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<p>Atmospheric flux inversions use observations of atmospheric <span class="inline-formula">CO₂</span> to provide anthropogenic and biogenic <span class="inline-formula">CO₂</span> flux estimates at a range of spatio-temporal scales. Inversions require prior flux, a forward model and observation errors to estimate posterior fluxes and uncertainties. Here, we investigate the forward transport error and the associated biogenic feedback in an Earth system model (ESM) context. These errors can occur from uncertainty in the initial meteorology, the analysis fields used, or the advection schemes and physical parameterisation of the model. We also explore the spatio-temporal variability and flow-dependent error covariances. We then compare the error with the atmospheric response to uncertainty in the prior anthropogenic emissions. Although transport errors are variable, average total-column <span class="inline-formula">CO₂</span> (<span class="inline-formula">XCO₂</span>) transport errors over anthropogenic emission hotspots (0.1–0.8&thinsp;ppm) are comparable to, and often exceed, prior monthly anthropogenic flux uncertainties projected onto the same space (0.1–1.4&thinsp;ppm). Average near-surface transport errors at three sites (Paris, Caltech and Tsukuba) range from 1.7 to 7.2&thinsp;ppm. The global average <span class="inline-formula">XCO₂</span> transport error standard deviation plateaus at <span class="inline-formula">∼0.1</span>&thinsp;ppm after 2–3&thinsp;d, after which atmospheric mixing significantly dampens the concentration gradients. Error correlations are found to be highly flow dependent, with <span class="inline-formula">XCO₂</span> spatio-temporal correlation length scales ranging from 0 to 700&thinsp;km and 0 to 260&thinsp;min. Globally, the average model error caused by the biogenic response to atmospheric meteorological uncertainties is small (<span class="inline-formula">&lt;0.01</span>&thinsp;ppm); however, this increases over high flux regions and is seasonally dependent (e.g. the Amazon; January and July: <span class="inline-formula">0.24±0.18</span>&thinsp;ppm and <span class="inline-formula">0.13±0.07</span>&thinsp;ppm). In general, flux hotspots are well-correlated with model transport errors. Our model error estimates, combined with the atmospheric response to anthropogenic flux uncertainty, are validated against three Total Carbon Observing Network (TCCON) <span class="inline-formula">XCO₂</span> sites. Results indicate that our model and flux uncertainty account for 21&thinsp;%–65&thinsp;% of the total uncertainty. The remaining uncertainty originates from additional sources, such as observation, numerical and representation errors, as well as structural errors in the biogenic model. An underrepresentation of transport and flux uncertainties could also contribute to the remaining uncertainty. Our quantification of <span class="inline-formula">CO₂</span> transport error can be used to help derive accurate posterior fluxes and error reductions in future inversion systems. The model uncertainty diagnosed here can be used with varying degrees of complexity and with different modelling techniques by the inversion community.</p>