二维复合极值分布理论在水利及防灾工程中的应用
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摘要
河口城市防洪设计水位是关系到人民生命、财产安全的重大研究课题。由于河口城市所处的特殊地理位置，其往往受到河流、海洋、气象等多种环境荷载的综合影响，因此如何合理确定极端环境荷载综合作用下的设计水位一直是工程人员普遍关心的问题。
针对中国最大的河口城市——上海，本文分析了三种极端环境荷载——天文潮、风暴增水和长江径流增水对上海市防洪设计水位的综合作用，应用二维复合极值分布的具体形式之一：泊松—混合冈贝尔二维复合极值分布(PGMCED)模型，预测了天文大潮发生时风暴增水和长江上游洪峰下泄增水的联合概率。同时也应用基于重点抽样法的随机模拟技术来预测了天文潮、风暴增水和长江径流增水三者的联合概率，并得出了合理的结果。以上两种方法得到的结果对比用传统方法(如年极值法)得到的防洪设计标准，显示出本文给出了更加合理的计算防洪设计标准的方法。
在本文中还将首次在洪水频率分析中应用PGMCED模型，即在考虑洪水发生频次符合泊松分布的条件下，对洪水的重要要素(洪峰流量、洪水总量)进行联合概率分析，并根据大通站洪水资料给出推算洪水设计值的实例，拓展了PGMECD模型在洪水频率分析方面的新应用，计算结果显示本模型具有更加合理可靠的优点。
It is one of the important problems to design the flood-prevention water level of the estuarine cities. Because of the special geographic location of the estuarine cities, they are affected by river ocean and meteorology environmental loads and so on. So how to determine the flood-prevention water level in the area is a question to need to study into it.
This paper proposes a method to estimate the hydrological disaster prevention design criteria for the estuarine city Shanghai, the biggest estuarine city in China. Considering the combined effect of typhoon storm surge, flood peak from upper river Yangtze and astronomical spring tide, one type of the Bivariate Compound Extreme Distribution: the Poisson-Gumbel Mixed Compound Extreme Distribution is adopted to predict the joint probability of storm surge and flood in the condition of spring tide. The stochastic simulation technique based on the Importance Sampling Procedure is also used to predict joint probability of storm surge, flood and spring tide. In comparison with the traditional method botn of them give more reasonable design criteria for coastal defence of Shanghai.
This paper also proposes the Poisson-Gumbel Mixed Compound Extreme
Distribution model to analyze flood frequency--the joint probability
of flood peaks and statistically corresponding volumes. The model is
tested and validated using observed flood data from the hydrological station Datong of river Yangtze.
针对中国最大的河口城市——上海，本文分析了三种极端环境荷载——天文潮、风暴增水和长江径流增水对上海市防洪设计水位的综合作用，应用二维复合极值分布的具体形式之一：泊松—混合冈贝尔二维复合极值分布(PGMCED)模型，预测了天文大潮发生时风暴增水和长江上游洪峰下泄增水的联合概率。同时也应用基于重点抽样法的随机模拟技术来预测了天文潮、风暴增水和长江径流增水三者的联合概率，并得出了合理的结果。以上两种方法得到的结果对比用传统方法(如年极值法)得到的防洪设计标准，显示出本文给出了更加合理的计算防洪设计标准的方法。
在本文中还将首次在洪水频率分析中应用PGMCED模型，即在考虑洪水发生频次符合泊松分布的条件下，对洪水的重要要素(洪峰流量、洪水总量)进行联合概率分析，并根据大通站洪水资料给出推算洪水设计值的实例，拓展了PGMECD模型在洪水频率分析方面的新应用，计算结果显示本模型具有更加合理可靠的优点。
It is one of the important problems to design the flood-prevention water level of the estuarine cities. Because of the special geographic location of the estuarine cities, they are affected by river ocean and meteorology environmental loads and so on. So how to determine the flood-prevention water level in the area is a question to need to study into it.
This paper proposes a method to estimate the hydrological disaster prevention design criteria for the estuarine city Shanghai, the biggest estuarine city in China. Considering the combined effect of typhoon storm surge, flood peak from upper river Yangtze and astronomical spring tide, one type of the Bivariate Compound Extreme Distribution: the Poisson-Gumbel Mixed Compound Extreme Distribution is adopted to predict the joint probability of storm surge and flood in the condition of spring tide. The stochastic simulation technique based on the Importance Sampling Procedure is also used to predict joint probability of storm surge, flood and spring tide. In comparison with the traditional method botn of them give more reasonable design criteria for coastal defence of Shanghai.
