High Detailed Lava Flows Hazard Maps by a Cellular Automata Approach - Simulation and Modeling Methodologies, Technologies and Application - page 84

log hc Tsol = c + dT sol
log hc Tvent = c + dT vent
It is known that, in general, deterministic CA for the simulation of macroscopic fluids
present a strong dependence on the cell geometry and directions of the cellular space.
In order to solve the problem, different solutions have been proposed in literature, such
as the adoption of hexagonal cells ([10], [30], [31]) or Monte Carlo approaches ([32],
[15]). The first solution, however, does not perfectly solve the problem on ideal surfaces,
while the second one has the disadvantage of giving rise to non-deterministic simulation
models. In order to solve the anisotropic problem, which is typical of deterministic
Cellular Automata models for fluids on ideal surfaces, a fictitious topographic alteration
along diagonal cells is considered with respect to those “individuated” by the DEM
(Digital Elevation Model). As a matter of fact, in a standard situation of non-altered
heights, cells along diagonals result in a lower elevation with respect to the remaining
ones (which belong to the von Neumann neighborhood), even in case of constant slope.
This is due since the distance between the central cell and diagonal neighbors is greater
than of the distance between the central cell and orthogonal adjacent cells (cf. Figure 1).
This introduces a side effect in the distribution algorithm, which operates on the basis
of height differences. If the algorithm perceives a greater difference along diagonals,
it will erroneously privilege them by producing greater outflows. In order to solve this
problem, we consider the height of diagonal neighbors taken at the intersection between
the diagonal line and the circle with radius equal to the cell side and centered in the
central cell, so that the distance with respect to the centre of the central cell is constant
for each cell of the Moore neighbourhood (Figure 1). Under the commonly assumed
hypothesis of inclined plane between adjacent cells [15], this solution permits to have
constant differences in level in correspondence of constant slopes, and the distribution
algorithm can work “properly”. Refer to [28] for other specifications on this issue.

3 A Methodology for Creating Hazard Maps

Volcanic hazard maps are fundamental for determining locations that are subject to
eruptions and their related risk. Typically, a volcanic hazard map divides the volcanic
area into a certain number of zones that are differently classified on the basis of the
probability of being interested by a specific volcanic event in future. Mapping both the
physical threat and the exposure and vulnerability of people and material properties to
volcanic hazards can help local authorities to guide decisions about where to locate crit-
ical infrastructures (e.g. hospitals, power plants, railroads, etc) and human settlements
and to devise mitigation measures that might be appropriate. This could be useful for
avoiding the development of inhabited areas in high risk areas, thus controlling land use
planning decisions.
While a reliable simulation model is certainly a valid instrument for analyzing vol-
canic risk in a certain area by simulating possible single episodes with different vent
locations, e.g. [33], the methodology for defining high detailed hazard maps here pre-
sented is based on the application of the SCIARA lava flows computational model for
simulating an elevated number of new events on topographic data. In particular, the