考虑矩阶数的最大熵方法及其在水文随机模拟中的应用

POME with constraints of moments and its application to hydrological stochastic simulations

最大熵原理(POME)是一种理论完善的非参数分布推断方法,近年来已开始应用于水科学领域。POME本质上作为多约束最优化问题,所得分布取决于约束条件的形式。以往基于POME的研究缺乏对约束条件的讨论,即主观规定最大矩阶数,这可能导致所得最大熵分布非最优分布。针对该问题,首先对常用分布下样本矩的收敛性进行讨论,并给出了确定最优矩阶数的理论–经验分析思路,从而提出了一种考虑矩阶数的POME推断框架。应用该方法对长江、黄河代表测站的水文分布模式进行识别,并探讨了POME在水文随机模拟中的适用性。对矩阶数的讨论进一步完善了POME方法,实例结果表明随机序列基本反映实测序列的统计特征,模拟效果优良。

The principle of maximum entropy （POME）, a non-parametric inference technique with complete mathematical framework, has been increasingly applied in water resources. POME is substantially an optimization problem and the probability density function （PDF） is derived with forms of constraints. However, previous studies have focused little attention on constraints that are in form of moments, subjectively specifying the order of moments, which may have limitations in determining optimal POME distributions. The main contribution of this study is to present a POME framework considering the optimal order of moments, with analyses of the convergence of different moments with common distributions and a theoretical-empirical approach determining the optimal order of moments. This technique has been applied with hydrological data collected from the Yangtze River and the Yellow River. The series simulated with the technique is analyzed by comparison with measured series. Results indicate a good performance with all the measured statistics falling within the boxplot.