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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I see that the fluxes at the

I see that the fluxes at the ground and top of atmosphere, though born of the same originating radiation from atmospheric matter, will differ owing to different degrees of absorption by that matter. They will be equal when the originating radiation is from the absorbent atmosphere’s centre of mass and the degree of absorption is equal for upward and downward fluxes. Radiation from altitudes lower than the centre of mass will produce the result F_atm-g > F_atm-space; and vice versa. While I also see that the degree of absorption is wavelength-dependent, I don’t see that these results are, as you say is the case.

Nor did I imply a blackbody atmosphere, merely that the emissivity of atmospheric matter must be less than for the surface. But Pierrehumbert R.T. does imply one: “Now, let’s stir an additional
gas into the atmosphere, and assume that it is well mixed with uniform mass concentration q.
This gas is transparent to solar radiation but interacts strongly enough with infrared that when a
sufficient amount is mixed into a parcel of air, it turns that parcel into an ideal blackbody.”

You’ve lost me on Venus. On Earth, a fully absorbing atmosphere generates 100% of OLR, the intensity of which is governed by the altitude at which it becomes fully absorbing, which in turn depends on the depth of atmosphere required to contain the critical absorbent mass. Adding absorbent mass reduces the depth and increases, via temperature and intensity, OLR. The system cools which is equivalent to an inward parallel shift of the adiabat and a reduction in surface temperature.

There is no point at which

There is no point at which "the originating radiation is from the absorbent atmosphere's centre of mass". Thermal radiation originates at every altitude in the atmosphere where you have infrared absorbers and emitters (GHG's). For a given wavelength, there is indeed some "fully absorbing depth" - but that distance applies both upwards and downwards.

That is, outgoing radiation, to space, has to originate within one "fully absorbing depth" of the top of the atmosphere. Downward radiation, to the surface, has to originate within one "fully absorbing depth" of the surface. Thermal radiation emitted at lower or higher altitudes would be fully absorbed before reaching space or the surface, respectively.

So even in the fully absorbing case (which we have almost across the thermal spectrum for Venus) a higher concentration of GHG's results in a shorter "fully absorbing depth". That raises the average altitude of final emission to space, meaning that radiation is coming from lower temperature regions of the atmosphere and thus reducing outgoing radiation. And it lowers the altitude of back-emission to the surface, raising that average temperature and the level of that back radiation.

So fully-absorbing or not, you have the same issue of increased GHG levels warming the planet.

Thanks, Arthur. I see that

Thanks, Arthur. I see that adding GHGs is the equivalent of shifting the adiabat outwards, not inwards. An outward shift in the adiabat implies an increase in OLR and a cooling system. That is, the surface warming effect of adding GHGs is self-correcting. Moreover, the shift is not a parallel one. Adding GHGs also decreases the lapse rate, by increasing molecular weight and specific heat with both of which it varies inversely. A lesser lapse rate implies a cooler surface for a given effective radiating temperature. These two effects on surface temperature of adding GHGs to the atmosphere, one self-correcting, the other opposing, spell ambiguity overall.

The lapse rate change (due to

The lapse rate change (due to the moist adiabat slope decreasing as water vapor levels increase) is a known negative feedback - it's included in IPCC AR4 WG1 discussion of feedbacks, in particular in section 8.6, and figure 8.14 (LR there represents the lapse rate feedback). It is a measurable but relatively small effect; when added to the water vapor feedback (due to water vapor's own GHG effects, as an infrared absorber) the net result is still, within quite tight bounds, a positive feedback. Any lapse rate change associated with other GHG's is infinitesimal in comparison to the water vapor one, so there really isn't any overall ambiguity on the size of the effects - it's quite calculable.

I came away with a slightly

I came away with a slightly different reading of this complex area. The lapse-rate and water vapour changes are treated as feedbacks - the former, negative- as a composite positive feedback. The lapse-rate effect is substantial; it halves the amplification due to water vapour alone. The lapse-rate effect would be even more substantial if taken account of when it should be - as a direct negative effect on surface temperature of adding GHGs - since water vapour content increases exponentially with temperature. I reckon there’s room, still, for ambiguity. Perhaps that explains models’ poor skill this century. The cooling trend in the decade just ended is evident in the declining 10-year increases in average annual temperatures over the course of the decade.

The water-vapor-related lapse

The water-vapor-related lapse rate effect is substantial in cutting the direct water vapor feedback - and it is a real and natural part of the response that models find, nothing particularly new about it. You seemed to be saying there should also be lapse rate changes due to the increase in CO2 or other GHG levels (besides water vapor) - but those changes are comparatively tiny, the only important one is the water vapor change.

But this issue of "water vapour content increases exponentially with temperature" is exactly what the calculated lapse rate feedback is all about - I don't know how else you propose to calculate it than the way the models do it. It is indeed a "direct negative effect on surface temperature of adding" water vapor (via the decrease in lapse rate caused by the exponential dependence you mention).

Climate models are not "weather models" - they are not intended as initial-value predictors of the details of Earth's weather in any given year; their purpose is to determine climate numbers - long term averages over periods of several decades. Since we have only had one decade so far this century, "poor skill this century" is meaningless. Given that this decade was warmer than any decade of the preceding century, it's hardly far from any predictions - "declining 10-year increases in average annual temperatures" seems a weird metric in the first place, where'd you get that from.

In any case, water vapor and lapse rate are among the things the models are best at - the uncertainty in those components of the calculation is comparatively very low. The real uncertainty in feedbacks is almost entirely in cloud effects (note that clouds are condensed water, so a completely separate atmospheric component from water vapor, despite many attempts in some quarters to conflate them).

“Let's suppose that the Earth

“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”.

In other words, Arthur, the effect of enveloping the continuously heated earth in a thick blanket of insulating material (with the low thermal conductivity of a gas) would be zero. In this situation the earth would be inside the blanket and receiving a steady flow of heat from the sun. You are suggesting that its surface temperature would not increase, which means that the atmosphere would offer no thermal resistance to conductive heat transfer.

The lapse rate, I hope we can agree, has nothing to do with radiation. It is a function of gravity and specific heat – the adiabatic compression and expansion of an ideal gas is a close approximation.

So, if you are correct, the temperature at top of the N2/O2 atmosphere would be about 30 degrees C below the surface, it would not be in radiative equilibrium with incoming solar radiation, and it would neither have been heated by conduction and convection nor cooled by radiation.

