Statistical Diagnostics of CO2 Inversions

Over the last decade, Bayesian synthesis inversion has become the most common technique for interpreting global-scale spatial distributions of CO{}₂. While the technique is formally based on statistical estimation, in few of the studies has there been any testing of the statistical model. The development of techniques has been a sequence of ad hoc adjustments in the light of problems experienced. This presentation describes a series of tests that revisit earlier calculations and investigate the extent to which problems could have been avoided if more comprehensive statistical testing had been adopted. These statistical tests can also be used in conjunction with current inversion studies, to evaluate whether results violate the assumptions inherent in the statistical model implemented. Problems such as biased priors, unrealistic covariance parameters, and residuals not following assumed distributions can be diagnosed. The test case uses 12 ocean regions, 4 regions of deforestation, and 8 regions each of CO{}₂ fertilisation and seasonal CO{}₂ exchange. Fossil CO{}₂ and oxidation of CO are treated separately. In the standard case, the distribution of normalised residuals is found to be consistent with the Gaussian distribution assumed in the statistical model. The distribution of normalised deviations of flux estimates from priors is found to have a smaller spread than expected from the notional statistical model. This is interpreted as a reflection of the common practice of using weak (minimally-informative) priors, informally regarding them as a regularization constraint rather than an equivalent source of information.