Supplementary material to "Catchments do not strictly follow Budyko curves over multiple decades but deviations are minor and predictable"

Abstract. Quantification of precipitation partitioning into evaporation and runoff is crucial for predicting future water availability. Within the widely used Budyko Framework, which relates the long-term aridity index to the long-term evaporative index, curvilinear relationships between these indices (i.e., parametric Budyko curves) allow for the quantification of precipitation partitioning under prevailing climatic conditions. A movement along a Budyko curve with changes in the climatic conditions has been used as a predictor for catchment behaviour under change. However, various studies have reported deviations around these curves, which raises questions about the usefulness of the method for future predictions. To investigate whether parametric Budyko curves still have predictive power, we quantified the global, regional, and local evolution of deviations of catchments from their parametric Budyko curves over multiple subsequent 20-year periods throughout the last century, based on historical long-term water balance data from over 2000 river catchments worldwide. This process resulted in up to four 20-year distributions of annual deviations from the long-term mean parametric curve for each catchment. To use these distributions of deviations to predict future deviations, the temporal stability of these four distributions of deviations was evaluated between subsequent periods of time. On average, it was found that the majority of 62 % of study catchments did not significantly deviate from their expected parametric Budyko curves. From the remaining 38 % of catchments that deviated from their expected curves, the long-term magnitude of median deviations remains minor, with 70 % of catchments falling within the range of ±0.025 of the expected evaporative index. Furthermore, a significant majority of catchments, constituting around the same percentage, were found to have stable distributions of deviations across multiple time periods, making them well-suited to statistically predict future deviations with high predictive power. These findings suggest that while trajectories of change in catchments do not strictly follow the expected long-term mean parametric Budyko curves, the deviations are minor and quantifiable. Consequently, taking into account these deviations, the parametric formulations of the Budyko Framework remain a valuable tool for predicting future evaporation and runoff under changing climatic conditions, within quantifiable margins of error.