Bivariate Characterization of Long-Term Hydrological Drought Risks Using SRI and Archimedean Copulas

Hydrological drought poses a major threat to water security-y in semi-arid regions, where prolonged runoff deficits can severely affect reservoir reliability and ecosystem sustainability. This study presents a bivariate probabilistic framework to characterize long-term hydrological drought risk in the Wadi Sahouat basin (northwestern Algeria) using the 12-month Standardized Runoff Index (SRI-12) for the period 1973/74–2014/15. Drought events were identified through run theory with a threshold level of SRI ≤ −1.0, and some drought characteristics, duration, and severity were extracted. Marginal distributions were fitted and evaluated using AIC, BIC, and Kolmogorov–Smirnov tests, leading to the selection of the Weibull distribution for both variables. The dependence structure between duration and severity was modeled using Archimedean copulas, and the Gumbel copula provided the best fit at both hydrometric stations, indicating significant upper-tail dependence. Univariate and bivariate return periods were estimated for target intervals from 10 to 200 years. Results demonstrate that multivariate return periods substantially differ from univariate estimates, particularly for extreme events, highlighting the compounded risk of prolonged and severe droughts.