基于游程理论和Copula函数研究岷江流域干旱特征
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摘要
为了合理评估区域干旱灾害风险,以岷江流域14个气象站1961-2012年逐月降水数据为研究对象,以阈值为变量设定3种游程截取水平识别干旱,然后利用经拟合优选的Copula函数构建干旱历时与干旱烈度的联合分布,并进行概率分析和重现期计算。结果表明:Gumbel Copula函数对整个流域的拟合效果最优;利用Gumbel Copula函数分析二维条件概率P(S≤60mm|D≥3月),3种截取水平的发生概率从流域东南到西北递增;联合重现期结果显示流域东北部和南部一带的旱情比中西部严重,而同现重现期结果则显示流域西部的旱情比东部严重;联合重现期比同现重现期的空间分布更稳定,任意一种截取水平下的联合重现期都比较接近。研究结果可为游程理论截取水平设定、Copula函数优选以及多变量干旱分析提供依据。
In order to assess the risk of regional drought disaster reasonably,we took the monthly precipitation data of 14 meteorological stations in Minjiang River Basin from 1961 to 2012 as the research object,and,with threshold as a variable,set three cutting levels according to the theory of runs to identify drought events.Then we used the best fit Copula function to construct the joint distribution of drought duration and severity and analyzed the probabilistic characteristics and return period.The results showed that Gumbel Copula function demonstrated the best fitness for Minjiang River Basin.After the analysis of the spatial distribution of conditional probability P(S≤60mm|D≥3 months),the results indicated that the probability of occurrence on the three cutting levels increased from the southeast to the northwest of the basin.The results of joint return period demonstrated that the drought in the northeastern and southern parts of the basin was more serious than that in the central and western regions,while the results of co-occurrence return period showed that the drought in the west of the basin was more serious than that in the east.The spatial distribution characteristics of joint return period were more stable than those of co-occurrence return period.The joint return periods of the whole basin on each cutting level were relatively close.This study could provide a basis for setting the cutting level of the theory of runs,choosing optimal Copula function,and conducting multivariate drought analysis.
In order to assess the risk of regional drought disaster reasonably,we took the monthly precipitation data of 14 meteorological stations in Minjiang River Basin from 1961 to 2012 as the research object,and,with threshold as a variable,set three cutting levels according to the theory of runs to identify drought events.Then we used the best fit Copula function to construct the joint distribution of drought duration and severity and analyzed the probabilistic characteristics and return period.The results showed that Gumbel Copula function demonstrated the best fitness for Minjiang River Basin.After the analysis of the spatial distribution of conditional probability P(S≤60mm|D≥3 months),the results indicated that the probability of occurrence on the three cutting levels increased from the southeast to the northwest of the basin.The results of joint return period demonstrated that the drought in the northeastern and southern parts of the basin was more serious than that in the central and western regions,while the results of co-occurrence return period showed that the drought in the west of the basin was more serious than that in the east.The spatial distribution characteristics of joint return period were more stable than those of co-occurrence return period.The joint return periods of the whole basin on each cutting level were relatively close.This study could provide a basis for setting the cutting level of the theory of runs,choosing optimal Copula function,and conducting multivariate drought analysis.
引文
[1] XU K,YANG D,XU X,et al.Copula based drought frequency analysis considering the spatio-temporal variability in Southwest China[J].Journal of Hydrology,2015,527:630-640.DOI:10.1016/j.jhydrol.2015.05.030.
[2]王晓峰,胡春艳,卫伟,等.基于SPI的渭北黄土高原干旱时空特征[J].生态环境学报,2016,25(3):415-421.(WANG X F,HU C Y,WEI W,et al.Temporal and spatial characteristics of drought based on standardized precipitation index in Weibei loess plateau[J].Ecology and Environmental Sciences,2016,25(3):415-421.(in Chinese))DOI:10.16258/j.cnki.1674-5906.2016.03.008.
[3]董前进,谢平.水文干旱研究进展[J].水文,2014(4):1-7.(DONG Q J,XIE P.Advances in hydrological drought research[J].Journal of China Hydrology,2014(4):1-7.(in Chinese))DOI:10.3969/j.issn.1000-0852.2014.04.001.
[4]于忱,陈隽,王红瑞,等.多变量Copula函数在干旱风险分析中的应用进展[J].南水北调与水利科技,2018,(1):14-21.(YU C,CHEN J,WANG H R,et al.Application progress of multi-variable Copula function in drought risk analysis[J].South-to-North Water Transfers and Water Science&Technology,2018,(1):14-21.(in Chinese))DOI:10.13476/j.cnki.nsbdqk.20180003.
