Energy analysis of a recent approximation to the atmospheric primitive equations

An approximation to the thermodynamic equation was introduced by Holton which was motivated by an energy principle involving a quadratic expression in temperature deviation, which he identified as available potential energy. The approximation consists of neglecting the component of adiabatic warming/cooling due to the temporally and horizontally variable part of the specific volume on a constant pressure surface, WKT*. If the approximation is made, the system lacks a total energy principle involving either total potential energy or available potential energy (except in one special case). Although this approximate form of the primitive equations does not cause substantial error in a numerical simulation of the annual cycle of a zonally-symmetric circulation, there appears to be no significant advantage to its application. Use of the standard set of primitive equations is suggested.