Flood Frequency Analysis Using Halphen Distribution and Maximum Entropy

Abstract

Flood frequency analysis (FFA) provides an important basis for determining the construction size of hydraulic facilities. The selection of a suitable distribution and parameter estimation method (D/E procedure) is of vital importance in FFA. In this study, the method of Halphen (HP) distribution, coupled with the principle of maximum entropy (ME), was proposed for FFA. First, the relations among Lagrange multipliers, constraints, and parameters were derived firstly. Annual maximum flood data series at 12 gauging stations and Monte Carlo simulation were used to evaluate the descriptive and predictive abilities of the proposed HP/ME procedure. The proposed HP/ME procedure was compared with the commonly used procedures. It is shown that the HP/ME procedure has the smallest root-mean-square error (RMSE) values for 1 of the 12 sites and the smallest Akaike information criterion (AIC) values for 7 of the 12 sites. The descriptive ability of the HP/ME procedure is good because of its flexible shapes and excellent tail properties. The Monte Carlo simulation results demonstrate that the HP/ME procedure performs well, which gives a narrower 9% confidence interval and produces higher efficiency than other compared procedures in several simulated cases. The proposed HP/ME procedure performs well to estimate design floods at two selected sites and might be suggested as an alternative candidate for hydrologic frequency analysis.