High Detailed Lava Flows Hazard Maps by a Cellular Automata Approach - Simulation and Modeling Methodologies, Technologies and Application - page 81

simulation of lava flows (e.g., [5], [6], [7]) or the simple paths followed by future lava
flows (e.g., [8], [9]). For instance, in 2001 the path of the eruption that threatened the
town of Nicolosi on Mt Etna was correctly predicted by means of a lava flows simulation
model [10], providing at that time useful information to local Civil Defense authorities.
However, in order to be efficiently and correctly applied, the above approaches require
an a priori knowledge of the degree of exposure of the volcano surrounding areas, to
allow both the realization of preventive countermeasures, and a more rational land use
planning. In the following, we illustrate a methodology for the definition of flexible
high-resolution lava invasion hazard maps, based on an improved version of SCIARA,
a reliable and efficient Cellular Automata lava flow model, and show some specific ap-
plications related to inhabited areas of Mt Etna, which demonstrate the validity of the
application for civil defense purposes and land use planning.

2 Cellular Automata and the SCIARA Model for Lava Flows

Simulation

The behavior of lava flows is difficult to be dealt with using traditional methods based on
differential equation systems (e.g., cf. [11], [12], [13]). In fact, due to the complexities
of its rheology, lava can range from fluids approximating Newtonian liquids to brittle
solids while cooling, and thus it is difficult to solve the differential equations without
making some simplifications. Nevertheless, many attempts of modelling real cases can
be found in literature.
In order to be applied for land use planning and civil defense purposes in volcanic
regions, a computational model for simulating lava flows should be well calibrated and
validated against test cases to assess its reliability, cf. e.g. ([6], [14], [15]). Another de-
sirable characteristic should be the model's efficiency since, depending on the extent
of the considered area, a great number of simulations could be required ([16], [17]). A
first computational model of basaltic lava flows, based on the Cellular Automata com-
putational paradigm and, specifically, on the Macroscopic Cellular Automata approach
for the modeling of spatially extended dynamical systems, was proposed in [18] called
SCIARA. In the following years, the SCIARA family of lava flows simulation models
have been improved and applied with success to the simulation of different Etnean cases
of study, e.g. [10], [14].
Cellular Automata (CA) [19] were introduced in 1947 by Hungarian-born American
mathematician John von Neumann in his attempt to understand and formalise the un-
derling mechanisms that regulate the auto-reproduction of living beings. While initially
studied from a theoretical point of view, CA are continuously gaining researchers at-
tention also for their range of applicability in different fields, such as Physics, Biology,
Earth Sciences and Engineering. However, researchers' major interest for CA regard
their use as powerful parallel computational models and as convenient tools for mod-
elling and simulating several types of complex physical phenomena (e.g. [7], [10], [20],
[21], [22]).
Classical Cellular Automata can be viewed as an n -dimensional space, R , subdivided
in cells of uniforms shape and size. Each cell embeds an identical finite automaton ( fa ),
whose state accounts for the temporary features of the cell; Q is the finite set of states.