A Thermodynamic Foundation for Modeling the Moist Atmosphere

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Abstract
With advances in numerical modeling of the atmosphere, we have experienced that the return to the first principles of physics often enables a model to cope more easily with the complexities of the real atmosphere. The return to the primitive equations of motion from historical balance approximations is an example. This paper proposes a way to return to the “primitive” form of moist themodynamics, in which prediction is made strictly in terms of conservative properties, such as mass and entropy. There is no conservation law that would apply directly to temperature or pressure. These intensive properties, therefore, should be diagnostically determined by thermodynamics, from the predicted conservative properties. The scope of the paper is limited to the thermodynamics of reversible processes. Irreversible processes, which would make a model alive with real weather, are not discussed here, since each of them requires a separate empirical treatment. It is shown, however, that the proposed formulation of thermodynamics facilitates modularization of various approximations within a model, and among models. For example, both the hydrostatic and nonhydrostatic models can be built under an identical design, differing only in the manner of calculating vertical motion. The proposed formulation is extended to include the ice phase within reversible thermodynamics. Also discussed are numerical problems in the spatial representation of thermodynamic discontinuities, which are caused by the phase transition of water substance.

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