含零值水文序列频率计算方法研究

Frequency estimation of hydrological samples with zero values

针对常规水文频率分析方法无法进行含零值水文序列频率计算的问题,研究3种含零值水文序列频率的计算方法。选用Gamma分布,推导极大似然法(ML)、最大熵原理(POME)和概率权重矩法(PWM)非零和含零值序列参数估计公式,研究非零值序列和含零值序列参数转换关系和设计值计算。应用蒙特卡洛试验,研究零值序列长度对参数估计方法不同重现期设计值的影响。以陕西省6个测站枯水期1月份月降水资料为例,研究不同参数估计方法的适用性,计算高尾部设计值的累积误差平方和,进行拟合优度评价。结果表明:最大熵原理和极大似然法对含零值降水序列均具有较好的拟合效果,研究结果可为含零值水文序列频率计算提供依据。

This paper presents a study on frequency analysis method of hydrological samples with zero values, focusing on the derivation of parameter estimation formulas of Gamma distribution for the nonzero values and full series using maximum likelihood method （ML）, the principle of maximum entropy （POME）, and probability weight moment method （PWM）. We also discuss the relationship between nonzero values and full series and the calculation of design values of hydrological samples. Monte-Carlo simulations are conducted to examine the influence of different sample lengths on the design values calculated using different methods of parameter estimation. Applicability of these methods are evaluated through a case study of six monthly precipitation samples observed in Shaanxi, including the effect and calculation error of fitting large sample events. The results indicate that both the principle of maximum entropy and maximum likelihood method have a good fitting effect, forming a theoretical basis for frequency analysis of the hydrological samples with zero values.