Macroscopic Cellular Automata Approach for Modeling Superficial Dangerous Geological Processes

D. D'Ambrosio (1,2,*), W. Spataro (1,2), G. Iovine (4), M.V. Avolio (3), G.M. Crisci (1,3), S. Di Gregorio (1,2), R. Rongo (1,3), G.A. Trunfio (5), V. Lupiano (3)

(1) Center of Excellence for High Performance Computing, University of Calabria, Italy; (2) Department of Mathematics, University of Calabria, Italy; (3) Department of Earth Sciences, University of Calabria, Italy; (4) CNR-IRPI, via Cavour, 6 – 87030 Rende (CS), Italy; (5) Department of Architecture and Planning, University of Sassari, Italy; (*)

The simulation of superficial dangerous geological processes represents an area of increasing interest for the scientific community, both for theoretical aspects and possible practical applications to risk assessment. Unfortunately, most of such processes (e.g. lava and pyroclastic flows, debris flows and avalanches) are characterized by an elevated degree of complexity, both in dynamic and rheological terms, which commonly implies serious difficulties for modelling. As they often pose serious risk conditions to urbanised areas and facilities, reliable computer-based and user-friendly techniques of estimation of susceptible areas are strongly needed for risk mitigation purposes. Fortunately, the common belief that models of high complexity are always required for simulating high-complexity phenomena has recently been refuted by Wolfram (2002): even quite simple “programs” may in fact be able to reproduce the dynamics of very complex systems. Among these approaches, Cellular Automata (CA) are simple but powerful parallel computational models (they simulate Turing Machines). They are particularly suitable for modelling phenomena whose evolution can be described my means of local interactions.

In case of “macroscopic” Cellular Automata (Di Gregorio and Serra, 1999), geological processes are modelled by means of proper but simple local rules of evolution within a macroscopic formal context. Contrarily to other types of CA, such as Lattice Gas or Boltzmann Models (cf. Chopard and Droz, 1998), a macroscopic level of description is considered, by ruling the motion of some quantities (e.g. lava or debris) among neighbouring cells. The approach deeply relies on the so called “minimization algorithm of the differences”, well described in Di Gregorio and Serra (1999), which expresses in local terms the principle for which Natural Systems tend toward equilibrium conditions. The algorithm in fact ultimately leads the system to a situation of global equilibrium. First applied to lava flow simulations (Crisci et al., 1982), the macroscopic CA approach has successively been refined, and applied to different natural phenomena, such as debris flows (cf. D’Ambrosio et al., 2003), pyroclastic flows (Crisci et al., 2005), flooding and land erosion (D’Ambrosio et al. 2001). Moreover, forest fire (Trunfio, 2004), bioremediation processes (Di Gregorio et al., 1999), and Artificial Life systems (Piscitelli et al., 2001) have also been simulated. Most significant practical applications have dealt with hazard evaluation through the models SCIARA (Crisci et al, 2004) and SCIDDICA (D’Ambrosio et al., 2003). SCIARA was employed for “real time” forecasting of lava emplacement during the 2001 crisis at Mt. Etna (Sicily, Southern Italy). SCIDDICA was deeply improved for the need of simulating high-energy flow-type landslides (i.e. extremely-rapid debris flows/avalanches) and adopted for hazard mapping purposes of the Sarno-Pizzo d’Alvano and of the S. Martino Valle CaudinaCervinara areas in Campania (Southern Italy), respectively stroke by the disasters of May 1998 and December 1999.

As concerns calibration, both sequential and parallel Genetic Algorithms have recently been applied with quite encouraging results (Iovine at al., 2005; D’Ambrosio et al., in press-a). Furthermore, aiming at evaluating the role of model parameters, of mesh geometry, and of accuracy of input data, sensitivity analyses have also been performed (some experiments are still in progress), by also considering ideal reference cases (D’Ambrosio et al., in press-b). First results confirmed the robustness of the model SCIDDICA, and its temporal and spatial scalability.

In this work, an outline of the “minimisation algorithm of the differences” and of the CA macroscopic approach for modelling and simulating superficial dangerous geological processes is presented, together with a review of its most recent developments. Particular emphasis is given to lava-flow and debris-flow simulations, to adopted techniques of model calibration, to results of sensitivity analyses, as well as to examples of application for Civil Defence purposes.

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