三峡库区香溪河流域多变量生态水文风险的不确定性分析
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摘要
本研究基于copula函数开发了一种多变量生态水文风险评估框架,用于分析三峡库区香溪河流域极端生态水文事件的发生频率。通过马尔可夫链蒙特卡罗(MCMC)方法量化边缘分布及copula函数中参数的不确定性,并基于后验概率揭示联合重现期的内在不确定性,同时可进一步得到双变量及多变量风险的概率特征。研究结果显示所得概率模型的预测区间可很好地匹配观测值,尤其对洪水持续时间而言。同时,"AND"联合重现期的不确定性随着单个洪水变量重现期的增加而增加。此外,低设计流量及高服务年限可能导致高洪水风险且伴随大量不确定性。
This study develops a multivariate eco-hydrological risk-assessment framework based on the multivariate copula method in order to evaluate the occurrence of extreme eco-hydrological events for the Xiangxi River within the Three Gorges Reservoir(TGR) area in China. Parameter uncertainties in marginal distributions and dependence structure are quantified by a Markov chain Monte Carlo(MCMC) algorithm.Uncertainties in the joint return periods are evaluated based on the posterior distributions. The probabilistic features of bivariate and multivariate hydrological risk are also characterized. The results show that the obtained predictive intervals bracketed the observations well, especially for flood duration.The uncertainty for the joint return period in ‘‘AND" case increases with an increase in the return period for univariate flood variables. Furthermore, a low design discharge and high service time may lead to high bivariate hydrological risk with great uncertainty.
This study develops a multivariate eco-hydrological risk-assessment framework based on the multivariate copula method in order to evaluate the occurrence of extreme eco-hydrological events for the Xiangxi River within the Three Gorges Reservoir(TGR) area in China. Parameter uncertainties in marginal distributions and dependence structure are quantified by a Markov chain Monte Carlo(MCMC) algorithm.Uncertainties in the joint return periods are evaluated based on the posterior distributions. The probabilistic features of bivariate and multivariate hydrological risk are also characterized. The results show that the obtained predictive intervals bracketed the observations well, especially for flood duration.The uncertainty for the joint return period in ‘‘AND" case increases with an increase in the return period for univariate flood variables. Furthermore, a low design discharge and high service time may lead to high bivariate hydrological risk with great uncertainty.
引文
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[3] Fan Y, Huang G, Huang K, Baetz BW. Planning water resources allocation under multiple uncertainties through a generalized fuzzy two-stage stochastic programming method. IEEE Trans Fuzzy Syst 2015;23(5):1488–504.
[4] Fan Y, Huang W, Li Y, Huang G, Huang K. A coupled ensemble filtering and probabilistic collocation approach for uncertainty quantification of hydrological models. J Hydrol 2015;530:255–72.
[5] Li Y, Nie S, Huang Z, McBean EA, Fan Y, Huang G. An integrated risk analysis method for planning water resource systems to support sustainable development of an arid region. J Environ Inform 2017;29(1):1–15.
[6] Chebana F, Dabo-Niang S, Ouarda TBMJ. Exploratory functional flood frequency analysis and outlier detection. Water Resour Res 2012;48(4):W04514.
[7] Guo Y, Baetz BW. Probabilistic description of runoff and leachate volumes from open windrow composting sites. J Environ Inform 2017;30(2):137–48.
[8] Chen B, Li P, Wu H, Husain T, Khan F. MCFP:a Monte Carlo simulation-based fuzzy programming approach for optimization under dual uncertainties of possibility and continuous probability. J Environ Inform 2017;29(2):88–97.
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[14] Kao SC, Govindaraju RS. A copula-based joint deficit index for droughts. J Hydrol 2010;380(1–2):121–34.
[15] Ma M, Song S, Ren L, Jiang S, Song J. Multivariate drought characteristics using trivariate Gaussian and Student t copulas. Hydrol Processes 2013;27(8):1175–90.
[16] Zhang L, Singh VP. Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 2007;332(1–2):93–109.
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[19] Kong X, Huang G, Fan Y, Li Y. Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi River, China.Stochastic Environ Res Risk Assess 2015;29(3):833–46.
[20] Fan Y, Huang G, Baetz BW, Li Y, Huang K. Development of a copula-based particle filter(CopPF)approach for hydrologic data assimilation under consideration of parameter interdependence. Water Resour Res 2017;53(6):4850–75.
[21] Fan Y, Huang G, Baetz BW, Li Y, Huang K, Chen X, et al. Development of integrated approaches for hydrological data assimilation through combination of ensemble Kalman filter and particle filter methods. J Hydrol 2017;550:412–26.
[22] Chen F, Huang G, Fan Y, Chen J. A copula-based fuzzy chance-constrained programming model and its application to electric power generation systems planning. Appl Energy 2017;187:291–309.
[23] Huang C, Nie S, Guo L, Fan Y. Inexact fuzzy stochastic chance constraint programming for emergency evacuation in Qinshan Nuclear Power Plant under uncertainty. J Environ Inform 2017;30(1):63–78.
