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Combining measurements of atmospheric CO2 and its radiocarbon ((CO2)-C-14) fraction and transport modeling in atmospheric inversions offers a way to derive improved estimates of CO2 emitted from fossil fuel (FFCO2). In this study, we solve for the monthly FFCO2 emission budgets at regional scale (i.e., the size of a medium-sized country in Europe) and investigate the performance of different observation networks and sampling strategies across Europe. The inversion system is built on the LMDZv4 global transport model at 3.75 degrees x 2.5 degrees resolution. We conduct Observing System Simulation Experiments (OSSEs) and use two types of diagnostics to assess the potential of the observation and inverse modeling frameworks. The first one relies on the theoretical computation of the uncertainty in the estimate of emissions from the inversion, known as "posterior uncertainty", and on the uncertainty reduction compared to the uncertainty in the inventories of these emissions, which are used as a prior knowledge by the inversion (called "prior uncertainty"). The second one is based on comparisons of prior and posterior estimates of the emission to synthetic "true" emissions when these true emissions are used beforehand to generate the synthetic fossil fuel CO2 mixing ratio measurements that are assimilated in the inversion. With 17 stations currently measuring (CO2)-C-14 across Europe using 2-week integrated sampling, the uncertainty reduction for monthly FFCO2 emissions in a country where the network is rather dense like Germany, is larger than 30 %. With the 43 (CO2)-C-14 measurement stations planned in Europe, the uncertainty reduction for monthly FFCO2 emissions is increased for the UK, France, Italy, eastern Europe and the Balkans, depending on the configuration of prior uncertainty. Further increasing the number of stations or the sampling frequency improves the uncertainty reduction (up to 40 to 70 %) in high emitting regions, but the performance of the inversion remains limited over low-emitting regions, even assuming a dense observation network covering the whole of Europe. This study also shows that both the theoretical uncertainty reduction (and resulting posterior uncertainty) from the inversion and the posterior estimate of emissions itself, for a given prior and "true" estimate of the emissions, are highly sensitive to the choice between two configurations of the prior uncertainty derived from the general estimate by inventory compilers or computations on existing inventories. In particular, when the configuration of the prior uncertainty statistics in the inversion system does not match the difference between these prior and true estimates, the posterior estimate of emissions deviates significantly from the truth. This highlights the difficulty of filtering the targeted signal in the model-data misfit for this specific inversion framework, the need to strongly rely on the prior uncertainty characterization for this and, consequently, the need for improved estimates of the uncertainties in current emission inventories for real applications with actual data. We apply the posterior uncertainty in annual emissions to the problem of detecting a trend of FFCO2, showing that increasing the monitoring period (e.g., more than 20 years) is more efficient than reducing uncertainty in annual emissions by adding stations.

The coarse spatial resolution of the atmospheric transport model used in this OSSE (typical of models used for global inversions of natural CO2 fluxes) leads to large representation errors (related to the inability of the transport model to capture the spatial variability of the actual fluxes and mixing ratios at subgrid scales), which is a key limitation of our OSSE setup to improve the accuracy of the monitoring of FFCO2 emissions in European regions. Using a high-resolution transport model should improve the potential to retrieve FFCO2 emissions, and this needs to be investigated.