Vulnerability for systems described by cellular automata: Application to flood phenomena

In this paper, we introduce the vulnerability and vulnerability index for systems described by cellular automata. A zone will be vulnerable to the space-time expansion of a given property during a time horizon if the property trajectory reaches the zone at a certain time. The space-time expansion of the property known as spreadability depends closely on the property definition, the cells properties and the transition function which governs the cellular automata evolution. These constraints exhibit two types of spreadability (inclusion sense and area sense) which affect vulnerable zones. When multiple zones are vulnerable during a given time horizon, we need criteria which describe whose are the most vulnerable. Then we consider iterative, average and global vulnerability index whose use depends on the considered phenomena. As an application we consider the flood phenomena. For this we use the two scale cellular automaton for flow dynamics modeling (2CAFDYM) over a given terrain. This application requires an adaptation of the general vulnerability index in order to take into account the both horizontal and vertical distributions of surface water. As practice application, we consider simulation for a basin in northern Morocco using a simulation software we have designed in Java Object Oriented Programming. Digital terrain model, geological maps and satellite image are used for input data.