Consistent and flexible thermodynamics in atmospheric models using internal energy as a thermodynamic potential. Part II: Non-equilibrium regime.

Abstract

In numerical models of the atmosphere, the non equilibrium thermodynamic processes involving moisture are not always treated consistently — possibly leading to inconsistencies and errors in the energy budget. Therefore, a more consistent formulation of (moist) thermodynamics is important, for short timescale weather models, and long-timescale climate models. In part I, we derived a thermodynamically consistent framework, describing condensation, evaporation, freezing, and melting of cloud droplets, in which all thermodynamic quantities of interest were derived from an internal energy potential, and with the moist thermodynamics coupled to a 2D semi-implicit semi-Lagrangian dynamical core. While this framework was primed to express non-equilibrium processes, it was solved for the equilibrium regime only. Here, we follow the methods in part I, but with the expression of the non-equilibrium processes ‘turned on’, e.g. allowing freezing of super-cooled water, or evaporation into subsaturated air. To implement the proposed approach it is necessary to translate conventional atmospheric microphysics expressions for transfer rates of matter and entropy in and around a cloud droplet into the formalism of non-equilibrium thermodynamics. This procedure is first derived for some simple idealised cases, beginning with liquid droplet growth by vapour diffusion, and proceeding to more complex three-phase cases. To demonstrate the approach we then simulate some idealised cloudy thermals, comparing the equilibrium and non-equilibrium regimes—finding a robust decrease in the vertical velocity in the non-equilibrium regime, as expected. Thus, this work demonstrates the feasibility of building a numerical model that includes a framework for consistently modelling the moist non-equilibrium thermodynamics of an atmospheric system and provides a step towards this type of more consistent atmospheric modelling.