Spatial-temporal dynamics of meteorological and soil moisture drought on the Tibetan Plateau: Trend, response, and propagation process

•From spatiotemporal dimension to analyze drought propagation of SPEI to SSMI on the TP.•There is a lag time of 2–3 months from SPEI to SSMI and increases from summer to winter.•Climate, vegetation and permafrost type have an impact on drought propagation.•In winter, drought duration decreases in 45% of the TP after drought propagation, and drought severity decreases in 52%, particularly in the Inner TP.•The direction of propagation from SPEI to SSMI is predominantly northwest.