Orthogonal Vertical Normal Modes for a Multilevel Model

Abstract

Orthogonal vertical normal modes are found for a multilevel sigma-coordinate model, linearized about a state of rest with a nonisothermal mean temperature profile. Orthogonality permits the partitioning of energy into the vertical modes, and simplifies the application of variational techniques to normal mode initialization in the multilevel case. Improved procedures are described for the vertical transforms required during normal mode initialization. We derive relationships between the time derivatives of the energy computed in vertical normal mode space and in gold point space, and analogous relationships between the changes made by initialization to the vertical normal mode coefficients and the corresponding changes made in grid point space.