A Non-Iterative Procedure for the Time Integration of the Balance Equations

Abstract

Recent work by Gent and McWilliams (1982) suggests that of all models intermediate in complexity between quasi-geostrophic (QG) and primitive equation (PE), the balance equations (BE) have the best performance when compared with the standard of the PE. The BE system [and the simpler linear balance equations (LBE)] have been infrequently integrated during the past 30 years because of problems with solvability conditions and the apparent necessity for iteration each timestep. The present article proposes a non-iterative procedure for the time integration of the BE and LBE systems. The procedure was tested on the barotropic (vertically integrated) equations on the sphere. High-resolution BE, LBE and QG integrations were compared with a control PE integration initialized with observed data. The growth of error in the various models as a function of time, latitude and scale was carefully monitored. The high accuracy of the BE equations was confirmed.