Estimating the Spatiotemporal Constraints and Uncertainties in a Mesoscale Inversion of Methane Emissions During SENEX

Our ability to properly interpret trace gas source inversions and to accurately assess their uncertainty is often hindered by, on one hand, the absence of a robust theoretical and computational framework to define the observational constraints, and, on the other hand, the necessity to rely on simplistic assumptions for the probability distributions in order to accommodate the high-dimensionality of the problems (e.g., Gaussian distributions for the prior emissions). In this study, we apply a novel dimension reduction technique to a mesoscale inversion of methane sources from shale production during the Southeast Nexus of Climate Change and Air Quality (SENEX) field campaign (June-July, 2013) that allows us to rigorously characterize the spatiotemporal emission patterns that are independently and most constrained by the observations. This information allows us to define an optimal reduced basis set of emissions, which is then incorporated into a Markov-Chain-Monte-Carlo (MCMC) sampling method. The latter approach enables to relax the Gaussian assumption for the prior distribution and to fully sample the posterior distribution of the estimated methane fluxes. Several prior distribution scenarios that are more representative of the true prior uncertainties in the methane fluxes over shale production facilities (e.g., log-normal, multi-modal) are tested in order to provide a better characterization of errors in the posterior fluxes arising from the simplified Gaussian framework generally adopted in mesoscale inversions.