Entropy-Based Method for Bivariate Drought Analysis

Abstract

Drought duration and severity are two main properties for characterizing droughts. These drought properties are mutually correlated and may have different marginal distributions. A bivariate (or joint) distribution of drought duration and severity is therefore needed that is capable of accommodating their different marginal distributions. This study proposes a method, based on entropy theory, for constructing the bivariate distribution of drought duration and severity with different marginal distribution forms. By specifying constraints for drought duration and severity, the entropy-based bivariate distribution can be derived and then marginal distributions can be obtained accordingly. Monthly streamflow data from Brazos River at Waco, Texas, are employed to illustrate the application of the proposed method to model drought duration and severity for drought analysis. The copula method is also applied for comparison with the proposed entropy method.