Abstract
Abstract. Decades of hydrograph separation studies have estimated the proportions of recent precipitation in streamflow using end-member mixing of chemical or isotopic tracers. Here I propose an ensemble approach to hydrograph separation that uses regressions between tracer fluctuations in precipitation and discharge to estimate the average fraction of new water (e.g., same-day or same-week precipitation) in streamflow across an ensemble of time steps. The points comprising this ensemble can be selected to isolate conditions of particular interest, making it possible to study how the new water fraction varies as a function of catchment and storm characteristics. Even when new water fractions are highly variable over time, one can show mathematically (and confirm with benchmark tests) that ensemble hydrograph separation will accurately estimate their average. Because ensemble hydrograph separation is based on correlations between tracer fluctuations rather than on tracer mass balances, it does not require that the end-member signatures are constant over time, or that all the end-members are sampled or even known, and it is relatively unaffected by evaporative isotopic fractionation. Ensemble hydrograph separation can also be extended to a multiple regression that estimates the average (or “marginal”) transit time distribution (TTD) directly from observational data. This approach can estimate both “backward” transit time distributions (the fraction of streamflow that originated as rainfall at different lag times) and “forward” transit time distributions (the fraction of rainfall that will become future streamflow at different lag times), with and without volume-weighting, up to a user-determined maximum time lag. The approach makes no assumption about the shapes of the transit time distributions, nor does it assume that they are time-invariant, and it does not require continuous time series of tracer measurements. Benchmark tests with a nonlinear, nonstationary catchment model confirm that ensemble hydrograph separation reliably quantifies both new water fractions and transit time distributions across widely varying catchment behaviors, using either daily or weekly tracer concentrations as input. Numerical experiments with the benchmark model also illustrate how ensemble hydrograph separation can be used to quantify the effects of rainfall intensity, flow regime, and antecedent wetness on new water fractions and transit time distributions.
Highlights
For nearly 50 years, chemical and isotopic tracers have been used to quantify the relative contributions of different water sources to streamflow following precipitation events (Pinder and Jones, 1969; Hubert et al, 1969); see reviews by Buttle (1994) and Klaus and McDonnell (2013), and references therein
Different catchment parameters and different precipitation forcings yield different patterns in the relationships between the new water fractions Qp Fnew and PFnew on the one hand and precipitation and discharge on the other. These patterns are accurately quantified by ensemble hydrograph separation, which matches the age-tracking www.hydrol-earth-syst-sci.net/23/303/2019/
Light blue and light green lines show the corresponding true new water fractions measured by age tracking in the benchmark model
Summary
For nearly 50 years, chemical and isotopic tracers have been used to quantify the relative contributions of different water sources to streamflow following precipitation events (Pinder and Jones, 1969; Hubert et al, 1969); see reviews by Buttle (1994) and Klaus and McDonnell (2013), and references therein. As reviewed by Klaus and McDonnell (2013), chemical and isotopic hydrograph separation studies have led to many important insights into runoff generation Foremost among these has been the realization that even at stormflow peaks, stream discharge is often composed primarily of “old” catchment storage rather than “new” recent precipitation (Sklash et al, 1976; Sklash, 1990; Neal and Rosier, 1990; Buttle, 1994). Isotope hydrograph separations showed that this intuition is often wrong, because the isotopic signatures of stormflow often resemble baseflow or groundwater rather than recent precipitation These observations have overthrown the previous dominant paradigm, and launched decades of research aimed at unraveling the paradox of how catchments store water for weeks or months, but release it within minutes following the onset of rainfall (Kirchner, 2003)
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