Modelling Landscape Evolution - Environmental Modelling: Finding Simplicity in Complexity - page 297

Landscape-evolution models have been used to address
problems on widely different space- and timescales, from
predicting landscape response to dam removal or mine
rehabilitation over a few years (e.g. Hancock, 2004; Cui
et al ., 2006), through the response of a single catchment
to Holocene climate and land-use change (e.g. Coulthard
and Macklin, 2001) to the evolution of entire orogens or
rifted margins over millions to tens of millions of years
(e.g., Beaumont et al ., 2000; Willett et al ., 2001). Here, I
will focus on applications on geological (i.e. million-year)
timescales, well beyond those to which direct observations
pertain, and on spatial scales that range from individual
folds or fault blocks to rifted margins and orogens (i.e.
several to several hundreds of kilometres).

models attempt to capture emerging properties of the
landscape as a self-organized system from general prin-
ciples such as energy minimization or space-filling laws
(e.g. Stark, 1994; Rodriguez-Iturbe and Rinaldo, 1997).
Although such a 'statistical realism' approach may provide
understanding of landscape development on a conceptual
level, model predictions are difficult to compare specifi-
cally to natural examples because they concern landscape
properties such as fractal dimension or network-scaling
laws that are overly general (Kirchner, 1993). Numerical
landscape-evolution (or surface-process) models attempt
to find a compromise between the above two approaches
in that they aim to identify specific erosional and trans-
port processes to be included in the model, define the
basic physics that control these processes and capture
them in numerical algorithms, while making the neces-
sary abstractions to limit the number of parameters. In
the ideal case, the algorithms can be parameterized from
field measurements. The idea is that such an 'essential
realism' approach will be able to predict the controls on
general landscape properties and explain the differences
between landscapes. There is a danger, however, that
such modelling leads to 'apparent realism' because the
models are used on spatial and temporal scales that are
much larger than those to which the processes pertain, or
because the processes are insufficiently understood and
model algorithms fail to fully capture their dynamics.
In that case, model predictions may appear to represent
a natural landscape correctly and predict its evolution
at large spatial and temporal scales, but aspects of the
model outcome may be physically implausible or impos-
sible (Dietrich et al ., 2003). The ongoing debate regarding
landscape-evolution models concerns the question of the
level of detail with which the different processes need to
be captured in order for the models to correctly represent
nature and have predictive power.
Landscape-evolution models operate on a two-
dimensional (planform) grid; the typical spatial scale
of the model domain is of the order of 10 4 -10 5 m with
model resolution between 10 2 -10 3 m. Early models were
implemented on regular grids (e.g. Chase, 1992; Kooi
and Beaumont, 1994; Tucker and Slingerland, 1994)
but since Braun and Sambridge (1997) developed a
method to solve the model equations on an irregular
grid, others (e.g. Tucker et al ., 2001) have also adopted
irregular meshing. Irregular meshes provide several
advantages, including the possibility to locally refine
the mesh and to include horizontal tectonic advection
of material; they also predict more 'natural'-looking
drainage networks (Figure 19.1). All landscape-evolution
models

19.2 Model setup and philosophy

Landscape-evolution or surface-process models are
defined here as numerical models that operate on a
two-dimensional (planform) surface and that explicitly
aim to model different processes that detach and
transport bedrock in natural landscapes. Generally, a
distinction is made between short-range processes that
act on hill slopes and transport sediment from drainage
divides toward the drainage net, and long-range fluvial
or glacial processes that set the boundary conditions for
hillslope processes and export sediment from the model
domain (Figure 19.1). First-order landscape characteris-
tics, such as drainage density or relief roughness, appear
to depend on the relative efficiency of these two types of
processes (Kooi and Beaumont, 1994; van der Beek and
Braun, 1998; Simpson and Schlunegger, 2003; Perron
et al ., 2008; Figure 19.2).
Different approaches exist to modelling erosion and
sediment-transport processes, which can be character-
ized by the degree to which the models are grounded
in physical or mechanical principles and by the spatial
and temporal scales addressed (see also Chapter 15). In
their review of geomorphic transport laws, Dietrich et al .
(2003) recognized three different approaches. On the one
hand, mechanistic models are capable of making detailed
predictions for the evolution of sediment flux, grain size
or river-bed morphology on small spatial and temporal
scales (e.g. Benda and Dunne, 1997; Parker et al ., 1998;
Cui et al ., 2006) but are difficult to extrapolate to the
scales relevant to landscape evolution because of the large
number of parameters involved and the lack of constraint
on their potential variability. This approach was termed
'detailed realism' by Dietrich et al . (2003). At the other
end of the spectrum, conceptually simple 'rules-based'

are fundamentally based on the continuity