基于相关系数的水文周期变异分级方法及验证
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摘要
周期成分是非一致性水文时间序列中的一种变异成分,对周期成分大小的定量描述与量化分级具有重要的现实意义。基于相关系数提出了一种周期变异程度分级方法,适用于可识别出简单周期成分的水文序列。首先通过计算水文序列和其含有的周期成分之间的相关系数,然后选定分级阈值,将周期变异程度划分为无、弱、中、强及巨变异5种等级。通过推导相关系数与周期成分半振幅之间的表达式,说明以相关系数作为分级指标的合理性,并分析各变量对相关系数求解结果的影响。将所提方法分别应用于人工生成序列和实测水文时间序列,结果显示该分级方法合理可靠,有助于理解和定量评估流域环境变化及其对水文过程的影响。
A periodic component is one of the time-varying components in an inconsistent hydrologic series, and quantifying and grading its significance level is practically significant. This paper presents a new method that uses the correlation coefficient to grade the significance level of periodicity in a hydrologic series containing only one simple periodic component. It calculates the correlation coefficient between the series and its periodic component, then uses four selected thresholds of this index to grade the corresponding periodicity significance into five levels: no, weak, mid, strong, and very strong. We derive a relationship of correlation coefficient versus half amplitude of periodicity demonstrating the reasonability of the index used in this method, and examine the influence of each variable on the correlation coefficient. Application to synthetic series and observed hydrologic series shows that our method is reliable and effective, thus helping quantify environmental change and its impact on hydrologic variability.
A periodic component is one of the time-varying components in an inconsistent hydrologic series, and quantifying and grading its significance level is practically significant. This paper presents a new method that uses the correlation coefficient to grade the significance level of periodicity in a hydrologic series containing only one simple periodic component. It calculates the correlation coefficient between the series and its periodic component, then uses four selected thresholds of this index to grade the corresponding periodicity significance into five levels: no, weak, mid, strong, and very strong. We derive a relationship of correlation coefficient versus half amplitude of periodicity demonstrating the reasonability of the index used in this method, and examine the influence of each variable on the correlation coefficient. Application to synthetic series and observed hydrologic series shows that our method is reliable and effective, thus helping quantify environmental change and its impact on hydrologic variability.
引文
[1]王文圣,丁晶,金菊良.随机水文学[M].北京:中国水利水电出版社,2008.WANG Wensheng,DING Jing,JIN Juliang.Stochastic hydrology[M].Beijing:China Water&Power Press,2008.(in Chinese)
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[6]王栋,朱元甡.基于MEM1谱分析的水文时间序列隐含周期特性研究[J].水文,2002(2):19-23.WANG Dong,ZHU Yuanshen.Research on cryptic period of hydrologic time series based on MEM1 spectral analysis[J].Journal of China Hydrology,2002(2):19-23.(in Chinese)
[7]谢平,李析男,刘宇,等.基于小波分析的非一致性洪水频率计算方法--以西江梧州站为例[J].水力发电学报,2014,33(1):15-22.XIE Ping,LI Xinan,LIU Yu,et al.Hydrological frequency calculation method of inconsistent flood series based on wavelet analysis[J].Journal of Hydroelectric Engineering,2014,33(1):15-22.(in Chinese)
[8]王红瑞,林欣,钱龙霞,等.基于异方差检验的水文过程隐含周期分析模型及其应用:Ⅰ.模型[J].水利学报,2008,39(11):1183-1189.WANG Hongrui,LIN Xin,QIAN Longxia,et al.Crytic period analysis model of hydrological process based on herteroskedasticity test and its application:Ⅰ.Model[J].Journal of Hydraulic Engineering,2008,39(11):1183-1189.(in Chinese)
