Diagnosing spatial error structures in CO<sub>2</sub> mole fractions and XCO<sub>2</sub> column mole fractions from atmospheric transport

Abstract

Abstract. 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.

Seasonal Characteristics of Model Uncertainties From Biogenic Fluxes, Transport, and Large‐Scale Boundary Inflow in Atmospheric CO2 Simulations Over North America

“…Previous studies from a large number of ensemble members show that the two outer bins are usually a factor of 3 greater than the ideal distribution even for a large ensemble (e. g., 50 members in Berner et al, ; 101 members in Garaud & Mallet, ; 45 member in Díaz‐Isaac et al, ). Lauvaux et al () showed that small size ensembles are sufficient to produce reliable statistics except spurious structures in space. We conclude that the transport ensemble suite is fairly representative and skillful despite our small number of members, but clearly not sufficient to represent the full spatiotemporal structures of model errors.…”

“…Previous studies from a large number of ensemble members show that the two outer bins are usually a factor of 3 greater than the ideal distribution even for a large ensemble (e. g., 50 members in Berner et al, 2009; 101 members in Garaud & Mallet, 2011;45 member in Díaz-Isaac et al, 2018b). Lauvaux et al (2019) showed that small size ensembles are sufficient to produce reliable statistics except spurious structures in space.…”

WOMBAT v1.0: A fully Bayesian global flux-inversion framework

“…introduces errors that could span hundreds of kilometres and several days (Lauvaux et al, 2019;McNorton et al, 2020).…”

“…The complexity of all modelled processes, from fluxes right up to satellite retrieval errors, inevitably leads to model misspecification (e.g., Engelen et al, 2002). The main causes of misspecification are (i) flux-process dimension-reduction error (e.g., Kaminski et al, 2001), which is a consequence of using a spatio-temporal model for the flux field that is low-dimensional and inflexible; (ii) an inaccurate prior flux mean, variance, and covariance (e.g., Philip et al, 2019); (iii) transport-model errors (e.g., Houweling et al, 2010;Basu et al, 2018;Schuh et al, 2019) arising from the underlying assumed physics, meteorology, and discretisation schemes used (e.g., Lauvaux et al, 2019;McNorton et al, 2020); (iv) retrieval biases (e.g., O'Dell et al, 2018) and incorrect associated measurement-error statistics (e.g., Worden et al, 2017); and (v) measurement-error spatio-temporal correlations that are not fully accounted for (e.g., Chevallier, 2007;Ciais et al, 2010). Two other causes of model misspecification worth noting are an incorrectly specified initial global mole-fraction field, and flux components assumed known in the inversion (i.e., assumed degenerate at their prior mean), such as anthropogenic emissions (e.g., Feng et al, 2019).…”

Representing model uncertainty for global atmospheric CO<sub>2</sub> flux inversions using ECMWF-IFS-46R1

“…Here, we investigate the forward transport error and the associated biogenic feedback in an Earth system model (ESM) context. Model transport error is usually larger than the observation error (Stephens et al, 2007;Law et al, 2008) and often consists of simplified assumptions. Depending on the configuration of the forward model, errors can occur from uncertainty in the initial meteorological conditions, the anal-ysis fields used, or the advection schemes and physical parameterisation of the model.…”