Multi-criteria decision-making analysis in selecting suitable plotting positions for IDF curves of storm events

Abstract

Selecting suitable distributions for rainfall data is usually subjective and complex since it requires decision-makers to consider results from various measures of goodness-of-fit indices. In this study, the VIKOR method in multi-criteria decision-making analysis is modified to select the most suitable plotting positions to represent extreme storm intensities in order to build the intensity–duration–frequency (IDF) curves of storm events. This is done by considering the rankings provided by all goodness-of-fit indices used to obtain a compromise solution. Nine plotting positions are considered: Weibull (W), Adamowski (A), Gringorten (G), Hazen (H) and Gumbel (EV I) and two known plotting positions for generalized extreme value (GEV) distribution using Pearson’s skewness and another two using L-skewness. The IDF curves obtained are compared to a reference IDF curves which was found using the GEV distribution. The mean and median for three goodness-of-fit indices, the coefficient of variation of root mean square error, CVRMSE, the mean percentage of difference, Δ, and the coefficient of determination, R 2, are taken as the criteria for selection process. The results show that six plotting positions, A, H, W, G and the two plotting positions with L-skewness, are equally superior compared to the other three plotting positions.