Multiscale Non-Linear Responses of Spatial Rainfall Distribution to Topographic Factors in Huairou District, Beijing

Mountainous rainfall exhibits strong spatial heterogeneity associated with topographic effects. Understanding modulating patterns and non-linear responses of rainfall to terrain factors supports mountain storm-disaster mitigation. Taking the Yanshan Mountains in Huairou (Beijing) as the study area, we divided the region by watershed divides into northern and southern zones. Elevation, slope, and sine-cosine transformed aspect served as independent variables, while annual, flood-season, maximum-daily, and maximum-3-day extreme rainfall were dependent variables. We applied Kriging interpolation, quadratic-polynomial ordinary least-squares (OLS), multiscale geographically weighted regression (MGWR), and XGBoost-SHAP to characterize terrain-rainfall statistical associations from global-linear, spatial-non-stationary, and non-linear empirical transition perspectives. Elevation and slope dominated rainfall spatial patterns, whereas aspect exerted minor local modulation. Southern rainfall generally corresponds to higher values with rising elevation, while northern rainfall presented a U-shaped non-linear elevation response. Extreme rainfall was more sensitive to slope than routine rainfall; empirical transition-response features lie at 700–800 m elevation and 20° slope. Multi-model coupling mitigated single-model limitations and provides references for extreme-precipitation understanding and geohazard risk assessment in the North China Yanshan Mountains.