A Method for Direct Solution of a Steady Linearized Spectral General Circulation Model

Abstract

A steady linearized version of a general circulation model (GCM) is a potentially useful tool for diagnosis and understanding of the time-mean solutions of the GCM. A method is developed for direct solution of the linearized equations. The method is efficient in the case that the GCM employs spectral horizontal discretization and finite differences in the vertical sigma coordinate, with seven or more vertical levels. The method uses a system of equations that is equivalent to the linearized GCM, but with an expanded number of variables. The resulting system of equations can then be solved by sparse matrix techniques. The method is applicable to general basic states.