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. Tracers have been used for over half a century in hydrology to quantifywater sources with the help of mixing models. In this paper, we build onclassic Bayesian methods to quantify uncertainty in mixing ratios. Suchmethods infer the probability density function (PDF) of the mixing ratios byformulating PDFs for the source and target concentrations and inferring theunderlying mixing ratios via Monte Carlo sampling. However, collectedhydrological samples are rarely abundant enough to robustly fit a PDF to thesource concentrations. Our approach, called HydroMix, solves the linearmixing problem in a Bayesian inference framework wherein the likelihood isformulated for the error between observed and modeled target variables,which corresponds to the parameter inference setup commonly used inhydrological models. To address small sample sizes, every combination ofsource samples is mixed with every target tracer concentration. Using aseries of synthetic case studies, we evaluate the performance of HydroMixusing a Markov chain Monte Carlo sampler. We then use HydroMix to show thatsnowmelt accounts for around 61 % of groundwater recharge in a SwissAlpine catchment (Vallon de Nant), despite snowfall only accounting for40 %–45 % of the annual precipitation. Using this example, we thendemonstrate the flexibility of this approach to account for uncertainties insource characterization due to different hydrological processes. We alsoaddress an important bias in mixing models that arises when there is a largedivergence between the number of collected source samples and their fluxmagnitudes. HydroMix can account for this bias by using composite likelihoodfunctions that effectively weight the relative magnitude of source fluxes.The primary application target of this framework is hydrology, but it is byno means limited to this field.

HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources