Estimation of observation errors for large-scale atmospheric inversion of CO2 emissions from fossil fuel combustion

National annual inventories of CO2 emitted during fossil fuel consumption (FFCO2) bear 5-10% uncertainties for developed countries, and are likely higher at intra annual scales or for developing countries. Given the current international efforts of mitigating actions, there is a need for independent verifications of these inventories. Atmospheric inversion assimilating atmospheric gradients of CO2 and radiocarbon measurements could provide an independent way of monitoring FFCO2 emissions. A strategy would be to deploy such measurements over continental scale networks and to conduct continental to global scale atmospheric inversions targeting the national and one-month scale budgets of the emissions. Uncertainties in the high-resolution distribution of the emissions could limit the skill for such a large-scale inversion framework. This study assesses the impact of such uncertainties on the potential for monitoring the emissions at large scale. In practice, it is more specifically dedicated to the derivation, typical quantification and analysis of critical sources of errors that affect the inversion of FFCO2 emissions when solving for them at a relatively coarse resolution with a coarse grid transport model. These errors include those due to the mismatch between the resolution of the transport model and the spatial variability of the actual fluxes and concentrations (i.e. the representation errors) and those due to the uncertainties in the spatial and temporal distribution of emissions at the transport model resolution when solving for the emissions at large scale (i.e. the aggregation errors). We show that the aggregation errors characterize the impact of the corresponding uncertainties on the potential for monitoring the emissions at large scale, even if solving for them at the transport model resolution. We propose a practical method to quantify these sources of errors, and compare them with the precision of FFCO2 measurements (i.e. the measurement errors) and the errors in the modelling of atmospheric transport (i.e. the transport errors). The results show that both the representation and measurement errors can be much larger than the aggregation errors. The magnitude of representation and aggregation errors is sensitive to sampling heights and temporal sampling integration time. The combination of these errors can reach up to about 50% of the typical signals, i.e. the atmospheric large-scale mean afternoon FFCO2 gradients between sites being assimilated by the inversion system. These errors have large temporal auto-correlation scales, but short spatial correlation scales. This indicates the need for accounting for these temporal auto-correlations in the atmospheric inversions and the need for dense networks to limit the impact of these errors on the inversion of FFCO2 emissions at large scale. More generally, comparisons of the representation and aggregation errors to the errors in simulated FFCO2 gradients due to uncertainties in current inventories suggest that the potential of inversions using global coarse-resolution models (with typical horizontal resolution of a couple of degrees) to retrieve FFCO2 emissions at sub-continental scale could be limited, and that meso-scale models with smaller representation errors would effectively increase the potential of inversions to constrain FFCO2 emission estimates.