[5]李明,张永清,张莲芝.基于Copula函数的长春市106年来的干旱特征分析[J].干旱区资源与环境,2017(6):147-153.(LI M,ZHANG Y Q,ZHANG L Z.Analysis on drought characteristics of Changchun city in 106years based on Copula function[J].Journal of Arid Land Resources&Environment,2017(6):147-153.DOI:10.13448/j.cnki.jalre.2017.193.
[6] REDDY M J,SINGH V P.Multivariate modeling of droughts using copulas and meta-heuristic methods[J].Stochastic environmental research and risk assessment,2014,28(3):475-489.DOI:10.1007/s00477-013-0766-2.
[7] SHIAU J T,SHEN H W.Recurrence analysis of hydrologic droughts of differing severity[J].Journal of Water Resources Planning and Management,2001,127(1):30-40.DOI:10.1061/(ASCE)0733-9496(2001)127:1(30).
[8]陆桂华,闫桂霞,吴志勇,等.基于copula函数的区域干旱分析方法[J].水科学进展,2010,21(2):188-193.(LU G H,YAN G X,WU Z Y,et al.Regional drought analysis approach based on copula function[J].Advances in Water Science,2010,21(2):188-193.(in Chinese))DOI:10.14042/j.cnki.32.1309.2010.02.004.
[9]张玉虎,刘凯利,陈秋华,等.区域气象干旱特征多变量Copula分析——以阿克苏河流域为例[J].地理科学,2014,34(12):1480-1487.(ZHANG Y H,LIU K L,CHEN Q H,et al.Bivariate probability distribution of meteorological drought characteristics in the Aksu Basin using Copula[J].Scientia Geographica Sinica,2014,34(12):1480-1487.(in Chinese))DOI:10.13249/j.cnki.sgs.2014.12.009.
[10]李计,李毅,宋松柏,等.基于Copulas函数的多维干旱变量联合分布[J].自然资源学报,2013,28(2):312-320.(LI J,LI Y SONG S B,et al.Multivariate joint distributions of drought variables based on Copulas function[J].Journal of Natural Resources,2013,28(2):312-320.(in Chinese))DOI:10.11849/zrzyxb.2013.02.012.
[11]肖名忠,张强,陈永勤,等.基于三变量Copula函数的东江流域水文干旱频率分析[J].自然灾害学报,2013,22(2):99-108.(XIAO M Z,ZHANG Q,CHEN Y Q,et al.Hydrological drought frequency analysis of East River basin based on trivariate Copulas function[J].Journal of Natural Disasters,2013,22(2):99-108.(in Chinese))DOI:10.13577/j.jnd.2013.0214.
[12]肖名忠,张强,陈晓宏.基于多变量概率分析的珠江流域干旱特征研究[J].地理学报,2012,67(1):83-92.(XIAO M Z,ZHANG Q,CHEN X H.Spatial-temporal patterns of drought risk across the Pearl River Basin[J].Acta Geographica Sinica,2012,67(1):83-92.(in Chinese))DOI:10.11821/xb201201009.
[13]刘文琨,裴源生,赵勇,等.区域气象干旱评估分析模式[J].水科学进展,2014,25(3):318-326.(LIU W K,PEI Y S,ZHAO Y,et al.Research of the regional meteorological drought assessment analysis model[J].Advances in Water Science,2014,25(3):318-326.(in Chinese))DOI:10.14042/j.cnki.32.1309.2014.03.002.
[14]罗艳青,邹滨,邱永红.华东地区干旱灾害时空演化特征研究[J].干旱区资源与环境,2013,27(10):58-64.(LUO Y Q,ZOU B,QIU Y H.Spatial-temporal evolution characteristics of drought disaster in East China[J].Journal of Arid Land Resources&Environment,2013,27(10):58-64.(in Chinese))DOI:10.13448/j.cnki.jalre.2013.10.013.
[15]刘永林,延军平,岑敏仪.中国降水非均匀性综合评价[J].地理学报,2015,70(3):392-406.(LIU Y L,YAN J P,CEN M H.Comprehensive evaluation of precipitation heterogeneity in China[J].Acta Geographica Sinica,2015,70(3):392-406.(in Chinese))DOI:10.11821/xb201201009.
[16] GB/T 20481-2006,气象干旱等级[S].(GB/T 20481-2006,Classification of Meteorological Drought[S].(in Chinese))
[17]李天水,王顺,庄文化,等.游程理论和Copula函数在二维干旱变量联合分布中的应用[J].干旱区资源与环境,2016,30(6):77-82.(LI T S,WANG S,ZHUANG W H,et al.Application of the theory of run and Copula function to the joint distribution of two-dimension drought variables[J].Journal of Arid Land Resources&Environment,2016,30(6):77-82.(in Chinese))DOI:10.13448/j.cnki.jalre.2016.185.
