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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00253 |
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Table of Contents:
- Geoscientific applications of ensemble Kalman filters face several computational challenges arising from the high dimensionality of the forecast covariance matrix, particularly when this matrix incorporates localization. For square-root filters, updating the perturbations of the ensemble members from their mean is an especially challenging step, one which generally requires approximations that introduce a trade-off between accuracy and computational cost. This paper describes an ensemble square-root filter which achieves a favorable trade-off between these factors by discretizing an integral representation of the Kalman filter update equations, and in doing so, avoids a direct evaluation of the matrix square-root in the perturbation update stage. This algorithm, which we call InFo-ESRF ("Integral-Form Ensemble Square-Root Filter"), is parallelizable and uses a preconditioned Krylov method to update perturbations to a high degree of accuracy. Through numerical experiments with both a Gaussian forecast model and a multi-layer Lorenz-type system, we demonstrate that InFo-ESRF is competitive or superior to several existing localized square-root filters in terms of accuracy and cost.