Across ecosystems, soil water is replenished by precipitation events and depleted by evapotranspiration. Evapotranspiration is driven by solar radiation and the aerodynamic evaporative demand of the atmospheric boundary layer (E_aero). However, vegetation regulates the rate of transpiration through species-specific stomatal closure mechanisms that depend on tree water status, which in turn depends on the tree’s water supply and the atmospheric water demand. Therefore, quantifying the effects of precipitation, solar radiation and E_aero on tree-mediated water fluxes is challenging. Here we use ERRA, a framework for de-mixing and de-convolving non-stationary system responses to multiple inputs, to quantify how atmospheric forcing affects ecosystem water fluxes and water content dynamics in a mixed beech and spruce forest. The resulting impulse-response functions describe how soil and tree water fluxes respond to three atmospheric forcing (precipitation, solar radiation, E_aero). Water contents of soils and trees responded positively and rapidly to precipitation pulses, indicating fast infiltration of precipitation into the soil and net increases in tree water contents. Tree water contents responded more clearly to precipitation inputs than sapflow rates did, suggesting that precipitation primarily reduced transpiration rather than enhancing tree water uptake. Trees responded quickly and strongly to impulses of solar radiation, but their responses to E_aero were less distinct, potentially reflecting stomatal closure effects on transpiration. The impulse-response functions reflected species-specific water use strategies and differences in hydraulic capacitance of trees, which buffered root water uptake during periods of high transpiration demand and thus prolonged the refilling of tree water storage after precipitation events. Impulse responses to solar radiation and E_aero were much less distinct in the soils than in the trees, illustrating how forest canopies shield the underlying soils from atmospheric forcing. Our study highlights how impulse-response functions can help to identify soil-plant-atmosphere relations, complementing our understanding of forest ecosystem functioning in response to atmospheric forcing.