Rainfall-induced landslides pose a growing risk worldwide as climate change intensifies extreme rainfall events. To provide sufficient evacuation time, landslide early warning systems (LEWS) for real-time disaster monitoring must estimate near-future landslide risk by integrating observed rainfall with short-term rainfall forecasts from spatio-temporal environmental data streams. Although recent landslide prediction methods have improved predictive performance using statistical and deep learning approaches, most assume accurate rainfall inputs. In operational settings, however, landslide prediction relies on rainfall forecasts, which often contain spatial displacement of rainfall fields due to forecasting uncertainties. Such displacement can alter local accumulated rainfall and degrade prediction accuracy. To address this challenge, we propose a novel LEWS robust to rainfall field displacement. The key idea is to learn latent representations from rainfall and terrain data that remain stable under displacement in rainfall field motion, enabling reliable geospatial data integration for landslide risk estimation. The landslide prediction model is trained using Rainfall-Motion-Aware Contrastive Learning (RMCL), which introduces temporally correlated rainfall field perturbations to emulate forecast-induced displacement in rainfall-driven spatio-temporal environmental data streams. Experiments were conducted using two years of rainfall and terrain data across Japan, covering 19 regions with landslide events. The proposed system achieved up to 37% higher precision than state-of-the-art baselines. These results demonstrate that modeling rainfall as a moving spatial field and addressing rainfall field displacement during learning significantly improve the reliability of short-term landslide prediction in operational early warning systems.