高阶线性矩法在陕北地区洪水频率分析中的应用
Using Higher-Order L-Moments for Flood Frequency Analysis in Northern Shaanxi
DOI: 10.12677/JWRR.2018.74045, PDF,   
作者: 王俊珍：贵州省大坝安全监测中心，贵州 贵阳；赵克宇：中国电建集团贵阳勘测设计研究院有限公司，贵州 贵阳
关键词: 设计洪水；参数估计；洪水设计值；高阶线性矩；广义极值分布；Design Flood； Parameter Estimation； Flood Quantile； Higher-Order L-Moments； GEV Distribution
摘要: 在介绍高阶线性矩原理的基础上，选取陕北交口河、张家山、赵石窖、绥德、刘家河、张村驿、林家村及神木8个水文站的洪峰流量资料进行广义极值分布高阶线性矩的参数估计，评价拟合效果和设计值的计算偏差，并与普通线性矩法拟合结果进行比较分析。利用高阶线性矩和普通线性矩对陕北8个水文站洪水频率进行的分析表明：随着阶数η的增大，设计值的相对偏差值越小，说明高阶线性矩法对洪峰序列的大洪水值拟合效果更好，提高了设计值估算精度。因此，高阶线性矩法是一种合理有效的洪水频率分析参数估计方法，可为大重现期设计洪水值的计算提供依据。
Abstract: In order to provide an efficient and reliable theoretical basis for design floods in the northern Shaanxi province, the higher-order L-Moments are applied in flood frequency analysis based on the principles of higher-order L-Moments. The annual maximum flood series of 8 hydrological stations at Jiaokou, Zhangjiashan, Zhaoshiyao, Sudie, Liujia, Zhangcunyi, Linjiacun and Shenmu Rivers are selected for case study. The parameters of Generalized Extreme Value (GEV) distribution and the design floods are estimated. The flood frequency curves are fitted, and the cumulative of squares error is regard as an indicator to evaluate the effect, and compared with the traditional Method of moments. The results show that higher-order L-Moments possess good statistical performance, which can describe the data series much better than lower-order L-Moments in flood analysis. Consequently, this method is reasonable and feasible, and would be provided the basis for the flood quantile calculation.
文章引用：王俊珍, 赵克宇. 高阶线性矩法在陕北地区洪水频率分析中的应用[J]. 水资源研究, 2018, 7(4): 404-411. https://doi.org/10.12677/JWRR.2018.74045

参考文献

[1] 李桃英. 陕西省灾害性洪水类型及成因分析[J]. 水文, 2004, 4(24): 39-42. LI Taoying. The types of disastrous floods in Shaanxi Province and the concerned genetic analysis. Hydrology, 2004, 4(24):39-42. (in Chinese)
[2] 刘攀, 郭生练, 闫宝伟, 李响, 陈璐. 再论分期设计洪水频率与防洪标准的关系[J]. 水力发电学报, 2011, 1(30): 187-192. LIU Pan, GUO Shenglian, YAN Baowei, LI Xiang and CHEN Lu. Supplementary of relationship between seasonal flood frequency and flood control standard. Journal of Hydroelectric Engineering, 2011, 1(30): 187-192.
[3] 王俊珍, 宋松柏. 基于高阶线性矩法的洪水设计值研究[J]. 水力发电学报, 2014,6(33): 33-42. WANG Junzhen, SONG Songbai. Application of higher-order L-Moments for flood quantile estimation. Journal of Hydroelectric Engineering, 2014, 6(33): 33-42. ( in Chinese)
[4] 王俊珍, 宋松柏. 具有历史洪水资料的期望矩法参数估计研究[J]. 水力发电学报, 待刊. WANG Junzhen, SONG Songbai. Expected moments algorithm method for parameters estimation with consideration of historical flood. Journal of Hydroelectric Engineering, in Press. (in Chinese)
[5] WANG, Q. J. Estimation of the GEV distribution from censored samples by method of partial probability weighted moments. Journal of Hydrology, 1990, (120): 103-114. [Google Scholar] [CrossRef] 
[6] WANG, Q. J. Using partial probability weighted moments to fit the extreme value distributions to censored samples. Water Resources Research, 1996, 32(6): 1767-1771.
[7] PANDEY, M. D. Extreme quantile estimation using order statistics with minimum cross-entropy principle. Engineering Mechanics, 2001, (16): 31-42.
[8] PANDEY, M. D. Minimum cross-entropy method for extreme value estimation using peaks-over-threshold data. Structural Safety, 2001, (23): 345-363. [Google Scholar] [CrossRef] 
[9] DENG, J., PANDEY, M. D. Using partial probability weighted moments and partial maximum entropy to estimate quantile from censored samples. Engineering Mechanics, 2009, (24): 407-417.
[10] DENG, J., PANDEY, M. D. Cross entropy quantile function estimation from censored samples using partial probability weighted moments. Journal of Hydrology, 2008, (363): 18-31.
[11] 詹道江, 徐向阳, 陈元芳. 工程水文学[M]. 北京: 中国水利水电出版社, 2011. ZHAN Daojiang, XU Xiangyang and CHEN Yuanfang. Engineering hydrology. Beijing: China Water Power Press, 2011. (in Chinese)
[12] 董闯, 宋松柏. 群智能优化算法在水文频率曲线适线中的应用[J]. 水文, 2011, 31(2): 20-26. DONG Chuang, SONG Songbai. Application of swarm intelligence optimization algorithm in optimization fitting of hydrologic frequency curve. Journal of China Hydrology, 2011, 31(2): 20-26. (in Chinese)
[13] 谢平, 郑泽权. 水文频率计算有约束加权适线法[J]. 武汉水利电力大学学报, 2000, 33(1): 49-52. XIE Ping, ZHENG Zequan. A constrained and weighted fitting method for hydrologic frequency calculation. Journal of Wuhan University of Hydraulic and Electric Engineering, 2000, 33(1): 49-52. (in Chinese)
[14] 邓育仁, 丁晶, 韦雪艳. 水文计算中的模糊优化适线法[J]. 水电站设计, 1995, 11(4): 43-47. DENG Yuren, DING Jing and WEI Xueyan. Fuzzy optimal curve fitting method in frequency analysis. Design of Hydroelectric Power Station, 1995, 11(4): 43-47. (in Chinese)
[15] WANG, Q. J. LH moments for statistical analysis of extreme events. Water Resources Research, 1997, 33(12): 2841-2848. [Google Scholar] [CrossRef] 
[16] WANG, Q. J. Using higher probability weighted moments for flood frequency analysis. Journal of Hydrology, 1997, 194(1): 95-106. [Google Scholar] [CrossRef] 
[17] HOSKING, J. R. M., WALLIS, J. R. and WOOD, E. F. Estimation of the generalized extreme value distribution by the method of probability weighted moments. Technometrics, 1985, 27(3): 251-261. [Google Scholar] [CrossRef] 
[18] GREENWOOD, J. A., LANDWEHR, J. M., MATALAS, N. C., et al. Probability weighted moments: Definition and relation to parameters of several distributions expressible in inverse form. Water Resources Research, 1979, 15(5): 1049-1054. [Google Scholar] [CrossRef]