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legitimate'; this echoes Kleindorfer et al. (1998) who argue that model validation
should be an open process involving model builder(s) and other stakeholders. Evalu-
ating models in this way represents a signifi cant departure from the objectivist
methods typically used in the natural sciences. Development of alternative ways to
evaluate models of all types remains fertile, if contested, ground.
Case Studies: Land-Use and Cover Change (LUCC)
Modelling LUCC is of active interest across geography and many other disciplines
3
.
To illustrate the points raised in previous sections, I will consider some of the
approaches taken to modelling LUCC. I do not intended to provide an exhaustive
overview of activity in the fi eld, but rather to provide an overview of the types of
approaches that have been adopted. I will consider models in terms of the typology
introduced in table 20.1, with the
caveat
that models typically span multiple of
these categories; for example, simulation models usually contain analytical and
empirical-statistical components. Finally, although LUCC is an obvious example of
socio-ecological modelling, there are many other areas of environmental geography
where models are routinely applied, including urban planning, climate change and
its implications, resource models of water use and agricultural production, transport
planning, reconstruction of palæo-environments, and prediction of the distribution
of species and ecological communities (past, present and future), among other
applications. The chapters in Wainwright and Mulligan (2004) provide a number
of examples of specifi c modelling applications across the broad fi eld of environ-
mental geography.
Analytical models
Analytical models of LUCC focus on changes in the abundance of different land
uses or conditions (e.g., economic values). These 'distributional models' (
sensu
Baker, 1989) are non-spatial and focus on how much change is taking place rather
than where change is occurring. Transition (Markov) matrices are a commonly used
type of distributional model. In Markov models, locations in the landscape are clas-
sifi ed as being in one of
n
discrete categories. Repeatedly multiplying a
n
n
matrix,
which describes the probability of transitions between each category, by a vector,
which contains the abundance of each category in the landscape, results in a projec-
tion of change in the abundance of the various categories present in the landscape
into the future under various restrictive assumptions. This approach has often been
used in modelling LUCC (e.g., Turner, 1987; Hall et al., 1991; Romero-Calcerrada
and Perry, 2004) because it is intuitive, conceptually simple and relatively easily
parameterised (e.g., via time-series of remotely sensed imagery). However, in their
simplest form, Markov models assume stationarity (constant rates of change in
space and time) and ignore spatial neighbourhood effects.
A discipline where analytical modelling of land-use change has been much applied
is economics. I will consider this economic framework here as much contemporary
simulation modelling of LUCC (especially the agent-based approach) has been
developed as a
reaction
to the microeconomic approach and its assumptions. The
standard economic approach to land-use change is the 'bid-rent model' in which
parcels of land (characterised by their location and other attributes) are allocated
to the use earning the highest rent. This framework, based on rational utility theory,
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