Nonlinear normal mode initialization and the bounded derivative method

Abstract

Recently, two new approaches have been proposed for the initialization of primitive equation models. One is called the nonlinear normal mode procedure, developed by Baer and Machenhauer. It is suitable for a global primitive equation model in which the construction of the model normal modes is feasible. The other approach is called the bounded derivative method, proposed by Kreiss. It can be applicable to both pure initial value and initial boundary value problems. Leith established a connection between the nonlinear normal mode procedure and the classical balancing based on quasi‐geostrophic theory. The purpose of this paper is to compare the three procedures of initialization for a baroclinic primitive equation model with beta plane geometry in pressure coordinates. To the degree of approximation employed, the initialization by the bounded derivative method agrees with the classical balance procedure with quasi‐geostrophic assumptions. We demonstrate for the same prediction model that nonlinear normal mode balancing leads to an initialization scheme identical to the one derived from the bounded derivative method within the degree of approximations. Since both new approaches to initialization are more general than the classical procedures, the connection of the two approaches with the quasi‐geostrophic formulation will enhance our understanding of the dynamics of large‐scale motions beyond the classical quasi‐geostrophic theory.