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

Related authors

Probabilistic retrieval of volcanic SO2 layer height and partial column density using the Cross-track Infrared Sounder (CrIS)
David M. Hyman and Michael J. Pavolonis
Atmos. Meas. Tech., 13, 5891–5921,,, 2020
Short summary

Related subject area

Volcanic Hazards
The characteristics of the 2022 Tonga volcanic tsunami in the Pacific Ocean
Gui Hu, Linlin Li, Zhiyuan Ren, and Kan Zhang
Nat. Hazards Earth Syst. Sci., 23, 675–691,,, 2023
Short summary
Scenario–based Modelling of Waves Generated by Sublacustrine Explosive Eruptions at Lake Taupō, New Zealand
Matthew W. Hayward, Emily M. Lane, Colin N. Whittaker, Graham S. Leonard, and William L. Power
EGUsphere,,, 2022
Short summary
Assessing minimum pyroclastic density current mass to impact critical infrastructures: example from Aso caldera (Japan)
Andrea Bevilacqua, Alvaro Aravena, Willy Aspinall, Antonio Costa, Sue Mahony, Augusto Neri, Stephen Sparks, and Brittain Hill
Nat. Hazards Earth Syst. Sci., 22, 3329–3348,,, 2022
Short summary
Insights into the vulnerability of vegetation to tephra fallouts from interpretable machine learning and big Earth observation data
Sébastien Biass, Susanna F. Jenkins, William H. Aeberhard, Pierre Delmelle, and Thomas Wilson
Nat. Hazards Earth Syst. Sci., 22, 2829–2855,,, 2022
Short summary
Risk communication during seismo-volcanic crises: the example of Mayotte, France
Maud Devès, Robin Lacassin, Hugues Pécout, and Geoffrey Robert
Nat. Hazards Earth Syst. Sci., 22, 2001–2029,,, 2022
Short summary

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.
Final-revised paper