Joint modelling of drought characteristics derived from historical and synthetic rainfalls: Application of Generalized Linear Models and Copulas

Abstract

Study region: Çoruh Basin in Northeastern Turkey. Study focus: In recent years, copulas have been widely used to model the joint distribution function of duration and severity series which are the major characteristics of a drought event to be considered in the planning and management of water resources systems. However, as the copula functions are typically fitted to the drought series that are derived from a limited amount of observed data, it may be insufficient to characterize the full range of the analyzed drought characteristics. Therefore, General Linear Models (GLMs) were used to model and simulate rainfall data in this study. The Standard Precipitation Index (SPI) method was used to obtain the drought characteristics from simulated and historical rainfall series. Four Archimedean copulas, namely Ali-Mikhail-Haq, Clayton, Frank and Gumbel-Hougaard, were evaluated to model the joint distribution functions of these characteristics. New hydrological insights for the region: The Gumbel-Hougaard copula was found to be the most suitable copula in modelling the joint dependence structure of the drought characteristics at five stations in the basin. The derived Gumbel-Hougaard copulas for each station were employed to obtain joint and conditional return periods of the historical and generated drought characteristics. The drought risks that are estimated based on bivariate return periods for different circumstances can provide useful information in planning, management and in assessing adequacy of the water structures in the basin. Keywords: Drought, Standard precipitation index (SPI), General linear models (GLMs), Copulas, Çoruh basin, Turkey