The Budyko hypothesis provides a reference condition of water balance and describes an empirical relationship between precipitation (P), evapotranspiration (E) and potential evapotranspiration (Ep). However, real-world catchments often deviate significantly from the theoretical Budyko curve. Recent advances of understanding in the impacts of seasonal water balances on long-term averaged water balance showed that phase difference between P and Ep is a major cause of downward departure from the Budyko curve. The phase difference and its processing by the catchments are in fact recorded over the globe in the form of Gravity Recovery and Climate Experiment satellite (GRACE) terrestrial water storage anomalies (TWSA). Here we present a GRACE-assisted Budyko-type formula that has improved predictive accuracy for long term E/P using the aridity index and storage patterns. We established an error model for the residual between Turk-Pike form of the Budyko curve and the observed E, based on a seamless United States basin water balance dataset. We found that the error model could improve the prediction efficiency by more than 60% comparing to Budyko model. The form of the error model was supported by Monte Carlo analysis. We compared the results with NLDAS predict E and found that the GRACE-corrected formula are in closer agreement with NLDAS than that without GRACE correction. In addition, we apply this error model to the whole world and global E was predicted. By comparing with other E products we found this error model can correct Budyko curve effectively.