A multiscale alignment method for ensemble filtering with displacement errors

Abstract

High-resolution models nowadays simulate phenomena across many scales and pose challenges to the design of efficient data assimilation methods that reduce errors at all scales. Smaller-scale features experience rapid nonlinear error growth that gives rise to displacement errors, which cause suboptimal ensemble filter performance. Previous studies have started exploring methods that can reduce displacement errors. In this study, a multiscale alignment (MSA) method is proposed for ensemble filtering. The MSA method iteratively processes the model state from the largest to the smallest scales. At each scale, an ensemble filter is applied to update the state with observations, and the analysis increments are utilized to derive displacement vectors for each member that align the ensemble at smaller scales before the next iteration. The nonlinearity in smallerscale 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 are 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.