The dynamics of error covariances in a barotropic model

Under the hypothesis of linear error growth, the tangent linear model can be used to provide a simplified form of stochastic-dynamic prediction, in which the uncertainty on a model forecast is defined by the error covariances between the model state variables. We apply this method on a global vorticity equation model with a simple initial condition for the covariance matrix. The forecast error variances and correlations undergo rapid modifications in relation with the atmospheric flow pattern. This may have some implications for operational assimilation schemes in numerical weather prediction. A deeper understanding of the relevant processes is sought, using an adjoint form of the prediction equation, in order to assess the impact of the initial variances and correlations, and of the intrinsic dynamics of the model flow. The application on some simplified flows shows the relevance of diffusion, advection, Rossby wave dispersion and barotropic instability to forecast skill prediction.