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Kirchner, J. W. (2023). Mixing Models With Multiple, Overlapping, or Incomplete End-Members, Quantified Using Time Series of a Single Tracer. Geophysical Research Letters, 50(12), 2023.
Abstract: Abstract Mixing models are used throughout earth and environmental science to quantify the relative contributions of sources to mixtures, based on chemical or isotopic tracers. Often, however, some end-members are missing or their tracer distributions overlap, precluding the use of conventional mixing models. Here I show how these constraints can be overcome by exploiting the information contained in tracer time-series fluctuations. This approach, ensemble end-member mixing analysis (EEMMA), can potentially quantify many sources using a single tracer, even if their mean concentrations are indistinguishable. EEMMA can also quantify source contributions when some sources are unknown, and even infer the tracer time series of a missing source. Benchmark tests with synthetic data verify the reliability of this approach, thus expanding the range of mixing models that can be quantified using tracer time series. An R script is provided for the necessary calculations, including error propagation.
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Külls, C., Jobin, J., & Weiler, M. (2015). Environmental analytics for water carbon management: enable WCM: Schlussbericht. Albert Ludwigs Universität, Professur für Hydrologie.
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Dahan, O., Tatarsky, B., Enzel, Y., Külls, C., Seely, M., & Benito, G. (2008). Dynamics of flood water infiltration and ground water recharge in hyperarid desert. Groundwater, 46(3), 450–461.
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Joseph, J., Külls, C., Arend, M., Schaub, M., Hagedorn, F., Gessler, A., et al. (2019). Application of a laser-based spectrometer for continuous in situ measurements of stable isotopes of soil CO2 in calcareous and acidic soils. Soil, 5(1), 49–62.
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Baram, S., Ronen, Z., Kurtzman, D., Külls, C., & Dahan, O. (2013). Desiccation-crack-induced salinization in deep clay sediment. Hydrology and Earth System Sciences, 17(4), 1533.
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Klaus, J., Zehe, E., Elsner, M., Külls, C., & McDonnell, J. J. (2013). Macropore flow of old water revisited: experimental insights from a tile-drained hillslope. Hydrology and Earth System Sciences, 17(1), 103.
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Mahindawansha, A., Külls, C., Kraft, P., & Breuer, L. (2020). Investigating unproductive water losses from irrigated agricultural crops in the humid tropics through analyses of stable isotopes of water. Hydrology and Earth System Sciences, 24(7), 3627–3642.
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Morin, E., Grodek, T., Dahan, O., Benito, G., Külls, C., Jacoby, Y., et al. (2009). Flood routing and alluvial aquifer recharge along the ephemeral arid Kuiseb River, Namibia. Journal of Hydrology, 368(1-4), 262–275.
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Klaus, J., Külls, C., & Dahan, O. (2008). Evaluating the recharge mechanism of the Lower Kuiseb Dune area using mixing cell modeling and residence time data. Journal of Hydrology, 358(3-4), 304–316.
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Müller, M., Alaoui, A., Külls, C., Leistert, H., Meusburger, K., Stumpp, C., et al. (2014). Tracking water pathways in steep hillslopes by δ18O depth profiles of soil water. Journal of hydrology, 519, 340–352.
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