[9]范钟秀.中长期水文预报[M].南京:河海大学出版社,1999.FAN Zhongxiu.Mid-and-long term hydrological forecasting[M].Nanjing:Hohai University Press,1999.(in Chinese)
[10]魏凤英.现代气候统计诊断与预测技术[M].北京:气象出版社,2007.WEI Fengying.Modern climate statistical diagnosis and prediction technology[M].Beijing:China Meteorological Press,2007.(in Chinese)
[11]黄嘉佑,李黄.气象中的谱分析[M].北京:气象出版社,1984.HUANG Jiayou,LI Huang.Spectral analysis in meteorology[M].Beijing:China Meteorological Press,1984.(in Chinese)
[12]王栋,朱元甡.最大熵原理在水文水资源科学中的应用[J].水科学进展,2001,12(3):424-430.WANG Dong,ZHU Yuanshen.Principle of maximum entropy and its application in hydrology and water resources[J].Advances in Water Science,2001,12(3):424-430.(in Chinese)
[13]崔锦泰,程正兴.小波分析导论[M].西安:西安交通大学出版社,1995.CUI Jintai,CHENG Zhengxing.An Introduction to wavelet[M].Xi'an:Xi'an Jiaotong University Press,1995.(in Chinese)
[14]桑燕芳,王中根,刘昌明.小波分析方法在水文学研究中的应用现状及展望[J].地理科学进展,2013,32(9):1413-1422.SANG Yanfang,WANG Zhonggen,LIU Changming.Applications of wavelet analysis to hydrology:Status and prospects[J].Progress in Geography,2013,32(9):1413-1422.(in Chinese)
[15]Huang N,Shen Z,Long S,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings of the Royal Society London A,1998,454(1971):903-995.
[16]王红瑞,叶乐天,刘昌明,等.水文序列小波周期分析中存在的问题及改进方式[J].自然科学进展,2006,16(8):1002-1008.WANG Hongrui,YE Letian,LIU Changming,et al.Existing problems and their improvement methods in wavelet periodic analysis of hydrological sequences[J].Progress in Natural Science,2006,16(8):1002-1008.(in Chinese)
[17]Sang Y F,Dong W,Wu J C,et al.The relation between periods'identification and noises in hydrologic series data[J].Journal of Hydrology,2009,368(1):165-177.
[18]Xie Y,Huang Q,Chang J,et al.Period analysis of hydrologic series through moving-window correlation analysis method[J].Journal of Hydrology,2016,538:278-292.
[19]桑燕芳,王栋.水文时间序列周期识别的新思路与两种新方法[J].水科学进展,2008,19(3):412-417.SANG Yanfang,WANG Dong.New idea and two new methods for identifying periodicities of hydrological time series[J].Advances in Water Science,2008,19(3):412-417.(in Chinese)
[20]Sang Y F,Wang Z,Liu C.Period identification in hydrologic time series using empirical mode decomposition and maximum entropy spectral analysis[J].Journal of Hydrology,2012,424-425(10):154-164.
[21]王红瑞,刘达通,王成,等,基于季节调整和趋势分解的水文序列小波周期分析模型及其应用[J].应用基础与工程科学学报,2013,21(5):823-836.WANG Hongrui,LIU Datong,WANG Cheng,et al.Hydrological series wavelet periodic model based on seasonal adjustment and trend decomposition with its application[J].Journal of Basic Science and Engineering,2013,21(5):823-836.(in Chinese)
[22]李平,卢文喜,辛欣,等.挠力河流域降水量序列的功率谱分析和最大熵谱分析[J].世界地质,2008,27(1):63-67.LI Ping,LU Wenxi,XIN Xin,et al.Power spectrum and maximum entropy spectrum analyses of precipitation series in Naolihe watershed[J].Global Geology,2008,27(1):63-67.(in Chinese)
[23]谢平,唐亚松,李彬彬,等.基于相关系数的水文趋势变异分级方法[J].应用基础与工程科学学报,2014,22(6):1089-1097.XIE Ping,TANG Yasong,LI Binbin,et al.Hydrological trend variation classification method based on correlation coefficient[J].Journal of Basic Science and Engineering,2014,22(6):1089-1097.(in Chinese)
