Uncertainty in water transit time estimation with StorAge Selection functions and tracer data interpolation

Abstract. Transit time distributions (TTDs) of streamflow are useful descriptors for understanding flow and solute transport in catchments. Catchment-scale TTDs can be modeled using tracer data (e.g. oxygen isotopes, such as δ18O) in inflow and outflows by employing StorAge Selection (SAS) functions. However, tracer data are often sparse in space and time, so they need to be interpolated to increase their spatiotemporal resolution. Moreover, SAS functions can be parameterized with different forms, but there is no general agreement on which one should be used. Both of these aspects induce uncertainty in the simulated TTDs, and the individual uncertainty sources as well as their combined effect have not been fully investigated. This study provides a comprehensive analysis of the TTD uncertainty resulting from 12 model setups obtained by combining different interpolation schemes for δ18O in precipitation and distinct SAS functions. For each model setup, we found behavioral solutions with satisfactory model performance for in-stream δ18O (KGE > 0.55, where KGE refers to the Kling–Gupta efficiency). Differences in KGE values were statistically significant, thereby showing the relevance of the chosen setup for simulating TTDs. We found a large uncertainty in the simulated TTDs, represented by a large range of variability in the 95 % confidence interval of the median transit time, varying at the most by between 259 and 1009 d across all tested setups. Uncertainty in TTDs was mainly associated with the temporal interpolation of δ18O in precipitation, the choice between time-variant and time-invariant SAS functions, flow conditions, and the use of nonspatially interpolated δ18O in precipitation. We discuss the implications of these results for the SAS framework, uncertainty characterization in TTD-based models, and the influence of the uncertainty for water quality and quantity studies.