The Budyko hypothesis provides a first-order estimate of water partitioning into runoff (Q) and evapotranspiration (E). Observations, however, often show significant departures from the Budyko curve; moreover, past improvements to Budyko curve tend to lose predictive power when migrated between regions or to small scales. Here, to estimate departures from the Budyko curve, we use hydrologic signatures extracted from Gravity Recovery And Climate Experiment (GRACE) terrestrial water storage anomalies. The signatures include GRACE amplitude as a fraction of precipitation (A/P), inter-annual variability, and 1-month-lag auto-correlation. We created a group of linear models embodying two alternate hypotheses that departures can be predicted by (a) Taylor series expansion based on deviation of physical characteristics (seasonality, snow fraction and vegetation index) from reference conditions; and (b) surrogate indicators co-varying with E, e.g., A/P. These models are fitted using a mesoscale USA dataset (HUC4) and then evaluated using world datasets and USA basins <1×10⁵ km². The model with A/P could reduce error by 50% compared to Budyko itself. We found that seasonality and fraction of precipitation as snow account for a major portion of the predictive power of A/P, while the remainder is attributed to unexplained basin characteristics. When migrated to a global dataset, type (b) models performed better than type (a). This contrast in transferability is argued to be due to dataset limitations and catchment co-evolution. The GRACE-base correction performs well for USA basins >1000 km² and, according to comparison with other global datasets, is suitable for data fusion purposes, with GRACE error as estimates of uncertainty. This article is protected by copyright. All rights reserved.