极限水文干旱历时概率分布解析法研究

Analytical study on probability distribution of critical hydrological drought duration

【目的】研究P-Ⅲ分布和Markove过程年径流序列极限水文干旱历时概率分布随水文参数的变化规律。【方法】以泾河和北洛河为例,根据游程理论与随机变量极值理论,采用解析法与模拟法,应用MATLAB编程技术,求解一定时期内极限水文干旱历时的概率分布,探讨极限水文干旱历时概率分布和数学期望值随径流序列一阶自相关系数、偏态系数的变化规律。【结果】在一定时期内,极限水文干旱历时的发生概率和数学期望随一阶自相关系数、偏态系数的增加而增大,且一阶自相关系数对极限水文干旱历时概率分布影响较为显著;泾河和洛河发生连续11年干旱的重现期均为1 000年。【结论】该解析法模型具有计算量小、精度高的特点,可用于年降水序列表征的气候干旱概率分析。

[Objective] The variation of the probability distribution of critical hydrological drought duration with hydrblogical parameters of runoff which was followed with P-Ⅲ distribution and Markove process was made. [Method] Based on the theory of run and extremes of random number of random variable and taking North Luo River and Jing River as examples,the probability distribution of critical drought duration in a certain period and the variation of the probability distribution and expected value of critical drought duration with first-order auto-correlation coefficient and skewed coefficient were completed. [Result] In a certain period,the probability and expected value of critical drought duration got larger with the increase of first-order auto-correlation coefficient and skewed coefficient, especially with first-order autocorrelation coefficient. The return periods of consecutive 11-year drought in North Luo River and Jing River were 1 000 years. [Conclusion] The analytical method in this paper avoided much calculation caused by simulation and had the traits of high accuracy and convenience, so it could be used in meteorological drought analysis.