Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 54

A similar approach is used in the long-term landscape
evolution modelling of De Boer (2001), which represents
larger catchments. Results from the model suggest that the
sediment dynamics of a drainage basin are an emergent
response from the whole system, rather than being con-
tingent upon local (i.e. within-basin) conditions. Thus to
understand how a particular drainage basin functions, it is
necessary to view the basin holistically, and to seek expla-
nation at the drainage basin level, rather than focusing
wholly on individual sites within the basin (cf. Trimble,
1981). Tucker and Bradley (2010) describe a particle-
based model that has a slope cross-sectional focus, rather
than the planview focus of most CA models. It is capable
of reproducing a broad range of slope forms, and raises
interesting theoretical issues regarding hillslope transport
laws. Finally, Valette et al . (2006, 2008) extend the normal
2D focus of CA models by using a 3D model 18 to simulate
the response of a cultivated soil, including changes in the
vertical structure, to erosive runoff.

SCAVATU is a CA model for soil erosion by water
on small watersheds (D'Ambrosio et al ., 2001); more
physically based than earlier models of its kind, it
nonetheless retains a good number of empirical ele-
ments. When used to simulate erosion on an Italian
watershed, results were encouraging when compared
with a conventional empirical model.

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More advanced is the CAESAR model (Coulthard et al .,
2002) which represents long-term landscape evolution
on small watersheds. It has a strong process focus,
although still has some empirical relationships. CAE-
SAR has been successfully used in a number of studies
(e.g. Welsh et al ., 2009; Van De Wiel et al ., 2011). In par-
ticular, it has given good results in a model validation
exercise, which involved comparison with a more con-
ventional process-based model (Hancock et al ., 2010).

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Kessler and Werner (2003) have developed a second-
generation process-oriented CA model of patterned
ground, which reproduces circles, labyrinths, and
islands when sorting dominates; polygonal networks
when stone domain squeezing and confinement dom-
inate; and stripes when hillslope gradient is increased.

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4.3.6.2 The next generation of geomorphological
CA models

The CATT model of Vanwalleghem et al . (2010) rep-
resents tillage translocation on a hillslope site, and is
capable of being validated against observed patterns
of soil movement derived by the

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All modelling approaches from this first generation of
studies have been 'conceptual' in the sense that arbitrary
units are often used for cell size, elevation and so forth.
Thus the scaling of the model is undefined and the
size of the landscape area being simulated is unclear, so
that validation of these models (by comparison of model
results with observations) is difficult or impossible. Whilst
this first generation of geomorphological models of self-
organizing systems has clearly established the general
validity and potential of the CA approach for landscape
modelling, an obvious next step is to use more realistic
units so that outputs from the models can be more
rigorously validated. A further desirable step is to improve
the physical basis of the models, removing or reducing
the reliance on empirical relationships.
Geomorphological CA models which are attempt these
next steps represent a 'second generation'. A selection of
such models is briefly described below.

137 Cs method. First

results appear realistic.

Finally, the CA model of hillslope erosion by Ting et al .
(2009), and version 5 of the RillGrow model (Favis-
Mortlock, in preparation), both have a much stronger
physical basis than earlier equivalents. Development of
RillGrow 5 is ongoing.

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4.4 Case study: modelling rill initiation
and growth

4.4.1 TheRillGrow1model

Conventional process-oriented models of soil erosion
by water represent flow in hillslope rills (channels cut by
erosive flow) by applying commonly used hydraulics rela-
tionships, just as can be done for flow in any open channel.
This is an empirically rooted, 'engineering' approach that
works well in many circumstances. However, it also leads
to a number of deficiencies in models that employ it.
The first major deficiency is that it is a poor description
of reality, since 'all rills are not created equal'. Hills-
lope erosion models represent rills as prismatic channels,
equally spaced, and with a similar hydrological efficiency.

Avolio et al . (2000) developed the SCIDDICA CA land-
slide model. While still possessing many empirical
features, this was capable of being validated for a real
event - the 1992 Tessina landslide.

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18 That is, operating on a regular 3D grid, rather than the 2D-grid-
with-elevation of many CA models.