On the statistical optimality of CO₂ atmospheric inversions assimilating CO₂ column retrievals

The extending archive of the Greenhouse Gases Observing Satellite (GOSAT) measurements (now covering about 6 years) allows increasingly robust statistics to be computed, that document the performance of the corresponding retrievals of the column-average dry air-mole fraction of CO2 (XCO2). Here, we demonstrate that atmospheric inversions cannot be rigorously optimal when assimilating current XCO2 retrievals, even with averaging kernels, in particular because retrievals and inversions use different assumption about prior uncertainty. We look for some practical evidence of this sub-optimality from the view point of atmospheric inversion by comparing a model simulation constrained by surface air-sample measurements with one of the GOSAT retrieval products (NASA's ACOS). The retrieval-minus-model differences result from various error sources, both in the retrievals and in the simulation: we discuss the plausibility of the origin of the major patterns. We find systematic retrieval errors over the dark surfaces of high-latitude lands and over African savannahs. More importantly, we also find a systematic over-fit of the GOSAT radiances by the retrievals over land for the high-gain detector mode, which is the usual observation mode. The over-fit is partially compensated by the retrieval bias-correction. These issues are likely common to other retrieval products and may explain some of the surprising and inconsistent CO2 atmospheric inversion results obtained with the existing GOSAT retrieval products. We suggest that reducing the observation weight in the retrieval schemes (for instance so that retrieval increments to the retrieval prior values are halved for the studied retrieval product) would significantly improve the retrieval quality and reduce the need for (or at least reduce the complexity of) ad-hoc retrieval bias correction.