Ensemble Kalman filtering with one-step-ahead smoothing

Abstract
The ensemble Kalman filter (EnKF) is widely used for sequential data assimilation. It operates as a succession of forecast and analysis steps. In realistic large-scale applications, EnKFs are implemented with small ensembles and poorly known model error statistics. This limits their representativeness of the background error covariances and, thus, their performance. This work explores the efficiency of the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to enhance the data assimilation performance of EnKFs. Filtering with OSA smoothing introduces an updated step with future observations, conditioning the ensemble sampling with more information. This should provide an improved background ensemble in the analysis step, which may help to mitigate the suboptimal character of EnKF-based methods. Here, the authors demonstrate the efficiency of a stochastic EnKF with OSA smoothing for state estimation. They then introduce a deterministic-like EnKF-OSA based on the singular evolutive interpolated ensemble Kalman (SEIK) filter. The authors show that the proposed SEIK-OSA outperforms both SEIK, as it efficiently exploits the data twice, and the stochastic EnKF-OSA, as it avoids observational error undersampling. They present extensive assimilation results from numerical experiments conducted with the Lorenz-96 model to demonstrate SEIK-OSA’s capabilities.

Citation
Raboudi NF, Ait-El-Fquih B, Hoteit I (2018) Ensemble Kalman Filtering with One-Step-Ahead Smoothing. Monthly Weather Review 146: 561–581. Available: http://dx.doi.org/10.1175/mwr-d-17-0175.1.

Acknowledgements
This work is supported by King Abdullah University of Science and Technology Award CRG3-2156.

Publisher
American Meteorological Society

Journal
Monthly Weather Review

DOI
10.1175/mwr-d-17-0175.1

Additional Links
https://journals.ametsoc.org/doi/10.1175/MWR-D-17-0175.1

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