The long-term safety of shallow disposal facility for short-lived low and intermediate level nuclear waste (LLW/ILW) relies on the performance of engineered barriers (caps and liners). Soil-atmosphere interaction may affect the capping material at shallow depths, due to changes of its coupled hydro-thermal-mechanical behavior under the effect of atmospheric conditions. This study aims to investigate the soil-atmosphere interaction at different time scales in the overburden of an LLW/ILW disposal facility, located in middle France. Actual meteorological data from Valencia El Saler station in Spain, including solar radiation, air temperature, latent heat, rainfall, and actual evaporation, at four different time scales (30 min, daily, weekly and monthly), were applied as the future climate conditions of the studied area based on climate analogues. A numerical approach combining a coupled hydro-thermal model and a soil-atmosphere interaction model was employed. Results show that the employment of meteorological data at a short time scale (30 min) can increase the simulation accuracy by capturing the rainfall events and accelerating the soil-atmosphere interactions. Furthermore, the effect of future climate conditions in the long-term (7 years) on soil hydro-thermal behavior was examined. This study allows a further detailed inspection of the climate’s role in the LLW/ILW storage system.