[18] SL 424-2008,旱情等级标准[S].(SL 424-2008,Standard of Classification for Drought Severity[S].(in Chinese))
[19]左冬冬,侯威,颜鹏程,等.基于游程理论和两变量联合分布的中国西南地区干旱特征研究[J].物理学报,2014,63(23):53-64.(ZUO D D,HOU W,YAN P C,et al.Research on drought in Southwest China based on the theory on run and 2-D joint distribution theory[J].Acta Physica Sinica,2014:63(23):53-64.(in Chinese))DOI:10.7498/aps.63.230204.
[20]佘敦先,夏军,杜鸿,等.黄河流域极端干旱的时空演变特征及多变量统计模型研究[J].应用基础与工程科学学报,2012(S1):15-29.(SHE D X,XIA J,DU H,et al.Spatio-temporal analysis and multi-variable statistical models of extreme drought events in Yellow River Basin,China[J].Journal of Basic Science&Engineering,2012(S1):15-29.(in Chinese))DOI:10.3969/j.issn.1005-0930.2012.s1.002.
[21]李计,李毅,宋松柏,等.基于Copulas函数的二维干旱变量联合分布[J].水文,2012,32(1):43-49.(LI J,LI Y,SONG S B,et al.Joint distribution of two-dimension drought variables based on copulas function[J].Journal of China Hydrology,2012,32(1):43-49.(in Chinese))DOI:10.3969/j.issn.1000-0852.2012.01.009.
[22] ZHANG L,SINGH V P.Bivariate flood frequency analysis using the copula method[J].Journal of Hydrologic Engineering,2006,11(2):150-164.DOI:10.1061/(ASCE)1084-0699(2006)11:2(150)
[2]王晓峰,胡春艳,卫伟,等.基于SPI的渭北黄土高原干旱时空特征[J].生态环境学报,2016,25(3):415-421.(WANG X F,HU C Y,WEI W,et al.Temporal and spatial characteristics of drought based on standardized precipitation index in Weibei loess plateau[J].Ecology and Environmental Sciences,2016,25(3):415-421.(in Chinese))DOI:10.16258/j.cnki.1674-5906.2016.03.008.
[3]董前进,谢平.水文干旱研究进展[J].水文,2014(4):1-7.(DONG Q J,XIE P.Advances in hydrological drought research[J].Journal of China Hydrology,2014(4):1-7.(in Chinese))DOI:10.3969/j.issn.1000-0852.2014.04.001.
[4]于忱,陈隽,王红瑞,等.多变量Copula函数在干旱风险分析中的应用进展[J].南水北调与水利科技,2018,(1):14-21.(YU C,CHEN J,WANG H R,et al.Application progress of multi-variable Copula function in drought risk analysis[J].South-to-North Water Transfers and Water Science&Technology,2018,(1):14-21.(in Chinese))DOI:10.13476/j.cnki.nsbdqk.20180003.
[5]李明,张永清,张莲芝.基于Copula函数的长春市106年来的干旱特征分析[J].干旱区资源与环境,2017(6):147-153.(LI M,ZHANG Y Q,ZHANG L Z.Analysis on drought characteristics of Changchun city in 106years based on Copula function[J].Journal of Arid Land Resources&Environment,2017(6):147-153.DOI:10.13448/j.cnki.jalre.2017.193.
[6] REDDY M J,SINGH V P.Multivariate modeling of droughts using copulas and meta-heuristic methods[J].Stochastic environmental research and risk assessment,2014,28(3):475-489.DOI:10.1007/s00477-013-0766-2.
[7] SHIAU J T,SHEN H W.Recurrence analysis of hydrologic droughts of differing severity[J].Journal of Water Resources Planning and Management,2001,127(1):30-40.DOI:10.1061/(ASCE)0733-9496(2001)127:1(30).
[8]陆桂华,闫桂霞,吴志勇,等.基于copula函数的区域干旱分析方法[J].水科学进展,2010,21(2):188-193.(LU G H,YAN G X,WU Z Y,et al.Regional drought analysis approach based on copula function[J].Advances in Water Science,2010,21(2):188-193.(in Chinese))DOI:10.14042/j.cnki.32.1309.2010.02.004.
[9]张玉虎,刘凯利,陈秋华,等.区域气象干旱特征多变量Copula分析——以阿克苏河流域为例[J].地理科学,2014,34(12):1480-1487.(ZHANG Y H,LIU K L,CHEN Q H,et al.Bivariate probability distribution of meteorological drought characteristics in the Aksu Basin using Copula[J].Scientia Geographica Sinica,2014,34(12):1480-1487.(in Chinese))DOI:10.13249/j.cnki.sgs.2014.12.009.
