Comparative frequency analysis with L moments between the Kappa distribution and six of general application

Abstract

Frequency analysis (FA) allows estimating magnitudes for the maximum annual data of floods and daily rains associated with low exceedance probabilities. Such estimates or predictions allow the hydrological design of hydraulic works of exploitation or protection. The FA comprehends five stages: (1) verification of the randomness of the data; (2) adoption of a probability distribution function (PDF); (3) fitting the PDF; (4) evaluation of the goodness of fit, and (5) selection of the results. In this study, the theoretical bases of the Kappa distribution of four parameters (u, α, k, h), obtained through the L-moment method, which is described in detail, are exposed. The Kappa distribution, when its second shape parameter h takes values of -1, 0, and 1 reproduces the Generalized Logistics (GLO), Generalized Extreme Value (GEV), and Generalized Pareto (GPA) distributions. Three joint records of annual floods of peak flow (Qp) and runoff volume (Vol) were processed, and two yearly records of Qp and three of maximum annual daily precipitation. Five distributions were used to fit each of the eleven processed records: Kappa, the distribution reproduced according to the value of h (GLO, GEV o GPA); Log-Pearson type III; Log-Normal, and Wakeby. The statistical quality of each fit was quantified with the standard error of fit and the mean absolute error. The Conclusions highlight the similarity of the results (errors and predictions) in the eleven records processed and suggest the systematic application of the Kappa distribution, to complement those prescribed by government agencies and those of generalized use.