This paper also proposes the Poisson-Gumbel Mixed Compound Extreme
Distribution model to analyze flood frequency--the joint probability
of flood peaks and statistically corresponding volumes. The model is
tested and validated using observed flood data from the hydrological station Datong of river Yangtze.
引文
[1] Liu Defu, Wen Shuqin and Wang Liping, "Poisson-Gumbel Mixed Compound Distribution and Its Application," Chinese Science Bulletin, 2002, Vol. 47, No. 22, pp. 1901-1906.
[2] Madsen, H.O., "Methods of Structural Safety", Prentice-hall, Inc., 1986, 18-26
[3] Bourgund, U. and 8ucher, C.G., "Importance Sampling Procedure Using Design Point", Research Report of Univ. of Innsbruck, Nov. 1986
[4] G. I. Schueller, and R. Atix, "a Critical appraisal of methods to determine failure probabilities", Univ. of Innsbruck, Institute of Mechanics, 1986,35-74
[5] 刘德辅，杨永春，王超．海洋设计标准的不确定性及联合分布概率分析[J]．海洋学报，1996，18(5)：110-116．
[6] Liu P-L, Der Kiureghian A. Multivariate distribution models with prescribed marginals and covariances [J]. Probabilitic Engineering Mechanics, 1986, 1(2):105～112.
[7] 刘德辅，王铮，施建刚，海洋环境条件联合设计标准[J]．海洋学报，1994，16(2)：116—123。
[8] Stuart G Coles and Jonathan A Tawn. "Modelling Extremes of the Areal Rainfall Process" [R],Yechnical Report 92-12. Nottingham University, Nottingham, 1992.
[9] Stuart G Coles and Jonathan A Tawn. "Statistics of Coastal Flood Prevention" [J].Phi1. Trans. R, Soc. A, 1990,332:457～476.
[10] Stuart G Coles and Jonathan A Yawn. Modelling extreme multivariate events[J]. J.R. Statist. Soc. B, 1991, 53(2): 377～392.
[11] Jonathan A Tawn. Modelling multivariate extreme value distributions[J]. Biometrika, 1990, 77(2) :245～253.
[12] R.L Smith, J.A Tawn, Yuen H R. "Statistics of multivariate extremes" [J].
Int. Statist. Inst. Rev., 1990,58(1): 47-58.
[13] S Nadarajah, C W Anderson and Jonathan A Tawn. "Ordered multivariate extremes" [J]. J. R. Statist. Soc. B, 1998, 60(2):473～496.
[14] Stuart GColes and Jonathan A Tawn. "Modelling Extremes of the Areal Rainfall Process" [J]. J. R. Statist. B, 1996, 58(2):329～347.
[15] S. Zachary, G. Feld, G. Ward, J. Wofram. (1998). "Multivariate Extrapolation in The Offshore Environment", Applied Ocean Research 20, 273-295
[16] Gumbel E J. Distributions de valeurs extremes en plusieurs dimensions[J]. Publ. Inst. Statist. Paris, 1960, 9:171～173.
[17] I.D. Morton, J. Bowers.(1997). "Extreme Value Analysis in A Multivariate Offshore Environment", Applied Ocean Research 18 303-317
[18] Stuart G Coles and Jonathan A Tawn. Statistical methods for multivariate extremes: an application to structural design[J]. Appl. Statist., 1994, 43 (1): 1～48.
[19] Liu T.F. and Ma, F.S.,(1980). "Prediction of Extreme Wave Heights and Wind Velocities", Journal of the Waterway Port Coastal and Ocean Division, ASCE, 106, No. WW4, 469-479
[20] T.F. Liu (1982) "Long Term Distributions of Hurrican Characteristics" Pro. Offshore Technology Conference OTC 4325, pp. 305-313
[21] Liu Defu, Li huajun, Wen Shuqin, Song Yah, Wang Shuqing (2001). "Prediction of Extreme Significant Wave Height from Daily Maxima" China Ocean Engineering Vol. 15, No.1, pp97-106
[22] Langley R.M., A.H. El-Shaarawi (1986). "On The Calculation of Extreme Wave Heights: A Review", Ocean Englneering Vo1.13. No.1, pp. 93-118
[23] W.H. Kirby, M.E. Moss (1987). "Summary of Flood-Frequency Analysis in The United States", Journal of Hydrology, 96 pp. 5-14
[24] Haring, R.E. and J.C. Heideman. "Gulf of Mexico Rare Wave Return Periods". OTC 3230, Offshore Technology Conferenc, Houston, Teexas, May 1978
[25] Gumbel E. J., (1960). "Multivariate Extreme Distributions". Bulletin of the International Statistical Institute 39(2), 471-475.
