泾河流域水沙联合分布特征分析及其不确定性评估
|
摘要
径流与泥沙是非独立的二维随机变量,若要对流域实现水沙并举的科学管理方案,开展水沙联合概率分析显得尤为必要。而在联合概率分析中,水沙样本系列容量一般较小,使得联合设计值估计具有不确定性。以泾河流域为例,本文提出基于蒙特卡洛法的两变量联合设计值不确定性量化方法。该方法基于Copula函数建立水沙联合分布模型,推求两变量联合设计值的最可能组合模式,利用蒙特卡洛抽样法分析样本不确定性对水沙联合设计值的影响,计算两变量设计值置信区间。结果表明,OR重现期为20年的情况下,联合设计值95%二元置信区间表现出较大的不确定性,对流域工程设计值的确定提出了巨大挑战,且随着重现期水平的增加,联合设计值的不确定性随之增加。
The flow and sediment are non-independent two-dimensional random variables,so it is very necessary to carry out joint probability analysis of flow and sediment in order to realize the scientific management scheme of flow and sediment. In the joint probability analysis,the limited flow and sediment sample size would induce quantile estimation uncertainty in bivariate probability analysis. Based on Monte Carlo method,this paper presents the quantitative uncertainty evaluation method of bivariate quantile estimation in the Jinghe River basin. The flow and sediment joint distribution model is established based on Copulas function and the most likely realizations of bivariate quantile estimation are derived. The Monte Carlo sampling method is used to analyze the influence of sample uncertainty of bivariate quantile estimation,and the confidence region of bivariate quantile estimation is calculated. The results demonstrate that when the OR return period is 20 years,the 95% confidence region of bivariate quantile estimation shows greater uncertainty. It is a great challenge to determine the quantile estimation of river basin engineering design. The uncertainty of bivariate quantile estimation increases with the increase of the joint return period level.
The flow and sediment are non-independent two-dimensional random variables,so it is very necessary to carry out joint probability analysis of flow and sediment in order to realize the scientific management scheme of flow and sediment. In the joint probability analysis,the limited flow and sediment sample size would induce quantile estimation uncertainty in bivariate probability analysis. Based on Monte Carlo method,this paper presents the quantitative uncertainty evaluation method of bivariate quantile estimation in the Jinghe River basin. The flow and sediment joint distribution model is established based on Copulas function and the most likely realizations of bivariate quantile estimation are derived. The Monte Carlo sampling method is used to analyze the influence of sample uncertainty of bivariate quantile estimation,and the confidence region of bivariate quantile estimation is calculated. The results demonstrate that when the OR return period is 20 years,the 95% confidence region of bivariate quantile estimation shows greater uncertainty. It is a great challenge to determine the quantile estimation of river basin engineering design. The uncertainty of bivariate quantile estimation increases with the increase of the joint return period level.
引文
[1]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(地球科学版),2011,41(4):1130-1135.
[2]李天元.基于Copula函数的设计洪水计算方法研究[D].武汉:武汉大学,2014.
[3]周念清,赵露,沈新平.基于Copula函数的洞庭湖流域水沙丰枯遭遇频率分析[J].地理科学,2014,34(2):242-248.
[4]冯平,毛慧慧,王勇.多变量情况下的水文频率分析方法及其应用[J].水利学报,2009,40(1):33-37.
[5]陈子燊,高时友,李鸿皓.基于二次重现期的城市两级排涝标准衔接的设计暴雨[J].水科学进展,2017,28(3):382-389.
[6]李天元,郭生练,刘章君,等.基于峰量联合分布推求设计洪水[J].水利学报,2014,45(3):269-276.
[7]梁忠民,戴荣,李彬权.基于贝叶斯理论的水文不确定性分析研究进展[J].水科学进展,2010,21(2):274-281.
[8] XU Y P,BOOIJ M J,TONG Y B. Uncertainty analysis in statistical modeling of extreme hydrological events[J].Stochastic Environmental Research&Risk Assessment,2010,24(5):567-578.
[9]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(3):302-314.
[10]冉大川,刘斌,罗全华,等.泾河流域水沙变化水文分析[J].人民黄河,2001,23(2):9-11.
[11]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.
[12]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.
[13]刘冰冰. Copula函数在金沙江干流随机水文分析中的应用[D].重庆:重庆交通大学,2016.
[14]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.
[15]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].华北水利水电学院学报,2013,34(3):51-54.
[16]尹军,杨志勇,袁喆,等. 1961-2011年黄淮海地区极端降水时空变化特征[J].灾害学,2015(3):71-75.
[17]诸裕良,周允谦,许陈澄.珠江三角洲洪水位重现期变化研究[J].科学技术与工程,2013,13(33):9894-9901.
[18]陈心池,张利平,闪丽洁,等.基于Copula函数的汉江中上游流域极端降雨洪水联合分布特征[J].长江流域资源与环境,2015,24(8):1425-1433.
[19]李运平,宋松柏,李丹丹.含零值水文序列频率计算方法研究[J].水力发电学报,2018,37(2):22-31.
[20]陈元芳,沙志贵,顾圣华,等.可考虑历史洪水的对数正态分布线性矩法[C]//中国水利学会2003学术年会论文集,2003.
[21] NELSON R B. An Introduction to Copulas[M]. Springer,New York,1999.
[22] SALVADORI G,DE MICHELE C,DURANTE F. On the return period and design in a multivariate framework[J]. Hydrol. Earth Syst. Sci.,2011,15:3293-3305.
[23]龚光鲁,钱敏平.应用随机过程教程及其在算法和智能计算中的应用[M].北京:清华大学出版社,2004.
