基于最大熵原理的水文干旱指标计算方法研究

Hydrological drought index calculation using Principle of Maximum Entropy

确定水文变量的概率分布,是计算各类标准化干旱指标的关键。提出了基于最大熵原理(POME)的月径流分布构建方法,采用多阶矩作为求解最大熵的约束条件,以拉格朗日乘子法估计分布参数,计算了不同时间尺度的标准化径流干旱指数SDI,评估了汉江30个子流域历史水文干旱情势。结果表明:与Normal、Gamma、Weibull、Pearson TypeⅢ等常用概率分布相比,POME分布模型可以最大程度地利用实测水文数据中的信息,有效拟合不同时间尺度的累积月径流量,表现出良好的适用性;随着时间尺度的增大,采用不同分布拟合同一尺度的月径流量,差别逐渐减小,月径流量概率分布特征趋于正态化。成果可为推求干旱指标,研究干旱特征的统计规律,进行干旱频率分析等提供新的手段。

Selecting the appropriate probability distribution function(PDF)for hydrological variables is of significant importance to calculating standardized drought indices.In this study,we used the Principle of Maximum Entropy(POME)method to model the PDFs of aggregated monthly streamflow on varying time scales for 30 sub-basins of the Hanjiang River Basin.The first three original moments of the cumulative monthly streamflow data were chosen as the constraint functions for maximizing the entropy by the Lagrange Multiplier.The Streamflow Drought Index(SDI)was computed based on monthly streamflow records derived from several theoretical probability distributions such as POME,Normal,Gamma,Weibull,and Pearson TypeⅢ.Results showed that the POME-based PDFs could make the best use of the information from observed records while avoiding mistakenly introducing redundant information.They showed satisfying applicability.We found that the PDFs of cumulative monthly streamflow would trend towards normalization as the time scale increased.The proposed method can be a practical tool for calculating hydrological drought indices,analyzing drought characteristics,and performing drought frequency analysis.