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

Abstract

Abstract. 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 spatio-temporally correlated. Using the GEOS-Chem atmospheric transport model, we show that WOMBAT is able to obtain posterior means and variances on non-fossil-fuel CO2 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). We also find that WOMBAT's predictions of out-of-sample retrievals obtained from the Total Column Carbon Observing Network (TCCON) are, for the most part, more accurate than those made by the MIP participants.

Discussion on “A combined estimate of global temperature”

“…It nevertheless will remain a challenge to quantify difficult to assess but non‐negligible errors such as consistent errors across all data products. The observing system simulation experiment approach described in, for example, Zammit‐Mangion et al (2021) in the context of trace gas flux inversion shows promise in this regard. The idea is to simulate both the underlying physical process—in the present case, the surface temperature as a function of space and time—together with the measurement process, including both random and systematic measurement errors and then apply the same analysis that was used on the actual data to this synthetic data.…”

Modelling the growth of atmospheric nitrous oxide using a global hierarchical inversion

“…The inversion uses a hierarchical Bayesian inversion framework called WOMBAT (the WOllongong Methodology for Bayesian Assimilation of Trace-gases), which has previously been used for estimating carbon dioxide emissions from satellite data (Zammit-Mangion et al, 2022). The WOMBAT framework was developed to reduce the problem of model misspecification caused by issues such as: an inaccurate prior flux field and uncertainty; retrieval biases for satellite data; and possible spatio-temporal correlations in the measurement error (Zammit-Mangion et al, 2022). WOMBAT tackles these problems by: specifying prior distributions on the uncertainty in the prior fluxes; modelling biases in the mole fraction data; adding a spatiotemporally correlated component of variability to the measurement error; and propagating uncertainty on all unknowns within a fully Bayesian statistical framework where inference is made using MCMC.…”

“…dioxide inversions is given byZammit-Mangion et al (2022). Here, we provide a brief description of the modified framework used here.…”

“…Here, we provide a brief description of the modified framework used here. This work is set up as for carbon dioxide inZammit-Mangion et al (2022), with four exceptions:1. No bias in observations and no correlation in model-measurement discrepancy are considered, as the monthly data used are less likely to have correlated errors than the higher frequency data used inZammit-Mangion et al (2022).…”

“…Zammit-Mangion et al (2022), with the step to sample α modified to use the method ofPakman and Paninski (2014) to 200 accommodate the truncated Gaussian prior. MCMC, of which a Gibbs sampler is one form, generates samples from a target distribution by simulating a Markov chain that has the target distribution as its equilibrium distribution.…”