Estimate of Truncation Error in Transformed Coordinate, Primitive Equation Atmospheric Models

Abstract

A comparison of truncation error for second-order difference schemes based on the σ and z coordinate systems is given. We also test a transformed z system based on s = (z − H)/(zT − H), where H ≤ z ≤ zT and H is surface elevation. The error is estimated by substitution of a known pressure function into the pressure gradient term. The σ and z systems show comparable error in the case of a level surface. The presence of a mountain greatly increases the error in the σ and z system calculations. A modification of the σ and s systems is developed to reduce this error.