Adaptive observations and assimilation in the unstable subspace by breeding on the data-assimilation system

Results of targeting and assimilation experiments in a quasi-geostrophic atmospheric model are presented and discussed. The basic idea is to assimilate observations in the unstable subspace (AUS) of the data-assimilation system. The unstable subspace is estimated by breeding on the data-assimilation system (BDAS). The analysis update has the same local structure as the observationally fozrced bred modes. Use of adaptive observations, taken 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 targeting and assimilation design is tested in an idealized context, under perfect model conditions. It is shown that the process of driving the control solution toward the true trajectory accomplished by the assimilation reduces the number and growth of unstable modes. By observing and assimilating the unstable structures it is then possible to stabilize the assimilation system so that few observations are sufficient to keep the analysis error within very low bounds, even in the presence of observational noise. In an idealized limited area model configuration the number and frequency of observations necessary to control the system is shown to be related to the properties of its unstable subspace.