[26] P. Todorovic, Stochastic Models of Floods, Water Resources Research ,1978, VOL. 14, No. 2
[27] Embrechts P, Kluppelberg C, Mikosch T. "Modeling Extremal Events". Berlin: Springer, 1997.
[28] Walshaw D. (1994) "Getting The Most from Your Extreme Wind Data: A Step By Step Guide", J Res Nat Inst Stand Technol 99, 399-411
[29] H．克拉美，统计学数学方法，魏宗叙等译，上海科技出版社，1966年。
[30] 丛树铮等编，水文学的概率统计基础，水利出版社，1980年。
[31] D E Reeve. Coastal Flood Risk Assessment [J],Journal of Waterway, Port. Coastal. and Ocean Engineering, 1998,124(5):219-228.
[32] 郭仲伟，风险分析与决策[M]．1986，机械工业出版社。
[33] Liu Defu, Wen Shuqin and Wang Liping, 2002, "Compound Bivariate Extreme Distribution of Typhoon Induced Sea Environments and Its Application," Proc. 12th ISOPE, ISSN 1098-6189, pp. 130-134.
[34] DET NORSKE VERITAS, Rules For The Design Construction and Inspection of Offshore Structures, 1997.
[35] E.G. Pitt, J. Oaruvala, J.B. Bole and O.B. Oriver, "Models of the Probability Distribution of Extreme Wave Crest Elevation", Proceedings of the Ninth (1999) International Offshore and Polar Engineering Conference, Brest, France, May 30-June 4,1999
[36] 王超编著，海洋工程环境，大津大学出版社，1993年。
[37] 天津大学水文力学教研室编，海洋石油工程环境，水文分析计算，石油工业出版社，
1983年。
[38] Madsen, H.O., "Methods of Structural Safety", Prentice-hall, Inc.,1986, 18-26
[39] Bourgund, U. and Bucher, C.G., "Importance Sampling Procedure Using Design Point", Research Report of Univ. of Innsbruck, Nov. 1986
[40] Srinivasan, Rajan, Importance Sampling: Applications in Communications and Detection, Berlin; New York: Springer, 2002.
[41] Bourgund, U., Ouypornprasert, W., Prenninger, P.H.W., Advanced Simulation Methods for the Estimation of Systems Reliability, Internal Working Report 19, Inst. of Eng. Mech., Univ. of Innsbruck, October 1986.
[42] Harbitz A. Efficient and Accurate Probability of Failure Calculation by Use of the Importance Sampling Technique, Proc 4th. International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Bologna, Italy: Pragora Editric, 1983, pp825-836.
[43] 傅旭东，相关变量下失效概率的计算机模拟，西南交通大学学报，1997，Vol．32，pp319-323．
[44] 吕震宙，多设计准则下多变量多模式结构可靠性理论及应用，西北工业大学博士论文，1993．10
[45] Melchers R E, Structural Reliability Analysis and Prediction, New York: Ellis Horwood Limited, 1987.
[46] 李亚东，重要抽样模拟及其在结构可靠度计算中的应用，西南交通大学学报，1992(4)：105-111
[47] 端义宏，秦曾灏，上海沿岸天文潮与风暴潮非线性相互作用的数值研究[J]．海洋与湖沼，1997．1，28(1)：15～19。
[48] Y.K. Wen., H. Banon. (1991). "Development of Environmental Combination Design Criteria for Fixed Platforms in the Gulf of Mexico", OTC 6540, The 23rd Annual Offshor Technology Conference in Houston,Texas,365-375
[49] G.Z. Foriistall, R.D. Larrabee, R.S. Mercier. (1991) "Combined Oceanographic Criteria for Deepwater Structures in the Gulf of Mexico", OTC 6541, The 23rd Annual Offshore Technology Conference Houston, Texas, 377-390
[50] I.D. Morton, J. Bowers. (1997). "Extreme Value Analysis in A Multivariate Offshore Environment", Applied Ocean Research 18 303-317
[51] M. N. Tsimplis and D. Blackman, (1997). "Extreme Sea-level Distribution and Return Periods in the Aegean an Ionian Seas", Estuarine, Coastal ands shelf Science 44: 79-89.
[52] Cavani? A. "Joint occurrence of extreme wave heights and wind gusts during severe storms on the Frigg Field" [R]. Exploration and Production Forum Wkshp Application of Joint Probability of Metocean Phenomena in the Oil Industry's Structural Design York, London, 1985.
