Quantifying and monitoring terrestrial water storage (TWS) is an essential task for understanding the Earth's hydrosphere cycle, its susceptibility to climate change, and concurrent impacts for ecosystems, agriculture, and water management. Changes in TWS manifest as anomalies in the Earth's gravity field, which are routinely observed from space. However, the complex underlying distribution of water masses in rivers, lakes, or groundwater basins remains elusive. We combine machine learning, numerical modeling, and satellite altimetry to build a downscaling neural network that recovers simulated TWS from synthetic space-borne gravity observations. A novel constrained training is introduced, allowing the neural network to validate its training progress with independent satellite altimetry records. We show that the neural network can accurately derive the TWS in 2019 after being trained over the years 2003 to 2018. Further, we demonstrate that the constrained neural network can outperform the numerical model in validated regions.
