Consistent and flexible thermodynamics in atmospheric models using internal energy as a thermodynamic potential. Part I: Equilibrium regime

Abstract

Approximations in the moist thermodynamics of atmospheric models can often be inconsistent; different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. To address these problems, all relevant thermodynamic quantities may be derived from a defined thermodynamic potential; approximations are instead made to the potential itself—this guarantees self‐consistency, as well as flexibility. Previous work showed that this concept is viable for vapour and liquid water mixtures in a moist atmospheric system using the Gibbs potential. However, on extension to include the ice phase, an ambiguity is encountered at the triple point. To resolve this ambiguity, here the internal energy is used instead. Constrained maximisation methods on the entropy can then be used to solve for the system equilibrium state. Nevertheless, a further extension is necessary for realistic atmospheric systems, where many importantnon‐equilibriumprocesses take place; for example, freezing of supercooled water and evaporation into subsaturated air. To capture processes such as these fully, the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. Here the principles of non‐equilibrium thermodynamics are used, beginning with a set of phenomenological equations, to show how non‐equilibrium moist processes may be coupled to a semi‐implicit semi‐Lagrangian dynamical core. Standard bubble test cases and simulations of idealised cloudy thermals are presented to demonstrate the viability of the approach for the equilibrium regime. Further details and results for non‐equilibrium regimes are presented in Part II.