## More on Entropy, MEP, and Climate . . . and more

HISASHI OZAWA AND ATSUMU OHMURA Thermodynamics of a Global-Mean State of the Atmosphere—A State of Maximum Entropy Increase

ABSTRACT

Vertical heat transport through thermal convection of the earth’s atmosphere is investigated from a thermo- dynamic viewpoint. The postulate for convection considered here is that the global-mean state of the atmosphere is stabilized at a state of maximum entropy increase in a whole system through convective transport of sensible and latent heat from the earth’s surface into outer space. Results of an investigation using a simple vertical gray atmosphere show the existence of a unique set of vertical distributions of air temperature and of convective and radiative heat fluxes that represents a state of maximum entropy increase and that resembles the present earth. It is suggested that the global-mean state of the atmospheric convection of the earth, and that of other planets, is stabilized so as to increase entropy in the universe at a possible maximum rate.

OLIVIER PAULUIS AND ISAAC M. HELD Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part II: Latent Heat Transport and Moist Processes

ABSTRACT

In moist convection, atmospheric motions transport water vapor from the earth’s surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes.

The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.

RICHARD GOODY Maximum Entropy Production in Climate Theory

ABSTRACT

R. D. Lorenz et al. claim that recent data on Mars and Titan show that planetary atmospheres are in unconstrained states of maximum entropy production (MEP). Their model as it applies to Venus, Earth, Mars, and Titan is reexamined, and it is shown that their claim is not justified. This does not necessarily imply that MEP is incorrect, and inapplicable to atmospheres, but it does mean that the difficult and unexplored problem of dynamical constraints on the MEP solution must be understood if it is to be of value for climate research.

Here’s some recent info on the topic.

I ran across this issue of Philosophical Transactions of The Royal Society B: Biological Sciences, May 12, 2010; 365 (1545):

Theme Issue ‘Maximum entropy production in ecological and environmental systems: applications and implications’ compiled and edited by Axel Kleidon, Yadvinder Malhi and Peter M. Cox. doi:10.1098/rstb.2010.0018

Full papers are available at no cost.

This paper:

G Grinstein and R Linsker, “Comments on a derivation and application of the ‘maximum entropy production’ principle” 2007 J. Phys. A: Math. Theor. 40 9717. doi:10.1088/1751-8113/40/31/N01

reports errors in these recent papers by Dewar:

Dewar R 2003. “Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states” J. Phys. A: Math. Gen. 36 631. doi: 10.1088/0305-4470/36/3/303

Dewar R C 2005, “Maximum entropy production and the fluctuation theorem” J. Phys. A: Math. Gen. 38 L371. doi: 10.1088/0305-4470/38/21/L01

Finally, additional papers here. And even more here.

Thanks for the links Dan!

I’ve always liked thermodynamics. And since it does not appear possible to IV&V the GCMs, we are in dire need of a less sophomoric computational approach to understanding and predicting the ultimate climatic consequences of anthropogenric greenhouse gases and other human influences on the climate.

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