  WOMBAT (the WOllongong Methodology for Bayesian Assimilation of Trace-gases)
is a fully Bayesian hierarchical statistical framework for flux inversion of
trace gases from flask, in situ, and remotely sensed data. WOMBAT extends the
conventional Bayesian-synthesis framework through the consideration of a
correlated error term, the capacity for online bias correction, and the
provision of uncertainty quantification on all unknowns that appear in the
Bayesian statistical model. We show, in an observing system simulation
experiment (OSSE), that these extensions are crucial when the data are indeed
biased and have errors that are correlated. Using the GEOS-Chem atmospheric
transport model, we show that WOMBAT is able to obtain posterior means and
uncertainties on non-fossil-fuel CO$_2$ fluxes from Orbiting Carbon
Observatory-2 (OCO-2) data that are comparable to those from the Model
Intercomparison Project (MIP) reported in Crowell et al. (2019, Atmos. Chem.
Phys., vol. 19). We also find that our predictions of out-of-sample retrievals
from the Total Column Carbon Observing Network are, for the most part, more
accurate than those made by the MIP participants. Subsequent versions of the
OCO-2 datasets will be ingested into WOMBAT as they become available.
