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Uncertainty for calculating transport on Titan: a probabilistic description of bimolecular diffusion parameters

Bimolecular diffusion coefficients are important parameters used by atmospheric models to calculate altitude profiles of minor constituents in an atmosphere. Unfortunately, laboratory measurements of these coefficients were never conducted at temperature conditions relevant to the atmosphere of Titan. Here we conduct a detailed uncertainty analysis of the bimolecular diffusion coefficient parameters as applied to Titan's upper atmosphere to provide a better understanding of the impact of uncertainty for this parameter on models. Because temperature and pressure conditions are much lower than the laboratory conditions in which bimolecular diffusion parameters were measured, we apply a Bayesian framework, a problem-agnostic framework, to determine parameter estimates and associated uncertainties. We solve the Bayesian calibration problem using the open-source QUESO library which also performs a propagation of uncertainties in the calibrated parameters to temperature and pressure conditions observed in Titan's upper atmosphere. Our results show that, after propagating uncertainty through the Massman model, the uncertainty in molecular diffusion is highly correlated to temperature and we observe no noticeable correlation with pressure. We propagate the calibrated molecular diffusion estimate and associated uncertainty to obtain an estimate with uncertainty due to bimolecular diffusion for the methane molar fraction as a function of altitude. Results show that the uncertainty in methane abundance due to molecular diffusion is in general small compared to eddy diffusion and the chemical kinetics description. However, methane abundance is most sensitive to uncertainty in molecular diffusion above 1200 km where the errors are nontrivial and could have important implications for scientific research based on diffusion models in this altitude range.