%0 Journal Article %T A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective %+ Centre national de recherches météorologiques (CNRM) %+ Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) %A Pannekoucke, Olivier %A Ménard, Richard %A El Aabaribaoune, Mohammad %A Plu, Matthieu %< avec comité de lecture %J Nonlinear Processes in Geophysics %V 28 %P 1-22 %8 2021 %D 2021 %Z 2021NPGeo..28....1P %R 10.5194/npg-28-1-2021 %Z Sciences of the Universe [physics]Journal articles %X 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. %G English %2 https://insu.hal.science/insu-03668384/document %2 https://insu.hal.science/insu-03668384/file/npg-28-1-2021.pdf %L insu-03668384 %U https://insu.hal.science/insu-03668384 %~ IRD %~ INSU %~ METEO %~ UNIV-TLSE3 %~ CNRS %~ CNES %~ OMP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP