Analyzing the propagation time and threshold from meteorological drought to groundwater drought is crucial for early groundwater drought warning. This study integrated meteorological station data, Gravity Recovery and Climate Experiment (GRACE) satellite data, and Global Land Data Assimilation System (GLDAS) data to construct the Standardized Precipitation Evapotranspiration Index (SPEI) and GRACE Groundwater Drought Index (GGDI) for the Haihe River Basin from 2002 to 2020. Using Copula functions and Bayesian conditional probability, we quantified the propagation time, risk, and thresholds of drought transition. The results show: (1) Validation showed strong agreement between GRACE-derived groundwater storage anomalies (GRACE-GWSA) and the WaterGAP Global Hydrology Model (WGHM)-GWSA (r=0.91, P＜0.01), as well as high correlations with observed groundwater data from two monitoring stations (r1=0.88, P＜0.01; r2=0.85, P＜0.01), confirming the reliability of GRACE-GWSA in this basin. (2) The average propagation time from meteorological to groundwater drought in the Haihe Basin was approximately 10 months, with significant spatial heterogeneity. In the western region, the propagation time primarily ranges from 1 to 3 months, while in the eastern region, it is predominantly between 21 and 24 months. (3) The triggering probability of groundwater drought under varying meteorological drought scenarios exhibited distinct spatial patterns, with higher risks in the southern basin and lower risks in the northwest. Severe and extreme meteorological droughts dominated the propagation thresholds for groundwater drought initiation. Notably, the required thresholds decreased progressively as groundwater drought severity intensified, highlighting cumulative drought impacts.