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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/npg-2020-14
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2020-14
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 08 May 2020

Submitted as: research article | 08 May 2020

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This preprint is currently under review for the journal NPG.

A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective

Olivier Pannekoucke1, Richard Ménard2, Mohammad El Aabaribaoune3, and Matthieu Plu4 Olivier Pannekoucke et al.
  • 1INPT-ENM, CNRM UMR 3589, Météo-France/CNRS, CERFACS, Toulouse, France
  • 2ARQI/Air Quality Research Division, Environment and Climate Change Canada, Dorval (Québec), Canada
  • 3CNRM UMR 3589, Météo-France/CNRS, CERFACS, Toulouse, France
  • 4CNRM UMR 3589, Météo-France/CNRS, Toulouse, France

Abstract. This contribution adresses the characterization of the model-error covariance matrix from the new theoretical perspective provided by the parametric Kalman filter method which approximates the covariance dynamics from the parametric evolution of a covariance model. The classical approach to obtain the modified equation of a dynamics is revisited to formulate a parametric diagnosis of the model-error covariance matrix. As an illustration, the particular case of the advection equation is considered as a simple test bed. After the theoretical derivation of both the forecast-error and the predictability-error covariance matrices, a numerical simulation is proposed which demonstrates the skill of the parametric methodology in reproducing the model-error covariance matrix information.

Olivier Pannekoucke et al.

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Olivier Pannekoucke et al.

Olivier Pannekoucke et al.

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Latest update: 10 Jul 2020
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Short summary
Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Numerical weather prediction involves numerically solving the mathematical equations, which...
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