Revisiting the Application of Halphen Distributions in Flood Frequency Analysis: Fid-Bau Portal

Revisiting the Application of Halphen Distributions in Flood Frequency Analysis

Zhang, Lan / Singh, Vijay P.

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.