Carbon flux bias estimation employing maximum likelihood ensemble filter (MLEF)

We evaluate the capability of an ensemble based data assimilation approach, referred to as Maximum Likelihood Ensemble Filter (MLEF), to estimate biases in the CO2 photosynthesis and respiration fluxes. We employ an off-line Lagrangian Particle Dispersion Model (LPDM), which is driven by the carbon fluxes, obtained from the Simple Biosphere -Regional Atmospheric Modeling System (SiB-RAMS). The SiB-RAMS carbon fluxes are assumed to have errors in the form of multiplicative biases. Our goal is to estimate and reduce these biases and also to assign reliable posterior uncertainties to the estimated biases. Experiments of this study are performed using simulated CO2 observations, which resemble real CO2 concentrations from the Ring of Towers in northern Wisconsin. We evaluate the MLEF results with respect to the truth'' and the Kalman Filter (KF) solution. The KF solution is considered theoretically optimal for the problem of this study, which is a linear data assimilation problem involving Gaussian errors. We also evaluate the impact of forecast error covariance localization based on a new distance'' defined in the space of information measures. Experimental results are encouraging, indicating that the MLEF can successfully estimate carbon flux biases and their uncertainties. As expected, the estimated biases are closer to the true'' biases in the experiments with more ensemble members and more observations. The data assimilation algorithm has a stable performance and converges smoothly to the KF solution when the ensemble size approaches the size of the model state vector (i. e., the control variable of the data assimilation problem).