Stable water isotopes and tritium tracers tell the same tale: no evidence for underestimation of catchment transit times inferred by stable isotopes in StorAge Selection (SAS)-function models
Authors: Wang Siyuan , Hrachowitz Markus , Schoups Gerrit , Stumpp Christine 
Published: August 2023

Abstract. Stable isotopes (δ18O) and tritium (3H)
are frequently used as tracers in environmental sciences to estimate 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 in
exacerbating the underestimation of water ages. This was done by comparing
water age distributions inferred from δ18O and 3H with a
total of 21 different model implementations, including time-invariant,
lumped-parameter sine-wave (SW) and convolution integral (CO) models as well
as StorAge Selection (SAS)-function models (P-SAS) and 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 (MTTs) of
∼ 1–2 years substantially lower than those obtained from
3H with the same models, reaching MTTs of ∼10 years. In
contrast, several implementations of P-SAS and IM-SAS models not only
allowed simultaneous representations of storage variations and streamflow as
well as δ18O and 3H stream signals, but water ages
inferred from δ18O with these models were, with MTTs of
∼ 11–17 years, also much higher and similar to those inferred
from 3H, which suggested MTTs of ∼ 11–13 years. Characterized by similar parameter posterior distributions, in particular
for parameters that control water age, P-SAS and 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 and in the temporal variability of transit time distributions (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 largely be attributed to choices of model approaches and complexity not
considering transient hydrological conditions next to tracer aspects. Given
the additional vulnerability of time-invariant, lumped 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 avoiding the use of this model
type in combination with seasonally variable tracers if possible and
instead adopting SAS-based models or time-variant formulations of CO models.