熵理论及其在水文水资源中的应用研究
Entropy Theory and Its Application in Hydrology and Water Resources

作者: 熊 丰 , 陈 璐 :华中科技大学水电与数字化工程学院,湖北 武汉; 张俊宏 :中南民族大学资源与环境学院,湖北 武汉;

关键词: 水文水资源熵理论最大熵原理相关性分析应用研究Hydrology and Water Resources Entropy Theory Principle of Maximum Entropy Correlation Analysis Application

摘要:
水文水资源系统是一个复杂的非线性系统,研究水资源系统中的不确定信息以及水文事件的相关性属性具有重要意义。熵理论是进行水文不确定性度量和相关性分析的有效方法。本文综述了最大熵原理和基于熵理论的相关性分析方法,探究了其在水文水资源学科中的应用,分析了其特点、优势和存在的问题,并对熵理论今后的研究方向进行了展望。

Abstract: Hydrology and water resources system is a complex and nonlinear system. It is of great significance to study how to deal with the uncertainty in water resources system and analyze the correlation among hydrological variables. Entropy theory can measure the uncertainty of hydrological information and analyze the dependences among hydrological variables. In this paper, the principle of maximum entropy (POME) and the correlation analysis method based on entropy theory were introduced. The application of entropy theory in hydrology and water resources was reviewed. The characteristics, advantages and disadvantages of these methods were analyzed. Finally, the future research on entropy theory and its application in hydrology and water resources was discussed.

文章引用: 熊 丰 , 陈 璐 , 张俊宏 (2016) 熵理论及其在水文水资源中的应用研究。 水资源研究, 5, 23-32. doi: 10.12677/JWRR.2016.51003

参考文献

[1] SINGH, V. P. On derivation of the extreme value (EV) type III distribution for low flows using entropy. Hydrological Sciences Journal, 1987, 32(4): 521-533.
http://dx.doi.org/10.1080/02626668709491209

[2] SINGH, V. P. On application of the Weibull distribution in hydrology. Water Resources Management, 1987, 1(1): 33-43.
http://dx.doi.org/10.1007/BF00421796

[3] 张明. 最大信息熵理论在地貌瞬时单位线中的应用[J]. 水文, 2000, 20(3): 13-14. ZHANG Ming. Application of maximum entropy in geomorphological instantaneous unit hydrograph. Journal of China Hy-drology, 2000, 20(3): 13-14. (in Chinese)

[4] PAPALEXIOU, S. M., KOUTSOYIANNIS, D. Entropy based derivation of probability distributions: A case study to daily rainfall. Advances in Water Resources, 2012, 45: 51-57.
http://dx.doi.org/10.1016/j.advwatres.2011.11.007

[5] HAO, Z., SINGH, V. P. Single-site monthly streamflow simulation using entropy theory. Water Resources Research, 2011, 47(9): W09528.
http://dx.doi.org/10.1029/2010WR010208

[6] ZHANG, L., SINGH, V. P. Joint and conditional probability distributions of runoff depth and peak discharge using entropy theory. Journal of Hydrologic Engineering, 2014, 19(6): 1150-1159.
http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000906

[7] CHIU, C. L. Entropy and probability concepts in hydraulics. Journal of Hydraulic Engineering, 1987, 113(5): 583-600.
http://dx.doi.org/10.1061/(ASCE)0733-9429(1987)113:5(583)

[8] CHIU, C. L. Entropy and 2D velocity distribution in open channels. Journal of Hydraulic Engineering, 1988, 114(7): 738-756.
http://dx.doi.org/10.1061/(ASCE)0733-9429(1988)114:7(738)

[9] MORAMARCO, T., CORATO, G., MELONE, F. and SINGH, V. P. An entropy-based method for determining the flow depth distribution in natural channels. Journal of Hydrology, 2013, 497: 176-188.
http://dx.doi.org/10.1016/j.jhydrol.2013.06.002

[10] FARINA, G., ALVISI, S., FRANCHINI, M., et al. Estimation of bathymetry (and discharge) in natural river cross-sections by using an entropy approach. Journal of Hydrology, 2015, 527: 20-29.
http://dx.doi.org/10.1016/j.jhydrol.2015.04.037

[11] CUI, H., SINGH, V. Computation of suspended sediment discharge in open channels by combining Tsallis entropy-based methods and empirical formulas. Journal of Hydrologic Engineering, 2014, 19(1): 18-25.
http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000782

[12] JAIN, D., SINGH, V. P. Estimating parameters of EV1 distribution for flood frequency analysis. Journal of the American Water Resources Association, 1986, 22(1): 59-72.

