The Arrogance of Physicists

First, apropos of some of the discussion below but more urgent than any of that, the council of the American Physical Society is considering revising its 2007 statement on climate change. If you are an APS member with an opinion on the issue, write immediately to one of the councillors; they need your input before the November 8th council meeting.

So... let me start by saying I love physics. I think I decided to be a physicist by age 13 or 14. My best friend in high school also got a physics PhD. I married a physicist. I published a couple of dozen physics research papers. I've met Nobel Prize winners in physics, talked with some of the most prominent names in the field. I work with dozens of physicists every day. I've had a wide variety of physicist friends and colleages for decades.

I hate to stereotype people, and the physicists I know span a huge variety of personality types. But training and experience in physics gives you a very powerful toolbox of techniques, intuitions and approaches to solving problems that molds your outlook and attitude toward the rest of the world. Other fields of science or engineering are limited in their scope. Mathematics is powerful and immense in logical scope, but in the end it is all tautology, as I tease my mathematician friends, with no implied or even desired connection to the real world. Physics is the application of mathematics to reality and the 20th century proved its remarkable effectiveness in understanding that world, from the behavior of the tiniest particles to the limits of the entire cosmos. Chemistry generally confines itself to the world of atoms and molecules, biology to life, wonderful in itself, but confined so far as we know to just this planet. The social sciences limit themselves still further, mainly to the behavior of us human beings - certainly a complex and highly interesting subject, but difficult to generalize from. Engineering also has a powerful collection of intuitions and formulas to apply to the real world, but those tend to be more specific individual rules, rather than the general and universal laws that physicists have found.

Computer scientists and their practical real-world programming cousins are perhaps closest to physicists in justified confidence in the generality of their toolbox. Everything real can be viewed as computational, and there are some very general rules about information and logic that seep into the intuition of any good programmer. As physics is the application of mathematics to the real world of physical things, so programming is the application of mathematics to the world of information about things, and sometimes those two worlds even seem to be merging.

But physics is older and has a lot more experience. Confidence in the tools of physics has proven itself in the weaponry of war from Archimedes to the nuclear era. The industrial revolution arose from application of physical understanding to energy - the steam engine and engines that followed, electricity. The basis of our modern information technology - semiconductors, magnetic devices, lasers, fiber optics as just recognized by the Nobel committee - all derive from the work of physicists. Many tools of advanced medicine - X-rays, MRI's, various radiation-based cancer therapies - derive from physical understanding. The need for basic understanding of the laws of physics are exemplified perhaps most in recent debates over energy policy - politicians who talk about being able to drive hydrogen cars by filling up the tank with water, for instance. Physics gives direct power over the world, but also imposes limits on what is physically possible, and understanding both is essential. In recent years physicists flocked to Wall Street to prove the worth of their skills in the world of finance - quantitative analysis, and several of my friends heard that siren song. But money is a fickle thing, much different from the solid world we're accustomed to thinking about, and I'm not sure my colleagues' toolbox is quite big enough yet to fully understand what they're dealing with in that realm.

In general though, physicists have good reason to be arrogant. Each of us in the intellectual world is like an armed policeman. A certain swagger is justified, we feel confident we have the tools to handle any situation. A problem asserts itself, and we walk in with the self-assurance of those who have tackled thousands of similar cases in the past. For a really challenging problem we know how to put out a call for reinforcements. One all-purpose tool is reductionism - breaking a problem into smaller more comprehensible pieces, and then tackling those one by one. Modeling, a topic I've written about before , is what reduces a problem of reality to a mathematical problem. Every model is an approximation, but a wide variety of intuitions guide the physicist in isolating the essential characteristics of a problem into an appropriate model. Consideration of energy scales, expected magnitude of perturbations, symmetries and the like provide ways to separate effects that are important from those that are likely irrelevant to the problem in question. Systems that exhibit seemingly universal behavior, for example the ubiquity of oscillations, or the prevalance of power laws in complex systems, give the physicist a diverse collection of analogues to compare with the model developed for any given problem.

But sometimes that arrogance and self-assurance and collection of intuitions lead us, or at least a few of us, astray. We forget that there are other smart people in the world, who have been thinking about their limited problem for a lot longer and perhaps have a deeper understanding than we give them credit for. We jump in with our simplified models and ideas and then wonder why they don't find them helpful. Or we too deeply trust the intuition of a colleague who has been often right before or who we trust for other reasons, but in a particular instance has not put in the effort to properly understand the problem, and ends up only embarrassing themselves, and us by association.

I experienced a bit of this myself when I first started working at my current job. I now work in scientific publishing, and back in late 1995, when the web was young, I knew deep down that the scientific publishing business model had to change, and I came in with many ideas for reform. There was a definite lack of respect in my attitude for the experience and background of the many others in my office. I was right about some of the things that needed to be done, but naive about how to initiate those changes. My approach was unhelpful - to the extent that my boss decided, after about a year of this, to have a big sit-down talk with me and send me off to a Dale Carnegie course. I learned a bit of humility then - but I am still regularly accused of arrogance in my communications elsewhere, so perhaps there's a bit of room for further improvement. On the other hand, when you have a proven track record of being right, it's hard not to be assertive about it.

I also find myself occasionally making what I later recognize as slightly embarrassing assertions, when I extrapolate from some simple model I've made of a situation or circumstance, and find my prediction turns out to be wrong. Life is endlessly complex and fascinating. And that includes the physical world that we typically take such pride in understanding.

Unfortunately there are a few cases I've witnessed recently when, instead of recognizing the embarrassment they are causing themselves, a group of physicists digs in, asserting that their naive assertions and understanding are the truth, and that everybody else has got it wrong. This sort of thing isn't too unusual in the normal course of science. As Thomas Kuhn (himself a physics PhD) pointed out in The Structure of Scientific Revolutions, there often seems to be a generation gap between those of the old understanding (or paradigm, in his usage) and those of the new one of greater explanatory power, and at least some of the individuals holding the old paradigm go to their graves without recognizing the value of the new.

Worse though, in the examples I'll show here, are cases where there is a clear objective truth and a well-reasoned collection of logical deductions from observations and theory, and yet an "old guard" insists on embarrassing itself by denying that reality using what are clearly bizarre, inconsistent and fundamentally unscientific arguments. Science relies on the assumption that there is a real underlying objective reality that manifests itself in ways we can come to agreement on through repeatable measurements. Is it just the typical arrogance of the physicist that sustains these strange denials of reality?

Gerlich and Tscheuschner

The subject in question is, as usual, human causation of climate change and the world's responsibility to fix the problem. Many well-respected and traditional climate scientists have training in physics. Jim Hansen, perhaps the most prominent advocate among scientists in the US for strong action to limit our CO2 emissions, has a PhD in physics. Sir Robert May, at the top of Tim Prall's most-cited climate authors list, also received a PhD in physics, as did many of the most prominent scientists on Prall's list.

There are also a number of climate "skeptics" who have a physics background. I'll talk a bit more about Freeman Dyson and Will Happer later in this note. Among blogger and blog-comment "skeptics" there are several who prominently tout their physics background - Lubos Motl for instance - asserting that their physics expertise in some way makes their commentary on the subject more relevant. Of course I have used much the same stance myself - arrogance isn't confined to those who are wrong... Most recently Nathan Myhrvold, with a triple dose of arrogance in his physics PhD, his information technology background and his long tenure at Microsoft has come out as a climate skeptic - or at least a skeptic on the merits of solar energy. Though perhaps he was misquoted, as others have been.

But the first example I want to look at in detail, because the violations of the standards of science are so egregious, is the case of two German physicists and some of their colleagues who have come to their defense. In July 2007, Gerhard Gerlich and Ralf D. Tscheuschner posted this article (a version of which has, even more remarkably, actually appeared in a scientific journal) that claims to "falsify" the "atmospheric CO2 greenhouse effects" - i.e. the entire premise of a greenhouse effect in the first place.

This isn't merely old-guard reactionism, in this case. Gerlich and Tscheuschner are claiming that the greenhouse effect discovered by some of the founders of thermodynamics itself over 100 years ago (Fourier and Tyndall) violates those same laws of thermodynamics. That is a stunningly bold and arrogant assertion. If they were actually right, it would be of monumental importance. Surely, to avoid embarrassing themselves, they must have been very careful to understand their subject before diving in? But the arrogance of physicists, in some cases at least, knows no bounds.

There are dozens of ways to show that the greenhouse effect indeed involves no violation of the second law of thermodynamics, that net heat flows in the system are always from the hot sun to the surface of the Earth and up through the atmosphere; the colder atmosphere does not "heat" the surface in the second-law violating sense that Gerlich and Tscheuschner assert. Figuring out why they think it does anyway is a problem of psychology, not physics.

But they also assert (essentially 4 of the six claims in their original abstract) that the whole framework describing the natural greenhouse effect is fundamentally wrong. That framework uses balance of energy flux (the first law of thermodynamics) and a variety of averages over Earth's surface to show the natural greenhouse effect has warmed our planet's surface by at least 33 degrees Celsius, above what it would be without infrared-trapping gases in the atmosphere. In February 2008 I posted a response using the most straightforward-possible mathematical reasoning in a Proof of the Atmospheric Greenhouse Effect. This was of course no new scientific result - Fourier and Tyndall had it right in the 19th century. Nevertheless my posting received several interesting responses. First from some very prominent global warming "skeptics" who thanked me for my clear refutation of the nonsense of Gerlich and Tscheuschner, an article that they found personally embarrassing to be in any way associated with. But second, I was vehemently attacked on a variety of grounds, including apparently my ignorance of basic mathematics, by one Gerhard Kramm, who seems to have allied himself with Gerlich and Tscheuschner and comes to their defense at every opportunity. Arrogance amplified - interestingly half of Kramm's arguments also logically contradict Gerlich and Tscheushcner's paper, but it doesn't seem to embarrass any of them.

