Information Technology Reference
In-Depth Information
4.
An Application: Cellular Automata of Land-Use Dynamics
4.1
Data and Steps in Inverse Problem Solving
Data available as a starting point of our study are maps of four European cities,
displaying the land use according to the Corine legend. For each city, four maps are
available, referring to different years and covering a period of about 40 years; in
details: Milan (1955, 1965, 1980, 1997), Palermo (1955, 1963, 1989, 1997), Grenoble
(1948, 1960, 1981, 1997) and Prague (1953, 1968, 1989, 1998), as shown in Fig. 2.
A number of steps are needed to reach our goal, headed on one hand to understand
which changes have affected every city during the period of analysis, on the other to
decompose these changes in their one-step evolution:
1.
comparing successive maps of each city, in order to draw three transition matrices
for each city; every matrix is square, 12X12 (as a consequence of our legend that
takes into account 12 land uses), and everyone of its elements means the number of
cells migrated from the row class to the column class (or the probability of
migration, after dividing for the total of the corresponding row);
2.
drawing transition rules that
effectively
took place;
3.
conveying all the information above in operational rules for the automaton. This is
a fundamental issue: information gained from data is not immediately useful for
the definition of transition rules because of the different span of real (that is,
coming from data) transitions; so it is necessary to elaborate a procedure that
allows us to obtain one-step transitions, that we may call “fictitious”, from the real
ones. The composition of fictitious transitions should have the real corresponding
transition as a result; this must be proved applying rules to a map and comparing
the result with the real subsequently map.
The approach used to manage all the issues arisen is based on
successive
approximations
: taking a simple set of rules as a starting point and then refining it on
the basis of the distance between simulations and reality.
4.2
Operational Problems
The first important operational problem is about the determination of the simulation
step, necessary to run the CA. As is shown in Table 1, the number of years between
maps is not the same, and we should keep in mind two issues in our calculations:
1.
the number of steps dividing each transition must be an integer;
2.
the approximation to reduce this number to an integer must be as least as possible.
As a consequence, considering three different spans, all feasible for the life of a
construction site (respectively 36, 40 and 42 months), the best choice resulting is 36
months, because every approximation is of one year, more or less, and this does not
implies significant changes in the distribution of land uses.