And if we could complete our thought experiment by returning the gas to space, it would retain its intra-atomic and molecular energy states, and not cool down.

Dr Kramm’s example above, from Eli, is even more astonishing. It confirms my own view that much of the AGW confusion results from a failure to appreciate the difference between heat and energy – the “naïve” second law.

The heat transfer in that example, from Stefan-Bolzmann, is (459 – 259) = 200 Joules per square meter from A to B, in one direction only. The negative term in the heat transfer equation is the energy transfer from B to A. The entropy calculation is correct

Fred - how can you call an

Fred - how can you call an infrared-transparent atmosphere "a thick blanket of insulating material"? A blanket works by reducing the flow of heat between the two sides. If the atmosphere is transparent to infrared radiation, then it is doing nothing to reduce the heat flow from Earth's surface into space.

I am indeed suggesting that Earth's surface temperature would not increase, but not that "the atmosphere would offer no thermal resistance to conductive heat transfer." You believe heat is conducted through the atmosphere, from surface into space? Isn't a vacuum the most perfect possible thermal insulator for heat conduction (and convection, obviously)? So how can this heat be conducted through the atmosphere into the most perfect possible form of conductive heat flow resistance?

Heat conduction has nothing to do with the net energy flux between our planet and the rest of the universe. The only significant form of energy flux between planet and universe is by radiation. There are some completely insignificant solar wind and related material particle flows, and some also very small gravitational tidal forces, but the only substantial flow is the radiative one. Incoming from the sun in the form of the Sun's visible spectrum, and outgoing from our planet in the form of thermal radiative emissions. And as far as radiation is concerned, an infrared-transparent atmosphere might as well not even exist. It is no "thick blanket". That is the point of this scenario!

No, what happens is that the heat flow bypasses the atmosphere (if it is transparent to thermal infrared radiation) and goes directly into space. And under steady-state conditions, those two energy flows must balance, hence the 255 K (or lower) average surface temperature.

As to the lapse rate, no it has nothing directly to do with radiation. But the altitude at which the lapse rate ceases to apply (the tropopause, above which temperatures increase with altitude) does depend on the detailed collection of heat flows through the atmosphere, including radiative absorption and emission. In an atmosphere transparent to radiation, the radiative portion of those heat flows disappears, and, as I have asserted repeatedly here, the altitude of the tropopause drops to zero.

In fact, I stated earlier that the atmosphere would be essentially isothermal, at the surface temperature. So your claim that I think the "temperature at top of the N2/O2 atmosphere would be about 30 degrees C below the surface" is wrong. Not that I see any significant logical conclusion you are drawing from the issue.

Fred, you seem to be having trouble picturing the details of the heat flows in the real atmosphere and in this hypothetical case; I'd suggest starting from the Kiehl-Trenberth diagram. In the hypothetical infrared-transparent case, the "back radiation", "absorbed by atmosphere" and "emitted by atmosphere" pieces all go to zero. What happens then?

Arthur, you write, "In an

Arthur, you write,

"In an atmosphere transparent to radiation, the radiative portion of those heat flows disappears, and, as I have asserted repeatedly here, the altitude of the tropopause drops to zero".

First, how would you comment on this short article by William C. Gilbert; Atmospheric Temperature Distribution in a Gravitational Field, from page 3 of the following pdf,

It states ...

"There still seems to be some confusion in the Climate Science Community about the temperature distribution in a gaseous atmosphere under the influence of a gravitational field.",


"Thus in a gravitational field an atmosphere in equilibrium must have a nonisothermal decreasing temperature distribution with altitude. This is true in an isolated air column and this basic physical phenomenon exists independent of any input/output of other energy sources such as ground temperature, convection, radiation, convection, etc."


"This static temperature lapse rate (in this model atmosphere) is identical to the dry adiabatic lapse rate theoretically derived in Meteorology for a convective adiabatic air parcel. In both situations it is solely a function of the magnitude of the gravitational field and the heat capacity of the atmospheric gas, and nothing else. And this relationship aptly describes the bulk of the 33ºC so-called “Greenhouse Effect” that is the bread and butter of the Climate Science Community."


Second, wouldn't there be a nonisothermal temperature gradient in the atmosphere due to conduction and convection from source, surface, to sink, atmosphere?

Gilbert is simply wrong. For

Gilbert is simply wrong. For example, in his "high school approach", he refers to the drop in pressure with altitude, but the ideal gas equation has a term he missed ('n', the number of moles of gas) and a variable (volume - V) that he does not account for. Not only does pressure drop with altitude, so does density (n/V). Between p, V (density) and T you have 3 variables and the one (near-ideal gas) constraint. Hydrostatic equilibrium forces a particular pressure dependence with altitude, but that only provides one additional constraint: density and temperature can (and do) vary with altitude going up and down, with one remaining constraint between them.

Think, if Gilbert was right, then the temperature increase with altitude observed in the stratosphere would be impossible!

The lapse rate is a limit to atmospheric temperature gradients. If temperature decreases with altitude faster than the lapse rate, then the atmosphere is unstable, and convection is induced to reduce the temperature gradient. But (again, see the stratosphere) it provides no constraint in the other direction - if temperature decreases less quickly than the lapse rate, or even increases with altitude, that configuration is stable. That's why temperature inversions are a problem for smog etc - suppressed convection.

Gilbert's discussion of equilibrium is simply wrong. Any system isolated from its surroundings tends to complete thermodynamic equilibrium - that is a single, uniform temperature. Temperature gradients cannot be sustained in an isolated system because on net heat must move, one way or another, from hot regions to cold, and cannot move back (second law).

On your "second" question - why is the atmosphere a "sink"? A "sink" must release its energy somewhere, but an atmosphere transparent to radiation cannot radiate out into space. So the only place energy could leave the atmosphere is by being returned back to the surface. If surface and atmosphere are at different temperatures, then yes there will be conduction and convection to resolve that difference. As the atmosphere becomes isothermal, however, all such heat flows cease and the state of the atmosphere becomes essentially irrelevant to the one source and sink in the system - the surface.

Arthur, I meant the example

Arthur, I meant the example at page four from the article starting from page three.

