Sensitivity of Statistical Models for Extremes Rainfall Adjustment Regarding Data Size: Case of Ivory Coast

Relwindé Abdoul-Karim Nassa,Makouin Louise Toure,Amani Michel Kouassi

doi:10.4236/jwarp.2021.138035

Abstract

The objective of this study is to analyze the sensitivity of the statistical models regarding the size of samples. The study carried out in Ivory Coast is based on annual maximum daily rainfall data collected from 26 stations. The methodological approach is based on the statistical modeling of maximum daily rainfall. Adjustments were made on several sample sizes and several return periods (2, 5, 10, 20, 50 and 100 years). The main results have shown that the 30 years series (1931-1960; 1961-1990; 1991-2020) are better adjusted by the Gumbel (26.92% - 53.85%) and Inverse Gamma (26.92% - 46.15%). Concerning the 60-years series (1931-1990; 1961-2020), they are better adjusted by the Inverse Gamma (30.77%), Gamma (15.38% - 46.15%) and Gumbel (15.38% - 42.31%). The full chronicle 1931-2020 (90 years) presents a notable supremacy of 50% of Gumbel model over the Gamma (34.62%) and Gamma Inverse (15.38%) model. It is noted that the Gumbel is the most dominant model overall and more particularly in wet periods. The data for periods with normal and dry trends were better fitted by Gamma and Inverse Gamma.

Highlights

Several authors who have worked with series of annual maximum daily rainfall of different sizes have come to different conclusions
It is possible to proceed with the frequency analysis
It is noted that the Gumbel law is the most dominant law overall and more in wet periods

Summary

Introduction

Rence of rare events [1] It is a branch of statistics which is interested in the asymptotic characterization of the maxima or minima of a random variable. According to the first group [6] [8] [9] [10] [11] [14] with size series ranging from 47 to 81 years, the authors reached the same conclusion according to which Gumbel’s law best adjusts the maximum annual rainfall. The question that guides this research is the following: are the statistical laws of extremes used for the statistical modeling of the annual maximum daily rainfall used for the sizing of hydraulic structures from the project flow rate sensitive to the size of the samples of the series?

Objectives

Methods

Results

Discussion

Conclusion