Department of Physics
University of Ferrara, Italy
A recently developed data assimilation method is discussed and applied to a quasi-geostrophic atmospheric model. The method exploits the flow-dependent unstable structures of the observationally forced analysis cycle solution to estimate and reduce the background error. The unstable subspace is estimated by breeding on the data assimilation cycle, so that the analysis update has the same structure as the forced bred modes. Use of adaptive observations, made at locations where bred vectors have maximum amplitude, enhances the efficiency of the procedure and allows the use of a very limited number of observations and modes.
The performance of the assimilation scheme is tested in an idealized context, under perfect model conditions. The observational network consists of fixed observations completely covering one third of the domain plus a single adaptive observation in the otherwise data void region. Statistics accumulated over two years analysis cycle experiments show that a major reduction of the RMS analysis error is obtained with this procedure compared to 3D-Var.
The reduction of the error, whose amplitude is large at the beginning of the experiment, is accompained by a corresponding stabilization of the analysis cycle solution. The initially positive exponent, corresponding to a typical doubling time of two days, becomes negative, pointing to an obvious reduction of the dimension of the unstable subspace. This finding confirms previous conclusions about the stabilizing effect of the observational forcing and the observability of the data assimilation system.