Four-Dimensional, Data Assimilation and the Slow Manifold

Abstract

Abstract Four-dimensional data assimilation is the analysis technique that has been devised to cope with the large quantities of asynoptic data received from the new remote observing systems. In this analysis method, an atmospheric simulation model is integrated in time with observed data being inserted into the model whenever it becomes available. In the present study, the four-dimensional data assimilation process is analyzed in terms of the normal modes of the assimilating model and the slow manifold concept of Leith (1979). The problem of “data rejection” and the spurious excitation of transient gravity waves can be shown to have a simple geometrical interpretation in the slow manifold methodology. Using these ideas it is possible to define an ideal assimilation technique. Various realizable assimilation techniques which approach this ideal are proposed and tested.