bivariate rainfall and runoff analysis using entropy and copula theories使用熵和二元降雨和径流分析的相关理论.pdfVIP

Entropy 2012, 14, 1784-1812; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Bivariate Rainfall and Runoff Analysis Using Entropy and Copula Theories Lan Zhang 1,* and Vijay P. Singh 2,3 1 Department of Civil Engineering, University of Akron, Akron, OH 44325, USA 2 Department of Biological and Agricultural Engineering, Texas A M University, College Station, TX 77843, USA; E-Mail: vsingh@ (V.P.S.) 3 Department of Civil and Environmental Engineering, Texas A M University, College Station, TX 77843, USA * Author to whom correspondence should be addressed; E-Mail: zhang@. Received: 1 August 2012; in revised form: 15 September 2012 / Accepted: 17 September 2012 / Published: 24 September 2012 Abstract: Multivariate hydrologic frequency analysis has been widely studied using: (1) commonly known joint distributions or copula functions with the assumption of univariate variables being independently identically distributed (I.I.D.) random variables; or (2) directly applying the entropy theory-based framework. However, for the I.I.D. univariate random variable assumption, the univariate variable may be considered as independently distributed, but it may not be identically distributed; and secondly, the commonly applied Pearson’s coefficient of correlation () is not able to capture the nonlinear dependence structure that usually exists. Thus, this study attempts to combine the copula theory with the entropy theory for bivariate rainfall and r