Elsevier

Computers & Geosciences

Volume 32, Issue 7, August 2006, Pages 876-889
Computers & Geosciences

SCIARA γ2: An improved cellular automata model for lava flows and applications to the 2002 Etnean crisis

https://doi.org/10.1016/j.cageo.2005.10.026Get rights and content

Abstract

Cellular automata are widely utilized for modelling and simulating complex dynamical systems whose evolution depends on the local interactions of their constituent parts. Simulation by Cellular Interactive Automata of the Rheology of Aetnean lava flows (SCIARA) is a Cellular Automata model for simulating lava flows; its release γ2 introduces innovations to the empirical method for modelling macroscopic phenomena that was utilized in the previous releases. The lava flows are described as “blocks”, individuated by their barycentre co-ordinates and velocities. This approach is different from the previous releases of SCIARA and from cellular automata derived models for fluid-dynamical phenomena such as lattice-gas and lattice-Boltzmann models. Block specifications permit to obtain a more physical description of the phenomenon and a more accurate control of its development. SCIARA γ2 was applied to the 2002 Etnean lava flows with satisfying results, obtaining better simulations in comparison with the previous releases.

Introduction

Lava flows represent one of the greatest dangers for people security and involve invasion of land and property. Lava flow simulation could abate this hazard by forecasting lava paths and evaluating the effects of human interventions such as the construction of embankments or channels. Nonetheless, lava flows are complex phenomena and need, in general, sophisticated modelling tools. In fact, the major difficulty in modelling lava flows arises since derived equations (i.e. conservation, state and constitutive equations) must also satisfy additional variables to describe the physical properties of lava and its environment. For instance, because of cooling and crystallization, lava may change from a viscous fluid to a brittle solid during emplacement. Consequently, it is extremely difficult to characterize the resistance of lava to motion (Kilburn and Luongo, 1993). This paper deals with a different approach, modelling flow field growth with Cellular Automata techniques.

Cellular Automata (CA) are one of the first Parallel Computing models (von Neumann, 1966); they capture the peculiar characteristics of systems, whose global evolution may be described on the basis of local interactions of their constituent parts (i.e. locality property).

A homogeneous CA (Worsch, 1999) can be considered as a d-dimensional space, the cellular space, partitioned into regular cells of uniform size, each one embedding an identical finite automaton, the elementary automaton (ea). Input for each ea is given by the states of the ea in the neighbouring cells, where neighbourhood conditions are determined by a pattern, which is invariant in time and constant over the cells. At time t=0 (step 0), ea are in arbitrary states and the CA evolves changing the state of all ea simultaneously at discrete times, according to the transition function of the ea.

Complex phenomena modelled by classical CA involve an ea with few states (usually no more than two dozens) and a simple transition function, easily specified by a lookup table (Toffoli and Margolus, 1987).

Fluid dynamics is an important field of CA application: lattice-gas automata models (Frisch et al., 1990) and lattice-Boltzmann models (Succi, 2001) were introduced for describing the motion and collision of “fluid particles” on a discrete space/time. It was shown that such models could simulate fluid-dynamical properties; the continuum limit of these models leads to the Navier–Stokes equations.

This CA approach does not permit to make velocity explicit in the local context of the cell: i.e., an amount moves from the central cell to an adjacent cell in a CA step (which is a constant time), implying a constant “velocity”. Nevertheless, velocities can be deduced by analysing the global behaviour of the system in time and space. In such models, the flow velocity is an emergent property. It can be deduced implicitly by averaging quantities on space (i.e. considering clusters of cells) or by averaging quantities on time (e.g. considering the average velocity of the advancing flow front in a sequence of Cellular Automaton steps).

Many complex macroscopic fluid-dynamical phenomena, which own the same locality property of CA, the surface flows, like lava flows, seem difficult to be modelled in these CA frames, because they take place on a large space scale and need practically a macroscopic level of description that involves the management of a large amount of data, e.g., the morphological data.

Simulation by Cellular Interactive Automata of the Rheology of Aetnean lava flows (SCIARA) γ2 adopts and extends some mechanisms (Di Gregorio and Serra, 1999), which permit to define the macroscopic phenomenon of lava flow in terms of CA formalism. In particular, the flows are characterized by a mass centre position (inside the cell), that changes according to the velocity and produces an outflow, when position moves to a neighbouring cell.

The second section considers some CA empirical criteria for modelling complex macroscopic surface flows and the introduction of the explicit velocity in the previous methods; the third section presents the main specifications of the release γ2 of SCIARA; the transition function with its innovations is described in the fourth section; the fifth section shows a result of the simulations of some of the numerous lava flows, which occurred in the 2002 Etnean eruption, Sicily, Italy1 together with a comparison with application results of the previous SCIARA release; finally, some conclusions are reported at the end.

Section snippets

Some criteria for modelling surface flows with CA

The criteria here reported are empirical and may be applied only to particular classes of macroscopic phenomena, involving surface flows. The recipes that are here presented have to be adapted to the special features of the phenomenon. However, in general, they do not guarantee by themselves success in the simulation. In fact, only when the model is validated on real cases of a certain typology, the model applications in similar conditions are reliable. SCIARA γ2 was validated on recent

The problem of modelling lava flows

Navier–Stokes equations represent a good, but perhaps not completely exhaustive approach in terms of systems of differential equations for accounting for the physical behaviour of lava flows (McBirney and Murase, 1984). Analytical solutions to these differential equations which govern debris flows, are a hopeless challenge, except for few simple, not realistic, cases. The possibility to successfully apply numerical methods for the solution of differential equations have been elevated

The SCIARA γ2 transition function

The “elementary” processes are specified in terms of equations, where names of parameters and substates are derived by the lower indexes specified in Section 3.2: the parameter pname is indicated as name; qname and n_qname indicate, respectively, the value of substate Qname and the new value; when the specification of the index i of a neighbourhood cell is necessary, the notation qname[i] is adopted; an index pair (i,j) is needed for the flows: qFname[i,j] means the value of the flow substate

Simulations of the lava flows of 2002

The event which occurred in the autumn of 2002 at Mount Etna (Sicily) was chosen for validating SCIARA γ2. Two major eruptions have characterized this event. The first, started on the NE flank of the volcano, with lava generated by a fracture between 2500 and 2350 m a.s.l., near the 1809 fracture and pointed towards the town of Linguaglossa (Fig. 4). The Linguaglossa forest and numerous tourist facilities were destroyed by the lava flow in the days following the eruption. Fortunately, after 8

Conclusions

SCIARA γ2 represents a quality leap in modelling lava flows with CA. The attribution of the velocity to blocks, which are identified by barycentre co-ordinates and move inside a neighbourhood, permits to overcome the limits of the previous versions of SCIARA, where the velocity was an emergent property of the system.

We do not need to univocally fix the CA clock in the validation phase on the basis of results of the simulations as in the previous versions of SCIARA, but we may choose the two

Acknowledgements

The authors are very grateful to Dr. Sonia Calvari of the “Istituto Nazionale di Geofisica e Vulcanologia” of Catania (Italy) for the logistic support and useful information on the 2002 Mt Etna event. We are grateful to Hideaki “Hirdy” Miyamoto for the precious suggestions he made in the revision phase of the paper and to the second anonymous reviewer.

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