"... Consider a vertical gas column containing a finite and constant specific energy level (U, J/kg) that is isolated from its surroundings (no input/output of energy or mass) but which is in a gravitational field. The column will in time reach equilibrium with respect to internal specific energy but the temperature will not be uniform. At static equilibrium (adiabatic equilibrium where no macro motion exists), internal specific energy (U) is composed of both thermal energy (the energy due to molecular motion) and potential energy (the energy due to position). The latter has to exist in a gravitational field. Thus, according to the first and second law of thermodynamics, the specific internal energy (U) for any mass parcel in the air column has to be constant and can be expressed as a sum of the thermal and potential energies. This law (expressed as specific energies) can be written:

U = CpT + gh or upon differentiation dU = CpdT + gdh (1)

where “CpT” is the enthalpy (or thermal energy) per mass unit, “g” is the gravitational acceleration, “h” is the vertical height and “gh” is the potential energy per mass unit. At static equilibrium dU = 0 and equation (1) becomes;

CpdT + gdh = 0 (2) ..."

You wrote: "Think, if Gilbert was right, then the temperature increase with altitude observed in the stratosphere would be impossible!".

As C. Ahrens states in his book, Essentials of Meteorology 2nd ed., p. 10,

"The reason for the inversion in the stratosphere is that the gas ozone plays a major part in heating the air at this altitude. Recall that ozone is important because it absorbs energetic ultraviolet (UV) solar energy. Some of this absorbed energy warms the stratosphere, which explains why there is an inversion. If ozone were not present, the air probably would become colder with height, as it does in the troposphere."

And finally, if we accept the fact that all material above absolute zero temperature radiates energy and the excerpt below from stating:

"... 5. The energy discharge from the troposphere takes place at its upper boundary layer, at the transition of the atmosphere from its gaseous state to a state approaching a vacuum. Only in this zone do gases start to emit even small quantities of energy by radiation. The other energy transfer mechanisms - thermal conduction and convection - which at denser pressure are far more efficient than radiation, no longer operate because of the low density of the atmosphere there. But from the surface where man lives and up to 10 to 17km altitude (depending on geographical latitude), gases transfer the small quantities of energy they might acquire from absorbed radiation by convection and conduction - not by radiation. ..."

, we should have essentially identical atmospheric conditions with or without "greenhouse gases".

"jvs" - when I said "if

"jvs" - when I said "if Gilbert was right" at that point I was referring to his first ("high school") argument which is obviously wrong. Despite decreasing pressure with altitude in the stratosphere, temperature increases (due to the energy fluxes you mention).

Gilbert's other arguments are equally wrong, but perhaps less obviously so since they are masked in more attempts at sophistication, such as the one you highlight here. This argument refers to a "parcel of air". But there is no such object in the atmosphere; air mixes and is not subdivided into definable "parcels". For a short period of time you can treat a parcel as isolated and of a constant internal energy - that is the adiabatic approximation as I mentioned in another response here. But over time, heat flows (second law of thermodynamics) from hot regions to colder ones - governed by temperature, not internal energy. If a given "parcel of air" moves from a lower altitude to a higher one, its potential energy is indeed raised as Gilbert notes, but if it moves slowly enough it can easily maintain a constant temperature by exchanges with neighboring "parcels" that are at that same original temperature. As you approach equilibrium in any isolated system, you always reach a constant temperature. That's how thermal equilibrium is defined. This (and the related feature of transitivity of temperature equality) is often referred to as the "zeroth" law of thermodynamics.

While it is indeed true that "all material above absolute zero temperature radiates energy", different materials at a given temperature radiate energy at different rates. The Stefan-Boltzmann T^4 rule has an emissivity factor that depends on material (and temperature!) - without that it applies to black bodies, but we know that not all materials are black - some not close at all. In particular, the difference between greenhouse gases and other atmospheric gases is that, at the temperatures associated with our planet's atmosphere (200-300 K) their emissivity is many orders of magnitude greater (billions or more) - the ratio in question is the Planck factor which has an exponential dependence on the energy of prominent spectral features divided by temperature. Without the GHG's, there would indeed be a very little amount of emission from the atmosphere. But relative to the situation with GHG's, it's essentially negligible.

Just as for visible radiation a cloudless sky is essentially transparent so we can see the stars at night, so without GHG's the atmosphere would be essentially transparent to Earth's thermal radiation. The correction due to atmospheric emission in that case is exceedingly small.

No, Arthur. A blanket works

No, Arthur. A blanket works by creating a thermal barrier between the two sides. The flow of heat (at equilibrium) is the same. The presence of the blanket requires a greater temperature differential to maintain the same flow of heat.

For the sake of the reductio ad absurdum argument, imagine that the incoming solar energy is generated at the surface, inside the blanket. The N2/O2 mixture has a very low thermal conductivity and is some 20 kms thick. Can we not agree that the surface temperature must increase to overcome the thermal resistance of the air blanket (string vests, for example, if you remember them)?

[remaining nonsense removed by moderator - Fred, please try comprehending the discussion before responding]

As I already patiently

As I already patiently explained, thermal conductivity is irrelevant to radiation to space. If N2/O2 is transparent to outgoing thermal radiation, then the surface temperature has absolutely no reason to increase.

Since you refer to "thermal resistance", let's think of the different modes of heat transport as analogous to a collection of electrical resistors. Conduction is one resistor. Convection is another. Latent heat transport is a third (dependent on convection). And radiation is a fourth. This analogy is applicable whenever we partition a system into two regions at different temperatures, considering the flow of energy between them.

The important thing to understand then, with this analogy, is that the resistors are all operating in parallel. The large resistances become irrelevant, because they are shorted out by the small ones. Of the four heat-flow mechanisms, it is the least resistant one that dominates, not the most resistant.

Now the second thing to understand with this analogy is that, when the two regions we are looking at are Earth's surface and outer space, conductive, convective, and latent heat heat flow resistances are always effectively infinite. No heat flows into space via material transfers from Earth. That means that the only important resistance, the only heat-flow that matters in the Earth-space case is radiation.

And if the atmosphere is transparent to radiation, it doesn't matter what other properties it has, it will have no effect on heat flow between surface and space.

I found this site via Rabett

I found this site via Rabett Run. It looks like just the place for me to ask a question.

Is the following roughly correct?

I have a certain mass of gas at a certain temperature. It therefore contains a certain amount of thermal energy at an average temperature. If I compress it, the thermal energy, and therefore temperature, increases. This is because of the work I've done to compress it, not because of the increased pressure in itself.

If this gas has been compressed into a pressure vessel which is a perfect insulator, the thermal energy (and temperature) is maintained indefinitely. If it is a normal pressure vessel, like a gas cylinder, the thermal energy leaks out until the temperature drops to ambient: the gas has lost all the added energy despite the pressure being maintained. If this were not the case, we would be violating the First Law of Thermodynamics.

