Application of Copulas for Regional Bivariate Frequency Analysis of Meteorological Droughts in Turkey

Abstract

The main objective of this study was to model the joint probability distributions of meteorological droughts of Turkey using copulas. Monthly rainfall data covering of period 1966-2006 from 173 gauge stations uniformly distributed across Turkey is considered for this aim. The principal component analysis is used to identify homogenous rainfall regions of Turkey. For meteorological drought analysis of the monthly rainfall series, standardized precipitation index method is used and the crucial drought characteristics, namely drought duration and severity, are determined. Marginal probability distributions of these characteristics are identified by fitting Weibull, two-parameter Lognormal, generalized Pareto, Gamma, Normal, Logistic, log-Logistic, generalized Extreme Value and Exponential distributions. Based on the Chi-square (chi (2)) goodness-of-fit test, the two-parameter Lognormal distribution is indicated as the best suitable for the duration series, whereas the Gamma, Weibull and generalized Pareto distributions show better fit for the severity series. As these drought characteristics are highly correlated and follow different probability distributions, copula functions are used to construct the joint distribution function of drought duration and severity series. Four types of bivariate copulas (i.e., Frank, Clayton, Gumbel-Hougaard and Ali-Mikhail-Haq) are evaluated for modeling and the best-fit copula for each homogenous region is then employed to estimate conditional probability properties and joint return periods of the drought characteristics. The drought properties of each region are hereby comprehensively explained and the results indicated here can be helpful in the assessment of the adequacies of water supply systems under drought conditions in all regions.