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xvi Models in Spatial Analysis
In order to illustrate the diversity of meanings that come with the word “model”
in a given application, in the following sections we will rely for the most part on two
concrete examples. In the first, the goal is to model the evolution of the spatial
distribution of the population over a few decades and, in the second, of the land use .
From a methodological perspective, each of these two examples involves dealing
with and modeling “spatial dynamics”. However, modeling spatial dynamics can
take on several different meanings: it can consist of describing changes as clearly as
possible, or of finding causality underlying the type and speed of the observed
evolution. These two approaches, the former used to describe and the latter to
explain, should logically complement each other and be conducted one after the
other. In practice, however, the line between the two is not always clear, and the
structure of the information itself leads to different attitudes in research. If this
structure is complex, the first step can constitute the entire work of modeling.
Indeed, the objective is then to provide a simplified picture, in the form of a map, for
example, of a complex information obtained from several sources. If, on the other
hand, the information is described by a simple and relatively regular structure, such
as in the case of statistical information, the first step is short and most of the
modeling work is done in the second. In order to study spatial differentials in
population growth, the geographer will build an explanatory model based on
mechanisms he knows are fundamental, the role of rent, the effects of competition
for space, urban polarization, the deterring effect of distance, etc. In order to study
the evolution of land use, the agriculture scientist will develop a model involving the
modes and structures of farming, the specializations and quality of soil.
In any case, the first step consists of identifying the elementary objects that give
the level at which the information has to be collected. These objects can be cells or
pixels (image analysis), households or firms (surveys or census results), or spatial
entities (morphological or administrative units). When studying a settlement system,
the elementary entities can be municipalities or agglomerations. When analyzing
land use, plots or farms can be used. This identification becomes more complicated
in a dynamic framework, since there can be changes in the object’s semantics (when
a given agglomeration “absorbs” another, for example), identifier (a plot can be
divided in two) or its spatial extent (expansion of a farm) [CHE 95]. Once the
objects are identified, we have to come up with ways of measuring changes that
make sense in regards to the topic, and which are compatible with the spatial scale.
Already, throughout this entire process of formalizing information, we are dealing
with models. These are, on the one hand, conceptual models concerning the meaning
of the chosen indicators, particularly the link between the phenomenon being studied
(which refers to a theoretical framework) and the set of data obtained from its
measurements (which refers to what is observable), given the observation levels that
were chosen. These are, on the other hand, models of data that are necessary to
organize thematic and geometric information in order to process them (relational ,
object-oriented, vector/raster, etc.).