洪兴骏　郭生练　王乐

摘要：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 Type Ⅲ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。

关键词：最大熵原理；水文干旱；标准化径流干旱指数；汉江流域

中图分类号：TV121文献标志码：A文章编号：

16721683（2018）02009307

Abstract：

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 subbasins 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 Type Ⅲ.Results showed that the POMEbased 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.

Key words：POME；hydrological drought；Streamflow Drought Index （SDI）；Hanjiang River basin

干旱是一種由水循环异常引起的水分持续性短缺现象，不仅会对生态环境造成严重破坏，同时对工农业生产和城市供水等也会产生负面影响，长期制约着经济社会和人类文明发展。干旱指标是研究干旱现象的基础，也是衡量干旱发生与否与量级大小最为直观的定量表达。天然状况下，翔实的实测水文资料是计算干旱指标，评估区域干旱演变特征的基础。将实测水文要素时间序列看作服从某种理论概率分布的随机变量，通过等概率转换原理将其标准化，以评估其偏离正常情形的程度，是最常见的干旱指标构建方法。……