基于熵原理的年降水频率分布参数估计研究

Estimation of annual precipitation frequency distribution parameters based on entropy methods

【目的】研究最大熵、Meilin变换和交互熵3种基于熵原理的方法在年降水频率分布参数估计中的应用效果,为水文分布参数估计方法的选择提供依据。【方法】选用P-Ⅲ分布,以陕西省关中地区扶风、麟游、眉县、太白、西安和长武6个水文站年降水序列为例,应用最大熵、Meilin变换和交互熵法估计分布参数,计算年降水量拟合值,将结果与传统的矩法和线性矩法结果进行比较,并采用OLS和AIC准则评价频率曲线对实测值序列的拟合效果。【结果】OLS和AIC准则评价曲线的拟合优度基本一致,采用最大熵法估计分布参数时上述6个水文站的AIC值分别为255.421,255.673,240.592,264.032,419.178,289.437,采用Meilin变换估计时各站的AIC值分别为255.421,255.673,240.592,264.032,419.178,289.437,采用交互熵估计时各站的AIC值分别为249.967,251.269,232.356,257.481,412.545,276.879,采用矩法估计时各站的AIC值分别为256.436,256.037,241.109,262.969,419.122,291.161,采用线性矩法估计时各站的AIC值分别为250.081,251.992,232.828,256.229,414.030,278.745。频率曲线图与拟合优度评价结果一致,5种方法均可以取得较好的拟合效果,最大熵法和Meilin变换估计结果基本相同且优于矩法,交互熵法优于其他方法。【结论】最大熵、Meilin变换和交互熵3种参数估计法均可借助于计算机求解,是可行的年降水频率分布参数估计方法。

【Objective】This paper studied three new methods in estimation of hydrologic computation parameter including maximum entropy,Meilin transformation and cross entropy.【Method】Based on the annual precipitation data of Fufeng,Linyou,Meixian,Taibai,Xi＇an and Changwu in central Shaanxi,the methods of maximum entropy,Meilin transformation and cross entropy were applied to estimate parameters according with P-Ⅲ distribution.The designed annual precipitation was calculated and compared with the methods of Moment and L-Moments.The best method was obtained based on OLS and AIC standards.【Result】OLS and AIC showed same results for the goodness of fit.Corresponding AIC values of the maximum entropy at Fufeng,Linyou,Meixian,Taibai,Xi＇an and Changwu were 255.421,255.673,240.592,264.032,419.178 and 289.437;those of the Meilin transformation were 255.421,255.673,240.592,264.032,419.178 and 289.437;those of the cross entropy were 249.967,251.269,232.356,257.481,412.545 and 276.879;those of the Moment method were 256.436,256.037,241.109,262.969,419.122and291.161;and those of the linear moment were 250.081,251.992,232.828,256.229,414.030 and 278.745.The results of frequency curves were same to goodness of fit,and all the five methods obtained good results.The methods of maximum entropy and Meilin transformation were better than the Moments method,and the cross entropy method was the best.【Conclusion】The three new methods to estimate parameters were reasonable to estimate parameters for of P-Ⅲ distribution.