Formulas for calculating available potential energy over uneven topography

Abstract

Formulas are derived that correctly account for the uneven surface topography (mountains) in calculations of atmospheric available potential energy and its rate of change. Two (barotropic) reference states for available potential energy are discussed: one is horizontally stratified, the other has uniform surface pressure. The former is a state of minimum total potential energy and the latter is a state of minimum enthalpy. Both proposed reference states lead to similar, simple expressions for generation of available potential energy. A numerical procedure is presented for calculating the horizontally stratified reference state from a given atmospheric state. For a simple case with mountains, various methods of computing available potential energy are compared, which illustrates the inherent errors in previous formulas. Potential applications of the “exact” expressions are mentioned in the concluding section.