Copula Entropy and Its Application in Hydrological Correlation Analysis
Abstract: Hydrological events are usually characterized by several correlated variables. There is a great need to estimate the correlation of hydrological variables. In this study, the current hydrologic correlation analysis methods were reviewed, the disadvantages of which were also discussed. The concept of copula entropy was introduced to estimate the dependences. The relationship between copula entropy and mutual information was discussed and the calculation procedures of copula entropy were given. Finally, the proposed method was used for selecting the inputs of artificial neural network for flood forecasting. The comparative study results show that the proposed method performs better than conventional linear regression method and provides a new way for hydrological correlation analysis.
文章引用: 陈 璐 , 郭生练 (2013) Copula熵理论及其在水文相关性分析中的应用。 水资源研究， 2， 103-108. doi: 10.12677/JWRR.2013.22015
 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 Hy-drological Analysis and Estimation. Journal of China Hydrology, 2008, 28(3): 1-7. (in Chinese)
 KAO, S. C., GOVINDARAJU, S. A bivariate frequency analysis of extreme rainfall with implica-tions for design. Journal of Geophysical Research-Atmospheres, 2007, 112(D13).
 VANDENBERGHE, S., VERHOEST, N. E. C. and DE BAETS, B. Fitting bivariate copulas to the dependence structure between storm characteristics: A detailed analysis based on 105 year 10 min rainfall. Water Resources Research, 2010, 46(1): W01512.
 ZHANG, L., SINGH, V. P. Trivariate flood frequency analysis using the Gumbel-Hougaard copula. Journal of Hydrological Engineering, 2007, 12(4): 431-439.
 GRIMALDI, S., SERINALDI, F. Asymmetric co-pula in multivariate flood frequency analysis. Advances in Water Resources, 2006, 29(8): 1155-1167.
 SHIAU, J. T. Fitting drought duration and severity with two- dimensional copulas. Water Resources Management, 2006, 20(5): 795-815.
 KAO, S. C., GOVINDARAJU, R. S. A copula-based joint deficit index for droughts. Journal of Hydrology, 2010, 380(1-2): 121-134.
 LI, W. Mutual information functions versus correlation functions. Journal of Statistical Physics, 1990, 60(5-6): 823-837.
 HARMANCIOGLU, N., YEVJEVICH, V. Transfer of hydrologic information among river points. Journal of Hy-drology, 1987, 91(1-2): 103-118.
 ALFONSO, L., LOB-BRECHT, A. and PRICE, R. Information theory-based approach for location of monitoring water level gauges in polders. Water Resources Research, 2010, 46(3): W03528.
 MA, J., SUN, Z. Mutual information is copula entropy. Tsinghua Science and Technology, 2008, 16(1): 51-54.
 ZHAO, N., LIN, W. T. A copula entropy approach to correlation measurement at the country level. Applied Mathematics and Computation, 2011, 218(2): 628-642.
 SHANNON, C. E. A mathematical theory of com-munication. The Bell System Technical Journal, 1948, 27: 379-423.
 BERNTSON, J., ESPELID, T. O. and GENZ, A. An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software, 1991, 17(4): 437- 451.
 ASCE Task Committee. Application of artificial neural networks in hydrology, artificial neural networks in hydrology, I: Preliminary concepts. Journal of Hydrologic Engi-neering, 2000, 5(2), 115-123.
 ASCE Task Committee. Ap-plication of artificial neural networks in hydrology, artificial neural networks in hydrology. II: Hydrologic applications. Journal of Hydrologic Engineering, 2000, 5(2), 124-137.
 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)
 SHARMA, A. Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 1 a strategy for system predictor identification. Journal of Hydrology, 2000, 239(1): 232-239.
 FERNANDO, T. M. K. G., MAIER, H. R. and DANDY, G. C. Selection of input variables for data driven models: An average shifted histogram partial mutual information estimator approach. Journal of Hydrology, 2009, 367(3-4): 165-176.