Pearson-Ⅲ型负偏频率曲线的权函数参数估计方法  

Weighted Function Parameter Estimation Methods for Pearson-Ⅲ Negative Skewed Frequency Curve

作　　者：陈斐[1] 谢平[1] 桑燕芳[2] 梁忠民[3] 袁苏 CHEN Fei;XIE Ping;SANG Yanfang;LIANG Zhongmin;YUAN Su(State Key Laboratory of Water Resources Engineering and Management,Wuhan University,Wuhan 430072,China;Key Laboratory of Water Cycle and Related Land Surface Processes,Institute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences,Beijing 100101,China;College of Hydrology and Water Resources,Hohai University,Nanjing 210024,China)

机构地区：[1]武汉大学水资源工程与调度全国重点实验室,湖北武汉430072 [2]中国科学院地理科学与资源研究所陆地水循环与地表过程重点实验室,北京100101 [3]河海大学水文水资源学院,江苏南京210024

出　　处：《水文》2023年第3期1-8,22,共9页Journal of China Hydrology

基　　金：国家自然科学基金资助项目(91547205,41971040)。

摘　　要：Pearson-Ⅲ型水文频率计算以正偏序列为主,但在处理水库水位、潮位序列时常出现负偏的情况。针对正偏序列的权函数参数估计方法,通过公式推导将其拓展应用到负偏序列,完善了这一水文参数估计方法体系。统计试验表明相比常规矩法,权函数参数估计方法能显著提高对Cs估计的无偏性,并在有效性方面有所提升。比较权函数框架下的三种参数估计方法,发现二阶权函数矩法(WFM2)整体优于一阶权函数矩法(WFM1),利用权函数矩结合法(WFM3)对Cv(或σ)进行估计的前提是要确保Cs的估计优于Cv,否则其不如WFM1和WFM2的参数估计结果。以某潮位站年最高潮位序列和某水文站年最高水位序列进行了实例验证,拟合优度检验表明WFM2方法的拟合误差小、精度高,是所有比较方法中应用效果最好的方法。Hydrological frequency calculation for Pearson-III is mainly based on positive skewed series,but negative skew often occurs in dealing with reservoir water level and tide level series.Through formula derivation,weighted function methods of parameter estimation for positive skewed series are extended to negative skewed series in this paper,which perfects the system of this hydrological parameter estimation method.Statistical experiments show that compared with the conventional moment method(CM),weighted function methods can improve the unbiasedness significantly and the effectiveness slightly of parameter estimation for Cs.And three parameter estimation methods under the weighted function framework are compared.It is found that the second-order weighted function moment method(WFM2)is better than the first-order weighted function moment method(WFM1)as a whole,and the premise for parameter estimation of Cv(orσ)by the weighted function moment combination method(WFM3)is to ensure that the estimation of Cs is better than Cv,otherwise it is not as good as WFM1 and WFM2.The annual maximum tide level series in a tide level station and the annual maximum water level series in a hydrological station were verified as examples.The goodness-of-fit test shows that WFM2 has small fitting error and high precision,and so it is the best parameter estimation method among all comparison methods.

关 键 词：Pearson-Ⅲ型分布 负偏特性 权函数法 蒙特卡洛试验 水文频率分析 

分 类 号：P333[天文地球—水文科学] TV11[水利工程—水文学及水资源]