To briefly summarize the Gerlich and Tscheuschner argument on the 33 K issue and my refutation (and to pause in wonder that such logic could have been approved by the editor of a scientific journal) first let's make note of the essential, agreed-upon observations of the system:

(1) Earth's surface absorbs a certain pretty steady amount of total incoming energy from the Sun (some is reflected by the atmosphere or surface, so leave that part out)
(2) Earth's surface radiates essentially as a black body everywhere, which by the Stefan-Boltzmann law means the rate of radiated energy flow varies as the fourth power of the local surface temperature
(3) If Earth had no atmosphere, (1) and (2) would be the only heat transfers touching Earth's surface, so they have to balance in the long run. Using the standard equations you find an effective radiating temperature for the Earth of 255 K (-18 degrees C).
(4) There is a mathematical relationship between first-power averages and fourth-power averages that ensures that the average temperature must always be less than the effective radiating temperature (3).
(5) But the real Earth does have an atmosphere, and it also has an observed average temperature that is much warmer than 255 K - satellite and surface measurements agree on close to 288 K (+15 degrees C), for a difference of 33 K.

So the question is, what explains the difference between these two numbers, the 255 K effective radiating temperature of (3), and the observed 288 K average temperature of (5)?

The standard answer, as explained in my "proof" paper, is that the atmosphere's blocking of infrared radiation presents a barrier to the flow from Earth's surface, so to get the same energy flow rate out to space to balance incoming sunlight, the surface needs to warm up. The greenhouse effect. The conflict between observations (5) and (3) given the mathematical relationship (4) is proof that the atmosphere is having this real effect on our planet.

In Gerlich and Tscheuschner's paper, while acknowledging (and using) each of the above assertions, they also throw confusion on every one of them at the same time, and it is hard to follow the logic. In section 3.7.4 of their paper they present calculations for a planet in instantaneous balance with local incoming radiation, so that on the dark side of the planet (where no radiation comes in) the temperature is absolute zero, and corresponding temperatures on the warm side are inordinately hot. Computing the average temperature for their model planet, they find it a very cold 140 K (-133 C). This clearly satisfies the inequality in question (4 above) - in fact the two averages are expected to become all the more unequal the greater the divergence in individual measured temperatures that go into the averages.

To illustrate this, rather than going through the Gerlich and Tscheuschner case in full, look at a slightly simpler model with our planet uniformly at 0 K on one half, and 304 K on the other. Then the average temperature of the planet is (0 + 304)/2 = 152 K, not much warmer than the 140 K they found. The effective radiating temperature is ((0 + 304^4)/2)^(1/4) = 256 K, a full 104 degrees warmer. So it's easy to find a model of a planet where the average temperature is much lower than the effective radiating temperature, satisfying the inequality (4).

But this says nothing about how to get a planet with a higher average temperature than the effective radiating temperature. If the fourth power average is kept fixed, as it must be on a planet with no atmosphere, then the highest possible average surface temperature is when the temperature is completely uniform, all at the same temperature (255 K in Earth's case). Without an atmosphere there is no way to maintain a higher average.

All this Gerlich and Tscheuschner appear to agree with. Their eq. 89 is the same as my assertion (4) above. But they conclude from their mathematical model that the greenhouse effect increase in temperature is not 33 K, but a much larger number (their calculation shows that the "difference temperature that defines the natural greenhouse effect [can] explode"). And therefore "something must be fundamentally wrong here". And go on to make essentially hand-waving arguments about the invalidity of energy balance and how local temperatures are so variable you can't really average them. How they believe that any such measurement errors could mean Earth's actual average temperature is well below freezing, with a mostly liquid water surface, is still beyond me.

They have found no logical contradiction, only a contradiction to their (poor) intuitions. Let 'G' stand for the assertion that Earth's average temperature without an atmosphere would be less than or equal to 255 K (combining (3) and (4) above). If some model could be found that showed 'G' to be false, showing a temperature distribution on the surface that gave a higher average than the effective radiating temperature, then we might have an explanation of Earth's observed average temperature of 288 K that didn't involve the greenhouse effect. That would be a stunning achievement, deserving of their paper's title. But in fact every one of their examples shows 'G' to be true, and they even essentially prove it to be true. They assert it in their eq. 89. There is no logical disproof of 'G' anywhere in Gerlich and Tscheuschner's paper. And therefore no logical counter to the simple truth that the presence of Earth's infrared-absorbing atmosphere does indeed raise our planet's surface temperature by at least 33 degrees C from what it would be otherwise.

Any ordinary person would surely be embarrassed by such illogic, once the error was pointed out. Understanding how they got there and still apparently claim they are right to this day (after well over a year of people pointing out how they're wrong) is definitely a matter for psychology, and not physics.

The APS Statement

My second example is less egregiously wrong, but a little more disturbing to me because it involves people I have met and have some respect for. The issue starts with the American Physical Society official Statement on Climate Change, adopted by the APS Council in 2007:

Emissions of greenhouse gases from human activities are changing the atmosphere in ways that affect the Earth's climate. Greenhouse gases include carbon dioxide as well as methane, nitrous oxide and other gases. They are emitted from fossil fuel combustion and a range of industrial and agricultural processes.

The evidence is incontrovertible: Global warming is occurring. If no mitigating actions are taken, significant disruptions in the Earth’s physical and ecological systems, social systems, security and human health are likely to occur. We must reduce emissions of greenhouse gases beginning now.

Because the complexity of the climate makes accurate prediction difficult, the APS urges an enhanced effort to understand the effects of human activity on the Earth’s climate, and to provide the technological options for meeting the climate challenge in the near and longer terms. The APS also urges governments, universities, national laboratories and its membership to support policies and actions that will reduce the emission of greenhouse gases.

This statement was adopted after the release of the 4th assessment report from the Intergovernmental Panel on Climate Change (IPCC), and the three simple paragraphs of the APS statement echo the three major sections of that report: working group 1's assessment of the physical science basis, working group 2's assessment of the impacts of climate change that has already occurred and projections of the disruptive effects of future impacts, and working group 3's analysis of the steps needed to avoid these dire consequences. As such the APS statement as it stands is founded on the work of the thousands of scientists involved in the IPCC reports, and the thousands of peer-reviewed publications those reports are in turn based on, and every portion of the statement can be strongly supported by reference to the peer-reviewed literature and the scientific understanding that has developed in recent decades around the subject.

Such a brief, assertive (even arrogant?) summary of the major science results was bound to come under attack from those who feel they somehow know better than the thousands of deeply committed scientists who have spent decades working in the field. The first volley of opposition became public with the July 2008 issue of an APS unit newsletter, "Physics and Society", where the editors, apparently at the urging of physicist Gerald Marsh, published a highly erroneous article on climate sensitivity by a non-scientist with a reputation for misrepresenting climate science.

Said non-scientist and his associates, upon publication of their screed, immediately pounced with a press release that made its way around the blogosphere and into the Drudge Report where it was announced that the American Physical Society has "reversed its stance on climate change". APS was forced to post a clear statement on the organization's home page asserting that in fact no such reversal had taken place, that this was merely the work of an unsupervised editor and the article and associated editorial commentary did not represent in any way official position or policy of the organization.

While disturbing, that incident gave some insight into the potential importance of such statements from scientific societies who have almost unanimously now signed on to the main consensus. And so the APS statement has now drawn the attention of a handful of "skeptic" members within the organization (almost uniformly among the very oldest members of the society - so perhaps it is in part a Kuhnian generational paradigm shift problem).

Robert Austin, the APS Council member who urged the society to "reconsider" the statement and seems to have been behind this open letter on the subject, is a person I have met a number of times and have had interesting discussions with in the past. When I heard he was behind this I contacted him and we've exchanged a few letters; from that I've become convinced his understanding of the issues is relatively shallow and that he's relying on his trust in a few other physicists on the subject - trust that they may deserve on many other issues, but not this one. In particular, since Austin is at Princeton, he has some associations with Freeman Dyson and Will Happer, well-known and highly respected physicists in their own fields. But no person can be right about everything, and the recent NY Times Magazine profile of Dyson gives some perspective on where Dyson has gone astray on this issue - he is shaky on many details of the underlying science, and merely repeats assertions without providing detailed reasoning or justification.

Which is characteristic of the open letter as well. This is the sort of scientific claim without foundation that would never pass normal peer-review (unless of the sort that Gerlich and Tscheuschner seem to have been favored with). Let's look at this display of arrogance (their proposed revision of the APS statement) in a little more detail:

Greenhouse gas emissions, such as carbon dioxide, methane, and nitrous oxide, accompany human industrial and agricultural activity.

This slightly restates the second and third sentences of the first paragraph in the current APS statement, but omits the first sentence that clearly states these gases have an effect on climate. Do the authors of this proposed statement actually believe, like Gerlich and Tscheuschner, that the effect of greenhouse gases on climate is zero?

While substantial concern has been expressed that emissions may cause significant climate change, measured or reconstructed temperature records indicate that 20th 21st century changes are neither exceptional nor persistent, and the historical and geological records show many periods warmer than today.

Today's temperatures are not "exceptional" in the historical or geological record, as the IPCC report describes (in particular section 6 of the working-group 1 report of IPCC's 4th assessment report - AR4 WG1 sec. 6 - discusses the paleo-climate record: 3 million years ago it was 2-3 C warmer than now). But how can it be claimed they are "not persistent"? Every year from 2001 through 2008 the measured average global temperature has been warmer than all but 1 to 4 years of the entire 20th century (depending on which analysis you look at). What scientific justification is there to claim that the 20th century warming is not persisting?

Moreover, this statement is clearly intended to imply that there should be no expectation of continued increases in temperatures, but a huge weight of evidence points to at least a 2 degrees C transient response for a doubling of CO2, as stated in the IPCC report. Given continued greenhouse emissions (which the first sentence of the proposed statement admits), that certainly brings us into temperature territory that the Earth has not seen since well before human civilization began. "Exceptional" is hardly a precise term, but I think to any ordinary person, higher temperatures than human civilization has ever seen should qualify, and by that definition exceptional temperatures are surely coming unless we cut back on CO2 emissions significantly.

In addition, there is an extensive scientific literature that examines beneficial effects of increased levels of carbon dioxide for both plants and animals.

