Abstract. This contribution adresses 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 diagnosis of the model-error covariance matrix. As an illustration, the particular case of the advection equation is considered as a simple test bed. After the theoretical derivation of both the forecast-error and the predictability-error covariance matrices, a numerical simulation is proposed which demonstrates the skill of the parametric methodology in reproducing the model-error covariance matrix information.

Abstract. In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemical transport model MOCAGE (MOdèle de Chime Atmospheric à Grand Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in numerical weather prediction centers. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm−1 to estimate the observation error covariance matrix. We computed hourly 3D-Var analyses and compared the resulting O3 fields against ozonesondes and the measurements provided by the Microwave Limb Sounder (MLS). The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance is employed in the assimilation system.

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.

Abstract. In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemistry transport model MOCAGE (Modèle de Chimie Atmosphérique à Grande Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in many numerical weather prediction centres. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm−1 to estimate the observation-error covariance matrix. This spectral range includes ozone-sensitive and atmospheric window channels. We computed hourly 3D-Var analyses and compared the resulting O3 fields against ozonesondes and the measurements provided by the Microwave Limb Sounder (MLS) and by the Ozone Monitoring Instrument (OMI). The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement, especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance matrix is employed in the assimilation system, by reducing the number of iterations needed for the minimizer to converge.