Entropy inference of recurrence models for variability analysis of extreme events

Abstract

A complete methodology is developed to analyze the recurrence of extreme environmental events and its variability as time without further events elapses. Firstly we investigate the conditioned recurrence inference problem consisting in the selection of a probability model for the interarrival time between extreme events, given a contexto-factual evidence conditioned by the time elapsed since the last of such events. Two ways to include this condition can be considered, which yield alternative conditioned evidences and convert the former problem into two distinct ones, thus giving rise to a possible consistency violation. These problems are formalized within the logical probability framework, in a plausible logic language that allows a suitable expression of the available observational data. They are solved using the REF relative entropy method with fractile constraints, and their solutions are compared at all inference levels. It is concluded that the two conditioning ways are not really mutually exclusive and that a unique global solution to the conditioned inference can be obtained using this procedure. An example illustrates an application of the methodology to the variability analysis of the recurrence time between historical inundations of the Guadalquivir river in Spain, as time elapses with no new floods.