This includes a radical assertion not backed up by any reference to the actual literature. I have, personally, never heard of a benefit of higher CO2 for animal life. According to this hazard sheet, CO2 leads to blood acidification, at 1% can be hazardous, and 5% is toxic. Granted, those levels are considerably higher than the 0.1% concentration that we might get in the next century under business-as-usual scenarios, but "beneficial"?

As for plant life - the question is whether the increase in CO2 compensates for higher temperatures and expected changes in precipitation, and that also depends on the type of plant (C3 or C4 respiration). This statement is extremely one-sided on the real issues here. Again, where is this "extensive scientific literature" that justifies such a statement of clear benefit? I've attended a lecture from folk at Brookhaven Lab who have been actually doing this research, and they're significantly less optimistic than this statement implies.

Studies of a variety of natural processes, including ocean cycles and solar variability, indicate that they can account for variations in the Earth’s climate on the time scale of decades and centuries.

On a time scale of 1 decade, certainly, variations in Earth's climate are determined by "natural processes" like the solar cycle, volcanoes, and ocean-atmosphere interactions. In fact, climate is not even well-defined for a single decade, since it represents the statistical distribution over all such short time-scale variations. Further in the past, orbital forcings (with ice-albedo and greenhouse-gas feedbacks) clearly account for the glacial-interglacial changes. But no known natural processes can account for the changes in Earth's climate observed in the 20th century. What scientific source could you possibly have for this statement that outweighs the very clear analyses the IPCC report is based on? The "can account for" in that context is a strong statement (implying anthropogenic GHG's have had no impact). We're back in the logic of Gerlich and Tscheuschner here, if this statement is to be believed at face value.

Current climate models appear insufficiently reliable to properly account for natural and anthropogenic contributions to past climate change, much less project future climate.

This statement doesn't even make logical sense. Climate models do not predict either natural or anthropogenic contributions to past climate change - they model the *response* to forcings, not the forcings themselves. Forcings are input (from other types of modeling). And in modeling responses they have been tremendously successful - one of the best examples of this is the response of the planet to the Pinatubo eruption's addition of stratospheric aerosols, which was predicted quite accurately by Jim Hansen at least 4 years before the eruption. And of course "climate models" ever since Arrhenius have predicted surface warming from increased CO2, as observed in the 20th century. What analysis of climate models is there in the literature that in any way justifies this statement?

Pure arrogance backed up by nothing.

The APS supports an objective scientific effort to understand the effects of all processes – natural and human --on the Earth’s climate and the biosphere’s response to climate change, and promotes technological options for meeting challenges of future climate changes, regardless of cause.

More research, always the call for more research. And "skeptics" complain that it's the climate scientists who are taking their positions in pursuit of more funding for themselves? To the contrary - most climate scientists recognize the problem and urge money to be spent not on themselves, but on solutions: clean energy, getting off coal. calls for action on October 24 - not to fund climate scientists, but to work to actually turn things around, and make the world a better place. Of course what this proposed revised statement omits is any call to action for governments or APS members to work to actually reduce greenhouse gas emissions.

Selfish arrogance.

Frankly I'm really disappointed in Austin, Dyson, and their colleagues. People like Gerlich and Tscheuschner, Kramm, Gerald Marsh, I never heard of them before this, and I have no expectation of their rationality. But I do expect better from people I've met and otherwise respected. What happened to clear scientific rational thinking, understanding problems, looking at the peer-reviewed literature and trying to really understand what's going on, what the previous work in the field shows?

I'll conclude with just one simple piece of advice: a little humility can save a lot of embarrassment. I urge all my physicist colleagues and friends to try it some time.


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My dear and respected

My dear and respected colleague: I thought you just went to Dale Carnegie because it was a good idea! But I'm glad I went, too...loads of fun and learning all rolled together.

ah, secrets revealed :) So do

ah, secrets revealed :) So do you remember me rubbing people the wrong way here at first? Ok, aside from Bruce and Bill?

Hi Arthur! Nice post. But,

Hi Arthur! Nice post. But, having been hanging out a lot at Watt's site, I would have to say that such a combination of arrogance and ignorance doesn't seem to be confined to physicists in particular. It seems to occur in a lot of engineers and chemists and other non-scientists too. And, perhaps even in greater proportions. But, perhaps we have higher standards for our physicist brethren.

It is interesting to hear that you know and have communicated with Robert Austin. I hadn't but immediately did a google search after I read the APSNews and found something he had written on climate and I was immediately surprised by how weak his arguments (really just standard "skeptic" talking points) were. I mean there are some arguments on the "skeptic" side that are somewhat thought-provoking...and even a few I have trouble coming up with a good answer to...but those weren't the sort of arguments that Austin was making. Certainly not as nutty as G&T but not that much better.

By the way, I think it is interesting to go to ExxonMobil's website and compare their statement ( ) to the one proposed in the "open letter". I think it is sort of a bad sign when a proposed statement by the American Physical Society would make ExxonMobil look like an organization of radical tree-hugging environmental wackos by comparison!

Maybe it's higher standards -

Maybe it's higher standards - you do expect that somebody getting a PhD in physics has learned a few things...

Bob Austin is actually, sadly, the only one of the current APS councillors I really know much about at all - I guess Bo Hammer with FPS I know a little from his writings there (and he's the one I emailed my comments to), but that's about it.

And yes, the proposed statement (along with comments from Austin, Dyson and a few of the others) really is surprisingly weak and confused. I mean, beneficial to animal life??? Have they been smoking those "CO2 = life" commercials?

In my lists of climate

In my lists of climate scientists, skeptics and signers of declarations, I've set up a listing of all signers of any of a dozen climate denial/skeptic petitions or open letters. Recently I added in the 61 physicists who wrote to the APS about their position on climate change. I use the tag "APS09" to annotate the signers, here:

The only two with a substantial number of published works on climate are Sultan Hameed and S. Fred Singer (though the latter is no climatologist, just really prolific in publishing climate denial claims.) Scafetta and West come next, the Robert S. Knox who has written on solar-climate links. David Douglass of Rochester U has also written on that, though he's not at all widely cited. After that, it's all people involved in other areas of physics not related to climate science.

I believe Dyson came on after the original letter was put together; he wasn't on the list of 61 that I found on the letter at Anyway Dyson is also on my skeptic authors page, above, as he signed a couple of other statements.

You'd think anyone with a degree in physics should be better equipped to sort through science vs. spin on such a topic, but the incentive to avoid such bad news in any way possible is quite strong. I've been blogging on recent work about the psychology of climate denial, here:

- Jim Prall
Toronto, Canada

Thanks Jim - I keep pointing

Thanks Jim - I keep pointing people to your lists, they're very impressive evidence of the overwhelming nature of the science. When you put it in terms of real people, and you see so many of them on one side, it's a pretty strong case. The implication of conspiracy or incompetence so pervasive on the denial side is hard to maintain in the face of that kind of collection of people.

I don't think Dyson has actually signed on to any of the APS-related petitions, I mention him here only because he's clearly been outspoken as a skeptic and I know has influenced Austin on this. John Mashey's been putting together a more comprehensive demographic profile of the actual signers and their social networks, it'll be very good if he gets that in a form suitable for publishing in the next week or too.

Some time ago, Eli pointed to

Some time ago, Eli pointed to a paper by Myanna Lahsen which makes much the same point

This paper identifies cultural and historical dimensions that structure US climate science politics. It explores why a key subset of scientists—the physicist founders and leaders of the influential George C. Marshall Institute—chose to lend their scientific authority to this movement which continues to powerfully shape US climate policy. The paper suggests that these physicists joined the environmental backlash to stem changing tides in science and society, and to defend their preferred understandings of science, modernity, and of themselves as a physicist elite - understandings challenged by on-going transformations encapsulated by the widespread concern about human-induced climate change.

I'm sure my observations are

I'm sure my observations are not particularly new. And it really is delving into psychology to try to figure out what's motivating these people. From some stuff John Mashey sent me it sounds like there actually is a strong political inclination among the majority of the physicists who seem to be prominent in anti-climate science pronouncements - the few with liberal leanings are a distinct minority.

Eli - thanks for the pointer

Eli - thanks for the pointer again to Lahsen's paper, it's very informative on the original George Marshall folks (by the way, George Marshall has long been one of my heroes for his advocacy for the restoration of Europe after WWII - it greatly annoys me the way various people have abused his good name since then...). By the way, the paper cites a couple of Roger P. Jr. papers... back when he was making sense I suppose...

I am working on a model of

I am working on a model of Dyson's 5 climate sinks (short term) that we proponents of carbon reduction don't understand, unlike him. I'll use it in a very unusual venue if and when it gets done, but believe me I don't respect most of his statements on climate nowadays.

That being said, I hate him being tied, or tying himself, to Wm. Happer, who has cast all standards to the wind. When he's not saying easily disproven things like that no H20 feedback exists, he says things that are childishly true, like "models have been wrong in the past."

I also don't think Happer has the same stature in the physics community that Dyson has, for good or ill.

G&T don't have much, and thanks to their dreadful work lately, they'll probably never have it.

G. Kramm was a

G. Kramm was a student/protege of some sort of Akasofu, who was a student of Sidney Chapman. Akasofu was interviewed on the Great Global Warming Swindle on Channel IV essentially saying the atmospheric analysis of AGW didn't add up. Since he's a very highly respected atmospheric physicist (emeritus), that would have been damning if he hadn't been so specific about the analysis involved that he left room to be right and still wrong about AGW, and yet too vague about the problems he had with the analysis. Overall, he gave cover to the GGWS while still, he probably assumed, giving himself cover.

Since GGWS Akasofu has left the public eye and Kramm - who seems to be a politically motivated climate denialist similar to Lubos Motl - has seemed to see himself as some sort of stand-in for Akasofu.

Just to give you background on Kramm. And I believe "rationality" is a good word. That's what's missing for him when AGW comes up, not scientific expertise or knowledge.