[13] FIORENTIAO, M., ARORA, K. and SINGH, V. P. The two-component extreme-value distribution for flood fre-quency analysis: Another look and derivation of a new estimation method. Stochastic Hydrology and Hydraulics, 1987, 1(3): 199-208.
http://dx.doi.org/10.1007/BF01543891

[14] SINGH, V. P., GUO, H. and YU, F. X. Parameter estimation for 3-parameter log-logistic distribution (LLD3) by PMOE. Stochastic Hydrology and Hydraulics, 1993, 7(3): 163-177.
http://dx.doi.org/10.1007/BF01585596

[15] SINGH, V. P., GUO, H. Parameter estimation for 2-parameter log-logistic distribution (LLD2) by maximum entropy. Civil Engineering Systems, 1995, 12(4): 343-357.
http://dx.doi.org/10.1080/02630259508970181

[16] SINGH, V. P., GUO, H. Parameter estimation for 2-parameter Pareto distribution by Pome. Water Resource Management, 1995, 9(2): 81-93.
http://dx.doi.org/10.1007/BF00872461

[17] SINGH, V. P., GUO, H. Parameter estimations for 3-parameter generalized Pareto distribution by the principle of maximum entropy (POME). Hydrological Science Journal, 1995, 40(2): 165-181.
http://dx.doi.org/10.1080/02626669509491402

[18] SINGH, V. P., GUO, H. Parmaeter estimation for 2-parameter gene-ralized Pareto distribution by POME. Stochastic Hydrology and Hydraulics, 1997, 11(3): 211-227.
http://dx.doi.org/10.1007/BF02427916

[19] SHANNON, C. E. A mathematical theory of communication. The Bell System Technical Journal, 1948, 27(3): 379-423.
http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x

[20] 李元章, 丛树铮. 熵及其在水文频率计算中的应用[J]. 水文, 1985, (1): 22-26. LI Yuanzhang, CONG Shuzheng. Entropy and its application in hydrological frequency calculation. Journal of China Hydrology, 1985, (1): 22-26. (in Chinese)

[21] 张明, 金菊良, 张礼兵. 信息论方法在水资源系统工程中的应用[J]. 中国人口资源与环境, 2007, 17(2): 79-83. ZHANG Ming, JIN Juliang and ZHANG Libing. Applications of information theory methods to water resources systems engi-neering. China Population, Resource and Environment, 2007, 17(2): 79-83. (in Chinese)

[22] Jaynes, E. T. On the rationale of maximum entropy methods. Proceedings of the IEEE, 1982, 70(9): 939-952.
http://dx.doi.org/10.1109/PROC.1982.12425

[23] 王栋, 朱元甡. 最大熵原理(POME)在水文水资源科学中的应用[J]. 水科学进展, 2001, 12(3): 424-430. WANG Dong, ZHU Yuanshen. Principle of maximum entropy and its application in hydrology and water resources. Advances in Water Science, 2001, 12(3): 424-430.(in Chinese)

[24] SONUGA, J. O. Principle of maximum entropy in hydrologic frequency analysis. Journal of Hydrology, 1972, 17(3): 177-219.
http://dx.doi.org/10.1016/0022-1694(72)90003-0

[25] SONUGA, J. O. Entropy principle applied to the rainfall-runoff process. Journal of Hydrology, 1976, 30(1): 81-94.
http://dx.doi.org/10.1016/0022-1694(76)90090-1

[26] SOGAWA, N., ARAKI, M. and IMAI, T. Studies on multivariate conditional maximum entropy distribution and its characteristics. Journal of Hydroscience and Hydraulic Engineering, 1986, 4(1): 79-97.

[27] SINGH, V. P., RAJAGOPAL, A. K. A new method of parameter estimation for hydrologic frequency analysis. Hydrological Science and Technology, 1986, 2(3): 33-40.

[28] SINGH, V. P., SINGH, K. Derivation of the Gamma distribution by using the principle of maximum entropy (POME). Journal of the American Water Resources Association, 1985, 21(6): 941-952.
http://dx.doi.org/10.1111/j.1752-1688.1985.tb00189.x

[29] 张明. 纳须模型参数估计矩法和熵法的关系及评价[J]. 人民珠江, 2004, (1): 15-17. ZHANG Ming. Relationship between moment and entropy methods and evaluation for estimating parameters of Nash Model. Pearl River, 2004, (1): 15-17. (in Chinese)

[30] HAO, Z., SINGH, V. P. Entropy-based parameter estimation for extended Burr XII distribution. Stochastic Environmental Research and Risk Assessment, 2009, 23(8): 1113-1122.
http://dx.doi.org/10.1007/s00477-008-0286-7

[31] 李娟, 陈元芳, 王文鹏, 等. 最大熵原理在P-Ⅲ型分布参数估计中的应用研究[J]. 水电能源科学, 2007, 25(5): 31-35. LI Juan, CHEN Yuanfang, WANG Wenpeng, et al. Application of maximum entropy principle toparameters estimation for Pearson-Ⅲ distribution. Water Resources and Power, 2007, 25(5): 31-35. (in Chinese)

