A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities

Abstract

This paper is of methodological nature, and deals with the foundations of Risk Assessment.\ud Several international guidelines have recently recommended to select appropriate/relevant Hazard Scenarios\ud in order to tame the consequences of (extreme) natural phenomena. In particular, the scenarios should\ud be multivariate, i.e., they should take into account the fact that several variables, generally not independent,\ud may be of interest. In this work, it is shown how a Hazard Scenario can be identified in terms of (i) a specific\ud geometry and (ii) a suitable probability level. Several scenarios, as well as a Structural approach, are presented,\ud and due comparisons are carried out. In addition, it is shown how the Hazard Scenario approach\ud illustrated here is well suited to cope with the notion of Failure Probability, a tool traditionally used for\ud design and risk assessment in engineering practice. All the results outlined throughout the work are based\ud on the Copula Theory, which turns out to be a fundamental theoretical apparatus for doing multivariate risk\ud assessment: formulas for the calculation of the probability of Hazard Scenarios in the general multidimensional\ud case (d 2) are derived, and worthy analytical relationships among the probabilities of occurrence of\ud Hazard Scenarios are presented. In addition, the Extreme Value and Archimedean special cases are dealt\ud with, relationships between dependence ordering and scenario levels are studied, and a counter-example\ud concerning Tail Dependence is shown. Suitable indications for the practical application of the techniques\ud outlined in the work are given, and two case studies illustrate the procedures discussed in the pape

Probability Analysis of the Water Table and Driving Factors Using a Multidimensional Copula Function

“…In recent years, it has been widely applied to various aspects of hydrological studies [13]. The main applications of the Copula Function include the analysis of: precipitation characteristics [12], the correlation between flood peak and flood volume [14,15], the frequency and recurrence interval of floods [16][17][18], characteristics of storms [19,20], the frequency and recurrence intervals of droughts [21], drought assessment [22], risk assessment [23], and an assessment of environmental hydrological model performance [24]. Due to the specialty of the water table, the establishment of the Copula Function for this purpose is relatively difficult; therefore, no research that uses the Copula Function to analyze the water table has been reported.…”

High-resolution marine flood modelling coupling overflow and overtopping processes: framing the hazard based on historical and statistical approaches

“…These, and especially the SWASH model (Simulating WAves till SHore), are able to reproduce the dynamics of wave surges and overtopping to an appropriate degree of reliability for coastal flooding studies (Suzuki et al, 2012). However, questions remain as to the order of magnitude of overtopping volumes, whether estimated empirically (Laudier et al, 2011;Gallien et al, 2014) or by digital modelling (Smith et al, 2012;Gallien, 2016). In some cases, the estimated value can vary by as much as an order of magnitude (Lynett et al, 2010).…”

“…As yet, only a few studies have attempted to couple flooding by overflowing and overtopping (Gallien et al, 2014;Stansby, 2013;Le Roy et al, 2015;Gallien, 2016). Le Roy et al (2015) have attempted to integrate the spatial and temporal variability of overtopping by simulating overtopping in 2-D.…”

“…Breilh et al, 2013), cellular automata (e.g. Dearing et al, 2005;Hawick, 2014) and hydrodynamic modelling (Martinelli et al, 2010;Gallien et al, 2011;Smith et al, 2012;Fortunato et al, 2013).…”

“…In the last few years, several process-based models have been developed and applied to address coastal flooding risks: VOF (volume of fluid) model (Tomás et al, 2016), Boussinesq model (Lynett et al, 2010;Andrade et al, 2013), nonhydrostatic phase-averaged model (Smith et al, 2012;Gallien, 2016), and NLSW (nonlinear shallow water) model (Suzuki et al, 2012;Guimarães et al, 2015;Le Roy et al, 2015). These, and especially the SWASH model (Simulating WAves till SHore), are able to reproduce the dynamics of wave surges and overtopping to an appropriate degree of reliability for coastal flooding studies (Suzuki et al, 2012).…”