The situation with a planet's atmosphere is similar. Increased pressure cannot, of itself, increase thermal energy (and temperature) and any transient increase due to external input would be quickly lost to space. If the temperature were high through pressure alone and without external inputs, we would again be violating the First Law. Pressure cannot explain the high surface temperature of Venus.

Yes, that's a good way to

Yes, that's a good way to explain it. Thanks.

Since this has been raised in context of the lapse rate, note that it is called the "adiabatic lapse rate". Adiabatic changes in a blob of gas are rapid changes in pressure or volume; the adiabatic assumption is that no heat flows in or out of the blob. That is a reasonable assumption for rapid motion. But slow things down, and heat does start to flow through the boundaries of the blob, tending to the other extreme of isothermal change. And the "isothermal lapse rate", applicable to an atmosphere where gas only convected very slowly, would of course be zero.

Where did my comment go? I

Where did my comment go? I expected it would be moderated but I got no message when I clicked Save.

Hmm, still some bugs to be

Hmm, still some bugs to be fixed with this site. It was a bit of an experiment with the drupal software... But see the "Policy" link above for what to expect with comment moderation. In this case I just didn't have a chance to check for comments for a few days, and got a bit behind. I have some responses to the most recent comments from people here, will hopefully get to tonight...

Personally, Arthur, I am

Personally, Arthur, I am ready to move on, and, with your help, try to eliminate some of the more egregious internal contradictions in AGW theory. However, having read William Gilberts paragraph, and your response, I can’t resist one more try.

You object to his use of the (notional) adiabatic expansion of an air parcel (a standard trick in Physics, to coin a phrase). You then propose the isothermal expansion of a similar parcel, eventually producing a column at constant temperature. We can avoid moving parcels altogether by considering individual molecules.

Consider two thin slices in your isothermal gas column, a distance deltah apart. Their potential energies, per mole, will differ by g.deltah, entirely due to gravity.

Their internal kinetic energies will be the same, because (in your column) their temperatures are the same. Consider a molecule moving upwards. Its potential energy increases, its kinetic energy does not reduce. It does work against gravity and its total energy increases. Where does the additional energy come from?

Now consider a molecule moving down. It gives up potential energy, but its kinetic energy does not increase. Where does the energy go?

In the adiabatic column potential energy is exchanged for kinetic energy for all molecular movements. Which is the more physical description?.

Fred, obviously, a single

Fred, obviously, a single molecule moving upwards will slow down. But it will also, under the conditions that prevail throughout the bulk of the atmosphere, quickly collide with other molecules that, in the isothermal case, are at the original temperature. So after a very short time its kinetic energy at the higher altitude will be randomized to the local thermal profile. That's the standard thermalization process. At equilibrium the number of molecules moving up balances the number moving down, and there is no energy conservation issue at all.

“Obviously, a single molecule

“Obviously, a single molecule moving upwards will slow down. But it will also, under the conditions that prevail throughout the bulk of the atmosphere, quickly collide with other molecules that, in the isothermal case, are at the original temperature.”

Obviously, Arthur. And to get into the isothermal case the higher molecules (originally colder) must gain heat from the rising molecules, which cool (slow) down as they move up.

Consider a single plane across the atmosphere, and the gains and losses across that plane.

Even if we start in the isothermal case rising molecules gain potential energy, do work against gravity, and lose kinetic energy. Falling molecules lose potential energy, have work done by gravity, and gain kinetic energy. Over time, lower levels would warm, and higher levels cool.

The isothermal case can neither be established nor sustained in a gravitational field.

You are saying there can be

You are saying there can be no thermodynamic equilibrium (constant uniform temperature) for a gas, or even a liquid by this argument, in the presence of a gravitational field?

That's an interesting claim. It is also patently false. Let us indeed consider individual molecules crossing a single plane. While temperature above and below is the same under isothermal conditions, density differs, and the density gradient must be taken into account: there are more molecules below than above. On the other hand, molecular flux across the plane (number per second) is proportional to the normal velocity component, so the fluxes are weighted toward faster, higher-energy molecules. These two factors together ensure that the net internal energy change per unit time at any altitude is exactly zero, under equilibrium conditions.

Fred, surely you are familiar with the Equipartition Theorem, fundamental to statistical mechanics? It applies not just to the kinetic energy, giving the Maxwell-Boltzmann distribution there, but also to the potential energy at equilibrium in a gravitational (or any!) field, given an exponentially decaying density dependence with altitude. Very basic fundamental physics here.

fredstaples, "more egregious


"more egregious internal contradictions in AGW theory." What do you mean? How does "AGW theory" differ from GW theory? Do you in fact mean greenhouse gas theory in general?

Hand-waving, Arthur. The

Hand-waving, Arthur. The equipartition theory divides internal energy between the molecular degrees of freedom. For an ideal gas there are only three, the spatial axes, so the gas laws can be readily deduced without considering energy states in the molecular bands or Maxwell Bolzmann electron distributions in the individual atoms.

Considering the single level in the atmosphere you say:
“there are more molecules below than above. On the other hand, molecular flux across the plane (number per second) is proportional to the normal velocity component, so the fluxes are weighted toward faster, higher-energy molecules”.

Are you suggesting that, in your isothermal column, more molecules move upwards than downwards? That implies upwards mass transfer. Your system will defy gravity as well as thermodynamics.

I shall retreat to the comfort zone of the standard adiabatic parcel, expanding and cooling as it rises, (or contracting and warming as it falls) to give a temperature lapse rate equal to –g/Cp, dependent on gravity and specific heat alone, as the Gilberts reference demonstrates.
To move on, [removed by moderator - let's focus on one wrong concept of yours at a time.]

Sorry, I mis-spoke when I

Sorry, I mis-spoke when I referred to equipartition. The relevant relationship is the standard Gibbs/Boltzmann/canonical distribution that describes the density of independent molecules in phase space under thermal equilibrium conditions at a given temperature. This is very basic statistical mechanics, fundamental to essentially every use of thermal equilibrium arguments to a physical system. In this case we are looking at the energy of an ideal gas molecule in a gravitational field; as far as center-of-mass coordinate, phase space is six dimensional: position and momentum in 3 dimensions. Explicitly:

E = m g z + (px^2 + py^2 + pz^2)/2m

(x, y, z being atomic position along three axes, px, py, pz representing momentum)

Internal energy is independent of x and y position, but dependent on z; since the energy is a simple sum the partition function is trivially separable into a product of the partition function for z, and px, py and pz separately. Applying the canonical distribution formula for a given temperature T means that the population density of atoms with a given momentum px is proportional to exp(-px^2/(2m k T)), the Maxwell-Boltzmann distribution, and similarly that the density of atoms at a given altitude z is proportional to exp(-mgz/kT) (the barometric formula).

