A generic probabilistic model for natural hazard assessment

Abstract

A generic methodology for probabilistic natural hazard assessment is presented. Three area-characteristic recurrence parameters are defined by combining a Poisson process with the relevant natural-hazard-frequency–event-size power law. The distribution of the Poisson process describes the temporal characteristics present in the data and the power law describes the relationship between the frequency of events and the event sizes. The estimates for the mean rate of occurrence λ and the power law parameter b are based on empirical datasets consisting of extreme prehistoric and historical data, along with more-recent instrumental data. Likelihood functions are defined to allow for datasets to be combined and for the application of both maximum likelihood estimation (MLE) and Bayesian inference (BI). The proposed methodology accounts explicitly for aleatory and epistemic uncertainty by making provision for incomplete datasets, uncertainty associated with the observed event sizes, uncertainty associated with the parameters of the applied occurrence and event size distributions, and uncertainty associated with the occurrence of events in the dataset. These types of uncertainty are introduced in the modelling process through convolution and mixture distributions, as well as weighted likelihood functions. Existing techniques to assess the third recurrence parameter, the maximum possible event size x_max, are discussed briefly. The applicability of the proposed methodology is demonstrated by using a synthetic earthquake dataset, real earthquake datasets for Central Italy and the Ceres–Tulbagh region in South Africa, tsunami data for three tsunamigenic regions in the Pacific Ocean, and HAILCAST ensemble re-analysis hail data for Gauteng province, South Africa. Various combinations of the different types of assumptions, data, and uncertainty are investigated. The methodology shows the universality of the power law in assessing natural hazards. In practice, the methodology is not restricted to natural hazard assessment, but can be applied to any instance in which the frequency–event-size relationship follows a power law distribution. To illustrate this statement, financial vehicle loss information related to hail damage, obtained from a short-term insurer in South Africa, is analysed. The versatility of the modelling process provides the researcher with various options to account for incomplete data, as well as data and parameter uncertainty.