Use of the Gibbs thermodynamic potential to express the equation of state in atmospheric models

Abstract

The thermodynamics of moist processes is complicated, and in typical atmospheric models numerous approximations are made. However, they are not always made in a self-consistent way, which could lead to spurious sources or sinks of energy and entropy. One way to ensure self-consistency is to derive all thermodynamic quantities from a thermodynamic potential such as the Gibbs function. Approximations may be made to the Gibbs function; these approximations are inherited by all derived quantities in a way that guarantees self-consistency. Here, the feasibility of using the Gibbs function in an atmospheric model is demonstrated through the development of a semi-implicit, semi-Lagrangian vertical slice model, and its application to a standard buoyant bubble test case. The flexibility of the approach is also demonstrated by running the test case with four different equations of state corresponding to dry air, moist air that is saturated, a pseudo-incompressible fluid, and an incompressible fluid. A recently presented ‘blended’ equation set that unifies the dry fully compressible case and the pseudo-incompressible case is also easily accommodated.