Introducing the coupling information in a limited-area variational assimilation

We address the problem of how to take advantage, in a limited-area variational assimilation, of the previously-performed global data analysis of the coupling system. We expect this information to add value to the limited-area analysis, since, for example, the global analysis can deal with observations close to but outside the domain of interest. The global analysis is treated as an extra source of information, and we derive the full least-square error problem for the augmented information vector. We are left with the specifications of a global analysis-error covariance matrix and extra cross-covariance terms, expressed in a lower-resolution grid covering all of the coupled domain. Simplifications are proposed to make the problem algorithmically more tractable, especially in order to benefit from the advances in the 'modelization' of the background-error covariance matrix. Further, we obtain a more classical minimization problem for the sum of three, instead of two, additive cost functions. We have tested the formulation in the framework of the coupled ARPEGE 4D-Var and ALADIN-France 3D-Var systems. Objective scores with respect to radiosonde and aircraft observations give neutral or slightly positive results for the proposed method. The information-augmented assimilation cycle produces background 6 h forecasts that are slightly closer to the verifying observations. Subjective case-by-case verification does not reveal a visible systematic beneficial impact on the quality of the forecasts, especially for small-scale parameters such as precipitation. We nevertheless propose to apply the method in future to very high-resolution assimilation systems, which are likely to be operated on fairly small domains. Copyright (C) 2008 Royal Meteorological Society.