Monitoring, reporting, and verification frameworks for greenhouse gas emissions are being developed by countries across the world to keep track of progress towards national emission reduction targets. Data assimilation plays an important role in monitoring frameworks, combining different sources of information to achieve the best possible estimate of fossil fuel emissions and, as a consequence, better estimates for fluxes from the natural biosphere. Robust estimates for fossil fuel emissions rely on accurate estimates of uncertainties corresponding to different pieces of information. We describe prior uncertainties in CO2 and CO fossil fuel fluxes, paying special attention to spatial error correlations and the covariance structure between CO2 and CO. This represents the first time that prior uncertainties in CO2 and the important co-emitted trace gas CO are defined consistently, with error correlations included, which allows us to make use of the synergy between the two trace gases to better constrain CO2 fossil fuel fluxes. CO:CO2 error correlations differ by sector, depending on the diversity of sub-processes occurring within a sector, and also show a large range of values between pixels within the same sector. For example, for other stationary combustion, pixel correlation values range from 0.1 to 1.0, whereas for road transport, the correlation is mostly larger than 0.6. We illustrate the added value of our definition of prior uncertainties using closed-loop numerical experiments over mainland Europe and the UK, which isolate the influence of using error correlations between CO2 and CO and the influence of prescribing more detailed information about prior emission uncertainties. For the experiments, synthetic in situ observations are used, allowing us to validate the results against a “truth”. The “true” emissions are made by perturbing the prior emissions (from an emission inventory) according to the prescribed prior uncertainties. We find that using our realistic definition of prior uncertainties helps our data assimilation system to differentiate more easily between CO2 fluxes from biogenic and fossil fuel sources. Using improved prior emission uncertainties, we find fewer geographic regions with significant deviations from the prior compared to when using default prior uncertainties (32 vs. 80 grid cells of 0.25°×0.3125°, with an absolute difference of more than 1 kg s−1 between the prior and posterior), but these deviations from the prior almost consistently move closer to the prescribed true values, with 92 % showing an improvement, in contrast to the default prior uncertainties, where 61 % show an improvement. We also find that using CO provides additional information on CO2 fossil fuel fluxes, but this is only the case if the CO:CO2 error covariance structure is defined realistically. Using the default prior uncertainties, the CO2 fossil fuel fluxes move farther away from the truth in many geographical regions (with 50 % showing an improvement compared to 94 % when advanced prior uncertainties are used). With the default uncertainties, the maximum deviation of fossil fuel CO2 from the prescribed truth is about 7 % in both the prior and posterior results. With the advanced uncertainties, this is reduced to 3 % in the posterior results.@en

Under the Paris Agreement, countries report their anthropogenic greenhouse gas emissions in national inventories, which are used to track progress towards mitigation goals, but they must be independently verified. Atmospheric observations of CO2, interpreted using inverse methods, can potentially provide that verification. Conventional CO2 inverse methods infer natural CO2 fluxes by subtracting a priori estimates of fuel combustion from the a posteriori net CO2 fluxes, assuming that a priori knowledge for combustion emissions is better than for natural fluxes. We describe an inverse method that uses measurements of CO2 and carbon monoxide (CO), a trace gas that is co-emitted with CO2 during combustion, to report self-consistent combustion emissions and natural fluxes of CO2. We use an ensemble Kalman filter and the GEOS-Chem atmospheric transport model to explore how satellite observations of CO and CO2 collected by the TROPOspheric Monitoring Instrument (TROPOMI) and Orbiting Carbon Observatory-2 (OCO-2), respectively, can improve understanding of combustion emissions and natural CO2 fluxes across the UK and mainland Europe in 2018–2021. We assess the value of using satellite observations of CO2, with and without CO, above what is already available from the in situ network. Using CO2 satellite observations leads to small corrections to a priori emissions that are inconsistent with in situ observations, due partly to the insensitivity of the atmospheric CO2 column to CO2 emission changes. When we introduce satellite CO observations, we find better agreement with our in situ inversion and a better model fit to atmospheric CO2 observations. Our regional mean a posteriori combustion CO2 emission ranges from 4.6–5.0 Gt a−1 (1.5 %–2.4 % relative standard deviation), with all inversions reporting an overestimate for Germany's wintertime emissions. Our national a posteriori CO2 combustion emissions are highly dependent on the assumed relationship between CO2 and CO uncertainties, as expected. Generally, we find better results when we use grid-scale-based a priori CO2:CO uncertainty estimates rather than a fixed relationship between the two species.@en