We investigate the observed positive trends in annual runoff in several basins in central Nebraska using the Budyko hypothesis as a diagnostic tool. In basins where runoff is dominated by base flow we found that the estimated annual evapotranspiration (ETa) to precipitation (P) ratio (ETa/P) from data is negatively related to the aridity index (ETp/P, where ETp is potential annual evapotranspiration). This observation is inconsistent with the Budyko hypothesis. We hypothesized that the observed negative trend results from significant interannual changes in basin water storage. This hypothesis is tested using data from groundwater monitoring wells in the Sand Hills region of Nebraska. Plots of the yearly changes in groundwater storage versus the annual aridity index revealed the mean annual aridity index as a critical climatological variable that controls basin storage gain-loss dynamics. For the same absolute deviation from the mean climate, we found that a wetter year leads to a larger gain in groundwater storage than the net loss in a drier year. We argue that this storage gain-loss behavior builds a climate memory in the hydrologic system, causing persistence and statistically significant trends in annual runoff. A parsimonious model was developed that couples the Budyko hypothesis with a linear reservoir equation for base flow and was used to examine the possible causes of observed positive trends of annual runoff. We found that subtle, statistically insignificant, increases in annual P have led to positive and statistically insignificant trends in annual ETa and P − ETa. Annual runoff, on the other hand, was predicted to have high persistence and statistical significance, consistent with observations. Further model sensitivity analyses showed that increasing the size of the groundwater reservoir is associated with increased long-term (multidecadal) persistence in annual runoff and translates high-frequency, high-amplitude variation in climate to low-frequency, low-amplitude runoff response. Our results underscore the importance of evaluating apparent trends in any system variable in a complete water budget context.