Towards a new approach for generating probabilistic hazard maps for pyroclastic flows during lava dome eruptions.

It is increasingly being understood that development of mathematical models of a geophysical phenomena, while a fundamental step, is only part of the process of modeling and predicting inundation limits for natural hazards. In this work we combine data from hundreds of observed pyroclastic flows at the Soufriere Hills Volcano, Montserrat, a geophysical flow model, and statistical modeling to derive a new methodology for generating probabilistic hazard maps. The initial step consists of estimating probabilities of inundation at particular discrete points of interest (e.g. airport and Plymouth). The methodology starts with a computer model of the geophysical process, in this case the TITAN2D model that has been developed for modeling geophysical mass flows. A key input to the computer model is the probability distribution for the initial volume and direction of the flows based on observed data. An important limitation is that for modeling purposes, the observations represent relatively scarce datasets, while from a volcanological perspective datasets such as those from the prolonged and relatively well-monitored eruption of the Soufriere Hills Volcano, are as complete as can be realistically obtained. By combining flow event data, probability modeling and statistical methods, a probability distribution of severity and frequency of flow events is derived. Understanding and predicting the effects of volcanic hazards involves understanding the extreme event tail (the largest flow events) but this is notoriously difficult, especially with the limited data and prohibitively expensive to compute.. Instead a statistical emulator (or surrogate of the computer model) is used, a computationally cheap response surface approximating the output of the flow simulations, which is constructed based on carefully chosen computer model runs. The speed of the emulator then allows to 'solve the inverse problem': that is, to determine regions of inputs values (characteristics of the flow) which result in a events of interest (such as one that that reaches a given critical point). The flow frequency distribution is then used to determine the probability of this region, that is, the probability that an event of a given magnitude will occur at a particular site. Using quantitative measures like these to solve for the probabilities across an area, zoned maps could be generated from which civil protection authorities can make more informed decisions about hazard mitigation.