最尤法アンサンブルフィルタを用いた非線形観測の同化

Abstract

We investigate the performance of the Maximum Likelihood Ensemble Filter (MLEF) in assimilation of nonlinear observations. MLEF is a variational-ensemble data assimilation method, and can treat differentiable or non-differentiable nonlinear observation operators. In this study, we compare MLEF with the Ensemble Transform Kalman Filter (ETKF) in assimilation experiments with a one-dimensional Burgers model. The ETKF analysis with a certain formulation of nonlinear operators diverges when the observation nonlinearity is strong and the observation error is small. This divergence is found to be associated with an extra rank of ensemble perturbation matrix. Optimization in MLEF can improve the analysis to the level comparable to or better than ETKF. In addition, the smaller observation error is, or the stronger observation nonlinearity is, MLEF with the nonlinear operators can assimilate observations more effectively than MLEF with the tangent linear operators. However, the strong nonlinearity hinders convergence. We found that re-evaluation of the Hessian preconditioning matrix can alleviate such poor convergence. These encouraging results indicate that MLEF can incorporate nonlinear effects and evaluate observations appropriately.