The Dry-Entropy Budget of a Moist Atmosphere

Abstract The entropy budget has been a popular starting point for theories of the work, or dissipation, performed by moist atmospheres. For a dry atmosphere, the entropy budget provides a theory for the dissipation in terms of the imposed diabatic heat sources. For a moist atmosphere, the difficulties in quantifying irreversible moist processes or the value of the condensation temperature have so far frustrated efforts to construct a theory of dissipation. With this complication in mind, one of the goals here is to investigate the predictive power of the budget of dry entropy (i.e., the heat capacity times the logarithm of potential temperature). Toward this end, the dry-entropy budget is derived for an atmosphere with realistic heat capacities and a solid-water phase, features that were absent from some previous studies of atmospheric entropy. It is shown that the dry-entropy budget may be interpreted as the sum of sources and sinks from six processes, which are, in order of decreasing magnitude, radiative cooling, condensation heating, sensible heating at the surface, wind-generated frictional dissipation, lifting of water, and transport of heat from the melting line to the upper troposphere. This picture leads to an alternative explanation for the low efficiency of the moist atmospheric engine. Numerical simulations are presented from a new cloud-resolving model, Das Atmosphärische Modell, which was designed to conserve energy and close the dry-entropy budget. Simulations with and without subgrid diffusion of heat and water are compared to investigate the impact of subgrid parameterizations on the terms in the dry-entropy budget. The numerical results suggest a particularly simple parameterization of wind-generated dissipation that appears to be valid for changes in sea surface temperature and mean wind. The dry-entropy budget also points to various changes in forcings and parameterizations that could be expected to increase or decrease the wind-generated dissipation.