布尔分布在辽宁省西部半干旱地区水文频率分析中的应用
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摘要
在我国洪水频率分析计算中,一般选取P-Ⅲ型分布曲线作为理论曲线,但P-Ⅲ型曲线并非在任何自然条件下均适用。据此,采用EB-Ⅻ分布,对辽宁省西部17个水文站点经一致性修正后的年最大日流量序列进行拟合,与包括P-Ⅲ型曲线在内的9种曲线的拟合效果进行对比,找寻拟合效果最优的频率分布。结果表明:EB-Ⅻ分布在整体以及频率小于50%、频率小于25%的上尾区间段的拟合效果均优于P-Ⅲ型分布及其他8种分布,具有拟合效果好且稳定的特点,此外,根据EB-Ⅻ分布曲线进行外延得到的设计值的大小比较适中。因此,推荐在辽宁省西部地区使用EB-Ⅻ分布作为P-Ⅲ型分布的替代曲线。
In China, P-Ⅲ distribution is widely used in flood frequency analysis, but it is not suitable to be used under any natural conditions. After the consistency modification of annual maximum daily discharge series, the EB-Ⅻ distribution is applied to fit it at 17 hydrological gauging stations in the western Liaoning Province. and then be compared with nine distributions including P-Ⅲdistribution to find the best fitting frequency distribution. The results indicate that the EB-Ⅻ distribution performs better than the other 9 distributions in validity and stability, and the T-year designed flood peaks of EB-Ⅻ distribution are moderate as the peaks of the other frequency distributions may be higher or lower. Therefore, the EB-Ⅻ distribution is recommended to substitute P-Ⅲ distribution for frequency analysis in the western Liaoning Province.
In China, P-Ⅲ distribution is widely used in flood frequency analysis, but it is not suitable to be used under any natural conditions. After the consistency modification of annual maximum daily discharge series, the EB-Ⅻ distribution is applied to fit it at 17 hydrological gauging stations in the western Liaoning Province. and then be compared with nine distributions including P-Ⅲdistribution to find the best fitting frequency distribution. The results indicate that the EB-Ⅻ distribution performs better than the other 9 distributions in validity and stability, and the T-year designed flood peaks of EB-Ⅻ distribution are moderate as the peaks of the other frequency distributions may be higher or lower. Therefore, the EB-Ⅻ distribution is recommended to substitute P-Ⅲ distribution for frequency analysis in the western Liaoning Province.
引文
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[14]王炳兴. Burr TypeⅫ分布的统计推断[J].数学物理学报,2008,28(6):1103-1108.(WANG Bingxing. Statistical inference for theBurr TypeⅫdistribution[J]. Acta Mathematica Scientia, 2008,28(6):1103-1108.(in Chinese))
[15] Tasker G, Hosking J R M, Wallis J R. Regional frequency anal-ysis:an approach based on L-Moments[J]. Journal of the Ameri-can Statistical Association, 1998, 93(443):1233.
[16] Watkins A J. An algorithm for maximum likelihood estimation inthe three parameter Burr XII distribution[J]. Computational Statis-tics&Data Analysis, 1999, 32(1):19-27.
[17] Quanxi Shao. Notes on maximum likelihood estimation for thethree-parameter Burr XII distribution[J]. Computational Statistics&Data Analysis, 45(3):675-687.
[18]叶长青,陈晓宏,邵全喜,张家鸣.考虑高水影响的洪水频率分布线型对比研究[J].水利学报,2013,44(06):694-702.(YE Changqing,CHEN Xiaohong,SHAO Quanxi,et al. A comparison study on dis-tribution for flood frequency analysis focus on the observed flowdata in the high flow part[J]. Journal of Hydraulic Engineering,2013,44(06):694-702.(in Chinese))
[19]金光炎.水文分析中的经验频率[J].水文,1994(1):1-9.(JINGuangyan. Empirical frequency in hydrological analysis[J]. Journalof China Hydrology, 1994(1):1-9.(in Chinese))
[20]成静清.非一致性年径流序列频率分析计算[D].陕西:西北农林科技大学,2010.(CHENG Jingqing. Hydrological Frequency Analysisfor Inconsistent Annual Runoff Series[D]. Shanxi:Northwest A&FUniversity,2010.(in Chinese))
[21]熊立华,江聪,杜涛等.变化环境下非一致性水文频率分析研究综述[J].水资源研究,2015,04(4):310-319.(XIONG Lihua, JIANGCong, DU Tao, et al. Review on nonstationary hydrological fre-quency analysis under changing environments[J]. Journal of WaterResources Research, 2015,04(4):310-319.(in Chinese))
