Aggregation in environmental systems – Part 2: Catchment mean transit times and young water fractions under hydrologic nonstationarity

Abstract

Abstract. Methods for estimating mean transit times from chemical or isotopic tracers (such as Cl − , δ 18 O, or δ 2 H) commonly assume that catchments are stationary (i.e., timeinvariant) and homogeneous. Real catchments are neither. In a companion paper, I showed that catchment mean transit times estimated from seasonal tracer cycles are highly vulnerable to aggregation error, exhibiting strong bias and large scatter in spatially heterogeneous catchments. I proposed the young water fraction, which is virtually immune to aggregation error under spatial heterogeneity, as a better measure of transit times. Here I extend this analysis by exploring how nonstationarity affects mean transit times and young water fractions estimated from seasonal tracer cycles, using benchmark tests based on a simple two-box model. The model exhibits complex nonstationary behavior, with striking volatility in tracer concentrations, young water fractions, and mean transit times, driven by rapid shifts in the mixing ratios of fluxes from the upper and lower boxes. The transit-time distribution in streamflow becomes increasingly skewed at higher discharges, with marked increases in the young water fraction and decreases in the mean water age, reflecting the increased dominance of the upper box at higher flows. This simple two-box model exhibits strong equifinality, which can be partly resolved by simple parameter transformations. However, transit times are primarily determined by residual storage, which cannot be constrained through hydrograph calibration and must instead be estimated by tracer behavior.Seasonal tracer cycles in the two-box model are very poor predictors of mean transit times, with typical errors of several hundred percent. However, the same tracer cycles predict time-averaged young water fractions (F yw ) within a few percent, even in model catchments that are both nonstationary and spatially heterogeneous (although they may be biased by roughly 0.1-0.2 at sites where strong precipitation seasonality is correlated with precipitation tracer concentrations). Flow-weighted fits to the seasonal tracer cycles accurately predict the flow-weighted average F yw in streamflow, while unweighted fits to the seasonal tracer cycles accurately predict the unweighted average F yw . Young water fractions can also be estimated separately for individual flow regimes, again with a precision of a few percent, allowing direct determination of how shifts in a catchment's 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.

Aggregation in environmental systems – Part 1: Seasonal tracer cycles quantify young water fractions, but not mean transit times, in spatially heterogeneous catchments

“…The results presented here suggest that nonstationarity (which is, very loosely speaking, heterogeneity in time) is likely to create its own aggregation bias, in addition to the spatial aggregation bias identified here. This aggregation bias can also be characterized using benchmark tests, as I show in a companion paper (Kirchner, 2016).…”

“…One would expect F yw to increase under wetter conditions, as the water table rises into more permeable near-surface zones and as the flowing channel network extends to more finely dissect the landscape (Godsey and Kirchner, 2014), thus shortening the path length of subsurface flows as well as multiplying the wetted catch-ment area in riparian zones. In a companion paper (Kirchner, 2016), I show that young water fractions can be estimated separately for individual flow regimes, allowing one to infer how shifts in hydraulic forcing alter the fraction of streamflow that is generated via fast flowpaths. I further demonstrate how one can estimate the chemistry of "young water" and "old water" end-members, based on comparisons of F yw and solute concentrations across different flow regimes.…”

“…In fitting sinusoidal cycles to real-world data, robust estimation techniques such as iteratively reweighted least squares (IRLS) regression can help in limiting the influence of outliers. Also, because precipitation and streamflow rates vary through time, it may be useful to weight each tracer sample by its associated volume, for example to reduce the influence of small rainfall events (for more on the implications of volume-weighting, see Kirchner, 2016). An R script for performing volumeweighted IRLS is available from the author.…”

Aggregation effects on tritium-based mean transit times and young water fractions in spatially heterogeneous catchments and groundwater systems

“…We conducted our investigation by combining two dissimilar water components in virtual experiments and comparing the true mixed MTTs with the tritium-inferred apparent MTTs, as Kirchner (2016a) did with seasonal tracer cycles. Our experiments did not include examination of non-stationary hydrological systems, for which Kirchner (2016b) had found similar underestimation of MTTs with seasonal tracer cycles. We also examined aggregation effects for young water fractions estimated using tritium.…”

Nonparametric lower bounds to mean transit times

“…Kirchner (2016b) suggested that the young water fraction is robust against nonlinear effects when 20 considering seasonal amplitude differences. It may happen that * values are similarly robust but this would require further investigation.…”