Diagnosing spatial error structures in CO2 mole fractions and XCO2 column mole fractions from atmospheric transport

Atmospheric inversions inform us about the magnitude and variations of greenhouse gas (GHG) sources and sinks from global to local scales. Deployment of observing systems such as spaceborne sensors and ground-based instruments distributed around the globe has started to offer an unprecedented amount of information to estimate surface exchanges of GHG at finer spatial and temporal scales. However, all inversion methods still rely on imperfect atmospheric transport models whose error structures directly affect the inverse estimates of GHG fluxes. The impact of spatial error structures on the retrieved fluxes increase concurrently with the density of the available measurements. In this study, we diagnose the spatial structures due to transport model errors affecting modeled in situ carbon dioxide (CO2) mole fractions and total-column dry air mole fractions of CO2 (XCO2). We implement a cost-effective filtering technique recently developed in the meteorological data assimilation community to describe spatial error structures using a small-size ensemble. This technique can enable ensemble-based error analysis for multiyear inversions of sources and sinks. The removal of noisy structures due to sampling errors in our small-size ensembles is evaluated by comparison with larger-size ensembles. A second filtering approach for error covariances is proposed (Wiener filter), producing similar results over the 1-month simulation period compared to a Schur filter. Based on a comparison to a reference 25-member calibrated ensemble, we demonstrate that error variances and spatial error correlation structures are recoverable from small-size ensembles of about 8 to 10 members, improving the representation of transport errors in mesoscale inversions of CO2 fluxes. Moreover, error variances of in situ near-surface and free-tropospheric CO2 mole fractions differ significantly from total-column XCO2 error variances. We conclude that error variances for remote-sensing observations need to be quantified independently of in situ CO2 mole fractions due to the complexity of spatial error structures at different altitudes. However, we show the potential use of meteorological error structures such as the mean horizontal wind speed, directly available from ensemble prediction systems, to approximate spatial error correlations of in situ CO2 mole fractions, with similarities in seasonal variations and characteristic error length scales.