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 calculated TTDs that contribute to streamflow via spatially and temporally variable flow paths in a sub-humid mountain headwater catchment in Arizona, United States. Our results indicate that composite TTDs (a combination of Piston Flow and Gamma TTDs) most accurately represented this system for periods up to approximately 1 month, and that a Gamma TTD was most appropriate thereafter during both winter and summer seasons and for the overall time-weighted TTD; a Gamma TTD type was applicable for all periods during the dry season. The TTD results also suggested that old waters, i.e., beyond the applicable tracer range, represented approximately 3% of subsurface contributions to streamflow. For ETTD and using δ¹⁸O as a tracer in precipitation and xylem waters, a Gamma ETTD type best matched the observations for all seasons and for the overall time-weighted pattern, and stable water isotopes were effective tracers for the majority of vegetation source waters. This study addresses a fundamental question in mountain catchment hydrology; namely, how do the spatially and temporally varying subsurface flow paths that support catchment evapotranspiration and streamflow modulate water quantity and quality over space and time.