On the relevance of molecular diffusion for travel time distributions inferred from different water isotopes

Abstract. Water isotopes are a tool of choice for assessing travel time distributions of water and chemical species in soils, aquifers and rivers. However, the question of whether different water isotopes tag the same travel time distributions of the water molecule, or whether the inferred travel time distribution is specific to the chosen water isotope, remains under debate. Here we conjecture that the latter is correct. We state that (a) travel time distributions of water and any tracer reflect the spectrum of fluid velocities and diffusive/dispersive mixing between the flow lines connecting the system in- and outlet, and (b) the self-diffusion coefficients of deuterium, tritium and ¹⁸O differ by as much as 10 %. Using particle tracking simulations, we show that these differences do indeed affect the variance of the travel time distribution – as one would expect for well-mixed advective-dispersive transport. Moreover, our simulations suggest that in the case of imperfect mixing, also the average travel time becomes sensitive to the differences in self-diffusion coefficients. We find that when advective trapping occurs in low conductive zones, an isotope with a smaller diffusion coefficient remains there for longer times compared to a substance exhibiting faster diffusion. This implies that for imperfectly mixed transport, average transit times ultimately increase with a decreasing self-diffusion coefficient: deuterium has the longest average travel time, followed by tritium, followed by ¹⁸O. Depending on the type of simulated system, we find differences in average travel times ranging from 10 days to more than 2 years. As these differences are in relative terms of order 5–10 %, one could be tempted to erroneously explain them as measurement errors. Our findings suggest instead that these differences are physics based. These differences persist and even grow with increasing space and time scales, rather than being averaged out. We thus conclude that travel time distributions inferred from O-H isotopes of the water molecule are conditioned by the chosen water isotope.