On Normal Mode Linear Initialization on the Sphere

Abstract

The normal mode initialization procedure is investigated. It is shown that a balance exists between the wind field and the mass field when the gravity modes have been removed from the initial fields. Adopting a representation in the spectral domain on the sphere it is shown that the vectors consisting of all amplitudes of the streamfunction and the velocity potential, respectively, are related to the vector consisting of all amplitudes of the geopotential by a square matrix which depends entirely on the eigenvalues and eigenvectors of the truncated systems. The balance which exists after normal mode initialization is compared with the quasi-geostrophic balance when this procedure is applied to the adjusted initial fields which are obtained when the contribution from the gravity waves has been removed. It turns out that the balance from the normal mode procedure is virtually identical to the quasi-geostrophic balance except on the largest scales. The difference on the largest scale between the Rossby or rotational modes obtained by the two procedures is in the linear case entirely due to the sphericity of the earth since the modes would be identical if the Coriolis parameter were constant. The modifications to the initial state created by the normal mode procedure are investigated in Section 5, and Section 6 contains an analysis of the first baroclinic mode analogous to the basic barotropic mode considered in the main body of the paper.