Accounting for Transport Error in Inversions: An Urban Synthetic Data Experiment

We present and discuss the use of a high-dimensional computational method for atmospheric inversions that incorporates the space-time structure of transport and dispersion errors. In urban environments, transport and dispersion errors are largely the result of our inability to capture the true underlying transport of greenhouse gas (GHG) emissions to observational sites. Motivated by the impact of transport model error on estimates of fluxes of GHGs using in situ tower-based mole-fraction observations, we specifically address the need to characterize transport error structures in high-resolution large-scale inversion models. We do this using parametric covariance functions combined with shrinkage-based regularization methods within an Ensemble Transform Kalman Filter inversion setup. We devise a synthetic data experiment to compare the impact of transport and dispersion error component of the model-data mismatch covariance choices on flux retrievals and study the robustness of the method with respect to fewer observational constraints. We demonstrate the analysis in the context of inferring CO₂ fluxes starting with a hypothesized prior in the Washington D.C. /Baltimore area constrained by a synthetic set of tower-based CO₂ measurements within an observing system simulation experiment framework. This study demonstrates the ability of these simple covariance structures to substantially improve the estimation of fluxes over standard covariance models in flux estimation from urban regions.