An Application Of Cross Entropy Method In Hydrological Frequency Analysis

The primary objective of hydrological frequency analysis is to relate the magnitude of extreme events to their frequency of occurrence through the use of probability distribution and make statistically quantitative prediction of the possible future long-term change of hydrologic phenomenon,so as to provide effective basis for water conservancy project planning, designing, construction and operation. With the global climate changing, human activities increasing and the rapid development of social economy, water conservancy project need to constantly improve the design standard, the calculation method of design flood also need to be constantly developed and improved.This paper reviewed Hydrological frequency analysis research progress at home and abroad in recent years and discussed the application of cross entropy method and the traditional parameter estimation method in the hydrologic frequency distribution curve parameter estimation.The research contents of this paper are as follows.(1) Introducing fractile-pair constraints, cross entropy function and its properties, Kullback minimum cross entropy principle and the derivation process of the cross entropy method when is with fractile-pair constraints and used to estimate distribution parameters. Based on Matlab2010 b platform, developing the program that the application of the cross entropy method constrainted by fractile-pair in P-Ⅲ distribution, two-parameters Gamma distribution and Gumbel distribution parameter estimation.(2) Selected P-Ⅲ distribution as reference distribution, then studied cross entropy method and the conventional parameter estimation methods(method of moments,probability weighted moment method, linear moments method,the weighted function method) in the hydrological frequency analysis. This paper applied these methods in the annual maximum flood peak flow series of six major hydrological stations in northern Shannxi region,and the annual precipitation data series of 34 weather station in Guanzhong plain, then analyzed and evaluated the fitting results.(3) Selected two-parameter Gamma distribution and the Gumbel distribution(extreme value type I), then studied the cross entropy method and the conventional parameter estimation methods(method of moments, maximum likelihood method and linear moments method) in hydrological frequency analysis.This paper applied these methods in the annual maximum flood peak flow series of six major hydrological stations in northern Shannxi region,and the annual precipitation data of 34 weather station in Guanzhong plain, then analyzed and evaluated the fitting results.(4) Selected three kinds of goodness-of-fit evaluation criterion(cumulative sum of squares relative deviation principles δ, from the rule of minimum sum of squared residuals OLS, Akaike information criterion AIC) to evaluate the design value of each station under different distribution, so as to conclude the optimal distribution of each station.Through the study above,we can get several conclusions as follows:(1) When using the cross entropy method to estimate distribution parameter, the initial value selection affected the optimal solution of convergence and computation speed.(2) The cross entropy method is a feasible method.When it is applicated in Pearson Ⅲ distribution,its effect was close to the linear moment method and probability weighted moment method,but superior to the weighted function method and the method of moments.When used in two-parameter Gamma distribution, although there’s a certain gap between cross entropy method and linear moment method has, but the overall difference is very tiny. When it is applicated in the Gumbel distribution, no matter in the high tail or low tail both have a good fitting effect, the design value deviation is also within a reasonable range.(3) Under different optimization criteria, the optimal distribution of each station and parameter estimation methods are different.Under the rule of cumulative sum of squares relative deviation, Gumbel distribution and Gamma distribution can better fit the study of hydrological data sequence.Under the rule of minimum sum of squared residuals and the rule of red pool information, P- Ⅲ and Gumbel distribution can better fit the measured data.P-Ⅲ distribution fitted well more stations than Gumbel distribution.P-Ⅲ distribution can better fit the flood data.