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

Water isotopes are a tool of choice for assessing
travel time distributions of water 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 con-
jecture 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
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 simula-
tions suggest that in the case of imperfect mixing, also the
average travel time becomes sensitive to the differences in
diffusion coefficients. We find that when advective trapping
occurs in low conductive zones, an isotope with a smaller dif-
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fusion 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 diffusion coefficient: deuterium
has the longest average travel time, followed by tritium, fol-
lowed by 18O. Depending on the type of simulated system,
we find differences in average travel times ranging from 10 d
to more than 2 years. As these differences are in relative
terms usually of order 5 %–10 %, one might erroneously ex-
plain them as measurement errors. Our findings suggest in-
stead that these relative differences are physics based and
may reach up to 50 % for strongly heterogeneous systems,
persisting and even growing 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.
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