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Environmental heterogeneity is ubiquitous, but environmental systems areoften analyzed as if they were homogeneous instead, resulting in aggregationerrors that are rarely explored and almost never quantified. Here I usesimple benchmark tests to explore this general problem in one specificcontext: the use of seasonal cycles in chemical or isotopic tracers (such asCl−, δ18O, or δ2H) to estimate timescales ofstorage in catchments. Timescales of catchment storage are typicallyquantified by the mean transit time, meaning the average time that elapsesbetween parcels of water entering as precipitation and leaving again asstreamflow. Longer mean transit times imply greater damping of seasonaltracer cycles. Thus, the amplitudes of tracer cycles in precipitation andstreamflow are commonly used to calculate catchment mean transit times. HereI show that these calculations will typically be wrong by several hundredpercent, when applied to catchments with realistic degrees of spatialheterogeneity. This aggregation bias arises from the strong nonlinearity inthe relationship between tracer cycle amplitude and mean travel time. Ipropose an alternative storage metric, the young water fraction instreamflow, defined as the fraction of runoff with transit times of lessthan roughly 0.2 years. I show that this young water fraction (not to beconfused with event-based "new water" in hydrograph separations) isaccurately predicted by seasonal tracer cycles within a precision of a fewpercent, across the entire range of mean transit times from almost zero toalmost infinity. Importantly, this relationship is also virtually free fromaggregation error. That is, seasonal tracer cycles also accurately predictthe young water fraction in runoff from highly heterogeneous mixtures ofsubcatchments with strongly contrasting transit-time distributions. Thus,although tracer cycle amplitudes yield biased and unreliable estimates ofcatchment mean travel times in heterogeneous catchments, they can be usedto reliably estimate the fraction of young water in runoff

hydrology and earth system sciences

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