An Economical Time–Differencing System for Numerical Weather Prediction

Abstract

A simple method for integrating the primitive equations is presented which allows for a timestep increment up to twice that of the conventional leapfrog scheme. It consists of a time-averaging operator, which incorporates three consecutive time levels, on the pressure gradient terms in the equations of motion. An attractive feature of the method is its case in programming, since the resulting finite-difference equations can he solved explicitly. Presented here are linear analyses of the method applied to the barotropic and two-layer baroclinic gravity waves. Also presented is an analysis of the method with a time-damping device incorporated, which is an alternative in controlling linearly amplifying computational modes.