The Unconstrainable Tails of Catchment Transit Time Distributions

Water transit times are key indicators of how catchments store and release water, as well as tracers and contaminants. Water exiting a catchment is characterized by a transit time distribution (TTD), which reflects the variability of flow paths and the mixing of individual water parcels before reaching the stream. Since TTDs cannot be measured directly, they are typically inferred from time series of tracers in precipitation and streamflow. However, not all water carries the same information, as streamflow TTDs usually consist of a narrow range of young waters that contribute significantly to streamflow, while a much broader range of older waters accounts for only a small stream water fraction. The concern is that the tracer signal from these older waters may be masked by measurement uncertainties, making it difficult to accurately capture the right tail of the transit time distribution and thus to determine the age of the oldest waters in streamflow. Previous studies suggest that seasonally variable tracers such as oxygen-18 (¹⁸O) cannot help inferring water ages beyond 4–5 years, whereas tritium (³H) may extend this limit up to 100 years. However, these results rely on limited theoretical evidence, which calls for more in-depth investigation.

In this study, we investigate the maximum age up to which the shape of the transit time distribution can be reliably constrained before the signal of the oldest waters becomes completely hidden among measurement uncertainties. Our analysis covers a wide range of typical transit time distribution shapes and two key tracers: ¹⁸O and ³H. Our results indicate that water with transit times longer than 1–3 years does not typically produce detectable variations in the ¹⁸O signal, while for ³H, this limit extends further, but unlikely beyond 10 years. This suggests that the maximum age that can be accurately estimated using these tracers is significantly lower than previously assumed. Furthermore, we show that this age limit has important implications for estimating mean transit times, as the tail of the transit time distribution strongly influences this metric. Our findings highlight the need for a more cautious interpretation of TTD tails and encourages the use of alternative statistics beyond mean transit times to characterize TTDs across catchments.