Marion Delgado, this is one

Marion Delgado,

this is one of your stupid arguments. I was never a student of Syun Akasofu. I earned my doctoral degree in meteorology at the Department of Physics of the Humboldt University of Berlin, Germany. My adviser was Karlheinz Bernhardt, one of the leading theoretical meteorologists in Germany. When I joint the Geophysical Institute of UAF in 2001, the Director was Roger Smith, but not Akasofu. The former was and is still GI Director and my supervisor, the latter was the Director of the International Arctic Research Center (IARC). I never worked for the IARC.

Gerhard Kramm

I stand corrected on any of

I stand corrected on any of that that I said or implied was different.

That being said, Kramm, you've been a very fatuous acolyte of Akasofu whenever you've pontificated on climate science, which is a lot. In particular, your emphasis on Akasofu being a protege of Sidney Chapman never made any sense to me, given that Hansen was a student of Van Allen.

Now that you've, quite properly, corrected ME on my "stupid argument?"

How about addressing the many mistakes you've made on the G&T paper, as has been detailed here?

“the colder atmosphere does

“the colder atmosphere does not "heat" the surface in the second-law violating sense that Gerlich and Tscheuschner assert”

Indeed it does not, Mr Smith, as all physicists can agree without further discussion. We know, do we not, that the quality (entropy) of the absorbed energy in the atmosphere (a heat sink) is not sufficient to transfer heat (net energy) back to the earth (a heat source). We understand that heat transfer is a function of a temperature difference, (not temperature alone) and we can see why power stations labour to reduce their sink temperatures and reject (to the atmosphere) vast quantities of sink energy.
So why do we introduce into our atmospheric heat transfer equations a quantity of energy travelling back from the sink to the source? This back-radiation is the negative term in the correct application of Stefan Bolzmann, where the heat transfer is proportional to the difference between the fourth powers of the surface and atmospheric temperatures.

“That means that this atmospheric layer continuously emits an amount f • Eemitted equal to what it absorbs from the ground. Since thermal re-emission is randomly directed, half the radiation from this atmospheric layer will go up, and half down.”

If f = 1 in your equations you can get your result easily by assuming that W is the solar energy received at the surface, 2W is the energy emitted, and W is the energy coming back down from the atmosphere. Viewed in isolation, the surface temperature must increase sufficiently to emit 2W. From Stefan-Bolzmann, (again applied to the surface in isolation) the temperature is increased by a factor equal to the fourth root of 2, or about 19%.

This seems reasonable, until we try the two atmospheric layers you suggest. Balance the energy flows (first law of thermodynamics) and the temperature ratio is the fourth root of 3, or 335 degrees K, the result you will find in Eli Rabetts paper attempting to refute G and T. But why stop there? Three layers increases the ratio to the fourth root of 4, and the surface temperature to 381 degrees K.

If n is the number of layers into which the atmosphere can be realistically divided the ratio of Tsurface to the top, bare earth temperature is the fourth root of (n+1).

Something wrong here, surely.

What is wrong (apart from the thermodynamics) is the assumption that the equilibrium temperatures of the earth, atmosphere, and space are determined by radiative balance. The lapse rate, the difference in temperature between the top and bottom of the atmosphere, (your famous 33 degrees K), has nothing to do with radiation. It is a function of gravity and specific heat.

Adiabatic expansion, convection, plus conduction and the latent heat of evaporation are responsible for most of the heat transfer from the earth to the troposphere. Radiation from the whole system, near the top of the atmosphere, is responsible for the transfer to space, where Stefan Bolzmann gives a temperature of 255 degrees K. Add the lapse rate difference, and you have the temperature we observe at the surface. No back heating, no thermal blanket, and no AGW.

Gavin Schmidt and the luminaries at RC recognise this by advocating the “higher is colder” explanation of AGW, in which “back-radiation” plays no part. Without the lapse rate there would be no greenhouse effect, they say.

Fred, the number of layers


the number of layers in that approximation is not an arbitrary quantity, but represents full absorption by the atmosphere. On Venus you do effectively have a very large number of fully-absorbing layers, and the result is an extremely high surface temperature. On Earth, the atmosphere never fully absorbs surface thermal radiation - some portion of the spectrum always leaks through from the surface directly to space, so the gray-approximation represented there doesn't work on those grounds alone. The most heavily absorbed spectral regions do get absorbed quite quickly (10s of meters of atmosphere at the peak), but they don't cover a sufficient portion of the spectrum to get much warming. When you plug in the actual measured absorption coefficients and thermal and compositional profiles of the atmosphere, the 33K is explained perfectly.

You ask about back-radiation (a perfectly measurable quantity by the way - check out the definition of "pyrgeometer" some time) - "why do we introduce into our atmospheric heat transfer equations a quantity of energy travelling back from the sink to the source?" The reason this is done is because radiation through the atmosphere is a "microscopic", i.e. quantum-mechanically based quantity, and not represented well by thermodynamic or statistical averages. Physically the issue is that, unlike the molecules of air, most of the photons have very long mean-free-paths and can travel from their emission point to an absorption point that is at a different temperature. In other words, the photons of atmospheric radiation are not constrained by the condition of local thermal equilibrium that applies to all the other relevant quantities that can be treated as simple thermodynamic/statistical averages.

When you get down to the microscopic quantum/single-particle level, the naive "2nd law" is violated all the time. Molecules don't know what the local temperature is, so "hot" molecules happily travel from cold regions to hot ones, and vice versa. It is only when you do the statistical averaging over the behavior of all molecules both going and coming that you see the net energy flow has to be from hot to cold. For radiation it's the same issue - the individual photons don't know whether they're going from a hot place to a cold one or vice versa. Only when you statistically average over all photons, both coming and going, do you find net energy flow in the right direction. And it always is. The second law is very powerful, but it applies only to statistical averages, not at the microscopic level of individual molecules or photons.

Finally - on your last comment "Without the lapse rate there would be no greenhouse effect, they say." Actually, it's the other way round. Without the greenhouse effect, there would be no lapse rate. The atmosphere would be isothermal at the surface temperature (aside from day/night fluctuations). This is the situation on Mars, for instance. Understanding the atmospheric temperature profiles of Venus and Mars is very instructive.

Dear Fred Staples, I do not

Dear Fred Staples,

I do not believe that Arthur Smith and his friends will accept that their physical considerations are highly erroneous. Here is an example. I found it in the COMMENT ON "FALSIFICATION OF THE ATMOSPHERIC CO2 GREENHOUSE EFFECTS WITHIN THE FRAME OF PHYSICS written by Halpern (Eli Rabett) et al. that was available on the web site of Eli Rabett. Arthur Smith is one of the co-authors, Joel Shore another. In the the subsection 2.1 of this comment entitled "A simple example of radiative heat flow between a colder and a hotter body" Halpern et al. stated:


Again we use two infinite, flat and parallel plates. In this case we will treat the two plates as infinite heat sinks. For the sake of argument Face A is at 300 K, face B at 260 K, which are close to the temperatures of the surface and the level of the atmosphere at which greenhouse gases radiate to space. Using the Stefan-Boltzmann law we can calculate the thermal energy and entropy exchanges between the two plates as shown in Fig. 4 above which is similar to that of GT09 except that includes heat transfer in both directions, which, as was discussed above, must be the case.

The radiative flux leaving each surface can be calculated from the Stefan-Boltzmann law.

From the First Law of Thermodynamics:

DQ_A = DQ_(AB) + DQ_(BA) = - 459 + 259 J/m^2 (1)
DQ_B = DQ_(BA) + DQ_(AB) = - 259 + 459 J/m^2 (2)
DQ = DQ_A + DQ_B = 0 (3)

And from the Second Law

DS_A = DQ_A/T_A = (-200 J/m^2) /300 K = -0.66 J/(K m^2) (4)
DS_B = DQ_B/T_B = (+200 J/m2) /260 K = 0.77 J/(K m^2) (5)
DS = DS_A + DS_B = +0.11 J/(K m^2) (6)

Only heat is transferred, energy is conserved, and the net entropy increase of the entire system is positive as the Second Law requires, but equally clearly, the colder body radiates thermal energy that the hotter body absorbs. The argument of GT09, which considers only part of the process is unphysical and wrong. The Clausius statement is about a complete process, not individual steps. The example makes clear that there is an
interchange of heat by radiation between the colder and the warmer surface. Such an interchange occurs because the net entropy change for the process is positive.


To show that this consideration is highly erroneous one might use an example in which T_B is close to the absolute zero (T_B = 2.7 K , the temperature of the space) and the temperature T_A is assumed to be equal to the blackbody temperature of the sun ( T = 5784 K ). This example yields DS_A = -1.11E4 W/(m^2 K) and DS_B = 2.35E7 W/(m^2 K). Thus, we have DS = 2.349E7 W/(m^2 K), i.e., the thermodynamically unimportant space would affect the sun.

It is clear that this example is based on physical nonsense. Nevertheless, Arthur Smith stated that Gerlich, Tscheuschner, and me are arrogant. Moreover, Barton Paul Levensen (a computer programmer and writer of science fiction and fantasy) who always supports Arthur Smith called me a scientific illiterate and stated that Gerlich and Tscheuschner are incompetent (see [Edited by moderator - really, do you need to do the Godwin thing so readily?]

Sincerely yours

Gerhard Kramm

Dr. Kramm - regarding your

Dr. Kramm - regarding your assertion of physical nonsense in that "the thermodynamically unimportant space would affect the sun" - I'm not sure why you think this is an example of something affecting the sun, but please do tell us what you believe the total change in entropy *should be* for the case of radiation from the sun becoming thermalized in empty space. Do you believe the net entropy change should be zero? Really? The process is thermodynamically reversible?

Let's take a much more down-to-earth example - the heat engine. Wikipedia has a fine discussion, including getting into the entropy changes. When you move heat (Q) from hot (Th) to cold (Tc) the entropy change on the hot side is given by dQh/Th, and the entropy change on the cold side is given by dQc/Tc. If dQh = -dQc (no work, just heat exchange, as in the radiative transfer case) and dQc > 0 (net heat flowing from hot to cold), then the entropy change is given by precisely the formula stated in our paper, quoted above, and calculated for the sun-space case as you did.

Do you deny that the laws of thermodynamics which apply in the case of the heat engine also apply to the sun? Or do you completely deny the basic heat engine laws in the first place?

