Flow-dependent observation errors for GHG inversions in an ensemble Kalman smoother

Abstract. Atmospheric inverse modeling is the process of estimating emissions from atmospheric observations by minimizing a cost function, which includes a term describing the difference between simulated and observed concentrations. The minimization of this difference is typically limited by uncertainties in the atmospheric transport model rather than by uncertainties in the observations. In this study, we showcase how a temporally varying, flow-dependent atmospheric transport uncertainty can enhance the accuracy of emission estimation through idealized experiments using the CTDAS-ICON-ART ensemble Kalman smoother system. We use the estimation of European CH₄ emissions from the in-situ measurement network as an example, but we also demonstrate the additional benefits for trace gases with more localized sources, such as SF₆. The uncertainty in flow-dependent transport is determined using meteorological ensemble simulations that are perturbed by physics and driven at the boundaries by an analysis ensemble from a global meteorology and CH₄ simulation. The impact of a direct representation of temporally varying transport uncertainties in atmospheric inversions is then investigated in an observation system simulation experiment framework in various setups and for different flux signals. We show that the uncertainty in the transport model varies significantly in space and time, and it is generally highest during nighttime. We apply inversions using only afternoon observations as is common practice, but also explore the option of assimilating hourly data irrespective of the hour of day using a filter based on transport uncertainty and taking into account the temporal covariances. Our findings indicate that incorporating flow-dependent uncertainties in inversion techniques leads to more precise estimates of GHG emissions. Differences between estimated and true emissions could be reduced by 9 % to 82 % more effectively, with generally larger improvements for the SF₆ inversion problem and for the more challenging setup with small flux signals.