[22]梁忠民,胡义明,王军.非一致性水文频率分析的研究进展[J].水科学进展,2011,22(6):864-871.(LIANG Zhongmin, HU Yiming,WANG Jun. Advances in hydrological frequency analysis of non-stationary time series[J]. Advances in Water Science,2011,22(6):864-871.(in Chinese))
[23]沈宏.天然径流还原计算方法初步探讨[J].水利规划与设计,2003(3):15-18.(SHEN Hong. Study in the calculation method of nat-ural runoff restore[J].Water Resources Planning and Design,2003(3):15-18.(in Chinese))
[24]谢平,陈广才,夏军.变化环境下非一致性年径流系列的水文频率计算原理[J].武汉大学学报:工学版,2005,38(6):6-9.(XIE Ping,CHEN Guangcai, XIA Jun. Hydrological frequency calculationprinciple of inconsistent annual runoff series under changing envi-ronments[J]. Engineering Journal of Wuhan University,2005,38(6):6-9.(in Chinese))
[25]胡义明,梁忠民.基于跳跃分析的非一致性洪量系列的频率计算[J].东北水利水电,2011(7):38-40.(HU Yiming, LIANG Zhongmin.Frequency analysis of non-stationary flood series based on jumpanalysis[J].Water Resources&Hydropower of Northeast China,2011(7):38-40.(in Chinese))
[26]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2):55-58.(WANG Guoqing,ZHANG Jianyun, LIU Jiufu, et al. Quantitative assessment forclimate change and human activities impact on river runoff[J].China Water Resources,2008(2):55-58.(in Chinese))
[27]胡义明,梁忠民,杨好周,等.基于趋势分析的非一致性水文频率分析方法研究[J].水力发电学报,2013,32(5):21-25.(HU Yiming,LIANG Zhongmin, YANG Haozhou, et al. Study on frequencyanalysis method of non-stationary observation series based ontrend analysis[J]. Journal of Hydroelectric Engineering,2013,32(5):21-25.(in Chinese))
[2] 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 andHydropower[S].(in Chinese))
[3]郭生练,刘章君,熊立华.设计洪水计算方法研究进展与评价[J].水利学报,2016,47(03):302-314.(GUO Shenglian, LIU Zhangjun,XIONG Lihua. Advances and assessment on design flood estimationmethods[J]. Journal of Hydraulic Engineering,2016,47(03):302-314.(in Chinese))
[4]张静怡,徐小明.极值分布和P-III型分布线性矩法在区域洪水频率分析中的检验[J].水文,2002,22(06):36-38.(ZHANG Jingyi, XUXiaoming. Test on L-moment estimation method for GEV and P-IIIdistribution in regional flood frequency analysis[J]. Journal of ChinaHydrology, 2002,22(06):36-38.(in Chinese))
[5]姚孝诚.对数P-Ⅲ型分布曲线在年最大流量频率分析中的应用[J].四川水利,1998,19(03):7-12.(YAO Xiaocheng.The application oflogarithmic PearsonⅢdistribution in annual maximum flow fre-quency analysis[J].Sichuan Water Conservancy, 1998,19(03):7-12.(in Chinese))
[6]李松仕.对数皮尔逊Ⅲ型频率分布统计特性分析[J].水利学报,1985(09):43-48.(LI Songshi. Statistical characteristic analysis of loga-rithmic PearsonⅢfrequency distribution[J]. Journal of HydraulicEngineering. 1985(09):43-48.(in Chinese))
[7]田万荣,朱健.几种频率分布线型对新疆天山北坡洪水适应性研究[J].干旱区地理,2000,23(04):353-357.(TIAN Wanrong, ZHU Jian.Study on suitability of some curve type on frequency distribution inanalyzing floods occurring on the northern slope of the Tianshanmountains, Xinjiang[J].Arid Land Geography, 2000,23(04):353-357.(in Chinese))
[8] Shao Q. Notes on maximum likelihood estimation for the three-pa-rameter Burr XII distribution[J]. Computational Statistics&DataAnalysis, 2004, 45(3):675-687.
[9]李诚,郭文娟,杜新忠. EB3Ⅲ分布在枯水频率分析中的应用[J].交通科学与工程,2011,27(01):64-68.(LI Cheng, GUO Wenjuan, DUXinzhong. Application of three-parameter Burr III distribution forlow-flow frequency analysis[J].Journal of Transport Science and En-gineering, 2011,27(01):64-68.(in Chinese))
[10] Shao Q, Chen Y D, Zhang L. An Extension of Three-parameterBurr III Distribution for Low-flow Frequency Analysis[M]. ElsevierScience Publishers B. V. 2008.
[11] Quanxi Shao, Heung Wong, Jun Xia, et al. Models for extremesusing the extended three-parameter Burr XII system with applica-tion to flood frequency analysis[J]. Hydrological Sciences Journal,2004, 49(4):685-702.
