基于最大熵分布模拟的干旱频率分析

Drought frequency analysis using stochastic simulation with maximum entropy model

为提高干旱频率分析结果的可靠性,提出了基于最大熵分布模拟的干旱频率分析方法。该模型首先用自回归模型剔除年径流量序列中的相依成分,分别计算年径流残差项序列各阶样本矩,并通过加速遗传算法求解获得残差项的最大熵概率分布函数,得到研究区域年径流量序列的最大熵分布随机模型;然后采用Monte Carlo随机模拟研究区域长、短序列的年径流量序列,在比较模拟效果的基础上,用轮次分析方法得到研究区域的干旱发生频率情况。区域干旱频率分析的实例研究结果显示,最大熵分布和P-III分布的模拟结果在各统计特性上较为接近,充分说明最大熵分布模拟结果的准确性;窟野河流域温家川站10 000年的年径流量序列轮次分析结果表明,温家川站发生连续12年严重干旱事件的概率为2.6%,重现期为203年。基于最大熵分布模拟残差项序列,由于不事先假定理论分布线型,使得最大熵分布模拟结果更具有适用性,适合于处理水资源系统中各种降水、径流等模拟分析工作。

This paper develops a model for drought frequency analysis using maximum entropy distribution to improve the reliability of analysis. This model adopts three steps. First, it calculates the probability density function （PDF） of the residual series of annual runoff after eliminating the dependent components with a auto- regression process. Second, it simulates the maximum entropy PDF of a purely random series generated by a Monte Carlo model with a rejection technique. Third, it calculates the negative run lengths for a simulated long-term annual runoff series, so that a frequency curve of these lengths was obtained and used in drought frequency analysis. Its application to the runoff at the Wenjiachuan station in the Kuye river basin indicates that its stochastic simulations are better than those with a P-III distribution method. And on the basis of a simulated annual runoff series of 10 000 years long for this station, the model predicts a probability of 2.6% and a return period of 203a for a severe 12a drought event. The stochastic simulation based on maximum entropy model, that does not rely on assumption and has better applicability, would be widely used in frequency analysis for hydrological and water resources systems.