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Current understanding of the dynamic and slow flow paths that support streamflow in mountain headwater catchments is inhibited by the lack of long-term hydrogeochemical data and the frequent use of short residence time age tracers. To address this, the current study combined the traditional mean transit time and the state-of-the-art fraction of young water ( F yw ) metrics with stable water isotopes and tritium tracers to characterize the dynamic and slow flow paths at Marshall Gulch, a sub-humid headwater catchment in the Santa Catalina Mountains, Arizona, USA. The results show that F yw varied significantly with period when using sinusoidal curve fitting methods (e.g., iteratively re-weighted least squares or IRLS), but not when using the transit time distribution (TTD)-based method. Therefore, F yw estimates from TTD-based methods may be particularly useful for intercomparison of dynamic flow behavior between catchments. However, the utility of 3 H to determine F yw in deeper groundwater was limited due to both data quality and inconsistent seasonal cyclicity of the precipitation 3 H time series data. Although a Gamma-type TTD was appropriate to characterize deep groundwater, there were large uncertainties in the estimated Gamma TTD shape parameter arising from the short record length of 3 H in deep groundwater. This work demonstrates how co-application of multiple metrics and tracers can yield a more complete understanding of the dynamic and slow flow paths and observable deep groundwater storage volumes that contribute to streamflow in mountain headwater catchments. 

We confirm that energy dissipation weighting provides the most accurate approach to determining the effective hydraulic conductivity (Keff) of a binary K grid. A deep learning algorithm (UNET) can infer Keff with extremely high accuracy (R2 > 0.99). The UNET architecture could be trained to infer the energy dissipation weighting pattern from an image of the K distribution, although it was less accurate for cases with highly localized structures that controlled flow. Furthermore, the UNET architecture learned to infer the energy dissipation weighting even if it was not trained directly on this information. However, the weights were represented within the UNET in a way that was not immediately interpretable by a human user. This reiterates the idea that even if ML/DL algorithms are trained to make some hydrologic predictions accurately, they must be designed and trained to provide each user-required output if their results are to be used to improve our understanding of hydrologic systems. 

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.