Revisiting the Application of Halphen Distributions in Flood Frequency Analysis

Abstract

Flood frequency analysis is the foundation for hydrological and hydraulic design, and fundamental to frequency analysis is the selection of a suitable probability distribution. This study therefore revisits the Halphen frequency distribution family, with parameters estimated by the maximum likelihood estimation (MLE) method and goodness-of-fit evaluated by the Kolmogorov-Smirnov (KS) test. Besides revising the Halphen family, this study (1) proposes the study of kurtosis to assist the selection of a probability density function; (2) applies the kernel density function as the parent distribution function to evaluate flood risk (using 100-year event as an example); and (3) evaluates the mixed Halphen distribution for the heavy-tailed peak flow falling into the Halphen-B region. Using 198 peak flow datasets selected from 18 hydrologic regions in 48 states in the continental US, the study showed that: (1) Halphen-A/Halphen-B distributions were the preferred distributions for 190 datasets; (2) the moment-ratio diagram was found to be a reliable indicator for selecting the appropriate distribution; (3) kurtosis may be a tool to assist with the distribution selection; (4) comparison and risk assessment indicated that the identified Halphen distributions may properly model the flood frequency distribution; and (5) overall, the study validated the applicability of Halphen distributions for flood frequency analysis.