Under the background of global change, the threshold for the propagation of meteorological drought to hydrological drought is crucial for drought early warning and water resource management. However, traditional threshold studies often adopt subjective and fixed conditional probabilities and lack the revelation of the driving mechanisms under macroscopic natural geographical differentiation. This study integrates terrestrial water storage anomaly (TWSA) data derived from the Gravity Recovery and Climate Experiment (GRACE) and its Follow-On (GRACE-FO) mission, the standardized precipitation evapotranspiration index (SPEI), and multi-source environmental data to construct an objective threshold identification method based on Copula joint distribution and "system resilience loss", and combines explainable machine learning to systematically explore the critical threshold for meteorological drought, triggering a TWSA deficit and its driving mechanisms from the perspectives of three major natural regions, the Eastern Monsoon Region (EMR), the Northwestern Arid Region (NAR), and the Tibetan Plateau Region (TPR). The results show that: (1) from 2005 to 2024, the TWSA significantly decreased in nearly half of China's regions, with significant regional differentiation; (2) the response of the TWSA to meteorological drought has a significant lag (an average of 9-12 months), and shows a spatial pattern of slower in the east and faster in the northwest; (3) the probability of a TWSA deficit and the triggering threshold both have obvious grade dependence and spatial heterogeneity, with the lowest threshold in the northwest arid region, which is the most sensitive; (4) the threshold is driven by the synergy of multiple factors, with "water dominance and energy modulation", and the dominant factors show regional differentiation; and (5) irrigation agriculture significantly reduces the drought triggering threshold and exacerbates system vulnerability. This study provides a scientific basis for understanding the geographical differentiation laws of drought propagation and regional early warning management.