Diffusion of water vapor and the mechanical efficiency of moist circulations

This paper investigates thermodynamic constraints on the atmospheric circulation with a particular attention to the impacts diffusion of water vapor on mechanical efficiency. Mechanical efficiency is defined here as the ratio of the surface energy flux to the work produced by the circulation. We compare here two distinct frameworks to determine the mechanical efficiency. In the first approach, the amount of work produced by the atmospheric circulation is obtained from the irreversible entropy production associated with frictional dissipation. The second method determines the amount of Available Potential Energy (APE - Lorenz 1955, 1979) generated by the surface heating that can be converted into kinetic energy.

The first framework derives mechanical efficiency from the entropy budget as discussed in Pauluis and Held (2002a,b). The combination of surface energy flux and radiative cooling acts as a net export of entropy which balances the internal production due to irreversible processes. By identifying the individual contribution of frictional dissipation to the total entropy production, one is then able to determine the mechanical efficiency. Pauluis and Held (2002a) show that diffusion and irreversible phase transition account for a large fraction of the total entropy production and greatly reduces the work performed in a moist atmosphere. This approach leads to a relatively low estimate of the mechanical efficiency on the order of 0.02 to 0.05. The second method is based on the formulations for the sources and sinks of APE obtained by Pauluis (2006). A surface energy flux corresponds to a source of APE equal to the energy flux multiplied by a potential efficiency. For typical conditions in the tropics, this potential efficiency can be quite high - up to one third. Such a large potential efficiency is indeed required to maintain the intense winds of a hurricane (Emanuel 1986).

The potential efficiency is an order of magnitude greater than the overall mechanical efficiency of 0.02-0.05 obtained from the entropy budget. This discrepancy can be explained only if some of the APE is not converted into kinetic energy but actually lost through internal processes such as diffusion of water vapor, precipitation or re-evaporation. A scaling argument indicates that of all atmospheric processes, only diffusion of water vapor can result in a destruction of APE that is comparable to the source term due to the surface flux. In order to reconcile the entropy and APE analyses, most of the surface energy flux must be diffused from unstable air parcels (with a low reference temperature) to stable air parcels (with a high reference temperature). This diffusion can occur through three different processes: (1) mixing within the subcloud layer; (2) mixing between shallow clouds and the environment; and (3) entrainment in deep convective updrafts. The impact of diffusion on mechanical efficiency is investigated in high-resolution simulations of radiativeconvective equilibrium. Analysis of the energy flux in the numerical experiments confirms the theoretical prediction that diffusion is the primary sink of APE. Furthermore, these simulations indicate that most of the diffusion between unstable and stable air parcels takes place above the subcloud layer where shallow cumulus clouds mix with the dryer environment.

The moistening of subsiding air by shallow cumulus clouds plays a key role in the energetics of moist convection. Mixing between clouds and the dryer environment acts as a sink of APE that is comparable to the APE generated by the surface energy sources. As a result of this mixing the mechanical efficiency of the atmosphere is much lower than the potential efficiency. If, under specific circumstances, this mixing does not occur, the mechanical efficiency should increase by an order of magnitude, becoming comparable to the potential efficiency. Extreme weather such as hurricanes might indeed correspond to these high efficiency regimes. However, from a global perspective, these extreme weather events should be rare, and diffusion acts as the main sink of APE in a moist atmosphere.

References

Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady maintenance. J. Atmos. Sci., 43, 585–604.

Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157–167.

Lorenz, E.N., 1979: Available energy and the maintenance of a moist circulation. Tellus, 30, 15–31.

Pauluis, O., 2006: Sources and sinks of Available Potenital Energy in a moist atmosphere. To be published in J. Atmos. Sci. Available at http://www.cims.nyu.edu/ pauluis/Pauluis Bibliography.htm.

Pauluis, O. and I. M. Held, 2002a: Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation . J. Atmos. Sci., 59, 125–139.

Pauluis, O. and I.M. Held, 2002b: Entropy budget of an atmosphere in radiative-convective equilibrium. Part II: Latent heat transport and moist processes . J. Atmos. Sci., 59, 140–149.