Articles | Volume 19, issue 7
Research article
08 Jul 2019
Research article |  | 08 Jul 2019

Statistical theory of probabilistic hazard maps: a probability distribution for the hazard boundary location

David M. Hyman, Andrea Bevilacqua, and Marcus I. Bursik

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Cited articles

Aghakhani, H., Dalbey K., Salac, D., and Patra, A. K.: Heuristic and Eulerian interface capturing approaches for shallow water type flow and application to granular flows, Comput. Meth. Appl. Mech. Eng., 304, 243–264,, 2016. a
Bayarri, M. J., Berger, J. O., Calder, E. S., Patra, A. K., Pitman, E. B., Spiller, E. T., and Wolpert, R. L.: Probabilistic Quantification of Hazards: A Methodology Using Small Ensembles of Physics-based Simulations and Statistical Surrogates, Int. J. Uncertain. Quant., 5, 297–325,, 2015. a, b
Bevilacqua, A.: Doubly stochastic models for volcanic hazard assessment at Campi Flegrei caldera, Thesis, 21, Edizioni della Normale, Birkhäuser/Springer, Pisa, 2016. a
Bevilacqua, A., Neri, A., Bisson, M., Esposti Ongaro, T., Flandoli, F., Isaia, R., Rosi, M., and Vitale, S.: The Effects of Vent Location, Event Scale, and Time Forecasts on Pyroclastic Density Current Hazard Maps at Campi Flegrei Caldera (Italy), Front. Earth. Sci., 5, 1-16,, 2017. a, b
Bevilacqua, A., Patra, A. K., Bursik, M. I., Pitman, E. B., Macías, J. L., Saucedo, R., and Hyman, D.: Probabilistic forecasting of plausible debris flows from Nevado de Colima (México) using data from the Atenquique debris flow, 1955, Nat. Hazards Earth Syst. Sci., 19, 791–820,, 2019. a, b, c, d, e, f, g
Short summary
In this work, we present new methods for calculating the mean, standard deviation, median, and modal locations of the boundaries of volcanic hazards. These calculations are based on a new, mathematically rigorous definition of probabilistic hazard maps – a way to map the probabilities of inundation by a given hazard. We apply this analysis to several models of volcanic flows: simple models of viscous flows, complex models of a tabletop granular flow, and a complex model of a volcanic mud flow.
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