Mixing Models With Multiple, Overlapping, or Incomplete End-Members, Quantified Using Time Series of a Single Tracer

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.