基于次序统计量理论的洪水频率分析方法研究
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摘要
针对目前参数估计方法存在稀遇洪水频率设计值偏大的问题,提出采用基于数值次序统计量期望值的适线法计算洪水频率设计初始值;针对目前参数估计方法存在常遇洪水频率设计值偏小的问题,提出采用周文德公式修正目前频率设计偏小的情形,计算洪水频率设计修正值;针对目前传统方法计算洪水频率设计值抽样误差大的问题,提出采用基于数值次序统计量标准差的方法计算洪水频率设计保证值。定量分析表明,提出的基于数值次序统计量期望值的优化适线法具有良好的无偏性和有效性;寸滩站洪水频率设计修正值大于频率设计初始值,且两者偏差随着频率减小而减小;寸滩站洪水频率设计保证值明显大于修正值。
As for the problem that the rare flood frequency design value is too large with parameter estimation methods, this paper used the FIT method of order statistic expectation value to calculate the initial value of design flood. For the problem that the common flood frequency design value is too small with parameter estimation methods, this paper used the Zhou Wende formula to calculate the correction value of design flood. As for the problem that the error of design flood is too large, this paper used the standard deviation of generalized order statistics method to calculate the safety value of design flood.The results show that the FIT method of order statistic expectation has a good unbiased and effectiveness properties. The correction value of design flood of the Cuntan station design flood is greater than the initial value of design flood, and both bias decreases as the frequency decreases.Obviously, the safety value of design flood of Cuntan Station design flood is greater than the correction value of design flood.
As for the problem that the rare flood frequency design value is too large with parameter estimation methods, this paper used the FIT method of order statistic expectation value to calculate the initial value of design flood. For the problem that the common flood frequency design value is too small with parameter estimation methods, this paper used the Zhou Wende formula to calculate the correction value of design flood. As for the problem that the error of design flood is too large, this paper used the standard deviation of generalized order statistics method to calculate the safety value of design flood.The results show that the FIT method of order statistic expectation has a good unbiased and effectiveness properties. The correction value of design flood of the Cuntan station design flood is greater than the initial value of design flood, and both bias decreases as the frequency decreases.Obviously, the safety value of design flood of Cuntan Station design flood is greater than the correction value of design flood.
引文
[1]丛树铮,胡四一.洪水频率分析的现状与展望[J].水文,1987,(6):52-58.(CONG Shuzheng,HU Siyi.Present situation and prospect of flood frequency analysis[J].Journal of China Hydrology,1987,(6):52-58.(in Chinese))
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[9]谢自银,刘九夫,张建云.P-Ⅲ型分布次序统计量期望值数值计算[J].水文,2005,25(6).(XIE Ziyin,LIU Jiufu,ZHANG Jianyun.A numerical arithmetric for computing expected values of Pearson type-IIIorder statistics[J].Journal of China Hydrology,2005,25(6).(in Chinese))
[10]刘九夫,张建云.水文概率P-Ⅲ型分布无偏绘点位置的数值计算方法[J].水利学报,2006,37(8).(LIU Jiufu,ZHANG Jianyun.Numerical arithmetic for computing unbiased plotting positions of hydrological probability statistics with Pearson type-Ⅲdistribution[J].Journal of Hydraulic Engineering,2006,37(8).(in Chinese))
[11]Arnold B C,Balakrishnan N.Relations,Bounds and Approximations for Order Statistics[M].New York:Springer,1989.
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[13]郭生练,叶守泽.论水文计算中的经验频率公式[J].武汉水利水电学院学报,1992,25(2):38-45.(GUO Shenglian,YE Shouze.Another look at plotting position formulae in hydrology[J].Journal.of Wuhan University of Hydr.&Elec Eng,1992,25(2):38-45.(in Chinese))
[14]刘光文.皮尔逊Ⅲ型分布参数估计[J].水文,1990,(4).(LIU Guangwen.Parameter estimation of Pearson type-Ⅲdistribution[J].Journal of China Hydrology,1990,(4).(in Chinese))
[15]Sorooshian S,Duan Q,Gupta V K.Optimal use of the SCE-UA global optimization method for calibrating watershed models[J].Journal of Hydrology,1994,158(1):265-284.
[16]鲍振鑫.水文频率分析适线法参数估计研究[D].南京水利科学研究院,2010.(BAO Zhenxin.Parameter Estimation on Curve-fitting Methodology in Hydrologic Frequency Analysis[D].Nanjing Hydraulic Research Institute,2010.(in Chinese))
[17]C Cunnane.Unbiased plotting positions-a review[J].Journal of Hydrology,1978,37:205-222.
[18]Chow.V.T.,Maidment,D.R.,Mays.L.W.Applied Hydrology[M].Me Graw Hill Internarlonal Editions,Mc Graw-Hill,1988:383-388.
