Fast short-term lava flow hazard assessment with graph theory

We explore the use of graph theory to assess short-term hazard of lava flow inundation, with Mt Etna as a case study. In the preparation stage, we convert into a graph the long-term hazard map produced using about 30,000 possible eruptive scenarios calculated by simulating lava flow paths with the physics-based MAGFLOW model. Cells in the original DEM-based representation are merged into graph vertices if reached by the same scenarios, and for each pair of vertices, a directed edge is defined, with an associated lava conductance (probability of lava flowing from one vertex to the other) computed from the number of scenarios that reach both the start and end vertex. In the application stage, the graph representation can be used to extract short-term lava flow hazard maps in case of unrest. When a potential vent opening area is identified e.g. from monitoring data, the corresponding vertices in the graph are activated, and the information about lava inundation probability is iteratively propagated to neighboring vertices through the edges, weighted according to the associated lava conductance. This allows quick identification of potentially inundated areas with little computational time. A comparison with the deterministic approach of subsetting and recomputing the weights in the long-term hazard map is also presented to illustrate benefits and downsides of the graph-based approach.