Optimization of end-members used in multiple linear regression geochemical mixing models

Abstract

Tracking marine sediment provenance (e.g., of dust, ash, hydrothermal material, etc.) provides insight into contemporary ocean processes and helps construct paleoceanographic records. In a simple system with only a few end-members that can be easily quantified by a unique chemical or isotopic signal, chemical ratios and normative calculations can help quantify the flux of sediment from the few sources. In a more complex system (e.g., each element comes from multiple sources), more sophisticated mixing models are required. MATLAB codes published in Pisias et al. () solidified the foundation for application of a Constrained Least Squares (CLS) multiple linear regression technique that can use many elements and several end-members in a mixing model. However, rigorous sensitivity testing to check the robustness of the CLS model is time and labor intensive. MATLAB codes provided in this paper reduce the time and labor involved and facilitate finding a robust and stable CLS model. By quickly comparing the goodness of fit between thousands of different end-member combinations, users are able to identify trends in the results that reveal the CLS solution uniqueness and the end-member composition precision required for a good fit. Users can also rapidly check that they have the appropriate number and type of end-members in their model. In the end, these codes improve the user's confidence that the final CLS model(s) they select are the most reliable solutions. These advantages are demonstrated by application of the codes in two case studies of well-studied datasets (Nazca Plate and South Pacific Gyre).