Probabilistic Risk Assessment of Meteorological and Hydrological Droughts with Copula Functions: A Multivariate Framework

Abstract Drought is a complex and gradually developing natural hazard with profound impacts on water resources, agriculture, and ecosystems. Its multifaceted nature, coupled with increasing frequency and severity under climate change, requires robust monitoring and risk assessment tools. Traditional univariate indices, such as the Standardized Precipitation Index (SPI), provide essential information on drought occurrence and intensity but cannot capture the interactions among hydroclimatic variables. Multivariate indices, including the Multivariate Standardized Drought Index (MSDI), address this limitation by integrating multiple variables, yet probabilistic characterization of drought characteristics remains limited. This study presents a sequential, copula-based framework to assess drought behavior in the Çoruh River Basin. First, univariate drought indices, Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Streamflow Index (SSFI), are calculated to quantify individual drought characteristics. Then, a copula-based MSDI is developed to integrate meteorological and hydrological drought, capturing compound drought events and their interdependencies. Finally, the dependence between drought duration and severity is modeled using copula functions to estimate joint return periods based on drought characteristics derived from both univariate indices and the MSDI. Results demonstrate that the integrated approach more accurately represents the interdependencies of drought events than univariate methods alone, improving estimates of recurrence and joint risk. The study highlights the potential of combining univariate indices, multivariate indices, and copula-based analysis to advance understanding of compound drought risks, supporting early warning systems, water resources planning, and climate adaptation strategies in regions vulnerable to prolonged hydroclimatic extremes.