[2]李扬.水文频率新型计算理论与应用研究[D].西北农林科技大学,2013.(LI Yang.Research on New Theory and Application of Hydrologic Frequency Analysis[D].North West Agriculture and Forestry University,2013.(in Chinese))
[3]胡素端,宋松柏.高阶概率权重矩在洪水频率分布参数估计中的应用研究[J].西北农林科技大学学报(自然科学版),2013,41(6).(HU Suduan,SONG Songbai.Application of higher probability weighted moments in the estimation of flood frequency distribution paramenters[J].Journal of Northwest A&F University(Nat.Sci.Ed),2013,41(6).(in Chinese))
[4]原秀红,宋松柏.基于部分概率权重矩的洪水频率分布参数估计方法研究[J].水资源研究,2012,(1):375-379.(YUAN Xiuhong,SONG Songbai.Estimation of GEV distribution parameters using partial probability weighted moments[J].Journal of Water Resources Research,2012,(1):375-379.(in Chinese))
[5]胡宏达.关于样本次序统计量众值中值期望值的研究[J].东北水利水电,1991,(3).(HU Hongda.Research on the expected value of the median value of the sample order statistics[J].Water Resources&Hydropower of Northeast China,1991,(3).(in Chinese))
[6]林炳章,邵月红.水文气象促进工程水文计算核心课题研究的发展[A].中国水文科技新进展[C],2012.(LIN Bingzhang,SHAO Yuehong.The development of hydrologic computing core research in hydrometeorology promotion project[A].New Advances in Hydrological Science and Technology in China[C],2012.(in Chinese))
[7]SL44-2006,水利水电工程设计洪水计算规范[S].(SL44-2006,Regulation for Calculating Design Flood of Water Resources and Hydropower Projects[S].(in Chinese))
[8]刘九夫,谢自银,鲍振鑫,等.洪水频率分析的次序统计量[J].水科学进展,2010,21(2).(LIU Jiufu,XIE Ziyin,BAO Zhenxin,et al.Order statistics in flood frequency analysis[J].Advances in Water Science,2010,21(2).(in Chinese))
[9]谢自银,刘九夫,张建云.P-Ⅲ型分布次序统计量期望值数值计算[J].水文,2005,25(6).(XIE Ziyin,LIU Jiufu,ZHANG Jianyun.A numerical arithmetric for computing expected values of Pearson type-IIIorder statistics[J].Journal of China Hydrology,2005,25(6).(in Chinese))
[10]刘九夫,张建云.水文概率P-Ⅲ型分布无偏绘点位置的数值计算方法[J].水利学报,2006,37(8).(LIU Jiufu,ZHANG Jianyun.Numerical arithmetic for computing unbiased plotting positions of hydrological probability statistics with Pearson type-Ⅲdistribution[J].Journal of Hydraulic Engineering,2006,37(8).(in Chinese))
[11]Arnold B C,Balakrishnan N.Relations,Bounds and Approximations for Order Statistics[M].New York:Springer,1989.
[12]朱元甡,梁家志.m/(n+1)公式可以休矣—水文频率分析中绘点位置的研究[J].水文,1991,11(5).(ZHU Yuansheng,LIANG Jiazhi.The m/(n+1)formula can be used to study the position of the drawing points in hydrological frequency analysis[J].Journal of China Hydrology,1991,11(5).(in Chinese))
[13]郭生练,叶守泽.论水文计算中的经验频率公式[J].武汉水利水电学院学报,1992,25(2):38-45.(GUO Shenglian,YE Shouze.Another look at plotting position formulae in hydrology[J].Journal.of Wuhan University of Hydr.&Elec Eng,1992,25(2):38-45.(in Chinese))
[14]刘光文.皮尔逊Ⅲ型分布参数估计[J].水文,1990,(4).(LIU Guangwen.Parameter estimation of Pearson type-Ⅲdistribution[J].Journal of China Hydrology,1990,(4).(in Chinese))
[15]Sorooshian S,Duan Q,Gupta V K.Optimal use of the SCE-UA global optimization method for calibrating watershed models[J].Journal of Hydrology,1994,158(1):265-284.
[16]鲍振鑫.水文频率分析适线法参数估计研究[D].南京水利科学研究院,2010.(BAO Zhenxin.Parameter Estimation on Curve-fitting Methodology in Hydrologic Frequency Analysis[D].Nanjing Hydraulic Research Institute,2010.(in Chinese))
[17]C Cunnane.Unbiased plotting positions-a review[J].Journal of Hydrology,1978,37:205-222.
[18]Chow.V.T.,Maidment,D.R.,Mays.L.W.Applied Hydrology[M].Me Graw Hill Internarlonal Editions,Mc Graw-Hill,1988:383-388.