The math from that point is tedious but straightforward to show that, through any given plane, net flow of atoms and energy is identically zero, due to the two factors I mentioned (together with downward acceleration). I suggest you attempt it, rather than doing your own hand-waving there. Of course, the zeroth law of thermodynamics (and the canonical distribution) ensures that this will work. [Note: slightly edited from original posted 2 hours earlier.]

Now Arthur, I hope you will

Now Arthur, I hope you will agree that practical Physicists must try to use the Physics appropriate to a problem. We do not reach for our Lorentz transformations to calculate how far a golf ball will fly.

We know that the ideal gas laws allow perfectly acceptable calculations at atmospheric pressures and temperatures, and Newton’s laws are an acceptable approximation to motions.

These things we know, how? Because they conform to measurements and experiments under the controlled conditions of a laboratory.

For example, we can measure the ratio of Cp to Cv from the expansion of a gas which resembles the expansion of our parcel of air in an atmospheric column. In the column, we can calculate the exponential fall in pressure with height by equating the upward pressure on a parcel to the force of gravity on the gas above it. We know that an upward moving parcel will do work against its environment. The crucial question is whether the work is adiabatic or isothermal.

If the expansion is adiabatic, (because of the very low thermal conductivity of air), the temperature will fall. If the expansion is isothermal the gas will be heated by the constant temperature atmosphere as it expands, and the temperature will remain constant.

Of all the various PV experiments I have looked at, the Clement Desormes method at most resembles our atmospheric situation. Gas is expanded across a very low pressure differential to the atmosphere, adiabatic expansion is assumed, and the pressure changes are used to calculate the ratio of specific heats Cp/Cv = y from the adiabatic formula PV to the power y = constant.

The fact that the answers are very close to the measured ratios for a wide range of polyatomic gasses, including those with vibrational degrees of freedom, proves that the conventional assumption of adiabatic expansion is correct, and hence that the atmospheric lapse rate in dry air is a function of gravity and specific heat, and nothing else.

I try not to quote authority, Arthur, but I would add that of all the gas law real and thought experiments I looked at, both from Google and my text books, absolutely nothing supported your suggestion of an isothermal atmosphere in the presence of gravity.

You appear to agree that

You appear to agree that sustaining the adiabatic lapse rate requires doing work, consuming free energy and creating entropy. It transmits net energy from the surface into the atmosphere. In contrast, sustaining an isothermal state requires no work. In the examples you have presented, there is heat flowing into the atmosphere. But in the isothermal case under gravity that we've been talking about, there is no heat flow through the atmosphere because it has nowhere to go.

What is the source of free energy to the atmosphere in your example? Remember this atmosphere can absorb and emit no radiation according to the transparency assumption here. If energy is entering the atmosphere from some source (the surface, or "gravity" in some way), then this energy must be dissipated in the atmosphere, warming it, or returned again to the surface; it has nowhere else to go.

With an adiabatic lapse rate,

With an adiabatic lapse rate, Arthur, there is no need to struggle to explain internal energy or entropy changes, because the expansion of a rising (or falling) parcel is isentropic.

However, for the sake of the argument I will accept your isothermal temperature distribution and add 30,000 ppm of water vapour to our transparent atmosphere. The effect would be dramatic. The lapse rate would become adiabatic. The absorption of surface infra-red radiation would move the tropopause high into the troposphere, the surface temperature would increase by some 30 degrees K, and the dry air lapse rate would be substantially modified by the absorption of latent heat at the surface, and the release of latent heat high in the troposphere.

A window of radiation direct to space would remain, together with a much smaller window around 15 microns where the H2O and (still missing) CO2 spectra do not quite overlap.

Conduction, convection, evaporation and radiation would combine to transfer heat into the troposphere, whence it would be radiated into space.

In other words we would have more or less what we observe.

We can then discuss exactly how these mechanisms work, and how they would be modified by the addition of the pre-industrial 250 ppm of CO2, and finally by the AGW addition of post-industrial CO2.

Your last comment is an excellent start-point, since it combines the contrasting AGW explanations of surface warming versus top-of-atmosphere adjustments.

I extracted the following quotations from an RC discussion of this topic, ('Plass and the Surface Budget Fallacy') and posted the following:

Ekholm in his 1901 paper:
. . . radiation from the earth into space does not go directly from the ground, but on the average from a layer of the atmosphere having a considerable height above sea-level. . . The greater is the absorbing power of the air for heat rays emitted from the ground, the higher will that layer be. But the higher the layer, the lower is its temperature relatively to the ground; and as the radiation from the layer into space is the less the lower its temperature is, it follows that the ground will be hotter the higher the radiating layer is.

Chris Colose
This is one of the problems I have with the simple layer model as it is introduced in some textbooks, such as Dennis Hartmann’s or David Archer’s “Understanding the Forecast.” This is where you simply add up the influence from successive blackbody “layers” with a final result of something that usually ends up looking like T_s=T_eff*(N+1)^0.25, where N is the number of layers, and T_s and T_eff are the surface and effective temperatures, respectively. Archer discusses some of the incompleteness of this model in his class lectures (lack of convection, layers are not fully transparent in the shortwave nor fully opaque in the longwave) but I think the whole presentation misses the point completely

Barton Paul Levenson
Your CO2 absorbs an infrared photon, one of its electrons jumps a level, and it either radiates another photon of the same level, or more likely, crashes into a nearby nitrogen or oxygen molecule and transfers some of the new stuff as kinetic energy. Temperature is a measure of kinetic energy at the molecular level; the faster the molecules jiggle, the hotter the object. Thus the atmosphere warms up. Those collisions transfer energy *back* to the CO2, which radiates by the (wavelength-specific) Stefan-Boltzmann law. Some of the energy goes back down to the surface and heats it above what it would be from sunlight alone.

