A multiscale alignment method for ensemble filtering with displacement errors

The nonlinearity in smaller-scale priors is reduced by removing larger-scale displacement errors. Because the displacement vectors are derived from analysis increments in the state space rather than the nonlinear observation-space cost function formulated in previous studies, this method provides a less costly and more robust way to solve for the displacement vectors. Observing system simulation experiments using a two-layer quasigeostrophic model were conducted to provide a proof of concept of the MSA method.

Results show that the MSA method significantly improves the accuracy of posteriors compared to the existing ensemble filter methods with or without multiscale localization. Advantage of the MSA method is more evident when the ensemble size is relatively small and the cycling period is comparable to the average eddy turnover time of the dynamical system.