On the vertical structure of the atmosphere

Abstract

Expanding dependent atmospheric variables in series of pressure functions and applying a condition of energy preservation on modes that exist alone, it is found possible in an approximate case to derive a nonlinear differential equation which, as eigensolutions, determine the structure of the pressure functions. These modes are not found to resemble in a definite way the modes determined in a previous paper (Holmström, 1963) through expansion of observed data into empirical orthogonal functions. The conditions for a similarity between theoretical and empirical results are determined and it is then shown in a less approximate system that comparatively consistent vertical ω-profiles can be determined separately from the continuity, the vorticity, the adiabatic and the balance equations if the condition of selfpreservation is applied to each equation and the empirical modes for geopotential height and for wind are assumed to represent orthogonal eigensolutions to the equations. The main condition for vertical consistency in a self-preserving mode is found to be that the advection by the divergent part of the wind should not be neglected in the thermodynamic equation. DOI: 10.1111/j.2153-3490.1964.tb00168.x