A long-standing challenge for hydrologists has been a lack of observational data on global-scale basin hydrological behavior. With observations from NASA's Gravity Recovery and Climate Experiment (GRACE) mission, hydrologists are now able to study terrestrial water storage for large river basins (>200,000 km2), with monthly time resolution. Here we provide results of a time series model of basin-averaged GRACE terrestrial water storage anomaly and Global Precipitation Climatology Project precipitation for the world's largest basins. We address the short (10 year) length of the GRACE record by adopting a parametric spectral method to calculate frequency-domain transfer functions of storage response to precipitation forcing and then generalize these transfer functions based on large-scale basin characteristics, such as percent forest cover and basin temperature. Among the parameters tested, results show that temperature, soil water-holding capacity, and percent forest cover are important controls on relative storage variability, while basin area and mean terrain slope are less important. The derived empirical relationships were accurate (0.54 ≤ Ef
≤ 0.84) in modeling global-scale water storage anomaly time series for the study basins using only precipitation, average basin temperature, and two land-surface variables, offering the potential for synthesis of basin storage time series beyond the GRACE observational period. Such an approach could be applied toward gap filling between current and future GRACE missions and for predicting basin storage given predictions of future precipitation.