Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF

The stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of t...

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Bibliographic Details
Published in:Monthly weather review 2015-07, Vol.143 (7), p.2918-2936
Main Authors: Hoteit, I, Pham, D-T, Gharamti, ME, Luo, X
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Atmospheric data
Covariance
Covariance matrix
Data assimilation
Data collection
Error analysis
Errors
Kalman filters
Mathematical models
Meteorology
Noise
Numerical experiments
Observational errors
Perturbation
Perturbation methods
Sampling
Sampling error
Serials
Stochasticity
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Summary:The stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of the observational error covariance, which is often the case in real oceanic and atmospheric data assimilation applications. This work introduces an efficient serial scheme to mitigate the impact of observations' perturbations sampling in the analysis step of the EnKF, which should provide more accurate ensemble estimates of the analysis error covariance matrices. The new scheme is simple to implement within the serial EnKF algorithm, requiring only the approximation of the EnKF sample forecast error covariance matrix by a matrix with one rank less. The new EnKF scheme is implemented and tested with the Lorenz-96 model. Results from numerical experiments are conducted to compare its performance with the EnKF and two standard deterministic EnKFs. This study shows that the new scheme enhances the behavior of the EnKF and may lead to better performance than the deterministic EnKFs even when implemented with relatively small ensembles.
ISSN:0027-0644
1520-0493
DOI:10.1175/MWR-D-14-00088.1