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Hydrologic functions of catchments are intrinsically diverse, and defined as the ways catchments partition, store, and drain rainfall and snowmelt. Large-sample hydrology (LSH) uses existing datasets of catchments to derive generalizable conclusions on hydrologic behaviours. LSH has the potential to synthesize the diversity of catchment hydrologic functions, allowing a robust extrapolation of prediction of streamflow signatures to poorly-gauged regions. However, the descriptors of hydrologic functions, required to synthesize and extrapolate, have not been developed in LSH methodologies. This has potentially resulted in unexpectedly small associations between catchments’ physical features and streamflow characteristics as well as poor predictability at describing the shape of streamflow hydrographs, as shown in recent LSH studies. Here, we propose three dimensionless indices—which directly quantify hydrologic functions—based on how interactions between a catchments’ climatic and physical attributes construct catchment functions. Using climatic and physical data as well as long-term streamflow observations at hundreds of gauged catchments across the United States and Canada, our results depict the use of interactive functional indices as catchment descriptors improve the performance of LSH methodologies (hierarchical clustering, multivariate regression, and random forests) in identifying hydrologic (dis)similarities in shape-based streamflow signatures among catchments, and in predicting shape-based streamflow signatures in poorly-gauged regions. This research highlights the importance of physical interpretability of LSH models and showcases the development of parsimonious and process-based catchment-scale frameworks allowing the analysis of globally available catchment data to progress the generalizable understanding of catchment hydrologic functions.

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