Stable water isotopes and tritium tracers tell the same tale: No evidence for underestimation of catchment transit times inferred by stable isotopes in SAS function models

Abstract. Stable isotopes (δ¹⁸O) and tritium (³H) are frequently used as tracers in environmental sciences to estimate the age distributions of water. However, it has previously been argued that seasonally variable tracers, such as δ¹⁸O, generally and systematically fail to detect the tails of water age distributions and therefore substantially underestimate water ages as compared to radioactive tracers, such as ³H. In this study for the Neckar river basin in central Europe and based on a >20-year record of hydrological, δ¹⁸O, and ³H data, we systematically scrutinized the above postulate together with the potential role of spatial aggregation effects to exacerbate the underestimation of water ages. This was done by comparing water age distributions inferred from δ¹⁸O and ³H with a total of 12 different model implementations, including lumped parameter sine-wave (SW) and convolution integral models (CO) as well as integrated hydrological models in combination with SAS-functions (IM-SAS). We found that, indeed, water ages inferred from δ¹⁸O with commonly used SW and CO models are with mean transit times (MTT) ~ 1–2 years substantially lower than those obtained from ³H with the same models, reaching MTTs ~ 10 years. In contrast, several implementations of IM-SAS models did not only allow simultaneous representations of stream flow as well as δ¹⁸O and ³H stream signals, but water ages inferred from δ¹⁸O with these models were with MTTs ~ 16 years much higher than those from SW and CO models and similar to those inferred from ³H, which suggested MTTs ~ 15 years. Characterized by similar parameter posterior distributions, in particular for parameters that control water age, IM-SAS model implementations individually constrained with δ¹⁸O or ³H observations, exhibited only limited differences in the magnitudes of water ages in different parts of the models as well as in the temporal variability of TTDs in response to changing wetness conditions. This suggests that both tracers lead to comparable descriptions of how water is routed through the system. These findings provide evidence that allowed us to reject the hypothesis that δ¹⁸O as a tracer generally and systematically “cannot see water older than about 4 years” and that it truncates the corresponding tails in water age distributions, leading to underestimations of water ages. Instead, our results provide evidence for a broad equivalence of δ¹⁸O and ³H as age tracers for systems characterized by MTTs of at least 15–20 years. The question to which degree aggregation of spatial heterogeneity can further adversely affect estimates of water ages remains unresolved as the lumped and distributed implementations of the IM-SAS model provided inconclusive results.

Overall, this study demonstrates that previously reported underestimations of water ages are most likely not a result of the use of δ¹⁸O or other seasonally variable tracers per se. Rather, these underestimations can be largely attributed to choices of model approaches and complexity not considering hydrological next to tracer aspects. Given the additional vulnerability of SW and CO model approaches in combination with δ¹⁸O to substantially underestimate water ages due to spatial aggregation and potentially other, still unknown effects, we, therefore, advocate to avoid the use of this model type in combination with seasonally variable tracers if possible, and to instead adopt SAS-based or comparable model formulations.