Presentation and applications of mixing elements and dissolved isotopes in rivers (MEANDIR), a customizable MATLAB model for Monte Carlo inversion of dissolved river chemistry

The dissolved chemistry of rivers has been extensively studied to elucidate physical and climatic controls of chemical weathering at local to global spatial scales, as well as the impacts of chemical weathering on climate over short to geologic temporal scales. Within this effort, mixing models with Monte Carlo uncertainty propagation are a common tool for inverting measurements of dissolved river chemistry to distinguish among contributions from end-members with distinct elemental and/or isotopic compositions. However, the methods underlying prior river inversion models have typically been opaque. Here we present Mixing Elements ANd Dissolved Isotopes in Rivers (MEANDIR), a set of MATLAB scripts that enable highly customizable inversion of dissolved river chemistry with Monte Carlo propagation of uncertainty. First, we present an overview of the mathematics underlying MEANDIR. This overview includes, among other topics, derivation of equations for mass balance, implementation of chlorine critical values, construction of cost functions, normalization to the sum of dissolved variables, quantification of river sulfate sourced from pyrite oxidation, resolution of petrogenic organic carbon oxidation, representation of secondary phase formation with isotopic fractionation, and calculation of the impact of weathering on atmospheric carbon dioxide. Second, we apply MEANDIR to five previously published datasets to demonstrate the sensitivity of results to parameter choices. We invert data from two global compilations of river chemistry (Gaillardet and others, 1999; Burke and others, 2018), the major element chemistry and sulfate sulfur isotope ratios of rivers in the Peruvian Amazon (Torres and others, 2016), the major element chemistry of Icelandic rivers (Gíslason and others, 1996), and the major and trace element chemistry of water samples from the Mackenzie River (Horan and others, 2019). MEANDIR and its user guide are freely available online.