[24] Huang K, Dai L, Yao M, Fan Y, Kong X. Modelling dependence between traffic noise and traffic flow through an entropy-copula method. J Environ Inform2017;29(2):134–51.
[25] Yu L, Li Y, Huang G, Fan Y, Nie S. A copula-based flexible-stochastic programming method for planning regional energy system under multiple uncertainties:a case study of the urban agglomeration of Beijing and Tianjin.Appl Energy 2018;210:60–74.
[26] Guo A, Chang J, Wang Y, Huang Q, Zhou S. Flood risk analysis for flood control and sediment transportation in sandy regions:a case study in the Loess Plateau, China. J Hydrol 2018;560:39–55.
[27] Guo A, Chang J, Wang Y, Huang Q, Guo Z, Zhou S. Bivariate frequency analysis of flood and extreme precipitation under changing environment:case study in catchments of the Loess Plateau, China. Stochastic Environ Res Risk Assess2018;32(7):2057–74.
[28] Merz B, Thieken AH. Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 2005;309(1–4):114–32.
[29] Liang Z, Chang W, Li B. Bayesian flood frequency analysis in the light of model and parameter uncertainties. Stochastic Environ Res Risk Assess 2012;26(5):721–30.
[30] Nelsen RB. An introduction to copulas. 2nd ed. New York:Springer; 2006.
[31] Ganguli P, Reddy MJ. Probabilistic assessment of flood risks using trivariate copulas. Theor Appl Climatol 2013;111(1–2):341–60.
[32] Salvadori G, De Michele C, Kottegoda NT, Rosso R. Extremes in nature:an approach using copula. Dordrencht:Springer; 2007. p. 292.
[33] Salvadori G, De Michele C, Durante F. On the return period and design in a multivariate framework. Hydrol Earth Syst Sci 2011;15(11):3293–305.
[34] Han JC, Huang GH, Zhang H, Li Z, Li YP. Bayesian uncertainty analysis in hydrological modeling associated with watershed subdivision level:a case study of SLURP model applied to the Xiangxi River watershed, China.Stochastic Environ Res Risk Assess 2014;28(4):973–89.
[35] Xu H, Taylor RG, Kingston DG, Jiang T, Thompson JR, Todd MC. Hydrological modeling of River Xiangxi using SWAT2005:a comparison of model parameterizations using station and gridded meteorological observations.Quat Int 2010;226(1–2):54–9.
[36] Yue S. The bivariate lognormal distribution to model a multivariate flood episode. Hydrol Processes 2000;14(14):2575–88.
[37] Yue S. A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Processes 2001;15(6):1033–45.
[38] Adamowski K. A Monte Carlo comparison of parametric and nonparametric estimation of flood frequencies. J Hydrol 1989;108:295–308.
[39] Kite GW. Frequency and risk analysis in Hydrology. Littleton:Water Resources Publications; 1988.
[40] De Michele C, Salvadori G. A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. J Geophys Res 2003;108(D2):4067.
[2] Karmakar S, Simonovic SP. Bivariate flood frequency analysis. Part 2:a copulabased approach with mixed marginal distributions. J Flood Risk Manag 2009;2(1):32–44.
[3] Fan Y, Huang G, Huang K, Baetz BW. Planning water resources allocation under multiple uncertainties through a generalized fuzzy two-stage stochastic programming method. IEEE Trans Fuzzy Syst 2015;23(5):1488–504.
[4] Fan Y, Huang W, Li Y, Huang G, Huang K. A coupled ensemble filtering and probabilistic collocation approach for uncertainty quantification of hydrological models. J Hydrol 2015;530:255–72.
[5] Li Y, Nie S, Huang Z, McBean EA, Fan Y, Huang G. An integrated risk analysis method for planning water resource systems to support sustainable development of an arid region. J Environ Inform 2017;29(1):1–15.
[6] Chebana F, Dabo-Niang S, Ouarda TBMJ. Exploratory functional flood frequency analysis and outlier detection. Water Resour Res 2012;48(4):W04514.
[7] Guo Y, Baetz BW. Probabilistic description of runoff and leachate volumes from open windrow composting sites. J Environ Inform 2017;30(2):137–48.
[8] Chen B, Li P, Wu H, Husain T, Khan F. MCFP:a Monte Carlo simulation-based fuzzy programming approach for optimization under dual uncertainties of possibility and continuous probability. J Environ Inform 2017;29(2):88–97.
[9] Reddy JM, Ganguli P. Bivariate flood frequency analysis of upper Godavari River flows using Archimedean copulas. Water Resour Manage 2012;26(14):3995–4018.
[10] Fan Y, Huang W, Huang G, Huang K, Li Y, Kong X. Bivariate hydrologic risk analysis based on a coupled entropy-copula method for the Xiangxi River in the Three Gorges Reservoir area, China. Theor Appl Climatol 2016;125(1–2):381–97.
[11] Fan Y, Huang W, Huang G, Li Y, Huang K, Li Z. Hydrologic risk analysis in the Yangtze River Basin through coupling Gaussian mixtures into copulas. Adv Water Resour 2016;88:170–85.
[12] Zhang L, Singh VP. Bivariate flood frequency analysis using the copula method.J Hydrol Eng 2006;11(2):150–64.
