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Discussion papers | Copyright
https://doi.org/10.5194/hess-2018-429
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 27 Aug 2018

Research article | 27 Aug 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Quantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark tests

James Kirchner James Kirchner
  • 1Dept. of Environmental Systems Science, ETH Zurich, 8092 Zürich, Switzerland
  • 2Swiss Federal Research 5 Institute WSL, 8903 Birmensdorf, Switzerland
  • 3Dept. of Earth and Planetary Science, University of California, Berkeley, CA, 94720, USA

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 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. It 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.

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Short summary
How long does it take for raindrops to become streamflow? Here I propose a new approach to this old problem. I show how we can use time series of isotope data to measure the average fraction of same-day rainfall appearing in streamflow, even if this fraction varies greatly from rainstorm to rainstorm. I show that we can quantify how this fraction changes from small rainstorms to big ones, and from high flows to low flows, and how it changes with the lag time between rainfall and streamflow.
How long does it take for raindrops to become streamflow? Here I propose a new approach to this...
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