Frequency Analysis Incorporating a Decision Support System for Hydroclimatic Variables

Abstract

Statistical criteria used to evaluate the best distribution fit give large weights to the center of distributions. This is, however, not consistent with the objective of frequency analysis which is to estimate the quantiles with large return periods. In this study, the usefulness of a recently proposed decision support system (DSS), which defines the class of distributions prior to a model selection practice with respect to tail behavior of sample data, was investigated using three large hydroclimatic databases [Reference Hydrometric Basin Network (RHBN), precipitation, and UNESCO]. According to the DSS, although a considerable majority of RHBN flood sample data belonged to Class C (regularly varying distributions), a slight and great majority of UNESCO discharge as well as annual precipitation sample data, respectively, belonged to Class D (subexponential distributions). This difference in classification is attributed to the nature of studied variables: RHBN sample data represent extreme events with heavy tails (Class C), whereas UNESCO and especially precipitation sample data come from relatively lighter tailed processes and therefore belong mostly to Class D distributions. The impact of classification on model selection was the largest for the RHBN and the smallest for precipitation sample data. This confirms that discriminating between classes of competing models prior to model selection is critical when the sample data come from extreme events. Observed inconsistency in model selection for the RHBN database resulted in an underestimation of quantiles in more than 2/3 of the cases regardless of class of distributions. For the UNESCO and precipitation data, however, inappropriate model selection resulted equally in over- and under-estimation in Class C, whereas it resulted in underestimation of quantiles in Class D in the majority of observed inconsistencies. It can be concluded that an inappropriate model selection due to choosing a wrong class of distributions leads, in the majority of cases, to an underestimation of the quantity of the variable under study which is associated with a higher socioeconomy risk compared to that corresponding to an overestimation of a specific quantile. It was also observed that model selection using Bayesian Information Criterion (compared to Akaike Information Criterion) is more consistent with tail behavior of the natural processes.