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Modeling of background error covariance matrix: non exhaustive review and challenges for convective scale DA of clouds a

Outlines. Introduction: CVT formulation in VAR Which variables shall we analyzed?- Choice of the control variables- Non-linear balance equationsHow to get weather-dependent statistics?- Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of

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Modeling of background error covariance matrix: non exhaustive review and challenges for convective scale DA of clouds a

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    2. Outlines Introduction: CVT formulation in VAR Which variables shall we analyzed? - Choice of the control variables - Non-linear balance equations How to get weather-dependent statistics? - Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of heterogeneous covariances Possible strategies for mesoscale applications

    3. Outlines Introduction: CVT formulation in VAR Which variables shall we analyzed? - Choice of the control variables - Non-linear balance equations How to get weather-dependent statistics? - Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of heterogeneous covariances Possible strategies for mesoscale applications

    4. Introduction: The Variational Assimilation (VAR)

    5. Introduction: The Variational Assimilation (VAR)

    9. Introduction: Challenges at mesoscale Main challenges in modeling B to analyze clouds and precipitations: Broad ranges of space and time scales involved The strong non-linearities in moist physical processes imply that balance constraints, that were initially developed for DA in global models, must probably be redesigned Error covariances of variables linked to clouds and precipitations are inhomogeneous, anisotropic and flow dependent: better spatial and spectral localization is needed

    10. Outlines Introduction: CVT formulation in VAR Which variables shall we analyzed? - Choice of the control variables - Non-linear balance equations How to get weather-dependent statistics? - Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of heterogeneous covariances Possible strategies for mesoscale applications

    26. Outlines Introduction: CVT formulation in VAR Which variables shall we analyzed? - Choice of the control variables - Non-linear balance equations How to get weather-dependent statistics? - Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of heterogeneous covariances Possible strategies for mesoscale applications

    46. Outlines Introduction: CVT formulation in VAR Which variables shall we analyzed? - Choice of the control variables - Non-linear mesoscale balance equations How to get weather-dependent statistics? - Ensemble flow-dependent B matrix - Spatial and spectral localization of correlations - Use of heterogeneous covariances Possible strategies for mesoscale applications

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