Constructing the Joint Probability Spatial Distribution of Different Levels of Drought Risk Based on Copula Functions: A Case Study in the Yellow River Basin

Joint multivariate distribution and calculation of return period are essential in enhancing drought risk assessment and promoting the sustainable development of water resources. Aiming to address the increasingly serious drought situation in the Yellow River Basin, this study first utilized the Soil and Water Assessment Tool (SWAT) distributed hydrological model combined with the Standardized Precipitation Evapotranspiration Index (SPEI), the Standardized Soil Moisture Index (SSMI), and the Standard Water Yield Index (SWYI); the duration, peak, and severity of meteorological, agricultural, and hydrological droughts were analyzed. Based on the selected copula function, a three-dimensional joint distribution of drought duration (D), drought severity (S), and maximum severity (M) was constructed. The corresponding copula joint probability was calculated, leading to the three-dimensional joint return period and concurrent return period of meteorological drought, agricultural drought, and hydrological drought. The findings reveal several key trends: (1) Meteorological drought intensifies over time. Although drought areas eased after the 1990s, the overall drought trend continues to rise. Agricultural drought has intensified in arid regions but eased in semi-humid areas after the 2000s. Hydrological drought was severe in the upstream regions during the 1990s but eased in the 2000s, while it was particularly severe in the midstream and downstream regions during the 2000s. (2) Meteorological droughts are more severe in arid and semi-arid temperate regions and milder in semi-humid cold temperate regions. Agricultural droughts are extreme in arid and semi-arid cold temperate regions. Hydrological drought events are fewer but more severe in semi-arid temperate regions and have the lowest probability of occurrence in semi-humid cold temperate regions. (3) The overall probability of the occurrence of meteorological drought is between 55.7% and 69%; that of agricultural drought is between 73.1% and 91.7%, and that of hydrological drought is between 66.9% and 84%. Drought risk assessment provides scientific references for the analysis of the uncertainty of water supply in the basin and the formulation of effective risk management strategies.