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

Pannekoucke, Olivier; Ménard, Richard; El Aabaribaoune, Mohammad; Plu, Matthieu

This contribution addresses 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 modelling of the model-error covariance matrix which applies when the numerical model is dissipative compared with the true dynamics. As an illustration, the particular case of the advection equation is considered as a simple test bed. After the theoretical derivation of the predictability-error covariance matrices of both the nature and the numerical model, a numerical simulation is proposed which illustrates the properties of the resulting model-error covariance matrix.

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Pannekoucke, Olivier / Ménard, Richard / El Aabaribaoune, Mohammad / et al: A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective. 2021. Copernicus Publications.

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Rechteinhaber: Olivier Pannekoucke et al.

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