Dear Dr. Smith, by

Dear Dr. Smith,

by considering the Stefan-Boltzmann-law the export of entropy (i.e., the flux of entropy) at A would be given by
S_A = sigma T_A^4/ T_A = sigma T_A^3 and that at B by S_B = sigma T_B^3 . This means that the arguments of Halpern et al. (2009) are wrong.

Sincerely yours

Gerhard Kramm

Dr. Kramm - you are changing

Dr. Kramm - you are changing the question from one of the total increase in entropy to "export of entropy". If entropy is being exported by a system, the total entropy of the universe is not changed. A "exports" S_A, and therefore reduces its own entropy by an amount S_A. The rest of space is then given that increase in entropy S_A, and the total entropy change is zero.

Similarly, from B, the entropy of B itself is reduced by its "export" S_B, and the entropy of the rest of the universe increases by S_B. Total entropy change is zero.

However, "export" is not the only process involved. A stipulation both in the real atmosphere and in the example provided in Halpern et al (2009) is that the energy "exported" from A is absorbed by B, and vice versa. It is in the process of absorption, or "import" of energy, if you prefer that term, leading to thermalization and loss of information, that the entropy of the universe increases. And the amount of that entropy increase is given by the formula we provided.

Dear Dr. Smith, this is not

Dear Dr. Smith,

this is not correct. I did not change the question. I only expressed the true amounts of S_A and S_B, respectively. These amounts have to be used to determine DS_A and DS_B, and hence DS (eqs. (4) to (6)). In doing so, one obtains with T_A = 5784 K and T_B = 2.7 K

S_A = 11971 W/(m^2 K)

S_B = 0.000001 W/(m^2 K)

DS_A = - S_A + S_B = - 11971 W/(m^2 K)


DS_B = S_A - S_B = 11971 W/(m^2 K)

DS = DS_A + DS_B = 0

For the purpose of comparison: According to Halpern et al. (2009) one would obtain with T_A = 5784 K and T_B = 2.7 K

DS_A = - 1.1E4 W/(m^2 K)

DS_B = 2.35E7 W/(m^2 K)


DS = DS_A + DS_B = 2.349E7 W/(m^2 K)

Do you really believe that this result correct is? Note that Halpern et al. considered a positive value as an indication that the so-called atmospheric greenhouse effect is in agreement with the 2nd law of thermodynamics.

By the way, Halpern et al. always used the units "J/(m^2 K)" for the radiation flux density in their. This is not correct. Using the unit "Joule" requires J/(m^2 s K). Since 1 J = 1 W s, one obtains for the radiation flux density W/m^2.

Sincerely yours

Gerhard Kramm

Yes, I believe the entropy of

Yes, I believe the entropy of the universe increases in this irreversible process. Do you really believe entropy is unchanged (DS = 0 in your 5th equation)?

Remember we're talking about radiation leaving object A and being absorbed by object B, and vice versa. You think this is a reversible process, with no change in entropy? In that case there would be no limit to the lifetime of stars, amazing news.

I have long admired Arthur

I have long admired Arthur for his carefully modulated comments, mostly if not quite always eschewing the ad homs that proliferate in the blogosphere! And I do not find him arrogant, and certainly no more so than most of the physicists I know or have corresponded with (eg Dyson) who are almost all remarkably modest.

But as an amateur empiricist I hope I may be allowed to point out that like Arthur like quite a few of the physicists' clan tends not to be very empircal when venturing outside their own expertise.

For example, Arthur states "The evidence is incontrovertible: Global warming is occurring." But is it?

[removed - moderator]

Tim, you are welcome to post

Tim, you are welcome to post things that have some basis in fact - but if you want to make wild unsupported claims, without any link or reference to back them up, such things are not welcome here. I believe you know other places where you've been able to post such things in the past; feel free to continue that.

I appreciate the compliment in your first paragraph, but your third already consists of a false claim - the statement is not mine, but that of the APS Council. I do agree with it, simply because it echoes the IPCC AR4 WG1 statement (summary for Policy Makers, p. 5):

Warming of the climate system is unequivocal, as is now evident from observations of increases in global average air and ocean temperatures, widespread melting of snow and ice, and rising global average sea level (see Figure SPM.3). {3.2, 4.2, 5.5}

One might quibble over whether "incontrovertible" is a stronger or weaker claim than "unequivocal", but both seem pretty definitive to me. There is no legitimate dispute about 20th century warming, and unsupported claims to the contrary are simply not welcome here.

I will take you at your word.

I will take you at your word. Temperature changes over time can be affected by various factors, including changes in Solar Radiation (SR) and in the Radiative Forcing (RF) attributable to rising atmospheric concentrations of anthropogenic greenhouse gases (leaving out pro tem anthropogenic economic activity and its associated energy use and entropy). It so happens that SR is much larger than RF, e.g. 63 W/sq.m. at Pt Barrow in Alaska in 2005 (NOAA), against total GG RF of 2.66 W/sq.m. in 2005 (AR4, WG1, p.141). The evident declining trend in SR at Pt Barrow between 1990 and 2005 (3 W/sq.m) far outweighs the rise in RF of c. 0.4 W/sq.m. over that period.

Now for some regression results, never previously computed AFAIK. Regressing changes in Mean Ann. Tmin at Barrow against changes in [CO2] and SR between 1990 and 2005, we obtain adj.R2 of 0.4, and very highly sig t-stats for dSR 11.33 p-value 4.79E-23 and RF minus 8.17 p-value r4.33E-14, with Durbin-Watson >2, so no auto-correlations. The coefficient for Tmin on d[CO2]/dt is negative. Back to the drawing board. No wonder the IPCC's AR4 never discloses any regression analysis.

Tim - why do you believe

Tim - why do you believe local insolation and radiative forcing should be the only factors affecting local temperature? It is called *global* warming for a reason: the local effects are extremely tiny compared to local weather, only on the global scale do the radiative changes make a substantial difference, over a matter of decades. Local correlations with radiative change have to be very close to zero, because there is so much else responsible for their variation. But on the global scale there have been no long-term changes in "SR" to within less than 0.1 W/m^2 since at least the 1970s; there are short-term fluctuations of order 0.2 W/m^2 (0.1%) associated with the solar cycle, but their recent correlation with global temperatures is very weak.

See Section 2.7 of IPCC AR4 WG1 (p. 188 and following) for details on solar irradiance measurements and historical data.

Many thanks for the response.

Many thanks for the response. It definitely helps me to understand the prolonged dialogue of the deaf between yourself, Eli, and professor Kramm about the G and T paper.
As a practical (nuclear reactor) physicist I am very well aware of the need to use Laws of Physics appropriate to the problem to be solved. The application of quantum mechanical effects to the climate is asking for trouble. Even the basics of molecular radiation absorption are best treated by classical wave theory :
“We see, to our amazement, that the photon frequency associated with the transition is just an integer multiple of the classical resonant frequency of the harmonic oscillator” from a First Course in Atmospheric Radiation, page 252, by Grant W Petty, University of Wisconsin Madison.” Not to my amazement, I have to say. I was regurgitating these equations half a life-time ago.

In engineering applications, at the macroscopic level of reality, the combined application of the “naïve” (your word) first and second laws of thermodynamics are taken for granted. Their equations and calculations have to work in the real world of heat engines, flight, transport, power generation etc. In Schaum’s Thermodynamics for Engineers, the word “photon” does not appear in the index, and once only in the text.

Engineers are, however, much concerned with the distinction between heat and energy, and are absolutely clear that the internal energy of a gas, in isolation from its surroundings, does not determine its ability to do work or raise temperatures. Their heat transfer equations rigorously relate source to sink temperatures. The idea that the colder atmosphere can directly heat the warmer earth is absurd, as G and T point out at inordinate length. However, if you think in terms of photon particles flashing (at light speed) to and fro along their independent mean free paths, the idea seems entirely reasonable. Energy appears in isolation both from its source and its sink.

So, let us use the radiative heat transfer equation to calculate the net radiative energy leaving the surface of the planet, and ask if this, alone, is in equilibrium with the solar input? It is the net outgoing radiation we need, after all the heat transfer mechanisms from the surface to the atmosphere have reached equilibrium.
Applying Stefan-Bolzmann as a heat transfer equation, we can easily calculate the net, radiated, infra-red energy for any given sink (atmosphere) and source (earth). For the bare rock case, 100% of the net absorbed solar energy will be radiated to space if the surface temperature is 255 degrees K and the space temperature is 3 degrees K.

With an atmosphere, the temperature differential at the surface will be far less, depending on the sink temperature as seen by the earth, taking into account the average depth of the radiation. Because of the lapse rate, the surface temperature we observe is about 288 degrees K.

The lapse rate is about 6.5 degrees per kilometre, and most of the absorption is near the surface, so the sink temperature is not likely to be greater than 285 degrees K.
The net energy radiated in this case is about 7% of the solar energy absorbed. The balance (the vast majority) is transferred to the atmosphere via convection, conduction and the latent heat of evaporation (more than 70% of the surface is water). Radiative absorption from increased CO2 might effect the atmospheric temperature, and hence the surface temperature, but in comparison with the other heat transfer mechanisms the effect must be negligible, just as the warmer glass (relative to the rock-salt) failed to heat the interior of RWWoods’ greenhouse.

High in the atmosphere, the effective emission temperature of 255 degrees K is just sufficient for outgoing radiation to balance the incoming solar radiation. Why is the surface temperature 33 degrees K higher than the atmospheric emission temperature? Because of the lapse rate. You assert that the lapse rate is a radiative effect It is not. It is a function of gravity (gas compression) and the specific heats (constant volume and constant pressure). It has nothing to do with radiation. It seems pointless to quote text books or Wiki. Tamino, the Real Climate statistician might help:

“If a parcel of air rises, because of the reduced pressure the parcel will expand. It generally takes much longer for a parcel of air to absorb/emit heat from/to its surroundings than to expand/contract, so during its expansion it will, for all practical purposes, exchange no heat with its surroundings; in other words, the expansion of the parcel of air will be adiabatic”

Why is the surface temperature on Venus so high? Because the atmosphere is so thick.

