Abstract/Summary

The task of this paper is to study and analyse transformed localization and generalized localization for ensemble methods in data assimilation. Localization is an important part of ensemble methods such as the ensemble Kalman filter or square root filter. It guarantees a sufficient number of degrees of freedom when a small number of ensembles or particles, respectively, are used. However, when the observation operators under consideration are non-local, the localization that is applicable to the problem can be severly limited, with strong effects on the quality of the assimilation step. Here, we study a transformation approach to change non-local operators to local operators in transformed space, such that localization becomes applicable. We interpret this approach as a generalized localization and study its general algebraic formulation. Examples are provided for a compact integral operator and a non-local Matrix observation operator to demonstrate the feasibility of the approach and study the quality of the assimilation by transformation. In particular, we apply the approach to temperature profile reconstruction from infrared measurements given by the infrared atmospheric sounding interferometer (IASI) infrared sounder and show that the approach is feasible for this important data type in atmospheric analysis and forecasting