Application of the heat engine framework to modeling of large-scale atmospheric convection

Abstract

The heat engine framework is examined in terms of large-scale atmospheric convection in order to investigate several theoretical and modeling issues related to the steady-state convecting atmosphere. Applications of the heat engine framework to convective circulations are reviewed. It is shown that this framework provides fundamental insights into the nature of various atmospheric phenomena and estimates of their potential intensity. The framework is shown to be valid for both reversible and irreversible systems; the irreversible processes' sole effect is to reduce the thermodynamic efficiency of the convective heat engine. The heat engine framework is then employed to demonstrate that the two asymptotic limits of quasi-equilibrium theory are consistent. That is, the fractional area covered by convection goes to zero, σ → 0, as the ratio of the convective adjustment to large-scale time scale (e.g. radiative time scale) go to zero, tADJ/tLS →0 , despite recent arguments to the contrary. Furthermore, the heat engine framework is utilized to develop a methodology for assessing the strength of irreversibilities in numerical models. Using the explicit energy budget, we derive thermodynamic efficiencies based on work and the heat budget for both open (e.g., the Hadley circulation) and closed (e.g., the general circulation) thermodynamic systems. In addition, the Carnot efficiency for closed systems is calculated to ascertain the maximum efficiency possible. Comparison of the work-based efficiency with that of the efficiency based on the heat budget provides a gauge for assessing how close to reversible model-generated circulations are. A battery of experiments is carried out with an idealized GCM. The usefulness of this method is demonstrated and it is shown that an essentially reversible GCM is sensitive (i.e., becomes more irreversible) to changes in numerical parameters and horizontal resolution.