[24]王红瑞,林欣,钱龙霞,等.基于异方差检验的水文过程隐含周期分析模型及其应用:Ⅱ.应用[J].水利学报,2008,39(12):1296-1301.WANG Hongrui,LIN Xin,QIAN Longxia,et al.Crytic period analysis model of hydrological process based on herteroscedasticity test and its application:Ⅱ.Application[J].Journal of Hydraulic Engineering,2008,39(12):1296-1301.(in Chinese)
[25]赵羽西,谢平,桑燕芳,等.基于相关系数的水文相依性变异分级方法:以自回归模型为例[J].应用生态学报,2018,29(4):1089-1097.ZHAO Yuxi,XIE Ping,SANG Yanfang,et al.Correlation coefficient-based classification method of hydrological dependence variability,with auto-regression model as example[J].Chinese Journal of Applied Ecology,2018,29(4):1089-1097.(in Chinese)
[2]翁文波.预测论基础[M].北京:石油工业出版社,1984.WENG Wenbo.Basis of prediction[M].Beijing:Petroleum Industry Press,1984.(in Chinese)
[3]谢平,陈广才,雷红富,等.水文变异诊断系统[J].水力发电学报,2010,29(1):85-91.XIE Ping,CHEN Guangcai,LEI Hongfu,et al.Hydrological alteration diagnosis system[J].Journal of Hydroelectric Engineering,2010,29(1):85-91.(in Chinese)
[4]谢平,陈广才,雷红富.变化环境下基于趋势分析的水资源评价方法[J].水力发电学报,2009,28(2):14-19.XIE Ping,CHEN Guangcai,LEI Hongfu.The assessment method of water resources based on trend analysis of changing environments[J].Journal of Hydroelectric Engineering,2009,28(2):14-19.(in Chinese)
[5]赵利红.水文时间序列周期分析方法的研究[D].南京:河海大学,2007.ZHAO Lihong.Study of analysis methods for the period of hydrological time series[D].Nanjing:Hohai University,2007.(in Chinese)
[6]王栋,朱元甡.基于MEM1谱分析的水文时间序列隐含周期特性研究[J].水文,2002(2):19-23.WANG Dong,ZHU Yuanshen.Research on cryptic period of hydrologic time series based on MEM1 spectral analysis[J].Journal of China Hydrology,2002(2):19-23.(in Chinese)
[7]谢平,李析男,刘宇,等.基于小波分析的非一致性洪水频率计算方法--以西江梧州站为例[J].水力发电学报,2014,33(1):15-22.XIE Ping,LI Xinan,LIU Yu,et al.Hydrological frequency calculation method of inconsistent flood series based on wavelet analysis[J].Journal of Hydroelectric Engineering,2014,33(1):15-22.(in Chinese)
[8]王红瑞,林欣,钱龙霞,等.基于异方差检验的水文过程隐含周期分析模型及其应用:Ⅰ.模型[J].水利学报,2008,39(11):1183-1189.WANG Hongrui,LIN Xin,QIAN Longxia,et al.Crytic period analysis model of hydrological process based on herteroskedasticity test and its application:Ⅰ.Model[J].Journal of Hydraulic Engineering,2008,39(11):1183-1189.(in Chinese)
[9]范钟秀.中长期水文预报[M].南京:河海大学出版社,1999.FAN Zhongxiu.Mid-and-long term hydrological forecasting[M].Nanjing:Hohai University Press,1999.(in Chinese)
[10]魏凤英.现代气候统计诊断与预测技术[M].北京:气象出版社,2007.WEI Fengying.Modern climate statistical diagnosis and prediction technology[M].Beijing:China Meteorological Press,2007.(in Chinese)
[11]黄嘉佑,李黄.气象中的谱分析[M].北京:气象出版社,1984.HUANG Jiayou,LI Huang.Spectral analysis in meteorology[M].Beijing:China Meteorological Press,1984.(in Chinese)
[12]王栋,朱元甡.最大熵原理在水文水资源科学中的应用[J].水科学进展,2001,12(3):424-430.WANG Dong,ZHU Yuanshen.Principle of maximum entropy and its application in hydrology and water resources[J].Advances in Water Science,2001,12(3):424-430.(in Chinese)
[13]崔锦泰,程正兴.小波分析导论[M].西安:西安交通大学出版社,1995.CUI Jintai,CHENG Zhengxing.An Introduction to wavelet[M].Xi'an:Xi'an Jiaotong University Press,1995.(in Chinese)
[14]桑燕芳,王中根,刘昌明.小波分析方法在水文学研究中的应用现状及展望[J].地理科学进展,2013,32(9):1413-1422.SANG Yanfang,WANG Zhonggen,LIU Changming.Applications of wavelet analysis to hydrology:Status and prospects[J].Progress in Geography,2013,32(9):1413-1422.(in Chinese)
[15]Huang N,Shen Z,Long S,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings of the Royal Society London A,1998,454(1971):903-995.
