Sources and Sinks of Available Potential Energy in a Moist Atmosphere

Abstract

Abstract Available potential energy (APE) is defined as the difference between the total static energy of the atmosphere and that of a reference state that minimizes the total static energy after a sequence of reversible adiabatic transformations. Determining the rate at which APE is generated in the atmosphere allows one to estimate the amount of kinetic energy that can be generated by atmosphere flows. Previous expressions for the sources and sinks of APE rely on a dry framework and are limited by the fact that they require prior knowledge of the distribution of latent heat release by atmospheric motion. In contrast, this paper uses a moist APE framework to derive a general formula for the sources and sinks of APE that can be equally applied to dry and moist circulations. Two key problems are addressed here. First, it is shown that any reorganization of the reference state due to diabatic heating or addition of water does not change its total static energy. This property makes it possible to determine the rate of change in APE even in the absence of an analytic formula for the reference state, as is the case in a moist atmosphere. Second, the effects of changing the total water content of an air parcel are also considered in order to evaluate the changes of APE due to precipitation, evaporation, and diffusion of water vapor. Based on these new findings, one can obtain the rate of change of APE from that of atmospheric entropy, water content, and pressure. This result is used to determine the sources and sinks of APE due to different processes such as external energy sources, frictional dissipation, diffusion of sensible heat and water vapor, surface evaporation, precipitation, and reevaporation. These sources and sinks are then discussed in the context of an idealized atmosphere in radiative–convective equilibrium. For a moist atmosphere, the production of APE by the surface energy flux is much larger than any observational or theoretical estimates of frictional dissipation, and, as is argued here, must be balanced by a comparable sink of APE due to the diffusion of water vapor from unstable to stable air parcels.