Regional Frequency Analysis applied to extreme rainfall events: Evaluating its conceptual assumptions and constructing null distributions.

Gabriel C Blain,Graciela Da R Sobierajski,Ana Carolina F Xavier,João Paulo De Carvalho

doi:10.1590/0001-3765202120190406

Abstract

Besides increasing the amount of data that can be used in a fitting process, the Regional Frequency Analysis (RFA) also assesses the quality of weather station networks. This technique assumes that it is possible to form homogeneous groups of meteorological series presenting independent and identically distributed data. Based on the hypothesis that such homogeneous groups can be formed under tropical-subtropical conditions, this study applied the RFA to assess the probability of one-day annual maximum rainfall in the State of São Paulo, Brazil. Critical limits used in previous studies to declare a region/group as 'acceptable homogeneous' (H≤1.00) or to select a distribution (|Z|≤1.64) were evaluated through Monte Carlo simulations. While the limit H≤1 is appropriate, the limit |Z|≤1.64 may lead to unacceptably high rates of rejecting a true null hypothesis. This statement is particularly true for the general logistic distribution. A computational algorithm allowing the selection of critical limits corresponding to pre-specified probabilities of rejecting a true null hypothesis is provided. Considering the new critical limits, data from one of the largest weather station networks of the State have been pooled into four homogeneous groups. Both generalized logistic and extreme value distributions are recommended for the probabilistic assessment of such groups.

Highlights

Improving the probabilistic assessment of extreme rainfall events has been a common goal for many statistical studies because such events pose serious hazards to human activities, human health, and the environment
The Regional Frequency Analysis can be used to assess the probability of daily-extremes of rainfall events in the State of São Paulo, Brazil
The Generalized Extreme Value and the Generalized Logistic distributions can be used to assess the probability of such extremes within the four groups

Summary

Introduction

Improving the probabilistic assessment of extreme rainfall events has been a common goal for many statistical studies because such events pose serious hazards to human activities, human health, and the environment. Estimating the probability of such events is a difficult task because - by definition - they occur at long return periods (>100 years), which usually surpass the available length of at-sites rainfall records (Goudenhoofdt et al 2017) On such context, parametric distributions, such as the generalized extreme value distribution (GEV), the Pearson type III distribution (PE3) and the generalized logistic (GLO), are frequently used to estimate the probability of such extremes (Khan et al 2017). Parametric distributions, such as the generalized extreme value distribution (GEV), the Pearson type III distribution (PE3) and the generalized logistic (GLO), are frequently used to estimate the probability of such extremes (Khan et al 2017) The parameters of these probabilistic functions are usually estimated from rainfall data recorded at individual weather stations, the so-called ‘at-site approach’. Increasing the amount of rainfall data that can be used to fit

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