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.

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 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.

As I have noted from time to time, these interactions are frequently used to tune hindcasts so that a better representation of the past response of the Earth’s climate systems is obtained. And that I find this situation to be somewhat disconcerting due to the fuzzy nature of the parameterizations that are used to characterize these inherently complex interactions.

Let’s consider an example as follows. Take the steady-state isothermal flow of an incompressible fluid through a straight round pipe and for which a known flow rate is imposed. We want to check the predictions of a model of the pressure gradient along the pipe with measured data. For this flow as described, we know that the friction factor between the pipe wall and the fluid is the most critically important aspect of the response of the pressure gradient. The physical phenomena and processes of importance relative to the response of interest are known without a doubt.

If the predictions by the model do not agree with the measured data we know exactly which aspect of the modeling is in error and we can adjust that single parameter with assurance that we can obtain the correct results solely by the actions of this single parameter. We get the correct response for the correct reason. We know we have gotten the correct response for the correct reasons based on both theoretical and empirical information. Especially, empirical data have shown the direct connection between the pressure gradient and the wall friction factor for several hundred years.

In my opinion aerosols, and their critically important interactions with radiative energy transport, are among the more inherently complex aspects of real-world, radiative-energy transport in the Earth’s atmosphere. While theoretical studies have provided insights into these phenomena and processes, these are basically for highly idealized situations. The parameterization of the interactions are at all levels; from estimation of the geometric characterization of the aerosols, to the numbers of particles, to connections with several important aspects of clouds, and finally to the interactions with radiative energy transport. See Chapters 7 and 8 of Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models [Paperback] and Chapters 5 and 8 of Thermodynamics of Atmospheres and Oceans, Volume 65 (International Geophysics) [Hardcover].

When so many different aspects of complex processes are described by parameterizations, it can be difficult to ensure that tuning of parameterizations can be directly linked to the response of interest. This is especially true, in my opinion, when the response of interest is a very high level solution functional in which all aspects of the total problem are mapped to a single number. It is very disconcerting that parameterization of the geometric details of aerosols, for example, have been linked to representation of the response of the global-average surface temperature.

“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.

For me, this situation speaks volumes.

Update: Today, this morning, September 3, 2010, I’m not seeing any ???

What a strange way to write about anything. The alleged subject does not appear in the discussion.