Joint CO₂ state and flux estimation with the 4D-Var system EURAD-IM

Abstract. This idealized regional atmospheric inversion study assesses the potential of the 4-dimensional variational (4D-Var) method to estimate CO₂ fluxes and the atmospheric CO₂ concentration state jointly. In order to distinguish and quantify the surface-atmosphere CO₂ fluxes, combining anthropogenic CO₂ emissions, photosynthesis, and respiration, we include uncertainties of initial values, which arise from highly uncertain surface fluxes and night-time transport. Therefor a new calculation of the background error standard deviation for the CO₂ fluxes was developed. To suppress spurious wiggles occurring from advection, an absolute monotone advection scheme with low numeric diffusion and its adjoint has been implemented. The inversion by the EURopean Air pollution Dispersion-Inverse Model (EURAD-IM) with 5 km resolution in Central Europe is validated by synthetic half hourly measurements from eleven concentration towers. A significant improvement of the analysis is shown if initial values and CO₂ fluxes are optimised jointly, compared to optimising CO₂ fluxes alone, without estimating uncertainty of atmospheric concentration. We find that joint estimation of carbon fluxes and initial states requires a careful balance of the background error covariance matrices but enables a more detailed analysis of atmospheric CO₂ and the surface-atmosphere fluxes.