We develop and test new methodologies to best estimate CO2 fluxes on the Earth's surface by assimilating observations of atmospheric CO2 concentration, using the Local Ensemble Transform Kalman Filter. We perform Observing System Simulation Experiments and assimilate simultaneously atmospheric observations and atmospheric carbon observations, but no surface fluxes of carbon. For the experiments, we modified an atmospheric general circulation model to transport atmospheric CO2 and coupled this model with a dynamical terrestrial carbon model and a simple physical land model.

 The state vector of the model prognostic variables was augmented by the diagnosed carbon fluxes CF, so that the carbon fluxes were updated by the background error covariance with other variables.  We designed three types of analysis systems: a C-univariate system where CF errors are coupled only with CO2, a multivariate system where all the error covariances are coupled, and a one-way multivariate analysis where the wind is included in the carbon error covariance, but there is no feedback on the winds.  With perfect model experiments, the one-way multivariate analysis has the best results in CO2 analysis.  For the imperfect model experiments, we applied techniques of model bias correction and adaptive inflation.  With those, we obtained a high-quality analysis of surface CO2 fluxes.  Furthermore, the adaptive inflation technique also provides a good estimate of observation errors.  

 A new approach in the multivariate data assimilation with "variable localization", where the error correlations between unrelated variables are zeroed-out further improved the multivariate analyses surface CO2 fluxes. We note that with the simultaneous assimilation of winds and carbon variables, we are able to transport atmospheric CO2 with winds as well as, for the first time, couple their error covariances. As a result, the multivariate systems perform well, and do not require any kind of a-priori information that should be pre-calculated by independent observations or model simulations.  

 The many new techniques that we developed and tested put us on a solid basis to tackle the assimilation of real atmospheric and CO2 observations, a project being carried out collaboratively by Dr. Junjie Liu under the direction of Prof. Inez Fung at UC Berkeley.