Increasingly accurate, and spatio-temporally dense, measurements of Earth surface movements enable us to identify multiple deformation patterns and highlight the need to properly characterize the related source processes. This is particularly important in tectonically active areas, where deformation measurement is crucial for monitoring ongoing processes and assessing future hazard. Long Valley Caldera, California, USA, is a volcanic area where frequent episodes of unrest involve inflation and increased seismicity. Ground- and satellite-based instruments show that volcanic inflation renewed in 2011, and is continuing as of early 2021. Additionally, Long Valley Caldera is affected by the large, but spatially and temporally variable, amounts of precipitation falling on the adjacent Sierra Nevada Range. The density and long duration of deformation measurements at Long Valley Caldera provide an excellent collection of data to decompose time-series and separate multiple superimposed deformation sources. We analyze Global Navigation Satellite System (GNSS) time-series and apply variational Bayesian Independent Component Analysis (vbICA) decomposition method to isolate inflation-related signals from other processes. We show that hydrological forcing causes significant horizontal and vertical deformation at different temporal (seasonal and multiyear) and spatial (few to hundreds of km) scales that cannot be ignored while analyzing and modeling the tectonic signal. Focusing on the last inflation episode, we then improve on prior simplistic models of the inflation reservoir by including heterogeneous subsurface material properties and topography. Our results suggest the persistence and stability of the reservoir (prolate ellipsoid at about 8 km beneath the resurgent dome) and indicate a 40-50% reduction of the inflation rate after about 3 years from the inflation onset. The onset of the reduced inflation rate corresponded in time with the occurrence of a strong seismic swarm in the Caldera, but also to the temporal variation of climatic conditions in the area.