Eli Rabett
The short answer to the question of where the energy comes to warm the surface is from energy that left the surface but was turned around by backradiation. Without the greenhouse gases it would just keep going

And RayPierre
“The way the greenhouse effect really works is that adding CO2 reduces the infrared out the top of the atmosphere, which means the planet receives more solar energy than it is getting rid of as infrared out the top. The only way to bring the system back into balance is for the whole troposphere to warm up. It is the corresponding warming of the low level air that drags the surface temperature along with it”

In Dr. Smith's paper "Proof

In Dr. Smith's paper "Proof of the Atmospheric Greenhouse Effect" and in his postings to this blog, I observe a semantic problem. This problem muddies the waters that surround the issue of the circumstances under which absorption of IR by the so-called "greenhouse gases" can warm Earth's surface.

The problem results from confusion of the terms "heat" and "work" with the term "energy." In thermodynamics, the ideas conveyed by the various terms differ. An apprehension of these differences is crucial to lucidity in a discussion of the import of the second law of thermodynamics for atmospheric physics.

Under the second law, heat may not flow from a region of the atmosphere at temperature TCold to a region of Earth's surface at temperature THot without the expenditure of work, where THot is greater than TCold. It follows that the matter which is at temperature TCold may not heat the matter which is at temperature THot in the absence of a heat pump and this conclusion is independent of whether the matter which is at TCold is absorbing IR. Are we all in agreement on this?

Thank you, Dr. Smith, for

Thank you, Dr. Smith, for affording we posters with the opportunity for discussion of the Gerlich & Tscheuschner (G&T) paper "Falsification...". In this posting, I suggest an import for climatology of ideas presented in my previous posting, dated 02/11/2010.; these ideas are consistent with a theme of the G&T paper. In particular, I show that the greenhouse effect which is described by a prominent climatological research organization is refuted by its violation of the second law of thermodynamics.

A belief evidently held by the climatological research organization UCAR is presented by a Web page ( ) at UCAR's Web site. UCAR's presentation references a diagram that is labelled "Global Heat Flows." One of these "heat flows" is 390 W/m2 of "back radiation." An arrow points the back radiation toward Earth's surface.

Under a heading entitled "The greenhouse effect," UCAR's Web page provides the following description of the purported "greenhouse effect":
[begin UCAR description]"Now let's look at the outgoing IR radiation. Note that 390 W/m2 of IR energy starts upward from the surface. But wait! We only had 168 W/m2 coming in! Where did all of that extra energy come from? This is where the atmospheric nearly-complete opacity to IR comes into play. Whenever any IR radiation starts upward, nearly 90% of it is trapped by greenhouse gases in the atmosphere before it can escape the "black box" and return to space. So the atmosphere is warmed by the 67 W/m2 of incoming sunlight plus most of the IR trying to escape from the surface to space. All of this generates IR radiation emissions from the atmosphere. Some of this IR from the atmosphere does escape to space (the 165 W/m2 arrow flowing upward from the atmosphere plus the 30 W/m2 flowing upward from clouds). Most, however heads back down towards the surface. That's what the 324 W/m2 of "back radiation" is all about. This downward flow is what really pumps up the surface temperature to the point that it can radiate 390 W/m2 of energy upward. The greenhouse gases act as a blanket covering Earth's surface; a lot of energy flows back and forth between the insulating blanket and the "body" of the planet beneath; but relatively little escapes from this efficient insulating cover." [end UCAR description]

Evidently, UCAR believes the 324 W/m2 of back radiation flows as heat to Earth's surface for, according to UCAR's description, the back radiation " what really pumps up the surface temperature"; also, as previously mentioned, UCAR's presentation references a diagram labelled "Global heat flows" with an arrow pointing the back radiation toward Earth's surface. However, as it emanates from matter which is colder than the matter at Earth's surface, this "heat" cannot be transferred from the colder matter to Earth's surface without a heat pump, under the second law of thermodynamics. However, no heat pump is in evidence. Under the second law, then, the heat flow to Earth's surface from the "back radiation" is not the 324 W/m2 claimed by UCAR but rather is nil.

As the magnitude of the back radiation increases monotonically with the concentrations of the various greenhouse gases, UCAR's "greenhouse effect" yields a sensitivity of the global average surface temperature to the concentrations of these gases. On the other hand, if the heat to Earth's surface from the back radiation is nil, this sensitivity is nil. Under the second law, this sensitivity is nil.

But you are not discussing

But you are not discussing the Gerlich and Tscheuschner result, you are discussing your own theory here. Did you actually read my article? Did you read the discussion which has gone on in the comments? You clearly did not understand it.

You seem to believe the "back radiation", whatever it may be called ("heat" is a poor word for it) is nil. Do you agree that your argument is based on their being no such thing as "back radiation"? And yet it is measurable (see above discussion). Therefore your theory of the effect is demonstrably falsified by the evidence. Perhaps UCAR's presentation of the theory is poor - I certainly don't agree with precisely the way they've phrased it. But every popularization of science includes statements that are, technically, incorrect. That doesn't make the general sense invalid - and the general sense of what UCAR presented there is perfectly accurate.

Sadly, Mr Oldberg, your

Sadly, Mr Oldberg, your comment, though quite correct, is not conclusive. The source of atmospheric warming, the earth, is warmed by the sun and the sink, the atmosphere, is warmed by the earth.

AGW propnebts argue that the net energy transfer (which is heat) is from the warmer earth to the cooler atmosphere, so the second law is never violated. But if the radiation absorption in the atmosphere increases the resulting warming will reduce the temperature differential and hence the net energy transfer from the surface. Since the net outgoing energy must equal the incoming energy from the sun, the surface will warm to compensate.

You can see this if you compare the bare rock case with the atmospheric earth. In a single slab model the absorptive atmosphere will radiate equally up and down.

If the bare rock radiation to space is R, and the corresponding temperature Tr, adding an absorptive atmosphere will return half of the outgoing radiation to earth. The radiation must increase to 2R and the surface temperature must be increased to Te, so that :

Te/Tr = fourth root of 2 = 1.19. (From the Stefan-Bolzmann equation for black bodies)

Since the radiation from the top of the atmosphere must equal the bare rock radiation, we seem to have a surface temperature increase from 255 to 303 Kelvins as a direct result of an absorptive atmosphere. The difference, 48 degrees C, is greater than the observed 33 degrees C, but reasonable “in view of the simplicity of the model”.

You can see this argument in Arthur’s refutation of the G and T paper, so if we are to persuade Arthur to modify his position we will need stronger arguments.

