Geoscience Reference
In-Depth Information
Our positioning is a little different: in the approaches that we will describe,
statistical models are used to interpret, enlighten and summarize spatio-temporal
data, in order to identify change. Here, the idea is to privilege the construction of
objects in time and to approach their dynamics in an abductive manner. Indeed, the
analyzes are used as successive interpretationfilters, with round-trips between
analysis of results, conjecture, and new filter. These approaches combine statistical
models and models of spatial analysis, by interpreting systematically the results
relatively to the theme. Furthermore, it is useful to identify if space and time are
integrated in the analysis, or on the contrary are the support of the results. We insist
on the use of the term “approach” that corresponds closely to the intellectual path
that the application of a sequence of methods gives rise to, producing
complementary insight of the analyzed phenomenon.
Let us consider two examples to illustrate the different roles that space and time
can take in the analysis. Clark's model, classical in urban geography, is a static
model of spatial analysis, where space is formalized through the variable “distance
to the center”. It describes the shape of the decrease of the density as a function of
the distance to the center
5
. If we apply this model to a same space at several dates,
then the result is a sequence of curves (that can also be summarized by the sequence
of the two parameters) evolving in time. An indicator can also be calculated: for
example, the distance at which the density decreases below a given threshold, which
provides information on the sprawling of the city, and permits to follow it up over
time. In this example, time acts as a “frame” to interpret the result. Conversely, if a
table of the evolution of temperatures over a number of meteorological stations is
analyzed and the diversity of the evolution is summarized by the first factor of a
factorial multivariate analysis, then time is integrated in the analysis. In addition,
space intervenes a posteriori during the interpretation of the spatial organization of
the first factor, summarizing the diversity of forms of temperature evolution of the
stations. From the point of view of methods, these two examples also illustrate two
different ideas for the elementary and general level: in the first example, it is the
overall structure that is described at each time step, and the evolution of this
structure is being followed. In contrast, the evolution of each station in the second
example is being described, and a summary of these dynamics is spatialized.
This decomposition according to the various statuses of time and space, as well
as the geographical level at which change is analyzed, allow identifying a series of
questions, which will be discussed and illustrated further in full length in Chapter 3:
5 Clark's model is written as D(x) = a exp(bx), where D(x) is the residential density, x is the
distance to the center of the city and a and b are two parameters (a represents the density in
the center, and b is the dissuasive effect of the distance).
