Variational non-linear normal mode initialization

Abstract

The non-linear normal mode initialization technique of Machenhauer (1977) and Baer (1977) has shown great potential in removing spurious high frequency gravity modes from primitive equation model integrations. In essence, this procedure orthogonalizes the time tendencies of the original fields to the time tendencies of the high frequency normal modes of the linearized model equations. In the present work this procedure is generalized by casting the problem in a variational framework. Thus a variational integral is minimized subject to strong constraints obtained from the theory of non-linear normal mode initialization. When applied to the shallow water equations, it is found that this variational approach includes most previous barotropic static initialization procedures as special cases. The procedure was tested under various conditions and the results displayed.