The spatial-temporal variations of rainfall-streamflow linkage across North America: A functional data analysis approach

Achieving improved predictions in ungauged-basins or inferring the effects of climate and land-use changes on streamflow requires hydrologists to first learn the underlying mechanisms behind streamflow generation in gauged-basins. One way to characterize streamflow generation is by quantifying how catchments filter rainfall into streamflow. A simple and popular technique that displays the rainfall-streamflow linkage is the unit hydrograph. Though one could characterize and classify catchments based on their unit hydrographs, this approach implicitly implies that the function and response-time that link rainfall to streamflow are time-invariant. The celerity, and the function that links rainfall to streamflow in a given catchment, could vary from catchment to catchment as well as from season to season. This is primarily due to variations in antecedent wetness, temperature, vegetation transpiration and the ways climatic factors interact with biophysical factors, over time and over space. In this study, we utilize sparse historical functional linear models to quantify the time-variant rainfall-streamflow response function, across hundreds of catchments in North America. The function reflects the temporally varying relationship between rainfall and streamflow and can be used to infer temporally varying response times. We then attempt to relate catchment characteristics such geology, climate, and topography to the characteristics of rainfall-streamflow response function and response time, spatially and temporally.  We argue that our study extracts generalizable and robust process understanding in a novel data-driven manner.