Representing model uncertainty for global atmospheric CO2 flux inversions using ECMWF-IFS-46R1

Atmospheric flux inversions use observations of atmospheric CO2 to provide anthropogenic and biogenic CO2 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 flowdependent 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 CO2 (XCO2) transport errors over anthropogenic emission hotspots (0.1-0.8 ppm) are comparable to, and often exceed, prior monthly anthropogenic flux uncertainties projected onto the same space (0.1-1.4 ppm). Average near-surface transport errors at three sites (Paris, Caltech and Tsukuba) range from 1.7 to 7.2 ppm. The global average XCO2 transport error standard deviation plateaus at - 0.1 ppm after 2-3 d, after which atmospheric mixing significantly dampens the concentration gradients. Error correlations are found to be highly flow dependent, with XCO2 spatio-temporal correlation length scales ranging from 0 to 700 km and 0 to 260 min Globally, the average model error caused by the biogenic response to atmospheric meteorological uncertainties is small (< 0.01 ppm); however, this increases over high flux regions and is seasonally dependent (e.g. the Amazon; January and July: 0.24 +/- 0.18 ppm and 0.13 +/- 0.07 ppm). In general, flux hotspots are wellcorrelated with model transport errors. Our model error es- timates, combined with the atmospheric response to anthropogenic flux uncertainty, are validated against three Total Carbon Observing Network (TCCON) XCO2 sites. Results indicate that our model and flux uncertainty account for 21 %-65 % 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 CO2 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.