[53] 俞聿修编著，随机波浪及其工程应用，大连理工大学出版社，2000年。
[54] 徐德伦，于定勇编著，随机波浪理论，高等教育出版社，2001年。
[55] 茆诗松，王静龙，濮晓龙，高等数理统计，高等教育出版社＆施普林格出版社，1998．
[2] Madsen, H.O., "Methods of Structural Safety", Prentice-hall, Inc., 1986, 18-26
[3] Bourgund, U. and 8ucher, C.G., "Importance Sampling Procedure Using Design Point", Research Report of Univ. of Innsbruck, Nov. 1986
[4] G. I. Schueller, and R. Atix, "a Critical appraisal of methods to determine failure probabilities", Univ. of Innsbruck, Institute of Mechanics, 1986,35-74
[5] 刘德辅，杨永春，王超．海洋设计标准的不确定性及联合分布概率分析[J]．海洋学报，1996，18(5)：110-116．
[6] Liu P-L, Der Kiureghian A. Multivariate distribution models with prescribed marginals and covariances [J]. Probabilitic Engineering Mechanics, 1986, 1(2):105～112.
[7] 刘德辅，王铮，施建刚，海洋环境条件联合设计标准[J]．海洋学报，1994，16(2)：116—123。
[8] Stuart G Coles and Jonathan A Tawn. "Modelling Extremes of the Areal Rainfall Process" [R],Yechnical Report 92-12. Nottingham University, Nottingham, 1992.
[9] Stuart G Coles and Jonathan A Tawn. "Statistics of Coastal Flood Prevention" [J].Phi1. Trans. R, Soc. A, 1990,332:457～476.
[10] Stuart G Coles and Jonathan A Yawn. Modelling extreme multivariate events[J]. J.R. Statist. Soc. B, 1991, 53(2): 377～392.
[11] Jonathan A Tawn. Modelling multivariate extreme value distributions[J]. Biometrika, 1990, 77(2) :245～253.
[12] R.L Smith, J.A Tawn, Yuen H R. "Statistics of multivariate extremes" [J].
Int. Statist. Inst. Rev., 1990,58(1): 47-58.
[13] S Nadarajah, C W Anderson and Jonathan A Tawn. "Ordered multivariate extremes" [J]. J. R. Statist. Soc. B, 1998, 60(2):473～496.
[14] Stuart GColes and Jonathan A Tawn. "Modelling Extremes of the Areal Rainfall Process" [J]. J. R. Statist. B, 1996, 58(2):329～347.
[15] S. Zachary, G. Feld, G. Ward, J. Wofram. (1998). "Multivariate Extrapolation in The Offshore Environment", Applied Ocean Research 20, 273-295
[16] Gumbel E J. Distributions de valeurs extremes en plusieurs dimensions[J]. Publ. Inst. Statist. Paris, 1960, 9:171～173.
[17] I.D. Morton, J. Bowers.(1997). "Extreme Value Analysis in A Multivariate Offshore Environment", Applied Ocean Research 18 303-317
[18] Stuart G Coles and Jonathan A Tawn. Statistical methods for multivariate extremes: an application to structural design[J]. Appl. Statist., 1994, 43 (1): 1～48.
[19] Liu T.F. and Ma, F.S.,(1980). "Prediction of Extreme Wave Heights and Wind Velocities", Journal of the Waterway Port Coastal and Ocean Division, ASCE, 106, No. WW4, 469-479
[20] T.F. Liu (1982) "Long Term Distributions of Hurrican Characteristics" Pro. Offshore Technology Conference OTC 4325, pp. 305-313
[21] Liu Defu, Li huajun, Wen Shuqin, Song Yah, Wang Shuqing (2001). "Prediction of Extreme Significant Wave Height from Daily Maxima" China Ocean Engineering Vol. 15, No.1, pp97-106
[22] Langley R.M., A.H. El-Shaarawi (1986). "On The Calculation of Extreme Wave Heights: A Review", Ocean Englneering Vo1.13. No.1, pp. 93-118
[23] W.H. Kirby, M.E. Moss (1987). "Summary of Flood-Frequency Analysis in The United States", Journal of Hydrology, 96 pp. 5-14
[24] Haring, R.E. and J.C. Heideman. "Gulf of Mexico Rare Wave Return Periods". OTC 3230, Offshore Technology Conferenc, Houston, Teexas, May 1978
[25] Gumbel E. J., (1960). "Multivariate Extreme Distributions". Bulletin of the International Statistical Institute 39(2), 471-475.
[26] P. Todorovic, Stochastic Models of Floods, Water Resources Research ,1978, VOL. 14, No. 2
[27] Embrechts P, Kluppelberg C, Mikosch T. "Modeling Extremal Events". Berlin: Springer, 1997.
