Uncertainty Quantification of CO2 Flux Estimates with a 4D-Var Inversion System

A 4-dimensional variational method (4D-Var) is a popular technique for inverse modeling of atmospheric constituents. Using the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system, named NICAM-TM 4D-Var, combines the icosahedral grid atmospheric transport model with a quasi-Newton optimization scheme. One prominent feature of the new system is that the optimization algorithm does not require difficult decomposition of a matrix that establishes the correlation among the prior flux errors, which enables us to design the prior error covariance matrix more freely.

Conducting an identical twin experiment of surface CO₂ flux inversion using a prescribed "true flux" dataset, we have investigated how the current observation network could be exploited better to constrain surface flux estimates. The results show that general features of the true flux variations are successfully retrieved from weekly flask observations obtained from ground-based stations. Moreover, a remarkable performance of the new system is demonstrated by the result that the inversion is able to detect regionally limited flux anomalies caused by biomass burnings. However, improvements in the flux estimate in some regions have been found to be limited due to the sparseness of the observations. For instance, large difference from the true flux can be seen for the ocean flux in the 30–90°S latitude band, particularly during the southern hemisphere fall.

In this study, we have further developed a new method to estimate posterior flux uncertainties. The method utilizes the algorithm of the quasi-Newton optimization in which an approximated inverse Hessian is used to update the search direction in the 4D-Var iterative calculation. Comparing with the analytical solution, we have confirmed that the posterior CO₂ flux uncertainties are well estimated by the newly developed method.