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

Olivier Pannekoucke (1, 2) , Richard Ménard , Mohammad El Aabaribaoune , Matthieu Plu

1 CNRM - Centre national de recherches météorologiques
2 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique

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.

Domaines: Planète et Univers [physics]

Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, Matthieu Plu. A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective. Nonlinear Processes in Geophysics, 2021, 28, pp.1-22. ⟨10.5194/npg-28-1-2021⟩. ⟨insu-03668384⟩