First, if we apply the above analysis to more than one slab, the results rapidly become nonsensical. You can see this in my debate with Eli Rabett over his refutation of G and T, or in Chris Colloose’s doubts in my selection (above) of pro AGW explanations taken from the RC web-site.

Next, you can apply exactly the same analysis to a terrestrial greenhouse, with the absorbent glass replacing the atmosphere. RW Woods tried to find the back radiation effect by comparing a glass greenhouse with a rock salt greenhouse. It was not there.

On R.W. Wood - why the effect

On R.W. Wood - why the effect was not there is explained rather nicely over at Eli Rabett's blog.

Dear Mr. Staples: Thanks for

Dear Mr. Staples:

Thanks for taking the time to comment!

I'm not focused on the AGW controversy but rather on a foundational issue for climatology. This issue is whether or not the Kiehl-Trenberth type of diagram is fundamentally flawed. If it is fundamentally flawed, this would have far reaching implications for climatology.

If it is flawed, this flaw is obscured by an ambiguous and confusing use of language in climatology. Under this language, the separate concepts of "heat," "work" and "internal energy" are described by the single word "energy." Additionally, a heat flow is confused with a radiation intensity. The confusion results in the need by climatologists to employ the neologism which they call the "net heat flow" to avoid violations of the second law of thermodynamics. For climatologists, the second law does not apply to a heat flow but rather to a "net heat flow." This is a non-standard and confusing usage of technical English. In technical English, the notion of a "net heat flow" does not exist.

In making the following remarks, I use standard technical English. Thus, my "heat flow" is the equivalent of the "net heat flow" of climatology. Also, unlike a climatologist, I distinguish between the concepts of heat flow and radiation intensity

According to one UCAR publication, the entity that flows through a Kiehl-Trenberth diagram is energy. According to another UCAR publication, this entity is heat. If it is heat, then the Kiehl-Trenberth diagram is invalidated by the violation of the second law of thermodynamics by the heat flow which UCAR calls the "back-radiation."

If an energy flow is not a heat flow, then it seems to me that it must be a radiation intensity. However, there is a problem for this interpretation. The Kiehl-Trenberth diagram implies there is a balance of energy flows. This implies there is a balance of radiation intensities. However, in their paper "Falsification...," Gerlich&Tscheuschner point out that the notion of a balance implies the existence of a conservation principle. However, they state, there is no such principle for radiation intensities. They state that to assume there is such a principle is the "cardinal error" of climatology.

I'm left with the conclusion that, whether an "energy flow" is interpreted as a heat flow or as a radiation intensity, there is something fundamentally wrong with the Kiehl-Trenberth diagram.

I'll end with a bit of speculation. A balance of heat flows is a valid concept. Perhaps, climatologists have fooled themselves into thinking there is a balance of radiation intensities by their failure to distinguish between a heat flow and a radiation intensity.

Terry, yes, of course

Terry, yes, of course back-radiation is a radiative energy flow ("radiation intensity" if you wish) - by definition it cannot be "heat" because heat requires thermalization (redistribution among degrees of freedom at a given temperature), and the radiation is not thermalized until it is absorbed at the other end. So in transit it is most certainly not "heat", but radiative energy flow. And from Kirchoff's law (as well as the second law) the net radiative energy flow which determines the actual heat exchange between the two sides must be from hot to cold. That's very straightforward. Perhaps UCAR mislabeled a diagram (though I don't actually see any such mis-labeling in the page you pointed to), but there's no question that back-radiation is definitely a radiative energy flow which is only one side of a heat exchange - the name says "radiation" for one.

Your "problem for this interpretation" as a radiative energy flow is completely illogical. For one, the most recently updated Kiehl-Trenberth diagram which I linked to earlier in this discussion is not balanced - there is net heat increase of about 1 W/m^2 on the surface. The cause of the imbalance is humanity's enormous increase in greenhouse gases in the atmosphere, which is sort of the whole point of this discussion. It is not balanced.

Of course it is close to being balanced (and the earlier iteration with less precision was numerically balanced) - but all that means is that the Earth is in close to a steady state, not heating or cooling. G&T's call for some sort of "conservation principle" is hilarious - the "conservation principle" in question here is simply the conservation of Earth's temperature. If Earth's temperature remains fixed, then no net heat is flowing to our planet, and incoming and outgoing radiation flows must balance. If there is an imbalance (as there is right now) then Earth's temperature must increase. Really, there's little more that needs to be said about their (and apparently your) misunderstanding of the whole problem.

I thank Arthur Smith for his

I thank Arthur Smith for his critique of my previous comment. His critique was quite valuable. I particularly valued his questioning of my claim that the "back radiation" is nil. I address this and other issues below.

My understanding of the physics was sharpened by an exchange over the past couple of days of ideas with an academic physicist. I'll leave him nameless as I don't have his permission to reveal his identity.

To respond to a question raised by Dr. Smith, I've read his paper "Proof of the Atmospheric Greenhouse Effect". In the following remarks, I don't reference the content of Smith's paper as I don't believe it to be pertinent to the topic which I address. This topic is violations of the second law of thermodynamics in relation to the so-called "greenhouse effects." That there are one or more greenhouse effects is a key element of the argument for regulation of CO2 emissions.

Second law violations are a theme of the Gerlich & Tscheuschner (G&T) paper that is referenced in Dr. Smith's essay "The Arrogance of Physicists"; it is this essay that has resulted in all of the various comments in this section of Dr. Smith's blog including my comments. In the following remarks, I clarify and expand upon remarks made by G&T in their paper that relate to second law violations.

In reviewing the literature, I've observed that several critics of the G&T paper appear to misunderstand the basis for the paper's implication that second law violations falsify one or more claimed greenhouse effects. Thus, I open my remarks by addressing these misunderstandings.

After addressing them, I falsify a greenhouse effect where, by this effect, one means the effect that is described as "The Greenhouse Effect" at UCAR's Web site. Note that UCAR's claim is not to have described A greenhouse effect but rather is the more sweeping claim of having described THE greenhouse effect.

In the course of my remarks, I expose the role of the "back radiation" in creating an appearance of a greenhouse effect that is not real. In particular, the "back radiation" is a photon flux from colder to hotter matter. In representing this flux to be a heat flux, UCAR violates the second law while making the heat flux from a region of Earth's surface to a region of Earth's atmosophere seem highly sensitive to CO2 and water vapor concentrations when this heat flux is insensitive to these concentrations.