[12]陈璐,何典灿,周建中,等.基于广义第二类beta分布的洪水频率分析[J].水文,2016,36(06):1-6.(CHEN Lu, HE Diancan, ZHOUJianzhong,et al. Application of generalized Beta distribution ofsecond kind for flood frequency analysis[J].Journal of China Hy-drology, 2016,36(06):1-6.(in Chinese))
[13]胡乃发,金昌杰,关德新,等.浑太流域降水极值的统计分布特征[J].高原气象,2012,31(04):1166-1172.(HU Naifa, JIN Changjie,GUAN Dexin,et al. Characteristic of statistical distribution of ex-treme precipitation in Hunhe-Taizihe Basins[J].Plateau Meteorolo-gy, 2012,31(04):1166-1172.(in Chinese))
[14]王炳兴. Burr TypeⅫ分布的统计推断[J].数学物理学报,2008,28(6):1103-1108.(WANG Bingxing. Statistical inference for theBurr TypeⅫdistribution[J]. Acta Mathematica Scientia, 2008,28(6):1103-1108.(in Chinese))
[15] Tasker G, Hosking J R M, Wallis J R. Regional frequency anal-ysis:an approach based on L-Moments[J]. Journal of the Ameri-can Statistical Association, 1998, 93(443):1233.
[16] Watkins A J. An algorithm for maximum likelihood estimation inthe three parameter Burr XII distribution[J]. Computational Statis-tics&Data Analysis, 1999, 32(1):19-27.
[17] Quanxi Shao. Notes on maximum likelihood estimation for thethree-parameter Burr XII distribution[J]. Computational Statistics&Data Analysis, 45(3):675-687.
[18]叶长青,陈晓宏,邵全喜,张家鸣.考虑高水影响的洪水频率分布线型对比研究[J].水利学报,2013,44(06):694-702.(YE Changqing,CHEN Xiaohong,SHAO Quanxi,et al. A comparison study on dis-tribution for flood frequency analysis focus on the observed flowdata in the high flow part[J]. Journal of Hydraulic Engineering,2013,44(06):694-702.(in Chinese))
[19]金光炎.水文分析中的经验频率[J].水文,1994(1):1-9.(JINGuangyan. Empirical frequency in hydrological analysis[J]. Journalof China Hydrology, 1994(1):1-9.(in Chinese))
[20]成静清.非一致性年径流序列频率分析计算[D].陕西:西北农林科技大学,2010.(CHENG Jingqing. Hydrological Frequency Analysisfor Inconsistent Annual Runoff Series[D]. Shanxi:Northwest A&FUniversity,2010.(in Chinese))
[21]熊立华,江聪,杜涛等.变化环境下非一致性水文频率分析研究综述[J].水资源研究,2015,04(4):310-319.(XIONG Lihua, JIANGCong, DU Tao, et al. Review on nonstationary hydrological fre-quency analysis under changing environments[J]. Journal of WaterResources Research, 2015,04(4):310-319.(in Chinese))
[22]梁忠民,胡义明,王军.非一致性水文频率分析的研究进展[J].水科学进展,2011,22(6):864-871.(LIANG Zhongmin, HU Yiming,WANG Jun. Advances in hydrological frequency analysis of non-stationary time series[J]. Advances in Water Science,2011,22(6):864-871.(in Chinese))
[23]沈宏.天然径流还原计算方法初步探讨[J].水利规划与设计,2003(3):15-18.(SHEN Hong. Study in the calculation method of nat-ural runoff restore[J].Water Resources Planning and Design,2003(3):15-18.(in Chinese))
[24]谢平,陈广才,夏军.变化环境下非一致性年径流系列的水文频率计算原理[J].武汉大学学报:工学版,2005,38(6):6-9.(XIE Ping,CHEN Guangcai, XIA Jun. Hydrological frequency calculationprinciple of inconsistent annual runoff series under changing envi-ronments[J]. Engineering Journal of Wuhan University,2005,38(6):6-9.(in Chinese))
[25]胡义明,梁忠民.基于跳跃分析的非一致性洪量系列的频率计算[J].东北水利水电,2011(7):38-40.(HU Yiming, LIANG Zhongmin.Frequency analysis of non-stationary flood series based on jumpanalysis[J].Water Resources&Hydropower of Northeast China,2011(7):38-40.(in Chinese))
[26]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2):55-58.(WANG Guoqing,ZHANG Jianyun, LIU Jiufu, et al. Quantitative assessment forclimate change and human activities impact on river runoff[J].China Water Resources,2008(2):55-58.(in Chinese))
[27]胡义明,梁忠民,杨好周,等.基于趋势分析的非一致性水文频率分析方法研究[J].水力发电学报,2013,32(5):21-25.(HU Yiming,LIANG Zhongmin, YANG Haozhou, et al. Study on frequencyanalysis method of non-stationary observation series based ontrend analysis[J]. Journal of Hydroelectric Engineering,2013,32(5):21-25.(in Chinese))