基于Copula函数的泾河流域水沙丰枯遭遇频率分析
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摘要
流域水沙关系变化是洪旱灾害防治、重大水利工程布局的重要理论基础,同时又对人们的生产、生活产生重大影响。根据泾河流域主要控制水文站的年径流量和年输沙量数据,采用P-Ⅲ型曲线分别拟合计算得到各水文站的径流量和输沙量序列的边缘分布函数,然后采用Copula函数建立了泾河流域水沙联合分布模型,计算泾河流域各水文站水沙丰枯遭遇频率。结果表明:(1)Clayton Copula,Frank Copula,Gumbel copula函数均能较好地拟合泾河流域各水文站的水沙数据,根据拟合优度评价结果选用Frank Copula函数拟合各站的水沙联合分布;(2)在所研究的泾河流域8个控制水文站水沙丰枯遭遇均表现为水沙丰枯同步频率大于异步频率。在水沙丰枯同步频率中,同丰的遭遇频率基本与同枯的遭遇频率相同,二者均大于同平的遭遇频率。(3)在水沙丰枯异步遭遇频率中,丰枯遭遇频率最小的组合是水枯沙丰和水丰沙枯。该水沙联合分布模型对流域治理规划、防灾减灾及生态恢复等具有重要意义。
Based on the annual runoff and sediment discharge data of the main control hydrological stations in the Jinghe River Basin,P-Ⅲ distribution curve was applied to fit the marginal distribution of annual runoff and sediment discharge.Then the Copula function was used to establish the joint distribution model of runoff and sediment discharge,to calculate the occurent probability of rich-scarce runoff and sediment discharge in Jinghe River Basin.The results showed that:(1)all of Clayton Copula,Frank Copula and Gumbel copula functions could well simulate the joint distribution of runoff and sediment discharge;according to the ordinary least square(OLS)and AIC(Akaike information criterion)information criterion,the Frank Copula function was used to simulate the joint distribution of runoff and sediment discharge in each hydrological station;(2)according to the occurrent probability of rich-scarce runoff and sediment discharge of 8 hydrological stations,the frequency synchronization of rich-scarce runoff and sediment was larger than the asynchronous frequency;the frequency of rich water-rich sediment approximately equaled the frequency of scarce waterscarce sediment,and the frequency of normal water-normal sediment was the lowest;(3)the frequency of the encounter of opposite status of runoff and sediment(the frequency of rich water-scarce sediment and the frequency of scarce water-rich sediment)was the lowest among the asynchronous frequencies of rich-scarce runoff and sediment occurrences.The research results can provide the theoretical basis for the planning of watershed management,ecological restoration and disaster prevention and reduction.
Based on the annual runoff and sediment discharge data of the main control hydrological stations in the Jinghe River Basin,P-Ⅲ distribution curve was applied to fit the marginal distribution of annual runoff and sediment discharge.Then the Copula function was used to establish the joint distribution model of runoff and sediment discharge,to calculate the occurent probability of rich-scarce runoff and sediment discharge in Jinghe River Basin.The results showed that:(1)all of Clayton Copula,Frank Copula and Gumbel copula functions could well simulate the joint distribution of runoff and sediment discharge;according to the ordinary least square(OLS)and AIC(Akaike information criterion)information criterion,the Frank Copula function was used to simulate the joint distribution of runoff and sediment discharge in each hydrological station;(2)according to the occurrent probability of rich-scarce runoff and sediment discharge of 8 hydrological stations,the frequency synchronization of rich-scarce runoff and sediment was larger than the asynchronous frequency;the frequency of rich water-rich sediment approximately equaled the frequency of scarce waterscarce sediment,and the frequency of normal water-normal sediment was the lowest;(3)the frequency of the encounter of opposite status of runoff and sediment(the frequency of rich water-scarce sediment and the frequency of scarce water-rich sediment)was the lowest among the asynchronous frequencies of rich-scarce runoff and sediment occurrences.The research results can provide the theoretical basis for the planning of watershed management,ecological restoration and disaster prevention and reduction.
引文
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[2]Walling D E.Human impact on land-ocean sediment transfer by the world′s rivers[J].Geomorphology,2006,79(3):192-216.
[3]刘成,王兆印,隋觉义.我国主要入海河流水沙变化分析[J].水利学报,2007,38(12):1444-1452.
[4]朱红艳,韩彩波,贾志峰,等.泾河张家山水文站水沙特性分析及工程实例[J].农业工程学报,2012,28(19):48-55.
[5]颜明,郑明国,舒畅,等.泾河流域径流-泥沙的尺度效应研究[J].水土保持通报,2016,36(6):184-188.
[6]崔小红,周祖昊,邱林.泾河流域水沙特性空间尺度变化分析[J].华北水利水电大学学报:自然科学版,2013,34(3):51-54.
[7]郭爱军,黄强,畅建霞,等.基于Copula函数的泾河流域水沙关系演变特征分析[J].自然资源学报,2015,30(4):673-683.
[8]张金萍,丁志宏,郭兵托.泾河水沙丰枯演化规律及组合遭遇风险研究[J].水力发电学报,2015,34(1):11-16.
[9]冉大川,刘斌,罗全华,等.泾河流域人为活动对水沙变化的影响分析:兼议泾河流域治理方略[J].水土保持学报,2001,15(6):32-35.
[10]赵姹,李志,刘文兆,等.泾河流域潜在蒸散量的时空变异[J].生态学报,2014,34(19):5600-5608.
[11] Sklar M.Fonctions de repartition an dimensions et leurs marges[J].Publ.Inst.Statist.Univ.Paris,1959,8:229-231.
[12]丁志宏,张金良,冯平.黄河中游汛期水沙联合分布模型及其应用[J].吉林大学学报(地),2011,41(4):1130-1135.
[13]邱小霞,刘次华,吴娟.Copula函数中参数极大似然估计的性质[J].经济数学,2008,25(2):210-215.
[14] Joe H.Multivariate models and multivariate dependence concepts[M].Chapman and Hall/Crc,1997.