“Venus has a heavy thick atmosphere with 96.5% CO2, 3.5% nitrogen and small amounts of other gases including sulphur dioxide and water which forms thick sulphuric acid clouds. The pressure at the surface is 92 times that of the earth. Boyle’s Law tells us high pressure = higher temp which would explain most of the warmth at the surface (750C). At the level in the Venusian atmosphere with earth’s surface pressure, the temperature is about the same as the earth (300K or 27C) even though the planet is closer to the sun.”

What, in your opinion, would happen to the surface temperature of the moon if a cloud of dry N2/O2 gas should appear from space at a temperature of 3 degrees K, and surround the surface? For a practical example, you can try putting on a thick coat on a cold night, and recording your skin temperature.

Fred - here's the key

Fred - here's the key question for you. Why does the tropopause exist, and what determines its height?

The reality is that the (dry or wet) adiabatic lapse rate is a *stability limit*. No larger (more negative) vertical temperature gradient can exist in the atmosphere without causing spontaneous overturning (Tamino's explanation). However, the temperature gradient can always be more positive than the lapse rate. It can be zero, it can even be absolutely positive. Environmental lapse rates near the surface are rarely at exactly the adiabatic limit, and sometimes you get inversions where warmer air lies above colder - that's completely stable.

And above the tropopause, in the stratosphere, the vertical gradient is positive, not negative. Then it switches sign again a couple more times before you hit really empty space. The lapse rate only limits the negative gradient, it does not control the temperature gradient in the atmosphere.

Think about it. You know thermodynamics, at least according to the claims in your comment. Suppose the surface of the earth was at some uniform fixed temperature maintained by some infinitely steady-state system. Suppose next that the atmosphere (for example your dry N2/O2 on the moon) played absolutely no role in heat absorption from the sun or heat radiation into space (i.e. no greenhouse gases in the atmosphere). That makes the atmosphere a completely passive system coupled only by contact with the surface. You have just defined an otherwise isolated system in contact with an infinite constant-temperature heat-bath, and we know where that system goes: to thermal equilibrium at that constant temperature. The atmosphere will warm or cool to precisely the surface temperature, and then stay at that temperature forever. Completely stable, there are no heat flows in or out of such a non-radiating atmosphere to alter that situation.

But on the real Earth, as on Venus, the atmosphere does play a role in radiating energy directly to space. It is able to act as a conduit for energy flux to the ultimate 2.2 K heat sink, and so the atmosphere, rather than being uniformly at the surface temperature, can cool itself down. The limit to that cooling is defined by the adiabatic lapse rate limit and the average altitude at which the atmosphere radiates to space.

In summary:
(1) a radiatively transparent atmosphere implies an isothermal atmosphere.
(2) a radiating atmosphere results in an average altitude corresponding to direct radiation to space where the atmosphere is coldest - the tropopause.
(3) The atmospheric temperature gradient caused by (2) is limited by the adiabatic lapse rate.

Fred says: "What, in your

Fred says: "What, in your opinion, would happen to the surface temperature of the moon if a cloud of dry N2/O2 gas should appear from space at a temperature of 3 degrees K, and surround the surface? For a practical example, you can try putting on a thick coat on a cold night, and recording your skin temperature."

That example may be practical but it is very different. Your skin temperature is determined by your body's production of heat and the heat transfer to the air occurs by a variety of methods: radiation, conduction, and convection. In that case, you can reduce the transfer of heat from your skin to the outside world by the addition of the thick coat.

By contrast, the amount of energy produced internally by the Earth is dwarfed by the amount it receives from the sun. Furthermore, the only way that heat is communicated (in any significant amount) between the Sun, the Earth, and space is by radiation. Let's suppose that the Earth had an IR-transparent atmosphere and its current surface temperature of ~288 K. What would happen? Well, it would radiate as a blackbody (or very close to it since the surface's emissivity in the IR is very close to 1) at 288 K, which would mean that it is emitting much more energy than it is receiving from the sun. It would be way out of radiative balance and would cool until it reached the surface temperature of ~255 K where its emission was now equal to what it was receiving from the sun.

Hence, it is nonsense to say that somehow the relation between temperature and pressure or what-not causes the Earth's surface to be warmer than the effective blackbody temperature of ~255 K that it must have (with current albedo) in order to be in radiative balance. In the absence of an IR-absorbing atmosphere, whatever the distribution of temperature and pressure, it would be subject to the boundary condition that the Earth's global surface temperature has to be at 255 K (or colder if the temperature distribution is non-uniform since it is that is constrained by radiative balance, not ).

Arthur, I disagree with some

I disagree with some of this. The dry adiabatic lapse rate is more than just a stability limit. It is the neutral gradient for the up/down motion of air. At -9.8 K/km in dry air, motion does not convey nett heat. At, say, -8 K/km, motion conveys heat downward. Descending air heats faster by compression relative to the stationary air nearby, and passes heat to it (it's not completely adiabatic). Rising air cools more rapidly (conveying "cold" upwards). This pushes the gradient back towards -9.6, It also damps the motion, so the atmosphere is more positively stable.

And if the gradient is -12, then the reverse happens and heat is conveyed upwards, again pushing the temp gradient back towards -9.6. There is now the difference that the air motion is augmented, and the atmosphere is dynamically unstable.

So it isn't true that dry air can be at any gradient less than -9.8, if it is in motion, and there is no other mechanism of heat transport. Of course, it does often happen that more positive gradients are found. Then the implication is that there is some other heat transfer mechanism which balances the heat moved by adiabatic motion. The moist adiabat is a clear case, where latent heat transport has a counter effect (provided there is phase change). I believe another neglected case is IR radiative transfer (with GHG) which also counters the adiabat, and leads to a more positive lapse rate.

So on your summary points
1. Isothermal only if motionless, which won't generally be the case, if only because of convection from surface inhomogeneity.
2. Yes, the level where radiation leaves for space is a heat sink, and the gradient above and below has to be towards it.
3. I didn't understand. Yes, The atmospheric temperature gradient ... is limited by the adiabatic lapse rate.. But why caused by (2)

Nick, how do you explain the

Nick, how do you explain the stability of the positive temperature gradient in the stratosphere? Or the stability of the positive temperature gradient in the ocean? Yes, water doesn't perceptibly compress so the gas laws don't apply, but by your argument any motion would cause the ocean to become close to isothermal, yet the temperature gradient is stable.

You are correct that vertical motion would drive a negative gradient in the atmosphere, but maintaining that gradient would require continued motion, and what has to drive that continued motion? A source of free energy. But there is none as you approach thermal equilibrium, free energy goes away.

The free energy driving the vertical motion of the lower atmosphere is clear though, it's the temperature difference between surface and tropopause created by the greenhouse effect. If there were no convection, that temperature difference would be even higher; the adiabatic lapse rate limits it, but infrared absorption and radiation by the atmosphere is the cause. That's why (2) causes (3).

You need something driving convection or it doesn't happen.

Arthur, Let me first expand a

Let me first expand a little on the above ideas. There are four possible modes of heat transfer in the air:
1. Molecular diffusion - negligible on the large scale
2. GHG-augmented radiative transfer - Rosseland conduction. This behaves like molecular diffusion, with a higher diffusivity. The flux is proportional to the deviation of the temperature gradient from zero. Important, and often overlooked.
3. Turbulent diffusion. With compressibility and gravity, this behaves like 1 and 2 with one significant difference. The heat flux is proportional to the deviation of the temperature gradient from the dry adiabat.
4. Latent heat transfer. This requires actual phase change, and so has a complex relation to temperature. But broadly, it varies with the temperature gradient.

So those four together relate the heat flux to the temperature gradient. Where there is no nett flux and 3 provides the greatest diffusivity, the gradient must follow the dry adiabat. If there is a sustained flux (eg solar heat being returned to space), that has to be adjusted. Where modes 2 and 4 are significant, the actual lapse rate is closer to zero. You can think of this as causing a turbulent heat flux downward, because of the deviation from the adiabat, but offset by LH and IR flux upwards.

So on your specific queries:

Stability of the positive gradient in the stratosphere? We have:
a. A more significant heat source, from UV absorption by ozone etc, which exceeds IR loss from GHG emission
b. Reduced air motion, and of course, low pressure
c. The nearest significant heat sink is the GHG emission region near the tropopause

So the nett heat flux through the air is downwards (from UV source to IR sink), which explains the temperature gradient.

In the ocean. Low water compressibility means that the "dry adiabat" gradient is effectively zero. Modes 2 and 4 don't apply, and there is a nett downward heat flux, because solar heat moves down to warm the cold deep water which has come from the arctic. Again, that means a positive temp grad.

Energy to drive motion? Well, the first thing to say is that we have it. Lapse rates vary, but the atmosphere is always in motion.

But solar energy flowing through will always produce motion. As I suggested, all you need is surface variation - eg different albedo. This is enough to produce local convection. When it comes to heat flux, we think in big averages. But turbulent KE arises on much smaller scales.

Nick - an atmosphere is not

Nick - an atmosphere is not "always in motion". You just mentioned that the stratosphere has "reduced air motion". That's *caused by* the fact that the temperature gradient in the stratosphere is in the opposite direction from the pressure gradient, forcing stability. The tropopause temperature itself varies significantly from equator to poles but that doesn't induce vertical stratosphere motion.

Or take Mars. Surface temperatures vary widely from equator to poles. There is lots of horizontal atmospheric motion, but the atmospheric temperature gradient on Mars is (except for some day/night variation) generally positive from the surface - vertical motion is suppressed to the extent that your #3 effect doesn't do anything.

Yes "solar energy flowing through will always produce motion" - but only if that energy is actually being absorbed by the atmosphere. Absent sufficient GHG absorption, if the atmosphere is transparent those energy flows, that does not happen, and the atmosphere becomes isothermal and static.

In the ocean case - my point was simply that here also you have energy flowing through, but there is not sufficient turbulent motion in surface waters to reach the (near-zero) adiabat in that case - and like the stratosphere that's caused by the stability of the upper water layers having a positive temperature gradient accompanied by a negative density gradient (except at the poles where cooling plus higher salinity results in a density inversion and overturning). Again there's plenty of latitudinal temperature difference and horizontal motion, but no vertical motion, and the positive temperature gradient is stable.

