Modelling Dry Spells by Extreme Value Distribution with Bayesian Inference

Abstract

Two theoretically justified models of extremes are applied to dry spell (DS) series: the generalized Pareto distribution is applied to peak-over-threshold data (POT-GP), and the generalized extreme value distribution is applied to the annual maxima (AM-GEV). DS data are categorized according to three precipitation-per-day limits (1, 5 and 10 mm). The inference on the corresponding parameters is evaluated within the Bayesian paradigm, where the fact that DS values are recorded discretely as a whole number of days (forming the rounded series) can be incorporated in a straightforward manner. The study confirmed precautionary estimations when applying the GEV model on annual maxima in comparison with a simpler Gumbel model. Regarding the POT-GP modelling, the Bayesian approach reveals a high uncertainty that can occur in parameter estimations when very high thresholds are considered. It is found that there are no clear criteria in the assessment of some optimal threshold, nor is there a necessity for its detection. Instead, Bayesian inference provides a reasonable overall picture of the range of thresholds compatible with the GP model. Furthermore, it is suggested that all three GP parameters should be assessed when using the rounded data. The location estimates should be compatible with the theoretical value of − 0.5. Although the present study was performed mainly on DS series from two stations in Croatia spanning the period 1961–2015, the methodology developed here should be applicable to other regions.