Articles | Volume 33, issue 3
https://doi.org/10.5194/npg-33-335-2026
https://doi.org/10.5194/npg-33-335-2026
Research article
 | 
06 Jul 2026
Research article |  | 06 Jul 2026

Noise-scaled accuracy of the ensemble Kalman filter with an instability-based minimum ensemble size

Kota Takeda and Takemasa Miyoshi

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Cited articles

Barreira, L. and Pesin, Y.: Lyapunov Exponents and Smooth Ergodic Theory, vol. 23, University Lecture Series, American Mathematical Society, Providence, Rhode Island, ISBN 978-0-8218-2921-9, https://doi.org/10.1090/ulect/023, 2002. a
Bishop, C. H., Etherton, B. J., and Majumdar, S. J.: Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects, Mon. Weather Rev., 129, 420–436, https://doi.org/10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2, 2001. a, b
Biswas, A. and Branicki, M.: A Unified Framework for the Analysis of Accuracy and Stability of a Class of Approximate Gaussian Filters for the Navier–Stokes Equations, Nonlinearity, 37, 125013, https://doi.org/10.1088/1361-6544/ad805b, 2024. a, b, c
Bocquet, M.: Ensemble Kalman filtering without the intrinsic need for inflation, Nonlin. Processes Geophys., 18, 735–750, https://doi.org/10.5194/npg-18-735-2011, 2011. a, b
Bocquet, M. and Carrassi, A.: Four-Dimensional Ensemble Variational Data Assimilation and the Unstable Subspace, Tellus A, 69, 1304504, https://doi.org/10.1080/16000870.2017.1304504, 2017. a, b, c, d
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Short summary
This study examines the minimum ensemble size for accurate geophysical forecasting using a method called the ensemble Kalman filter. We reformulate accuracy via observation noise-dependency to classify filter performance qualitatively. Through numerical experiments with a chaotic model, we link the minimum ensemble size for the accuracy to system's instability and propose an effective ensemble downsizing method that ensures both stability and accuracy.
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