In other words, your item #3 applies only if there is sufficient vertical "turbulent diffusion". What induces a fluid to have enough diffusive motion of that sort? The only possible cause is an energy flow through the atmosphere that sustains a density inversion. The only such cause for Earth's atmosphere (and much greater on Venus, but too small to do this on Mars) is GHG radiative transfer.

Why does the tropopause

Why does the tropopause exist, you ask? Because, at a sufficiently low pressure and density bulk convective movement ceases and the atmosphere becomes stratified. (Tropos and stratos, if I remember correctly). Above the tropopause radiation dominates, and is responsible for heat transfer to space. Convection ceases, and with it the lapse rate.

Conversely, below the tropopause, convection, evaporation and sensible heat transfer (molecular kinetic energy) dominate, and transfer heat from the surface to the upper atmosphere, whence it is radiated into space. That is what you have said in your last paragraph, and I agree.

However, it is not the explanation for the increased surface temperature which you give in your blog paper. There, you assume that the atmosphere and the surface radiate against each other, more or less independently, in radiative balance with incoming solar energy. A simplified single slab statement of your explanation is as follows:

Without an atmosphere, the surface would be at 255 kelvins, radiating W and receiving W. With an atmosphere, W is absorbed in the troposphere and half of it is re-emitted downwards. To correct the outgoing imbalance the sun must heat the surface to a temperature where it emits 2W, and the increase in the “bare rock” temperature, from Stefan Bolzmann, will be about 19%, or 48 kelvins. It is this analysis, on which most (but by no means all) of the AGW explanations are based, with which I (and G and T) profoundly disagree.

Fundamental thermodynamics insists that, for energy to be converted either into work or a temperature increase, it must be transferred from a higher to a lower temperature, For two bodies at the same temperature there will be no net energy transfer, no work, and no heating. The type of energy involved, and its spectroscopy is irrelevant. I believe that the surface and the atmosphere act as a conventional source and sink, and that the outward and back radiation are the positive and negative terms in the Stefan-Bolzmann heat transfer equation.

Since, at the absorption point, the surface and the atmospheric temperatures are similar, the terms are much the same, and there will be relatively little net radiative energy transfer. It is the work done by gravity (effectively an external force) which increases the air temperature. In the troposphere convection, conduction, and evaporation cool down the atmosphere, not radiation.

How can I prove this? A reduction ad absurdum argument is to increase the number of atmospheric layers, as Eli did in his response to G ant T, where he added an absurd explanation for the much higher surface temperature which resulted from 2 radiating layers.

More convincingly, we can look at the terrestrial greenhouse experiment of RWWoods. Houghton reproduces the basic greenhouse argument in the first chapter of “Global Warming” : W in from the sun, 2W out from the interior, W back from the absorbent glass, W out. If we replace the glass by rock-salt, eliminating the absorption, we are left with W in, W out.

If your view is correct, the glass greenhouse should be much hotter than the rock-salt. Since the glass (and the rock-salt) are not much warmer than the interior, I would expect their internal temperatures to be the same, which they were.

If we can agree that it is the lapse rate, not back radiation, which increases the surface temperature by 6.5 degrees per kilometre over the tropopause, we can move on to discuss my moon example, where I do not accept that my N2/O2 atmosphere will play no part in heat absorption or radiation, nor that the atmosphere will be an “infinite constant temperature heat bath”. Everything with a temperature radiates.

The tropopause exists because

The tropopause exists because ozone absorbs UV light.

You want another sentence? The O3 dissociates into O2 + O and deposits a huge load of energy into heating the ozone layer.

The stratosphere is stratified because of this temperature inversion. Nuff said.

Well, ok, good point, that's

Well, ok, good point, that's why temperatures increase with height in the stratosphere. But why do they decrease in height from the surface? There's ozone down low too! Without GHG's temperatures would be flat or rising slightly (not as fast as in the ozone layer), not dropping from the surface to some point in the middle of the atmosphere.

Fred, your claims are simply

Fred, your claims are simply contrary to both well-founded physical theory and actual observation.

You just admitted the importance of radiation in distinguishing stratosphere from troposphere, but you continue to talk as if there is no radiation from the cold parts of the atmosphere to the surface. This is wrong. That radiation is observable.

I mentioned from the start the pyrgeometer. You can try running one yourself. There are thousands of measurements that show this atmospheric radiation coming to the ground, do a search and you'll find tons of examples.

For example, here's one I just ran across via Google, observing and modeling the spectrum of downward infrared radiation in Antarctica:

lots of data, that completely contradicts your apparent belief that this radiation does not occur.

I'm afraid I'm going to trim any further posts of yours on this subject unless you acknowledge these real observations and the contradiction with the claims in G&T.

Measurement of long wave

Measurement of long wave downward radiation

The atmosphere and the pyrgeometer (in effect the earth surface) exchange long wave IR radiation. This results in a net radiation balance according to:

Enet = Ein - Eout

Enet - net radiation at sensor surface [W/m²]
Ein - Long-wave radiation received from the atmosphere [W/m²]
Eout - Long-wave radiation emitted by the earth surface [W/m²]
“Note that for an upward facing pyrgeometer, the thermopile output voltage will in most instances be negative. This is because the upwelling irradiance from the pyrgeometer is likely to be greater than the incoming irradiance from the sky.”

My point exactly, Mr Smith. The radiative heat transfer from the earth is the net energy transfer, which is proportional to the difference between the fourth powers of the surface and atmosphere temperatures. If the temperatures were the same it would be zero, and convection, conduction and evaporation would be responsible for all the heat transfer to the atmosphere.

Here is a simple example, extrapolated from Schaum’s Thermodynamics for Engineers, page 51.

A 20cm sphere is suspended in a cold volume maintained at 20 degrees C What is the heat input required to maintain the sphere’s temperature at 200degrees C, if the emissivity is 0.8. The value of the constants is 5.7 e to the minus 9.

Using the difference between the fourth powers of the temperatures in degrees K, the answer is 262 Joules per second.

What is the heat input if the surround temperature is 350, 400, and 473 degrees K? The answers are respectively 200, 139, and zero Joules per second.

The energy radiated by the surround is the negative term in Stefan Bolzmann. In the 473 degree K case it is 262 Joules per second, which is what a pyrgeometer would measure.

Fred - that's absolutely

Fred - that's absolutely correct. But your earlier arguments (and those of Gerlich and Tscheuschner) appear to depend on a claim that Ein = 0 if the atmosphere is at a lower temperature than the surface. For example, in an earlier comment you said:

The idea that the colder atmosphere can directly heat the warmer earth is absurd, as G and T point out at inordinate length.

If you believe "Ein" is positive (proportional to 4th power of atmospheric temperature - or more accurately at each wavelength according to the Planck distribution at the lowest altitude that has close to 100% absorption/emissivity at that wavelength to the surface) and yet is not "directly heating" the warmer earth, then I have to say I don't understand your argument at all. Perhaps you can state it more clearly in mathematical terms.

Resolving the

Resolving the apsmith-fredstaples difference? Consider: the sun's energy spectrum envelops that for the earth's surface which in turn envelops that for any atmospheric altitude. The surface pyrgeometer doesn't know the source of the downwelling longwave flux it measures - the higher-intensity sun's spectrum or the lower-intensity atmosphere's. If the former, Stefan-Boltzmann would generate a positive value and the measured flux would heat the surface in conformity with the second law of thermodynamics. If the latter, S-B would generate a negative value, denoting non-warming also in accord with the second law.

Um, no, that's not correct at

Um, no, that's not correct at all. The solar spectrum "envelops" that for earth's surface only if you are looking at the same solid angle. But the sun's solid angle on Earth's surface (during the daytime) is 6 × 10−5 steradian, vs 2 pi steradian for the entire sky, a factor of 100,000. The solar spectrum in the infrared is far, far less than that from Earth and atmosphere, when you account for solid angle. Plus, you can run the pyrgeometer at night and see the same downwelling spectrum from the atmosphere. It's not from the sun. Sorry John - what were you trying to resolve here?

Good to be back in contact,

Good to be back in contact, Arthur.
Does the night pyrgeometer know whether the downwelling flux originates from atmospheric matter or from the surface, reflected/scattered by atmospheric matter? Is there any reason to think that the atmosphere, which reflects a substantial proportion of incoming radiation, doesn't perform a similar function on the outgoing variety? Do wavelength or intensity make the difference?
On the G&T front, allow me to gently recall that your 'with-absorbing-atmosphere' model generated an 'average

Looks like your comment was

Looks like your comment was cut off for some reason - want to try again?

Whether reflected or absorbed and retransmitted, the atmosphere would be in both cases assisting in trapping Earth's surface emissions and therefore forcing the surface to be warmer. Reflection isn't the traditional greenhouse effect, but it has a similar influence. With clouds and aerosol particles you will certainly get some reflection, but the downwelling radiation is pretty clear even on cloudless nights; as far as I'm aware the vast majority of the downwelling radiation comes from absorption and retransmission, not reflection. This can also be seen from the spectrum, which shows a longer peak wavelength for the downwelling radiation than for that coming from the surface, indicating it's coming from a lower-temperature source.

As an example of such published measurements, see this paper on downwelling infrared radiation measured in Antartica. You definitely get a lot more coming down when it's cloudy (partially reflection I expect, and partially re-emission from the cloud layer).

Yes, a glitch evaporated the

Yes, a glitch evaporated the interesting bit to which I shall return. Meanwhile, thank you for the reference to the Town et al paper which will take some time to digest. You say that reflection and emission have the same effect - trapping surface emissions and forcing the surface to be warmer. How so? In the case of reflection, radiation source and destination are one and the same and S-B would generate zero flux, that is, no warming, in accordance with the second law. For atmospheric emission, on the other hand, S-B generates negative flux, construed mathematically as non-warming of the surface or warming of the atmosphere, all in accordance with the second law. In your original post you counter this by inventing a physical property, "net heat", and recasting the second law accordingly so that as long as the net heat flow is from the sun to surface to atmosphere, surface warming by cooler atmospheric radiation is strictly in accord with the second law. The truth is the accord is with an invalidly revised second law, "net" being an accounting term, not a physical property. One model that I examined by kind invitation to further my education, which simulated the surface and atmosphere as opposing radiators, did raise the temperature of both; but in doing so the system output exceeded input, a violation of the first law of thermodynamics.