[13] Sraj M, Bezak N, Brilly M. Bivariate flood frequency analysis using the copula function:a case study of the Litija Station on the Sava River. Hydrol Processes2015;29(2):225–38.
[14] Kao SC, Govindaraju RS. A copula-based joint deficit index for droughts. J Hydrol 2010;380(1–2):121–34.
[15] Ma M, Song S, Ren L, Jiang S, Song J. Multivariate drought characteristics using trivariate Gaussian and Student t copulas. Hydrol Processes 2013;27(8):1175–90.
[16] Zhang L, Singh VP. Bivariate rainfall frequency distributions using Archimedean copulas. J Hydrol 2007;332(1–2):93–109.
[17] Vandenberghe S, Verhoest NEC, De Baets B. Fitting bivariate copulas to the dependence structure between storm characteristics:a detailed analysis based on 105 year 10 min rainfall. Water Resour Res 2010;46(1):W01512.
[18] Lee T, Salas JD. Copula-based stochastic simulation of hydrological data applied to Nile River flows. Hydrol Res 2011;42(4):318–30.
[19] Kong X, Huang G, Fan Y, Li Y. Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi River, China.Stochastic Environ Res Risk Assess 2015;29(3):833–46.
[20] Fan Y, Huang G, Baetz BW, Li Y, Huang K. Development of a copula-based particle filter(CopPF)approach for hydrologic data assimilation under consideration of parameter interdependence. Water Resour Res 2017;53(6):4850–75.
[21] Fan Y, Huang G, Baetz BW, Li Y, Huang K, Chen X, et al. Development of integrated approaches for hydrological data assimilation through combination of ensemble Kalman filter and particle filter methods. J Hydrol 2017;550:412–26.
[22] Chen F, Huang G, Fan Y, Chen J. A copula-based fuzzy chance-constrained programming model and its application to electric power generation systems planning. Appl Energy 2017;187:291–309.
[23] Huang C, Nie S, Guo L, Fan Y. Inexact fuzzy stochastic chance constraint programming for emergency evacuation in Qinshan Nuclear Power Plant under uncertainty. J Environ Inform 2017;30(1):63–78.
[24] Huang K, Dai L, Yao M, Fan Y, Kong X. Modelling dependence between traffic noise and traffic flow through an entropy-copula method. J Environ Inform2017;29(2):134–51.
[25] Yu L, Li Y, Huang G, Fan Y, Nie S. A copula-based flexible-stochastic programming method for planning regional energy system under multiple uncertainties:a case study of the urban agglomeration of Beijing and Tianjin.Appl Energy 2018;210:60–74.
[26] Guo A, Chang J, Wang Y, Huang Q, Zhou S. Flood risk analysis for flood control and sediment transportation in sandy regions:a case study in the Loess Plateau, China. J Hydrol 2018;560:39–55.
[27] Guo A, Chang J, Wang Y, Huang Q, Guo Z, Zhou S. Bivariate frequency analysis of flood and extreme precipitation under changing environment:case study in catchments of the Loess Plateau, China. Stochastic Environ Res Risk Assess2018;32(7):2057–74.
[28] Merz B, Thieken AH. Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 2005;309(1–4):114–32.
[29] Liang Z, Chang W, Li B. Bayesian flood frequency analysis in the light of model and parameter uncertainties. Stochastic Environ Res Risk Assess 2012;26(5):721–30.
[30] Nelsen RB. An introduction to copulas. 2nd ed. New York:Springer; 2006.
[31] Ganguli P, Reddy MJ. Probabilistic assessment of flood risks using trivariate copulas. Theor Appl Climatol 2013;111(1–2):341–60.
[32] Salvadori G, De Michele C, Kottegoda NT, Rosso R. Extremes in nature:an approach using copula. Dordrencht:Springer; 2007. p. 292.
[33] Salvadori G, De Michele C, Durante F. On the return period and design in a multivariate framework. Hydrol Earth Syst Sci 2011;15(11):3293–305.
[34] Han JC, Huang GH, Zhang H, Li Z, Li YP. Bayesian uncertainty analysis in hydrological modeling associated with watershed subdivision level:a case study of SLURP model applied to the Xiangxi River watershed, China.Stochastic Environ Res Risk Assess 2014;28(4):973–89.
[35] Xu H, Taylor RG, Kingston DG, Jiang T, Thompson JR, Todd MC. Hydrological modeling of River Xiangxi using SWAT2005:a comparison of model parameterizations using station and gridded meteorological observations.Quat Int 2010;226(1–2):54–9.
[36] Yue S. The bivariate lognormal distribution to model a multivariate flood episode. Hydrol Processes 2000;14(14):2575–88.
[37] Yue S. A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Processes 2001;15(6):1033–45.
[38] Adamowski K. A Monte Carlo comparison of parametric and nonparametric estimation of flood frequencies. J Hydrol 1989;108:295–308.
[39] Kite GW. Frequency and risk analysis in Hydrology. Littleton:Water Resources Publications; 1988.
[40] De Michele C, Salvadori G. A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas. J Geophys Res 2003;108(D2):4067.