[28] Walshaw D. (1994) "Getting The Most from Your Extreme Wind Data: A Step By Step Guide", J Res Nat Inst Stand Technol 99, 399-411
[29] H．克拉美，统计学数学方法，魏宗叙等译，上海科技出版社，1966年。
[30] 丛树铮等编，水文学的概率统计基础，水利出版社，1980年。
[31] D E Reeve. Coastal Flood Risk Assessment [J],Journal of Waterway, Port. Coastal. and Ocean Engineering, 1998,124(5):219-228.
[32] 郭仲伟，风险分析与决策[M]．1986，机械工业出版社。
[33] Liu Defu, Wen Shuqin and Wang Liping, 2002, "Compound Bivariate Extreme Distribution of Typhoon Induced Sea Environments and Its Application," Proc. 12th ISOPE, ISSN 1098-6189, pp. 130-134.
[34] DET NORSKE VERITAS, Rules For The Design Construction and Inspection of Offshore Structures, 1997.
[35] E.G. Pitt, J. Oaruvala, J.B. Bole and O.B. Oriver, "Models of the Probability Distribution of Extreme Wave Crest Elevation", Proceedings of the Ninth (1999) International Offshore and Polar Engineering Conference, Brest, France, May 30-June 4,1999
[36] 王超编著，海洋工程环境，大津大学出版社，1993年。
[37] 天津大学水文力学教研室编，海洋石油工程环境，水文分析计算，石油工业出版社，
1983年。
[38] Madsen, H.O., "Methods of Structural Safety", Prentice-hall, Inc.,1986, 18-26
[39] Bourgund, U. and Bucher, C.G., "Importance Sampling Procedure Using Design Point", Research Report of Univ. of Innsbruck, Nov. 1986
[40] Srinivasan, Rajan, Importance Sampling: Applications in Communications and Detection, Berlin; New York: Springer, 2002.
[41] Bourgund, U., Ouypornprasert, W., Prenninger, P.H.W., Advanced Simulation Methods for the Estimation of Systems Reliability, Internal Working Report 19, Inst. of Eng. Mech., Univ. of Innsbruck, October 1986.
[42] Harbitz A. Efficient and Accurate Probability of Failure Calculation by Use of the Importance Sampling Technique, Proc 4th. International Conference on Application of Statistics and Probability in Soil and Structural Engineering, Bologna, Italy: Pragora Editric, 1983, pp825-836.
[43] 傅旭东，相关变量下失效概率的计算机模拟，西南交通大学学报，1997，Vol．32，pp319-323．
[44] 吕震宙，多设计准则下多变量多模式结构可靠性理论及应用，西北工业大学博士论文，1993．10
[45] Melchers R E, Structural Reliability Analysis and Prediction, New York: Ellis Horwood Limited, 1987.
[46] 李亚东，重要抽样模拟及其在结构可靠度计算中的应用，西南交通大学学报，1992(4)：105-111
[47] 端义宏，秦曾灏，上海沿岸天文潮与风暴潮非线性相互作用的数值研究[J]．海洋与湖沼，1997．1，28(1)：15～19。
[48] Y.K. Wen., H. Banon. (1991). "Development of Environmental Combination Design Criteria for Fixed Platforms in the Gulf of Mexico", OTC 6540, The 23rd Annual Offshor Technology Conference in Houston,Texas,365-375
[49] G.Z. Foriistall, R.D. Larrabee, R.S. Mercier. (1991) "Combined Oceanographic Criteria for Deepwater Structures in the Gulf of Mexico", OTC 6541, The 23rd Annual Offshore Technology Conference Houston, Texas, 377-390
[50] I.D. Morton, J. Bowers. (1997). "Extreme Value Analysis in A Multivariate Offshore Environment", Applied Ocean Research 18 303-317
[51] M. N. Tsimplis and D. Blackman, (1997). "Extreme Sea-level Distribution and Return Periods in the Aegean an Ionian Seas", Estuarine, Coastal ands shelf Science 44: 79-89.
[52] Cavani? A. "Joint occurrence of extreme wave heights and wind gusts during severe storms on the Frigg Field" [R]. Exploration and Production Forum Wkshp Application of Joint Probability of Metocean Phenomena in the Oil Industry's Structural Design York, London, 1985.
[53] 俞聿修编著，随机波浪及其工程应用，大连理工大学出版社，2000年。
[54] 徐德伦，于定勇编著，随机波浪理论，高等教育出版社，2001年。
[55] 茆诗松，王静龙，濮晓龙，高等数理统计，高等教育出版社＆施普林格出版社，1998．
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