Arthur, allow me to gently recall that in your rebuttal of G&T, your "with absorbing atmosphere" model produced the un-earthlike "average< effective radiative" result. The difference was minor, as it was in G&T's numerical explanation of the Holder inequality, and as it is in a reworking of your example above substituting the more realistic 273K for the assumed zero as the night temperature: average, 288.5K; effective, 289.7K. In your paper you deal with the discrepancy by reference to multiple absorbing layers. However, the simplest way to produce the earthlike result is to relax the blackbody constraint on the surface. Reducing emissivity to 0.99 would do it.

Is the blackbody constraint justified? Amongst a plethora of blackbody definitions, which in itself suggests a less than complete understanding of the phenomenon, one referred to an idealisation only imperfectly observed in nature. Another claimed values for most natural matter between 0.9 and 1. However, emissivity tables covering a comprehensive range of materials give a much wider range of values, though not always in exact agreement with each other. From the IPCC's global mean energy budget and associated discussion, values for emissivity of the climate system can be deduced in the range 0.62 to 0.64, implying magnitudes of the natural greenhouse effect in the range 2 - 5 degrees Celsius. Allowing atmospheric reflection of outgoing longwave radiation, absent in the IPCC's budget, turns the effect negative.

John, what precisely do you

John, what precisely do you mean by "In the case of reflection ... S-B would generate zero flux, ... For atmospheric emission, ... S-B generates negative flux" ?

The question is the effect on net flux at the surface, and net outgoing flux to space. The flux to space is what cools the Earth, balancing the input of heat from the Sun; flux to the surface is what determines the warming of the surface that has to be re-emitted by thermal radiation. So if total flux to the surface increases through reflection or re-emission, the surface will warm. If total flux to space is reduced by radiation being blocked by reflection or absorption, the surface will warm also (actually just the same effect expressed differently).

The effective emissivity of the Earth's surface for thermal radiation is somewhere between 0.9 and 1. When you see numbers like 0.62 or 0.64, that's referring to Earth's response to radiation at visible light wavelengths, not thermal.

This is what I mean. E =

This is what I mean. E = e.rho.(T^4 - T'^4) where T is source temperature and T' is sink temperature. In the case of surface radiation reflected back to the surface by the atmosphere, T=T' and E=0. In the case of atmospheric emission to the surface, T<T' and E<0. The condition for surface warming is E>0, which neither case meets.

Reading from the IPCC's global mean energy budget: the atmosphere interacts with 342 Wm2 of incoming radiation and 390 of outgoing, a total of 732 Wm2. It reflects 77 and transmits 238 implying absorptivity = emissivity = 0.57 (as a first approximation; I am aware that this equivalence applies strictly to the same wavelength). Similarly, surface emissivity = 0.85. The atmosphere and surface emit to space in the ratio 0.83:0.17, giving a weighted average emissivity for the system = 0.62. The emissivity tables displaying these sorts of values are designed for use in measuring infrared temperatures - see - not visible light, as you claim.

Incidentally I learnt from the Town et al paper that temperature inversion in the Antarctic winter ensures that the downwelling longwave radiation measured there accords with the second law of thermodynamics.

I would like to run something by you. Professor Pierrehumbert, in his forthcoming textbook Principles of Planetary Climate, defines the condition for optical thickness thus: kqdelta_p/g = 1 where k is the coefficient of absorption of the GHG, q is its mass concentration, delta_p is a height interval in pressure coordinates in an atmospheric column with unit cross-sectional area, and g is earth's gravity. Delta_p/g is the mass of air contained in the interval and qdelta_p/g, the mass of the GHG. k has the units area per unit mass and is a measure of the proportion of the surface area at the top of the interval rendered opaque by a unit mass of GHG. When the product of these two quantities equals unity the surface is fully opaque and emits radiation direct to space. The required mass of GHG to achieve this state can come from either increasing the column interval, delta_p, or the mass concentration, q. Adding GHG to the interval increases q and allows for a reduction in delta_p without loss of critical GHG mass. That is, adding GHG increases the pressure and reduces the height at which radiation escapes freely to space as well as increasing the intensity of the radiation. This means the system is dissipating more heat to space than it is absorbing from the sun and will cool until the energy flows are again balanced. This conclusion, of course, is the exact opposite of the professor's and invalidates the AGW hypothesis. If it is nevertheless correct, Arthur, you will never again have to redefine the laws of thermodynamics to accommodate atmospheric back-radiation.

[edited to fix inequality coding - moderator]

John - your "condition for

John - your "condition for surface warming" is incoherent. Warming with respect to what?

The meaning of the "warming" in global warming, the increase in the amplitude of the greenhouse effect (and the warming in the basic greenhouse effect itself) is a comparison between two systems, one of which has more greenhouse gases in the atmosphere.

That is, the condition for "warming" has to be a comparison of the input energy to the Earth's surface under two different sets of conditions, one with less GHG's and one with more. Your calculation only involves one Earth model, not two.

Of course your formula is also wrong, because the relevant emissivity of atmosphere and surface are different (no common "e" or "rho") and for the atmosphere there is a strong wavelength dependence in the thermal spectral region that makes the "T^4" a poor approximation.

In any case, replacing your "e rho T^4" with a generic F_atm, representing the flux of energy from the atmosphere to the surface (about F_atm = 360 W/m^2 for the present atmosphere) the relevant question on warming is then whether F_atm increases, when you increase the amount of greenhouse gases in the atmosphere. It does, for two reasons: first overall emissivity (and absorptivity) increases as the higher gas levels start to fill in some of the gaps in the spectrum, and second emissions that reach the surface come from a lower altitude and therefore on average a higher temperature.

That is, the relevant comparison to see whether you should expect warming is not between F_atm and F_surface (flux from surface up), but between F_atm (low GHG levels) and F_atm (high GHG levels). If F_atm (high GHG levels) > F_atm (low GHG levels), then the surface will be warmed by the increased gas levels in the atmosphere. End of story.

"condition for surface

"condition for surface warming" is incoherent. Warming with respect to what?”

Warming with respect to the temperature due to absorption of solar radiation.

“If F_atm (high GHG levels) > F_atm (low GHG levels), then the surface will be warmed by the increased gas levels in the atmosphere. End of story.”

Not so fast, Arthur. Higher (isotropic) F_atm implies enhanced cooling of the atmosphere as well as alleged surface warming, that is, a steepening of the adiabat, the slope of which varies inversely with molecular weight, specific heat at constant pressure and humidity. Adding GHGs increases all three of these variables, lessening the slope of the adiabat, contrary to the change allegedly due to higher F_atm. This contradiction loops back to the one alluded to in my previous post.

F_atm is not isotropic -

F_atm is not isotropic - where did you get that? It's the flux of heat from the atmosphere to the surface. And there is no necessary relationship to the adiabat - to get that you have to understand all the heat flows, but you haven't even coherently explained what it is you're trying to calculate. Sorry.

You’re right, F_atm is not

You’re right, F_atm is not isotropic; but its source radiation is, so that F_atm-g = F_atm-space. Now to your two earth model comparison. Assuming Tg > T_atm (true in the real world) and equal emissivities, the simultaneous, continuous energy transfers between the surface and the atmosphere constitutes an evolution - a cooling surface, a warming atmosphere, a falling lapse rate - the end point of which is an isothermal atmosphere. As T_atm increases, so does F_atm-space and the system dissipates more energy to space than it absorbs from the sun - it cools down until Tg = T_atm. This is the radiative equilibrium for earth model one in which equal emissivities are assumed. The transfer from atmosphere to surface (prohibited by the classical second law, allowed by your recast one) affects only the speed of evolution, not the equilibrium state.

In earth model two, with GHG concentrations, atmospheric emissivity and temperature and energy transfers to the surface and to space all increased, the model evolves more slowly and cools more quickly to its equilibrium state, again an isothermal atmosphere and Tg = T_atm, but at a higher level than in model one. However, since the equilibrium temperature varies inversely with emissivity, the equilibrium flux being constant and equal to the incoming flux, model 2's equilibrium temperature should be lower than model 1's. The contradiction implies that atmospheric emissivity can’t exceed that at the surface, as assumed.

Relaxing the assumption, equilibrium in either model features Tg<T_atm. The temperature difference in the second model, where the emissivity difference is smaller, would be less than in the first. Compared with the real world, Tg falls in both models; but, because the atmospheric temperature difference between the two models is unknown, we can’t say in which model it falls less or more. Adding GHGs has an ambiguous effect on surface temperature.

John - "F_atm-g =

John - "F_atm-g = F_atm-space" is false, although it becomes approximately true in the limit as F_atm goes to zero. This is because some of what is emitted by the atmosphere close to the ground is absorbed higher up. For the strongest absorption lines this is the most true, so that the emission to ground at those wavelengths from the atmosphere is considerably higher than the emission to space, which comes from a portion of the atmosphere at a colder temperature.

As to the rest of your argument - "assuming equal emissivity" is nonsensical from the start. The comparison I'm talking about is to an atmosphere with zero emissivity, and zero absorptivity. Introducing GHG's increases emissivity (and absorptivity). But at no point has anybody been talking about a "black-body" atmosphere, as you seem to be implying is the relevant comparison.

However, in the case the atmosphere did behave as a black body (or with emissivity equivalent to that of the surface) your argument is still wrong because this is not a thermal equilibrium system, but dynamical equilibrium or steady state. It does not tend to a uniform temperature, it tends to a point where the various fluxes balance. Under a fully absorbing atmosphere, you would have a situation like Venus, where the surface temperature can increase essentially without limit (the temperature being determined by the height of the point where the atmosphere starts to become transparent to outgoing radiation, and the lapse rate to that point).