Abstract
Abstract. A four-dimensional variational method (4D-Var) is a popular technique for source/sink inversions 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 offline 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. In this paper, the inversion problem is simplified by assuming the prior flux errors to be reasonably well known and by designing the prior error correlations with a simple function as a first step. It is found that a system of forward and adjoint models with smaller model errors but with nonlinearity has comparable optimization performance to that of another system that conserves linearity with an exact adjoint relationship. Furthermore, the effectiveness of the prior error correlations is demonstrated, as the global error is reduced by about 15 % by adding prior error correlations that are simply designed when 65 weekly flask sampling observations at ground-based stations are used. With the optimal setting, the new inversion system successfully reproduces the spatiotemporal variations of the surface fluxes, from regional (such as biomass burning) to global scales. The optimization algorithm introduced in the new system does not require 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.
Highlights
Using the Bayesian algorithm, an inverse model estimates spatiotemporal variations of surface fluxes from observations of atmospheric concentrations with the help of a priori information
global root mean square error (GRMSE) shows a smooth reduction as the iterative calculation proceeds in all the cases, except for the case of NONLINEAR+DR89 with the diagonal B (Fig. 4a), where the GRMSE reduction in value matches that of its corresponding LINEAR case
After about 30 iterations, the two curves diverge rapidly as the NONLINEAR case increases in GRMSE to a value at the 60th iteration that is greater than the value at the beginning of the iteration
Summary
Using the Bayesian algorithm, an inverse model estimates spatiotemporal variations of surface fluxes from observations of atmospheric concentrations with the help of a priori information. The power of such techniques has been demonstrated in previous studies, such as the synthesis inversion analysis by Peylin et al (2013) that demonstrated significant variations in regional carbon budgets at seasonal to interannual timescales. We have developed a new inversion system based on the four-dimensional variational (4D-Var) method.
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