Tracer Cycles and Water Ages in Heterogeneous Catchments and Aquifers

Estimates of catchment mean transit times are often based on seasonal cycles of stable isotope tracers in precipitation and streamflow. In many cases these transit time estimates are derived directly from sine-wave fitting to the observed seasonal isotope cycles. Broadly similar results are also obtained from time-domain convolutions or explicit tracer modeling, because here too the dominant tracer signal that these techniques seek to match is the seasonal isotopic cycle. Here I use simple benchmark tests to show that estimates of mean transit times based on seasonal tracer cycles will typically be wrong by several hundred percent, when applied to catchments with realistic degrees of spatial heterogeneity. This aggregation bias arises from the strong nonlinearity in the relationship between tracer cycle amplitude and mean travel time. A similar bias arises in estimates of mean transit times in nonstationary catchments. Since typical real-world catchments are both spatially heterogeneous and nonstationary, this analysis poses a fundamental challenge to tracer-based estimates of mean transit times. I propose an alternative storage metric, the fraction of "young water" in streamflow, defined as the fraction of runoff with transit times of less than roughly 0.2 years. I show that young water fractions are virtually free of aggregation bias; that is, they can be accurately estimated from tracer cycles in highly heterogeneous mixtures of subcatchments with strongly contrasting transit time distributions. They can also be reliably estimated in strongly nonstationary catchments. Young water fractions can be estimated separately for individual flow regimes, allowing direct determination of how shifts in hydraulic regime alter the fraction of water reaching the stream by fast flowpaths. One can also estimate the chemical composition of idealized "young water" and "old water" end-members, using relationships between young water fractions and solute concentrations across different flow regimes. These results demonstrate that mean transit times cannot be estimated reliably from seasonal tracer cycles, and that, by contrast, the young water fraction is a robust and useful metric of transit times, even in catchments that exhibit strong nonstationarity and heterogeneity.