights include: (1) quantitative testing of the
models against experimental evolving landforms
and field landforms (both natural and man-made);
(2) inclusion of more physical processes for hill-
slopes (e.g. mass movements such as landslides
and debris flows); (3) models for the dynamics of
meandering rivers; (4) different numeric algorithms
(although testing of their relative merits has been
limited); and (5) extra-terrestrial geomorphology
applications (mostly for Mars). For the purpose of
this Handbook the main areas of active develop-
ment are in the modelling of soil and vegetation
dynamics and understanding how they co-evolve
with the evolving landform. Vegetation and soil
dynamics are at the research frontier, and we will
return to them later in the chapter.
When we simultaneously model the evolution
of environmental states (e.g. vegetation) as well
as the landform elevations, the models should
rightly be called landscape evolution models
rather than landform evolution models. However,
the original terminology has stuck, and in the lit-
erature the names are used interchangeably, com-
monly abbreviated in both cases to LEM.
18.2
Using LEMs as Erosion Models
At their most fundamental level, and at the risk
of oversimplifying, LEMs are erosion models
where the landform evolves with time in response
to erosion and where the erosion changes in
response to the changing landform. For instance,
if a landform is allowed to evolve for one year,
then the difference between the landform at the
start and end of the year gives the erosion and/or
deposition during that year. If the physics mod-
elled is the same, and the amount of landform
change in that year is small, then LEMs will (and
do) give the same result as traditional erosion
models (we use 'traditional' in this chapter to
refer to models that do not simulate the evolu-
tion of the landform, models as discussed in
the previous chapters of this topic). It is from
this starting point that we will discuss the use
of LEMs.
All LEMs simulate some form of fluvial ero-
sion for the hillslopes and channels. They may
also model other processes that are crucial once
the landform begins to evolve (e.g. soil creep,
debris flows) and which may or may not be impor-
tant for any specific application. If we focus for a
moment just on the fluvial erosion models that
are used in LEMs, the debate about the correct-
ness and/or adequacy of the underlying physics is
no different from traditional models. That said,
there are some aspects of erosion physics that are
central to how the landform will evolve, but
which are typically not as critical in traditional
models. We will highlight some of the important
ones (e.g. the relative importance of discharge
and slope in the erosion equation) below. Typically
because of the computational effort in running an
LEM simulation, the erosion physics is simpler
relative to traditional models, though the core
mechanism of shear-stress driven processes is
correctly implemented.
Inter-rill erosion, typically rainsplash and rain-
flow, is also normally modelled in LEMs (usually
with a Fickian diffusion term), although at the
catchment scale for which most LEMs are applied,
rainsplash is rarely a significant component.
Inter-rill erosion is generally considered by
