Identification of the Non-Stationarity of Meteorological Drought in the Yellow River Basin and Assessment of the Applicability of the GAMLSS Model

Taking the Yellow River Basin (YRB) as an example, this study explores the non-stationary drought evolution features in large river basins under climate change. This study utilized precipitation and multiple climate factor data to establish the non-stationary standardized precipitation index (NSPI) through the GAMLSS model. Combined with the run theory, Copula function and a cascaded RF-LSTM machine learning model, the drought characteristics and retrospective predictive patterns were systematically assessed. The results show that: (1) The Arctic Oscillation, the Pacific Decadal Oscillation, the Southern Oscillation and the North Pacific Index are the primary climate drivers of non-stationary precipitation variation in the YRB, with the former three being selected most frequently and NPI additionally influencing April–June and September, and their effects are both different and lagging. Compared with the traditional SPI, the NSPI assigned higher drought grades and greater severity to typical drought years (e.g., the 1974 event was rated D3 with a severity of 17.935 by NSPI versus D2 with 11.733 by SPI), and thus better captured non-stationary drought evolution. (2) The duration of droughts exhibited a decreasing trend that was not statistically significant ( p > 0.05), whereas drought intensity and severity decreased significantly ( p < 0.05); the peak severity showed a significant upward trend ( p = 0.0078). Spatially, the northwest of the Loess Plateau was a compound core area with high severity, high frequency and long duration of droughts, while the upper reaches were mainly characterized by low severity, short duration and sudden droughts. (3) The drought risk in the YRB shows a higher frequency in the lower reaches and a lower frequency in the upper reaches. The middle and lower reaches were high-risk areas, with shorter AND-type joint exceedance return periods for moderate drought (2.46–5.83 years) and severe drought (3.77–9.15 years). The upper reaches were low-risk areas, with longer return periods reaching up to 5.83 years for moderate drought and 9.15 years for severe drought. The study shows that the NSPI, considering the driving of multiple climate factors, can more effectively identify and assess non-stationary drought risks, providing a scientific basis for drought prevention and control in river basins.