Discharge as a confounding control on geochemical mixing inferences, and implications on catchment-scale weathering flux estimates

End-member mixing models are widely used in catchment geochemistry to interpret the observed stream chemistry as a linear combination of underlying end-members, and infer lithological source contributions, carbon fluxes or weathering rates. In pursuit of their conceptual simplicity, these models rely on a set of assumptions including conservative behavior of tracers, exactly identified (a-priori) number of sources with known and constant tracer signatures. While the conservativity of certain tracers is well-established, the accurate identification of geochemical end-member signatures from field investigations remains a challenge, contributing to uncertainties in inferred mixing fractions and subsequent interpretations. However, another layer of uncertainty, pertaining to the validity of the mixing model is often overlooked in this process. 

Here, we use high-frequency stream chemistry and discharge datasets from multiple small and mesoscale catchments to demonstrate the existence of large inaccuracies in inferred mixing fractions, irrespective of the perfect identification of (supposed) end-members. We employ a geometrical approach to visualize observed stream chemistry with reference to an ideal mixing space spanned by a given set of tracers. We then relate deviations from this reference space to hydrology (using discharge as a proxy) to argue that such deviations cannot be explained by the existence of another static unidentified end-member, but only through either discharge-dependent shifts in the source signatures themselves, or secondary geochemical processes correlated with discharge. This is evidenced by strong synchronization between the mixing model residuals and discharge time series, highlighting the role of discharge as a confounding factor in geochemical mixing analyses.

Preliminary results indicate that the variance unaccounted for by the mixing model due to the violation of its assumptions is comparable to, or even exceeds, the magnitude of the inferred mixing contributions. This raises questions on treating mixing as the primary control of observed variability in stream chemistry. Furthermore, we also demonstrate how data-driven inference of the number/nature of geochemical end-members using Principal Component Analysis, a frequently adopted practice, could be heavily biased due to this uncertainty. 

Overall, our results dispute the common practice of using mixing models to infer catchment geochemical processes, and call for exercising caution in downstream analyses such as calculating weathering and solute fluxes. We suggest that establishing the existence of a tenable mixing space must be a prerequisite for any subsequent geochemical interpretation.