A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0): 2. Optimization scheme and identical twin experiment of atmospheric CO2 inversion

A 4-dimensional variational method (4D-Var) is a popular technique for inverse modeling of atmospheric constituents, but it is not without problems. Using an icosahedral grid transport model and the 4D-Var method, a new atmospheric greenhouse gas (GHG) inversion system has been developed. The system combines off-line forward and adjoint models with a quasi-Newton optimization scheme. The new approach is then used to conduct identical twin experiments to investigate optimal system settings for an atmospheric CO2 inversion problem, and to demonstrate the validity of the new inversion system. It is found that a system of forward and adjoint models that has less model errors but with non-linearity performs better than another system that conserves linearity with exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is confirmed; the global error is reduced by about 15 % by adding prior error correlations that are simply designed. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to a global scale. The optimization algorithm introduced in the new system does not require difficult decomposition of a matrix that establishes the correlation among the prior flux errors. This enables us to design the prior error covariance matrix more freely.