Study region: The headwaters region of the Kriya River in the inland river basins of arid Northwest China. Study focus: Using remote sensing and observed runoff data (2001-2019), this study applied STL decomposition and trend tests to assess multi-timescale variations in precipitation, air and land surface temperature, snow cover, soil moisture, and runoff. A physically-constrained SVAR model was subsequently constructed to discern driving mechanisms through impulse response and Forecast Error Variance Decomposition (FEVD) analyses. New hydrological insights for the region: From 2001-2019, precipitation showed a weak increasing trend (Sen's (3 = 0.078, p = 0.484) while runoff declined slightly (Sen's (3 =-0.074, p = 0.441). Land surface and air temperatures decreased marginally; soil moisture and snow cover showed no significant trends. Precipitation dominated short-term runoff variability, accounting for 15.2% in the first period. Snow cover produced a lagged accumulation release effect that increasingly influenced medium-to long-term runoff. By period eight, air temperature together with land surface temperature explained 18.27% of runoff variance, reflecting energy control on snowmelt and release dynamics. The proposed framework, merging physical constraints, STL, SVAR responses, and FEVD, offers precise lag resolution and causal runoff diagnosis. It provides quantitative guidance for improving runoff forecasting, snowmelt management, and climate adaptation in cold, arid alpine headwaters. Its methodology is adaptable to other similar basins, supporting model calibration and water resource planning.