On modeling the maximum duration of dry spells: a simulation study under a Bayesian approach

Dry spell and drought are hydrological phenomena with serious socioeconomic effects and, despite recent efforts, substantial scientific and statistical comprehension are still lacking—especially when considering their extreme events. Such events are usually modeled using the generalized extreme value (GEV) distribution, whose prediction performance, at least under a Bayesian approach, remain poorly understood when fitted to a discrete series (the simplest way to record dry spell occurrence and duration). Thus, in this study, we aim at evaluating point and interval prediction performances of the GEV distribution when fitted to dry spell data, using computer simulations of different realistic scenarios (variations in the number of days per dry spells, number of dry spells per year, sample sizes, and available prior information). While sample size increase produced generally expected results over point performance (i.e., stronger bias in small samples), counterintuitive patterns arose when we evaluated the accuracy of prediction credible intervals. We also found a positive correlation between prediction bias and the GEV shape parameter estimate, a fact we believe to be related to the discrete nature of the data. Furthermore, we noticed the best interval performances occurred in increasing levels of information rendered by prior distributions. Finally, we consider all these results to be general enough to apply to different extreme discrete phenomena, since we found no effect of neither the duration nor the frequency of dry spells. Although typical issues in discrete data (e.g., overdispersion) and time series data (e.g., trend) should be considered in future investigations, one must be aware that whenever attempting to fit dry spell duration series to the GEV distribution in the absence of substantial prior information will frequently lead to underestimated predictions—the worst kind for dry spell strategic management—which may further compromise scientists, practitioners, and their community responsibilities.