[32] 臧红霞, 郑华山, 陈长茵. 三参数对数正态分布最大熵参数估计方法探讨[J]. 水利科技与经济, 2014, 20(5): 1-4. ZANG Hongxia, ZHENG Huashan and CHEN Changyin. Maximum entropy estimation methods for LN3 distribution consi-dering. Water Conservancy Science and Technology and Economy, 2014, 20(5): 1-4. (in Chinese)

[33] 张明, 张阳. 水文频率分析中参数估计最大熵法的梅林变换推导[J]. 水资源与水工程学报, 2015(4): 105-107. ZHANG Ming, ZHANG Yang. Mellin transform derivation of maximum entropy for parameter estimation in hydrologic fre-quency analysis. Journal of Water Resources and Water Engineering, 2015(4): 105-107. (in Chinese)

[34] 何玲, 陈晓宏. 一个基于熵最大原理的地下水评价模型[J]. 水科学进展, 2001, 12(1): 61-65. HE Ling, CHEN Xiaohong. A model for groundwater quality assessment based on the maximum entropy theory. Advances in Water Science,2001, 12(1): 61-65. (in Chinese)

[35] 张成科. 基于熵的水质模糊评价模型及应用[J]. 系统工程理论与实践, 1998, (6): 81-86. ZHANG Chengke. Model and application of the water quality fuzzy assessment based on entropy. System Engineering Theory and Practice, 1998, (6): 81-86. (in Chinese)

[36] 赵庆良, 马建华, 管华. 基于信息熵的评价模型在惠济河水质评价中的应用[J]. 河南大学学报(自然科学版), 2002, 32(4): 76-80. ZHAO Qingliang, MA Jianhua and GUAN Hua. Application of the model for water quality assessment based on the information entropy—In the case of Huiji River. Journal of Henan University (Natural Science), 2002, 32(4): 76-80. (in Chinese)

[37] 王栋, 朱元甡. 基于最大熵原理的水环境模糊优化评价模型[J]. 河南大学学报(自然科学版), 2002, 30(6): 56-60. WANG Dong, ZHU Yuanshen. POME-based fuzzy optimal evaluation model of water environment. Journal of Hohai University (Natural Science), 2002, 30(6): 56-60. (in Chinese)

[38] 姜志群, 朱元甡. 基于最大熵原理的水资源可持续性评价[J]. 人民长江, 2004, 35(1): 41-42. JIANG Zhiqun, ZHU Yuanshen. Sustainable evaluation of water resources based on maximum entropy. The Changjiang River, 2004, 35(1): 41-42.

[39] KULLBACK, S., LEIBLER, R. A. On Information and Sufficiency. Annals of Mathematical Statistics, 1951, 22(1): 79-86.
http://dx.doi.org/10.1214/aoms/1177729694

[40] 陈颖, 袁艳斌, 袁晓辉. 基于信息熵的水文站网优化研究[J]. 水电能源科学, 2013, 31(7): 188-190. CHEN Yin, YUAN Yanbin and YUAN Xiaohui. Hydrologic network optimization based on information entropy. Water Re-sources and Power, 2013, 31(7): 188-190. (in Chinese)

[41] LANGBEIN, W. M. Stream gaging networks. Assemblée Générale de Rome, 1954, 3: 293-303.

[42] RODRIGUEZ-ITURBE, I., MEJIA, J. M. On the transformation of point rainfall to areal rainfall. Water Resources Research, 1974, 10(4): 729-735.
http://dx.doi.org/10.1029/WR010i004p00729

[43] HARMANCIOGLU, N. Measuring the information content of hydro-logical process by the entropy concept. Journal of Civil Engineering Faculty, 1981: 13-40.

[44] MARKUS, M., KNAPP, H. V. and TASKER, G. D. Entropy and generalized least square methods in assessment of the regional value of stream gages. Journal of Hydrology, 2003, 283(1-4): 107-121.
http://dx.doi.org/10.1016/S0022-1694(03)00244-0

[45] SARLAK, N., SORMAN, A. U. Evaluation and selection of stream-flow network stations using entropy methods. Turkish Journal of Engineering and Environmental Sciences, 2006, 30: 91-100.

[46] CASELTON, W. F., HUSAIN, T. Hydrologic networks: Information trans-mission. Journal of the Water Resources Planning and Management Division, 1980, 106(2): 503-520.

