Three-dimensional spectral prediction equation, A
T. J. Simons · Digital Collections of Colorado (Colorado State University) · 2007
A generalization of the two-dimensional spectral forecast equations is suggested, whereby the atmospheric flow field in horizontal and vertical directions is represented in terms of orthogonal functions, which are eigenfunctions of certain differential operators in the three-dimensional equations.The technique is applied to the quasi-geostrophic potential vorticity equation.The quasi-geostrophic potential vorticity is related to the stream function of the horizontal wind by a three-dimensional Laplacian in which the vertical derivative is modified by the standard static stability of the atmosphere.The orthogonal functions are chosen to be characteristic functions of this quasi-Laplacian operator for a given variation of static stability with height.The resulting spectral form of the potential vorticity equation is very similar to that of the barotropic vorticity equation.