Ecological drought evolution analysis and risk assessment based on three-dimensional Copula function and cloud model

Flow‑chart‑style graphical abstract illustrating the study workflow: multi‑source data pre‑processing, Ecological Drought Index (EDI) construction via three‑dimensional Copula functions, EDI validation using matching rate and Spearman rank correlation tests, spatiotemporal drought identification, and risk‑uncertainty assessment adopting run theory and the MBCT‑SR inverse cloud model for the Yellow River Basin. Global warming increases drought frequency, worsening ecological challenges and requiring urgent assessment. Utilizing monthly data from the Yellow River Basin, this study constructed an Ecological Drought Index by coupling the Standardized Precipitation-Evapotranspiration Index, the Standardized Soil Moisture Index, and the Normalized Difference Vegetation Index via a three-dimensional Copula function. Furthermore, we applied run theory to analyse the ecological drought. We employed the MBCT-SR inverse cloud model for risk assessment to elucidate spatiotemporal patterns and uncertainty features. The results demonstrate the following: (1) The proposed index performs well in capturing ecological drought occurrences. It responds stably to asynchronous meteorological and soil droughts and detects vegetation water stress more sensitively. (2) Distinct spatiotemporal heterogeneity was observed in the YRB, with drought frequency peaking in winter and intensity increasing from the southeast to the northwest. (3) The Loess Plateau was identified as a critical high-risk zone by the MBCT-SR model, showing more pronounced stochasticity and fuzziness in drought evolution compared to other basin areas. In summary, this framework integrates multi-source monitoring and uncertainty-aware risk assessment, providing a useful reference for ecological conservation and drought management in the Yellow River Basin.