Satellite remote sensing is commonly used to observe the hydrologic cycle at spatial scales ranging from river basins to the globe. Yet it remains difficult to obtain a balanced water budget using remote sensing data, which highlights the errors and uncertainties in earth observation (EO) data. Various methods have been proposed to correct EO datasets to make them more coherent, so that they result in a more balanced water budget. This study aimed to improve estimates of water budget components (precipitation, evapotranspiration, runoff, and total water storage change) at the global scale using the methods of optimal interpolation (OI) and neural network (NN) modeling. We trained a set of NNs on a set of 1,358 river basins and validated them on an independent set of 340 basins and in-situ observations of evapotranspiration and river discharge. We extended the models to make pixel-scale predictions in 0.5° grid cells for near-global coverage. Calibrated datasets result in lower water budget residuals in validation basins: the mean and standard deviation of the imbalance is 11 ± 44 mm/mo when calculated with uncorrected EO data and 0.03 ± 24 mm/mo after calibration by the NN models. This study suggests to data producers where corrections should be made to the EO datasets, and demonstrates the benefits of physically-driven NN models for studying the hydrologic cycle at the global scale.