Articles | Volume 19, issue 7
Nat. Hazards Earth Syst. Sci., 19, 1347–1363, 2019
https://doi.org/10.5194/nhess-19-1347-2019
Nat. Hazards Earth Syst. Sci., 19, 1347–1363, 2019
https://doi.org/10.5194/nhess-19-1347-2019
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 et al.

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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, https://doi.org/10.1016/j.cma.2016.02.021, 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, https://doi.org/10.1615/Int.J.UncertaintyQuantification.2015011451, 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, https://doi.org/10.3389/feart.2017.00072, 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, https://doi.org/10.5194/nhess-19-791-2019, 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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