[10]李计,李毅,宋松柏,等.基于Copulas函数的多维干旱变量联合分布[J].自然资源学报,2013,28(2):312-320.(LI J,LI Y SONG S B,et al.Multivariate joint distributions of drought variables based on Copulas function[J].Journal of Natural Resources,2013,28(2):312-320.(in Chinese))DOI:10.11849/zrzyxb.2013.02.012.
[11]肖名忠,张强,陈永勤,等.基于三变量Copula函数的东江流域水文干旱频率分析[J].自然灾害学报,2013,22(2):99-108.(XIAO M Z,ZHANG Q,CHEN Y Q,et al.Hydrological drought frequency analysis of East River basin based on trivariate Copulas function[J].Journal of Natural Disasters,2013,22(2):99-108.(in Chinese))DOI:10.13577/j.jnd.2013.0214.
[12]肖名忠,张强,陈晓宏.基于多变量概率分析的珠江流域干旱特征研究[J].地理学报,2012,67(1):83-92.(XIAO M Z,ZHANG Q,CHEN X H.Spatial-temporal patterns of drought risk across the Pearl River Basin[J].Acta Geographica Sinica,2012,67(1):83-92.(in Chinese))DOI:10.11821/xb201201009.
[13]刘文琨,裴源生,赵勇,等.区域气象干旱评估分析模式[J].水科学进展,2014,25(3):318-326.(LIU W K,PEI Y S,ZHAO Y,et al.Research of the regional meteorological drought assessment analysis model[J].Advances in Water Science,2014,25(3):318-326.(in Chinese))DOI:10.14042/j.cnki.32.1309.2014.03.002.
[14]罗艳青,邹滨,邱永红.华东地区干旱灾害时空演化特征研究[J].干旱区资源与环境,2013,27(10):58-64.(LUO Y Q,ZOU B,QIU Y H.Spatial-temporal evolution characteristics of drought disaster in East China[J].Journal of Arid Land Resources&Environment,2013,27(10):58-64.(in Chinese))DOI:10.13448/j.cnki.jalre.2013.10.013.
[15]刘永林,延军平,岑敏仪.中国降水非均匀性综合评价[J].地理学报,2015,70(3):392-406.(LIU Y L,YAN J P,CEN M H.Comprehensive evaluation of precipitation heterogeneity in China[J].Acta Geographica Sinica,2015,70(3):392-406.(in Chinese))DOI:10.11821/xb201201009.
[16] GB/T 20481-2006,气象干旱等级[S].(GB/T 20481-2006,Classification of Meteorological Drought[S].(in Chinese))
[17]李天水,王顺,庄文化,等.游程理论和Copula函数在二维干旱变量联合分布中的应用[J].干旱区资源与环境,2016,30(6):77-82.(LI T S,WANG S,ZHUANG W H,et al.Application of the theory of run and Copula function to the joint distribution of two-dimension drought variables[J].Journal of Arid Land Resources&Environment,2016,30(6):77-82.(in Chinese))DOI:10.13448/j.cnki.jalre.2016.185.
[18] SL 424-2008,旱情等级标准[S].(SL 424-2008,Standard of Classification for Drought Severity[S].(in Chinese))
[19]左冬冬,侯威,颜鹏程,等.基于游程理论和两变量联合分布的中国西南地区干旱特征研究[J].物理学报,2014,63(23):53-64.(ZUO D D,HOU W,YAN P C,et al.Research on drought in Southwest China based on the theory on run and 2-D joint distribution theory[J].Acta Physica Sinica,2014:63(23):53-64.(in Chinese))DOI:10.7498/aps.63.230204.
[20]佘敦先,夏军,杜鸿,等.黄河流域极端干旱的时空演变特征及多变量统计模型研究[J].应用基础与工程科学学报,2012(S1):15-29.(SHE D X,XIA J,DU H,et al.Spatio-temporal analysis and multi-variable statistical models of extreme drought events in Yellow River Basin,China[J].Journal of Basic Science&Engineering,2012(S1):15-29.(in Chinese))DOI:10.3969/j.issn.1005-0930.2012.s1.002.
[21]李计,李毅,宋松柏,等.基于Copulas函数的二维干旱变量联合分布[J].水文,2012,32(1):43-49.(LI J,LI Y,SONG S B,et al.Joint distribution of two-dimension drought variables based on copulas function[J].Journal of China Hydrology,2012,32(1):43-49.(in Chinese))DOI:10.3969/j.issn.1000-0852.2012.01.009.
[22] ZHANG L,SINGH V P.Bivariate flood frequency analysis using the copula method[J].Journal of Hydrologic Engineering,2006,11(2):150-164.DOI:10.1061/(ASCE)1084-0699(2006)11:2(150)
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