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

Abstract

Abstract. This contribution addresses the characterization of the model-error\ncovariance matrix from the new theoretical perspective provided by the\nparametric Kalman filter method which approximates the covariance dynamics\nfrom the parametric evolution of a covariance model.\nThe classical approach to obtain the modified equation of a dynamics is revisited to\nformulate a parametric modelling of the model-error covariance matrix which\napplies when the numerical model is dissipative compared with the true dynamics.\nAs an illustration, the particular case of the advection equation\nis considered as a simple test bed. After the theoretical derivation of\nthe predictability-error covariance matrices of both the nature and the numerical model,\na numerical simulation is proposed which illustrates the properties\nof the resulting model-error covariance matrix.\n