[24]闫宝伟,刘彦成,段美壮,等.基于两变量核密度估计的枯水频率分析[J].人民珠江,2017,38(4):15-19.
[25]王文圣,丁晶.基于核估计的多变量非参数随机模型初步研究[J].水利学报,2003(2):9-14.
[26]辛军霞,吴兴征,高伟,等.基于Copula函数的CFG桩复合地基载荷—变形曲线的概率分析[J].岩土力学,2016(S1):424-434.
[27]龚伟.基于信息熵和互信息的流域水文模型不确定性分析[D].北京:清华大学,2012.
[28]王星.非参数统计[M].北京:清华大学出版社,2009.
[29]李隆章.实用非参数统计方法[M].北京:中国财政经济出版社,1989.
[30]赵冬泉,王浩正,陈吉宁,等.城市暴雨径流模拟的参数不确定性研究[J].水科学进展,2009,20(1):45-51.
[31] PIL J,SALVDOR R. BEVEN K1 Model Calibratin and Uncertainty Prediction of Fire Spread[M]. Coimbra:Lu?so,2002.
[32]史黎翔.多变量水文事件重现期计算研究[D].杨凌:西北农林科技大学,2016.
[33]金鑫,郝振纯,张金良.黄河中游水沙频率关系研究[J].泥沙研究,2006(3):6-13.
[34]胡义明,梁忠民,王军,等.考虑抽样不确定性的水文设计值估计[J].水科学进展,2013,24(5):667-674.
[2]李天元.基于Copula函数的设计洪水计算方法研究[D].武汉:武汉大学,2014.
[3]周念清,赵露,沈新平.基于Copula函数的洞庭湖流域水沙丰枯遭遇频率分析[J].地理科学,2014,34(2):242-248.
[4]冯平,毛慧慧,王勇.多变量情况下的水文频率分析方法及其应用[J].水利学报,2009,40(1):33-37.
[5]陈子燊,高时友,李鸿皓.基于二次重现期的城市两级排涝标准衔接的设计暴雨[J].水科学进展,2017,28(3):382-389.
[6]李天元,郭生练,刘章君,等.基于峰量联合分布推求设计洪水[J].水利学报,2014,45(3):269-276.
[7]梁忠民,戴荣,李彬权.基于贝叶斯理论的水文不确定性分析研究进展[J].水科学进展,2010,21(2):274-281.
[8] XU Y P,BOOIJ M J,TONG Y B. Uncertainty analysis in statistical modeling of extreme hydrological events[J].Stochastic Environmental Research&Risk Assessment,2010,24(5):567-578.
[9]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(3):302-314.
[10]冉大川,刘斌,罗全华,等.泾河流域水沙变化水文分析[J].人民黄河,2001,23(2):9-11.
[11]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.
[12]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.
[13]刘冰冰. Copula函数在金沙江干流随机水文分析中的应用[D].重庆:重庆交通大学,2016.
[14]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.
[15]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].华北水利水电学院学报,2013,34(3):51-54.
[16]尹军,杨志勇,袁喆,等. 1961-2011年黄淮海地区极端降水时空变化特征[J].灾害学,2015(3):71-75.
[17]诸裕良,周允谦,许陈澄.珠江三角洲洪水位重现期变化研究[J].科学技术与工程,2013,13(33):9894-9901.
[18]陈心池,张利平,闪丽洁,等.基于Copula函数的汉江中上游流域极端降雨洪水联合分布特征[J].长江流域资源与环境,2015,24(8):1425-1433.
[19]李运平,宋松柏,李丹丹.含零值水文序列频率计算方法研究[J].水力发电学报,2018,37(2):22-31.
[20]陈元芳,沙志贵,顾圣华,等.可考虑历史洪水的对数正态分布线性矩法[C]//中国水利学会2003学术年会论文集,2003.
[21] NELSON R B. An Introduction to Copulas[M]. Springer,New York,1999.
[22] SALVADORI G,DE MICHELE C,DURANTE F. On the return period and design in a multivariate framework[J]. Hydrol. Earth Syst. Sci.,2011,15:3293-3305.
[23]龚光鲁,钱敏平.应用随机过程教程及其在算法和智能计算中的应用[M].北京:清华大学出版社,2004.
[24]闫宝伟,刘彦成,段美壮,等.基于两变量核密度估计的枯水频率分析[J].人民珠江,2017,38(4):15-19.
[25]王文圣,丁晶.基于核估计的多变量非参数随机模型初步研究[J].水利学报,2003(2):9-14.
[26]辛军霞,吴兴征,高伟,等.基于Copula函数的CFG桩复合地基载荷—变形曲线的概率分析[J].岩土力学,2016(S1):424-434.
[27]龚伟.基于信息熵和互信息的流域水文模型不确定性分析[D].北京:清华大学,2012.
[28]王星.非参数统计[M].北京:清华大学出版社,2009.
[29]李隆章.实用非参数统计方法[M].北京:中国财政经济出版社,1989.
[30]赵冬泉,王浩正,陈吉宁,等.城市暴雨径流模拟的参数不确定性研究[J].水科学进展,2009,20(1):45-51.
[31] PIL J,SALVDOR R. BEVEN K1 Model Calibratin and Uncertainty Prediction of Fire Spread[M]. Coimbra:Lu?so,2002.
[32]史黎翔.多变量水文事件重现期计算研究[D].杨凌:西北农林科技大学,2016.
[33]金鑫,郝振纯,张金良.黄河中游水沙频率关系研究[J].泥沙研究,2006(3):6-13.
[34]胡义明,梁忠民,王军,等.考虑抽样不确定性的水文设计值估计[J].水科学进展,2013,24(5):667-674.