Geoscience Reference
In-Depth Information
The comparisons in time require, however, a certain degree of caution, the
settlements considered being able to change delimitation and meaning over time.
While many works have focused on methodological aspects (such as the choice of
which probability laws to use), the first question to pose, faced with change in the
rank-size distribution of a system of cities, is of an ontological nature (Chapter 1).
Berry and Okulicz-Kozaryn [BER 11b] hence form the hypothesis that the deviation
to Zipf's law observed for the hierarchy of American cities would be essentially due
to the mobilization of empirical entities not corresponding to what are today the real
functioning areas of cities. With respect to the top of the urban hierarchy, the urban
areas consisting of several urban units are the areas that make sense and not the
urban units themselves. This reflection again illustrates the importance of a critical
discussion on what is the reference when studying a system's transformations.
Figure 3.9.
Evolution of the hierarchical structure of the South-African cities
with more than 5,000 inhabitants during the 20th Century [GIR 09]
These four examples present a temporal perspective of indicators conventionally
used in a spatial analysis approach. It is a way to account for the three dimensions
that are thematical, spatial and temporal. Some of these examples mobilize statistical
models, for the sole purpose to represent space at time t, and to account for the
evolution by repeating this representation over time.
3.2.2.
Change, temporalities and statistical explanations
The statistical models can be interpreted as using a mathematical formalism to
study the variations of a variable as a function of the variations of other variables
said to be explanatory. The simple or multiple linear regressions are examples. In
