An improved practical approach for estimating catchment‐scale response functions through wavelet analysis

Catchment-scale response functions, such as transit time distribution (TTD) and evapotranspiration time distribution (ETTD), are considered fundamental descriptors of a catchment’s hydrologic and ecohydrologic responses to spatially and temporally varying precipitation inputs. Yet, estimating these functions is challenging, especially in headwater catchments where data collection is complicated by rugged terrain, or in semi-arid or sub-humid areas where precipitation is infrequent. Hence, we developed practical approaches for estimating both TTD and ETTD from commonly available tracer flux data in hydrologic inflows and outflows without requiring continuous observations. Using the weighted wavelet spectral analysis method of Kirchner and Neal [2013] for δ18O in precipitation and stream water, we specifically calculated TTDs that contribute to streamflow via spatially and temporally variable flow paths in a sub-humid mountain headwater catchment in Arizona, USA. Our results indicate that composite TTDs most accurately represented this system for periods up to approximately one month and that a Gamma TTD was most appropriate thereafter. The TTD results also suggested that some contribution of subsurface water was beyond the applicable tracer range. For ETTD and using δ18O as a tracer in precipitation and xylem waters, a Gamma ETTD type best matched the observations, and stable water isotopes were capable tracers for the majority of vegetation source waters. This study contributes to a better understanding of a fundamental question in mountain catchment hydrology; namely, how tracer input fluxes are modulated by spatially and temporally varying subsurface flow paths that support evapotranspiration and streamflow at multiple time scales.