Orthogonal Vertical Normal Modes of a Vertically Staggered Discretized Atmospheric Model

Abstract

Abstract In the formulation of nonlinear normal mode initialization (NNMI), we apply the separation of variables to a primitive equation model which is linearized about a basic state at rest. This results in the vertical and horizontal structure equations from which normal mode functions are constructed as their solutions. This paper is concerned with the property of the vertical normal mode functions. They vertical structure functions constructed in the framework of a vertically staggered discretized atmospheric model may not, in general, be orthogonal. There is an obvious advantage in using an orthogonal set of expansion functions. We propose in this paper the construction of orthogonal vertical structure functions for the NNMI with an atmospheric prediction model for which non-orthogonal vertical structure functions have been adopted in the past. We discuss the difference between the new formulation which yields orthogonal vertical structure functions and the old formulation which does not, in general,...