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.
Post of Record
I have moved this post to here.
U. S. Environmental Protection Agency: The Science is Settled
EPA Chief Goes Toe-To-Toe With Senate GOP Over Climate Science.
U.S. EPA Administrator Lisa Jackson today defended the science underpinning pending climate regulations despite Senate Republicans’ claims that global warming data has been thrown into doubt.
“The science behind climate change is settled, and human activity is responsible for global warming,” Jackson told the Senate Environment and Public Works Committee.
Administrator Jackson was speaking for the EPA, and the Climate Science communicated to the US EPA by Climate Scientists.
The Science is Settled, it’s on the EPA Web site:
Statement on Litigation on EPA Endangerment Finding.
The question of the science is settled.
Here’s the Introduction to The Statement on Litigation on EPA Endangerment Finding:
Statement on Litigation on EPA Endangerment Finding
The evidence of, and threats posed by a changing climate are right before our eyes.
EPA issued its endangerment finding because the U.S. Supreme Court ruled three years ago that greenhouse gas emissions constitute air pollution and that EPA therefore must determine whether that pollution threatens the health and welfare of Americans. EPA proceeded to carry out the instructions of the highest court in the land, and in doing so undertook a comprehensive and transparent review of the soundest available science. That science came from an array of highly respected, peer-reviewed sources from both within the United States and across the globe, and took into consideration hundreds of thousands of comments from members of the public, which were addressed in the finding. The conclusion: the scientific evidence of climate change is overwhelming and greenhouse gases pose a real threat to the American people.
The question of the science is settled. [ my em-bolding ] The debate that should be taking place now is how to address this challenge and take advantage of the opportunity it offers. EPA is proceeding with common sense measures that are helping to protect Americans from this threat while moving America into a leadership position in the 21st Century green economy, creating millions of good-paying jobs along the way. Unfortunately, special interests and other defenders of the status quo are now turning to the courts in an attempt to stall progress, with the added effect, if they are successful, of halting the creation of millions of new jobs.
EPA is confident the finding will withstand legal challenge, allowing the Agency to protect the American people from the significant dangers posed by greenhouse gases and carbon pollution.
The US EPA is committed to science-based policy. In this case, its findings are based The Science as determined by The Climate Science Community and the associated Climate Scientists.
Implicit Function Theory Applications; Part 0
I developed analytical solutions for a couple of simple transient compressible fluid flow problems that include fluid-structure interactions. I think the problems and solutions might be candidates for standard problems / benchmarks / Method of Exact Solutions.
Implicit function theory is an important aspect of the analytical solutions. Getting the required implicit function theory results was proving to take more pages and space that the analytical solutions. I decided to document those results in these separate notes. The results needed for the analytical solutions are given in the latter part of the notes, beginning with Variable Fluid Control Volume.
I have uploaded a Table that is in landscape and that I don’t now how to get into a portrait layout-document. That Table is here and should open in a separate window.
There are tons and tons of algebra associated with this work; straightforward but tedious algebra. I have checked and re-checked but maybe haven’t cleared out all the errors. If you plan to use any of this material, let me know what is of interest and I’ll work with you to ensure that the equations are correct.
The PDF file is here and should open in a separate window.
Update February 26, 2011
A corrected version of Table 3 is here. There was a bug in the first column of the third row.
Update January 14, 2011
There’s a typo in Eq. (1.8). The X_sub i in the last line ( the bottom part of the bottom ) should be Y_sub i. That’s a strange kind of bug; a typo in a nemonic device.
In the Section, The Bridgman Method, I say:
I have uploaded the table as a PDF file and provided this URL link in my post: http://edaniel.files.wordpress.com/2011/01/testbridgmantable.pdf . You’ll have to copy-n-paste the link into your browser.
That is the same Table mentioned in the Post, and you don’t have to copy-n-paste the URL; it’ll open from the PDF.
Note that Eq. (1.33) can be written in terms of the square of the sound speed.
And in a few places following Tables of derivatives, I said that the entropy derivatives had not been reduced when in fact they are shown reduced form in the tables.
Let me know if you find any problems.
An Interesting and Important Discussion
Steve Fitzpatick is summarizing important aspects of radiative energy transport and its interaction with material in the Earth’s atmosphere, at Jeff Id’s tAV. I think many of these phenomena and processes are represented by parameterizations.
Physical Realizations of Oxymoron
A Climate Scientist pleads for ( understanding / belief / sympathy / faith / acceptance ) and taking politics out of science by writing an Editorial Opinion column about politics, and while stating:
“Overloading the atmosphere with carbon dioxide from burning fossil fuels is heating the planet, shrinking the Arctic ice cap, melting glaciers and raising sea levels. It is leading to more widespread drought, more frequent heat waves and more powerful hurricanes. [ My bold ]
A two-fer; injecting politics into science and making statements not supported by science.
Americans are Fully Committed to Protecting the Environment
So long as it doesn’t make too much noise.
For me, this situation speaks volumes.
Google Ads
Where are those Google Ads coming from ? Or, more nearly correctly, from where are those Google Ads coming?
Update: Today, this morning, September 3, 2010, I’m not seeing any ???
Do-it-Yourself at RealClimate.Org
This post at realclimate.org is very strange. The phrase do-it-yourself is in the Title for the post and repeated once in the first sentence. Searches show that the phrase does not appear anywhere else in the post.
What a strange way to write about anything. The alleged subject does not appear in the discussion.
