A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, Matthieu Plu
Abstract
Abstract. 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.