[47] ALFONSO, L., LOBBRECHT, A. and PRICE, R. Information theory-based approach for location of monitoring water level gauges in polders. Water Resources Research, 2010, 46(3): W03528.
http://dx.doi.org/10.1029/2009WR008101

[48] HUSAIN, T. Hydrologic uncertainty measure and network design. Journal of the American Water Resources Association, 1989, 25(3): 527-534.
http://dx.doi.org/10.1111/j.1752-1688.1989.tb03088.x

[49] YANG, Y., BURN, D. H. An entropy approach to data collec-tion network design. Journal of Hydrology, 1994, 157(1-4): 307- 324.
http://dx.doi.org/10.1016/0022-1694(94)90111-2

[50] HARMANCIOGLU, N. B., ALPASLAN, N. Water quality moni-toring network design: A problem of multi-objective decision making. Journal of the American Water Resources Association, 1992, 28(1): 179-192.
http://dx.doi.org/10.1111/j.1752-1688.1992.tb03163.x

[51] OZKUL, S., HARMANCIOGLU, N. B. and SINGH, V. P. Entropy-based assessment of water quality monitoring networks. Journal of Hydrologic Engineering, 2000, 5(1): 90-100.
http://dx.doi.org/10.1061/(ASCE)1084-0699(2000)5:1(90)

[52] AL-ZAHRANI, M., HUSAIN, T. An algorithm for de-signing a precipitation network in the southwestern region of Saudi Arabia. Journal of Hydrology, 1998, 205(3-4): 205-216.
http://dx.doi.org/10.1016/S0022-1694(97)00153-4

[53] YOO, C., JUNG, K. and LEE, J. Evaluation of rain gauge network using entropy theory: Comparison of mixed and continuous distribution function applications. Journal of Hydrologic Engineering, 2008, 13(4): 226-235.
http://dx.doi.org/10.1061/(ASCE)1084-0699(2008)13:4(226)

[54] 陈颖. 基于信息熵理论的水文站网评价优化研究[D]: [硕士学位论文]. 武汉: 武汉理工大学资源与环境工程学院, 2013. CHEN Yin. Evaluation and optimization of hydrologic network. Wuhan: Wuhan University of Technology, 2013. (in Chi-nese)

[55] SU, H., YOU, G. J. Developing an entropy-based model of spatial information estimation and its application in the design of precipitation gauge networks. Journal of Hydrology, 2014, 519: 3316-3327.
http://dx.doi.org/10.1016/j.jhydrol.2014.10.022

[56] 赵铜铁钢, 杨大文. 神经网络径流预报模型中基于互信息的预报因子选择方法[J]. 水力发电学报, 2011, 20(1): 24-30. ZHAO Steel, YANG Dawen. Mutual information-based input variable selection method for runoff-forecasting neural network model. Journal of Hydroelectric Engineering, 2011, 20(1): 24-30. (in Chinese)

[57] 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]: [博士学位论文]. 北京: 清华大学水利水电工程系, 2012. GONG Wei. Watershed model uncertainty analysis based on information entropy and mutual information. Beijing: Tsinghua University, Department of Hydraulic Engineering, 2012. (in Chinese)

[58] SKLAR, M. Fonctions de répartition à n dimensions et leursmarges. Paris: Université Paris 8, 1959.

[59] 郭生练, 闫宝伟, 肖义, 等. Copula函数在多变量水文分析计算中的应用及研究进展[J]. 水文, 2008, 28(3): 1-7. GUO Shenglian, YAN Baowei, XIAO Yi, et al. Multivariate hydrological analysis and estimation. Journal of China Hydrology, 2008, 28(3): 1-7. (in Chinese)

[60] MA, J., SUN, Z. Mutual information is copula entropy. Tsinghua Science and Technology, 2008, 16(1): 51-54.
http://dx.doi.org/10.1016/S1007-0214(11)70008-6

[61] 陈璐, 郭生练. Copula熵理论及其在水文相关性分析中的应用水资源研究[J]. 水资源研究, 2013, (2): 103-108. CHEN Lu, GUO Shenglian. Copula entropy and its application in hydrological correlation analysis. Journal of Water Resources Research, 2013, (2): 103-108. (in Chinese)

[62] 卢韦伟, 周建中, 陈璐, 等. 考虑预报因子选择的神经网络降雨径流模型[J]. 水电能源科学, 2013, 31(6): 21-25. LU Weiwei, ZHOU Jianzhong, CHEN Lu, et al. Neural network model of rainfall-runoff process considering selection of pre-diction factors. Water Resources and Power, 2013, 31(6): 21-25. (in Chinese)

[63] CHEN, L., SINGH, V. P. and GUO, S. Measure of correlation between river flows using the Copula-entropy method. Journal of Hydrologic Engineering, 2013, 18(12): 1591-1606.
http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000714

[64] SINGH, V. P., SINGH, K. Derivation of the Pearson type (PT) III distribution by using the principle of maximum entropy (POME). Journal of Hydrology, 1985, 80(3-4): 197-214.
http://dx.doi.org/10.1016/0022-1694(85)90117-9

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