Performance assessment of the maximum likelihood ensemble filter and the ensemble Kalman filters for nonlinear problems

This study presents a thorough investigation of the performance comparison of three ensemble data assimilation (DA) methods, including the maximum likelihood ensemble filter (MLEF), the ensemble Kalman filter (EnKF), and the iterative EnKF (IEnKF), with respect to solution accuracy and computational efficiency for nonlinear problems. The convection-diffusion-reaction (CDR) problem is first tested, and then, the chaotic Lorenz 96 model is solved. Both linear and nonlinear observation operators are considered. The study demonstrates that MLEF consistently produces more accurate and efficient solution than the other two methods and provides more information on both states and their uncertainties. The IEnKF and MLEF are used to estimate model parameters and uncertainty in initial conditions using a nonlinear observation operator. The assimilation performance is assessed based on the quality metrics, such as the squared true error, the trace of the error covariance matrix, and the root-mean-square (RMS) error. Based on these DA performance assessments, MLEF demonstrates better convergence and higher accuracy. Results of the CDR problem show significant improvements in the estimate of model parameters and the solution accuracy by MLEF compared to the EnKF family. This study provides evidence supporting the choice of MLEF when solving large nonlinear problems.