Strongly coupled data assimilation (SCDA) generates coherent integrated Earth system analyses by assimilating the full Earth observation set into all Earth components. We describe SCDA based on the ensemble Kalman filter with a hierarchy of coupled models, from a coupled Lorenz to the Climate Forecast System v2. SCDA with a sufficiently large ensemble can provide more accurate coupled analyses compared to weakly coupled DA. The correlation-cutoff method can compensate for a small ensemble size.

We introduced a novel algorithm that assimilates a better a priori knowledge to improve the estimation of global surface carbon flux. The algorithm aims at separating the first-order systematic biases in the a priori "bottom-up" flux estimations out of the inversion framework from a comprehensive data assimilation perspective.

We described the application of a constrained ensemble Kalman filter (CEnKF) in a joint CO₂ and surface carbon fluxes estimation study. By assimilating the pseudo-surface and OCO-2 observations, the annual global flux estimation is significantly biased without mass conservation. With the additional CEnKF process, the CO₂ mass is strictly constrained, and the estimation of annual fluxes is significantly improved.

We developed a new carbon data assimilation system to estimate the surface carbon fluxes using the LETKF and GEOS-Chem model, which uses a new scheme with a short assimilation window and a long observation window. The analysis is more accurate using the short assimilation window and is exposed to the future observations that accelerate the spin-up. In OSSE, the system reduces the analysis error significantly, suggesting that this method could be used for other data assimilation problems.

The ensemble forecast sensitivity to observation (EFSO) method can efficiently clarify under what conditions observations are beneficial or detrimental for assimilation. Based on EFSO, an offline assimilation method is proposed to accelerate the development of data selection strategies for new observing systems. The usefulness of this method is demonstrated with the assimilation of global satellite precipitation data.