Multivariate Drought Risk Evolution in the Danube River Basin: A Copula-Based Analysis of Duration and Severity Across Sub-Basins

Projected climate change in the Danube River Basin (DRB) indicates significant shifts in temperature, precipitation patterns, and hydrological cycles, with pronounced spatial and seasonal variability. Among these impacts, drought risk is projected to escalate dramatically, particularly in the southern and eastern DRB (e.g., Romania, Bulgaria, Serbia), due to synergistic effects of reduced summer precipitation, higher temperatures, and increased evapotranspiration. Existing studies, however, focus on single sub-regions of the DRB or rely on a limited number of Global Circulation Models (GCMs) and Representative Concentration Pathways (RCPs).

This study encompasses the entire DRB, divided into its Upper, Middle, and Lower sub-basins, and examines the projected evolution of meteorological drought characteristics under three RCPs, targeting the joint probability of drought duration and severity using a multivariate Copula-based framework and the Standardized Precipitation Evapotranspiration Index (SPEI) months to model the dependence structure between drought variables.

The workflow consisted of two stages: validation and projection. Initially, historical simulations from five GCMs under three RCPs were validated against the Climate Research Unit (CRU) observational dataset. The Kolmogorov-Smirnov (KS) test confirmed that all selected GCM-RCP datasets reliably reproduced the empirical cumulative distribution functions of historical drought duration and severity.

In the second stage, we contrasted a Pooled Ensemble Analysis—where all GCM events were aggregated to fit a single Copula—with a Per-GCM Analysis. The latter fitted separate Copulas for each model and used model-specific thresholds to define historical extremes. By anchoring the definition of a "100-year event" to each GCM’s historical climatology rather than a universal baseline, this method normalised inherent model biases (e.g., "wetter" vs. "drier" base states), allowing for a more accurate assessment of relative change and internal climatological shifts.

Results from the Ensemble analysis indicate a clearer signal of intensification, particularly for extreme events under high-emission scenarios (RCP 8.5). For example, historical 100-year events are projected to occur every 37 years in the Middle sub-basin and every 13 years in the Upper sub-basin. Furthermore, an analysis of "Risk Multipliers" reveals that extreme events are disproportionately affected compared to moderate events; the rarest droughts of the past are those projected to see the most dramatic increase in frequency.

However, the Per-GCM analysis exposes significant inter-model variability that the ensemble average obscures. When analysed against their own baselines, individual GCM trajectories diverge: while some models (e.g., GFDL-ESM4) depict a doubling of drought frequency, others (e.g., MRI-ESM2-0) project stability or even a decrease in frequency (wetting). This "fanning out" of projections highlights that, while the aggregate consensus points towards drying, the specific magnitude of local change remains subject to structural model uncertainty. Consequently, adaptation strategies must look beyond ensemble means and account for this wide range of plausible hydrometeorological futures.