Quantifying uncertainty in stable isotope mixing models

Mixing models are powerful tools for identifying biogeochemical sources and determining mixing fractions in a sample. However, identification of actual source contributors is often not simple, and source compositions typically vary or even overlap, significantly increasing model uncertainty in calculated mixing fractions. This study compares three probabilistic methods, Stable Isotope Analysis in R (SIAR), a pure Monte Carlo technique (PMC), and Stable Isotope Reference Source (SIRS) mixing model, a new technique that estimates mixing in systems with more than three sources and/or uncertain source compositions. In this paper, we use nitrate stable isotope examples (N-15 and O-18) but all methods tested are applicable to other tracers. In Phase I of a three-phase blind test, we compared methods for a set of six-source nitrate problems. PMC was unable to find solutions for two of the target water samples. The Bayesian method, SIAR, experienced anchoring problems, and SIRS calculated mixing fractions that most closely approximated the known mixing fractions. For that reason, SIRS was the only approach used in the next phase of testing. In Phase II, the problem was broadened where any subset of the six sources could be a possible solution to the mixing problem. Results showed a high rate of Type I errors where solutions included sources that were not contributing to the sample. In Phase III some sources were eliminated based on assumed site knowledge and assumed nitrate concentrations, substantially reduced mixing fraction uncertainties and lowered the Type I error rate. These results demonstrate that valuable insights into stable isotope mixing problems result from probabilistic mixing model approaches like SIRS. The results also emphasize the importance of identifying a minimal set of potential sources and quantifying uncertainties in source isotopic composition as well as demonstrating the value of additional information in reducing the uncertainty in calculated mixing fractions.