Evaluation of generalized extreme value and Gumbel distributions for estimating maximum daily rainfall

Álvaro José Back,Fernanda Martins Bonfante

doi:10.5327/z217694781015

Abstract

Extreme rain events can cause social and economic impacts in various sectors. Knowing the risk of occurrences of extreme events is fundamental for the establishment of mitigation measures and for risk management. The analysis of frequencies of historical series of observed rain through theoretical probability distributions is the most commonly used method. The generalized extreme value (GEV) and Gumbel probability distributions stand out among those applied to estimate the maximum daily rainfall. The indication of the best distribution depends on characteristics of the data series used to adjust parameters and criteria used for selection. This study compares GEV and Gumbel distributions and analyzes different criteria used to select the best distribution. We used 224 series of annual maximums of rainfall stations in Santa Catarina (Brazil), with sizes between 12 and 90 years and asymmetry coefficient ranging from -0.277 to 3.917. We used the Anderson–Darling, Kolmogorov-Smirnov (KS), and Filliben adhesion tests. For an indication of the best distribution, we used the standard error of estimate, Akaike’s criterion, and the ranking with adhesion tests. KS test proved to be less rigorous and only rejected 0.25% of distributions tested, while Anderson–Darling and Filliben tests rejected 9.06% and 8.8% of distributions, respectively. GEV distribution proved to be the most indicated for most stations. High agreement (73.7%) was only found in the indication of the best distribution between Filliben tests and the standard error of estimate.

Highlights

The study of intense rainfall events is important for understanding the climatic reality of a place and for understanding and evaluating the consequences of the impacts they generate on different sectors of society. Selge et al (2015) showed a high vulnerability of agricultural production and regional income due to the low adaptation to local climate conditions.Most of the extreme rain events when they reach occupied areas, especially urban areas, negatively impact the socioeconomic system of these locations (Souza et al, 2014). Fernandes and Valverde (2017) highlighted that located and extreme climatic events impact, especially, the most socioeconomically susceptible populations, with higher levels of exposure and less resilience
The use of 224 series of maximum annual rainfall data ranging from 12 to 90 years, with asymmetry coefficient ranging from -0.277 to 3.917, allows important conclusions on parameter adjustment and selection of probability distributions to estimate maximum extreme rainfall
The Kolmogorov–Smirnov test is little rigorous as adhesion test criterion to adjust probability distributions to maximum annual rainfall data

Summary

Introduction

The study of intense rainfall events is important for understanding the climatic reality of a place and for understanding and evaluating the consequences of the impacts they generate on different sectors of society. Selge et al (2015) showed a high vulnerability of agricultural production and regional income due to the low adaptation to local climate conditions.Most of the extreme rain events when they reach occupied areas, especially urban areas, negatively impact the socioeconomic system of these locations (Souza et al, 2014). Fernandes and Valverde (2017) highlighted that located and extreme climatic events impact, especially, the most socioeconomically susceptible populations, with higher levels of exposure and less resilience. The study of intense rainfall events is important for understanding the climatic reality of a place and for understanding and evaluating the consequences of the impacts they generate on different sectors of society. Most of the extreme rain events when they reach occupied areas, especially urban areas, negatively impact the socioeconomic system of these locations (Souza et al, 2014). Fernandes and Valverde (2017) highlighted that located and extreme climatic events impact, especially, the most socioeconomically susceptible populations, with higher levels of exposure and less resilience. Impacts related to extreme rainfall events cause a huge number of disorders and loses (Bork et al, 2017). Investigation of spatial and temporal distributions of heavy rains provides information for planning actions to prevent and minimize their impact

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Conclusion