Estimation of global CO₂ fluxes at regional scale using the maximum likelihood ensemble filter

We use an ensemble-based data assimilation method, known as the maximum likelihood ensemble filter (MLEF), which has been coupled with a global atmospheric transport model to estimate slowly varying biases of carbon surface fluxes. Carbon fluxes for this test consist of hourly gross primary production and ecosystem, respiration over land, and air-sea gas exchange. Persistent multiplicative biases intended to represent incorrectly simulated biogeochemical or land-management processes such as stand age, soil fertility, or coarse woody debris were estimated for 1 year at 10° longitude by 6° latitude spatial resolution and with an 8-week time window. We tested the model using a pseudodata experiment with an existing observation network that includes flasks, aircraft profiles, and continuous measurements. Because of the underconstrained nature of the problem, strong covariance smoothing was applied in the first data assimilation cycle, and localization schemes have been introduced. Error covariance was propagated in subsequent cycles. The coupled model satisfactorily recovered the land biases in densely observed areas. Ocean biases, however, were poorly constrained by the atmospheric observations. Unlike in batch mode inversions, the MLEF has a capability of assimilating large observation vectors and hence is suitable for assimilating hourly continuous observations and satellite observations in the future. Uncertainty was reduced further in our pseudodata experiment than by previous batch methods because of the ability to assimilate a large observation vector. Propagation of spatial covariance and dynamic localization avoid the need for prescribed spatial patterns of error covariance centered at observation sites as in previous grid-scale methods.