[16]王红瑞,叶乐天,刘昌明,等.水文序列小波周期分析中存在的问题及改进方式[J].自然科学进展,2006,16(8):1002-1008.WANG Hongrui,YE Letian,LIU Changming,et al.Existing problems and their improvement methods in wavelet periodic analysis of hydrological sequences[J].Progress in Natural Science,2006,16(8):1002-1008.(in Chinese)
[17]Sang Y F,Dong W,Wu J C,et al.The relation between periods'identification and noises in hydrologic series data[J].Journal of Hydrology,2009,368(1):165-177.
[18]Xie Y,Huang Q,Chang J,et al.Period analysis of hydrologic series through moving-window correlation analysis method[J].Journal of Hydrology,2016,538:278-292.
[19]桑燕芳,王栋.水文时间序列周期识别的新思路与两种新方法[J].水科学进展,2008,19(3):412-417.SANG Yanfang,WANG Dong.New idea and two new methods for identifying periodicities of hydrological time series[J].Advances in Water Science,2008,19(3):412-417.(in Chinese)
[20]Sang Y F,Wang Z,Liu C.Period identification in hydrologic time series using empirical mode decomposition and maximum entropy spectral analysis[J].Journal of Hydrology,2012,424-425(10):154-164.
[21]王红瑞,刘达通,王成,等,基于季节调整和趋势分解的水文序列小波周期分析模型及其应用[J].应用基础与工程科学学报,2013,21(5):823-836.WANG Hongrui,LIU Datong,WANG Cheng,et al.Hydrological series wavelet periodic model based on seasonal adjustment and trend decomposition with its application[J].Journal of Basic Science and Engineering,2013,21(5):823-836.(in Chinese)
[22]李平,卢文喜,辛欣,等.挠力河流域降水量序列的功率谱分析和最大熵谱分析[J].世界地质,2008,27(1):63-67.LI Ping,LU Wenxi,XIN Xin,et al.Power spectrum and maximum entropy spectrum analyses of precipitation series in Naolihe watershed[J].Global Geology,2008,27(1):63-67.(in Chinese)
[23]谢平,唐亚松,李彬彬,等.基于相关系数的水文趋势变异分级方法[J].应用基础与工程科学学报,2014,22(6):1089-1097.XIE Ping,TANG Yasong,LI Binbin,et al.Hydrological trend variation classification method based on correlation coefficient[J].Journal of Basic Science and Engineering,2014,22(6):1089-1097.(in Chinese)
[24]王红瑞,林欣,钱龙霞,等.基于异方差检验的水文过程隐含周期分析模型及其应用:Ⅱ.应用[J].水利学报,2008,39(12):1296-1301.WANG Hongrui,LIN Xin,QIAN Longxia,et al.Crytic period analysis model of hydrological process based on herteroscedasticity test and its application:Ⅱ.Application[J].Journal of Hydraulic Engineering,2008,39(12):1296-1301.(in Chinese)
[25]赵羽西,谢平,桑燕芳,等.基于相关系数的水文相依性变异分级方法:以自回归模型为例[J].应用生态学报,2018,29(4):1089-1097.ZHAO Yuxi,XIE Ping,SANG Yanfang,et al.Correlation coefficient-based classification method of hydrological dependence variability,with auto-regression model as example[J].Chinese Journal of Applied Ecology,2018,29(4):1089-1097.(in Chinese)