Communication about my topic is hampered by a semantic problem. For simplicity and for comparison to experimental data to be described, it is convenient to expose this problem in the context of a pair of square flat plates that are separated by a gap and aligned so they oppose each other; each plate is a black body radiator. One plate is at temperature TCold. The other is at temperature THot. The gap is evacuated. Let the magnitude of this gap be designated by the variable "Gap."

A flux of photons passes from the plate which is at temperature TCold to the plate which is at temperature THot; this flux has power density PCold (W/square meter). A flux of photons passes from the plate which is at Temperature THot to the plate which is at temperature TCold; this flux has power density PHot (W/square meter). PHot and PCold can be calculated by the Stefan-Boltzmann equation as sigma * T^4 where "sigma" is the Stefan-Bolzmann constant and T is the temperature of the plate. The characteristics of the photons belonging to each flux are measurable. However, neither flux is a heat flux, as "heat" is defined in thermodynamics.

By the definition of "heat," the "heat flux" is PHot - PCold. By these semantics, the "heat" is non-negative and travels from the plate at temperature THot to the plate at temperature TCold, as required by thermodynamics.

In the chart on UCAR's Web page, there is a flux of photons from colder matter in Earth's atmosphere to hotter matter in Earth's surface. UCAR calls this flux the "back radiation." UCAR claims that the "back radiation" heats Earth's surface. This is incorrect, for the photon flux of the "back radiation" is not a heat flux. In claiming that the photon flux is a heat flux, UCAR violates the second law, for the photon flux is from colder to hotter matter. The second law violation has the repercussions which I next address.

Let us introduce air into the evacuated gap between the two plates. With the air in place, the heat flux changes from ( PHot - PCold ) to Q' (W/square meter). By definition, the thermal conductivity k of the air is Q'/[(THot - TCold) * Gap].

Now, let us mix CO2 or water vapor into the air. If there is a greenhouse effect, k drops significantly. However, according to G&T this effect never has been observed. What has always been observed is that, at atmospheric temperatures, k stays fixed as the CO2 or water vapor concentration varies; k stays fixed, rather than decreasing as is required for the existence of a greenhouse effect. At much higher than atmospheric temperatures, k increases with the concentration of CO2 or water vapor; k increases, rather than decreasing as is required for the existence of a greenhouse effect.

Experimental data on convective heat transfer has yielded models of convective heat transfer through the agency of dimensional analysis. The data and the analysis suggest the existence of a functional relation among the dimensionless Nusselt number, the dimensionless Prandtl number and one additional dimensionless number. In free convection, the additional number is the Grashof number; in forced convection, it is the Reynolds number.

The thermal conductivity k appears in the Nusselt number and Prandtl number. The Nusselt number is hL/k where h is the convective heat transfer coefficient and L is a characteristic length.

To apply facts cited above to the transfer of heat from Earth's surface into Earth's atmosphere, the thermal conductivity of air is independent of the CO2 or water vapor concentration. It follows from the dimensional analysis and empirical data on convective heat transfer that the convective heat transfer coefficient h of a region of Earth's surface is unaffected by the CO2 or water vapor concentration.

For simplicity assume it is a sunny day. It follows from facts cited above that a) heat transfer from Earth's surface to Earth's atmosphere is entirely by convection and b) the "back radiation" does not heat Earth's surface. That the "back radiation" seems to heat Earth's surface results from the semantic problem in which UCAR confuses with a heat flux the flux of photons flowing from colder matter in Earth's atmosphere to hotter matter in Earth's surface.

Let Tlocal designate the temperature of a region of Earth's surface. The heat flux from a region of Earth's surface to a region of Earth's atmosphere is h(Tlocal - Tatmos), where h is the convective heat transfer coefficient. I address the definition of Tatmos in the next paragraph.

From experiments on the flow of heat from a solid to an adjacent fluid, it is known that hydrodynamical and thermal boundary layers form in in the portion of Earth's atmosphere which is adjacent to the Earth's surface; the thermal boundary layer resists heat transfer from Earth's surface to Earth's atmosphere. Tatmos designates the temperature of the air outside the thermal boundary layer. Due to turbulent mixing in the atmosphere outside the two boundary layers, Tatmos is approximately fixed over a relatively large volume of the atmosphere near the surface.

As argued above, the heat flux from a region of Earth's surface to the adjoining atmosphere is insensitive to the concentration of CO2 or water vapor. That this heat flux appears to people who read and believe the content of UCAR's Web site to be highly sensitive to these concentrations results from UCAR's error in equating to a heat flux the photon flux from relatively cold matter in the atmosphere to relatively warm matter in Earth's surface. As the photon flux is sensitive to CO2 and water vapor concentrations, UCAR incorrectly concludes that the heat flux from Earth's surface to Earth's atmosphere is sensitive to these concentrations. By this error, UCAR violates the second law and produces a "greenhouse effect." Once this error is corrected, UCAR's "greenhouse effect" vanishes.

Now, to respond to Dr. Smith's questioning of the claim I made in my previous posting that the magnitude of the "back radiation" was nil, communication was garbled by the semantic problem addressed earlier in this posting. If the "back radiation" is interpreted as a heat flux from colder matter in Earth's atmosphere to warmer matter in Earth's surface, the magnitude of this "back radiation" is nil, by the second law. If, on the other hand, the "back radiation" is interpreted as a photon flux from colder matter in Earth's atmosphere to warmer matter in Earth's surface, the magnitude of this photon flux is not nil.

In a different question, Dr. Smith asks whether UCAR might deliberately have erred in its description of the "greenhouse effect" in an attempt at reaching the lay public. This question goes to UCAR's motive in making a false claim of a greenhouse effect. I have no information about the motive and wish to avoid speculating about one for to speculate would be to make an an hominem argument that would be illogical and inappropriate in the context of a scientific discussion. In the context of a scientific discussion, it suffices to demonstrate that UCAR's claim is false.

I have falsified the existence of a greenhouse effect which UCAR, one of the pre-eminent climatological research organizations in the world, claims for public consumption to be THE greenhouse effect. This result is surely significant for climatology. One message I'd like to deliver to climatologists is that it is crucial for them to accurately distinguish between the ideas of heat, work, energy and electromagnetic radiation. Failure by them to make this distinction makes their literature a muddle and conceals mistakes such as the disastrous one made by UCAR.

The error which I have exposed is foundational in nature. When a foundational error is exposed in a science, this science collapses and must be rebuilt upon a solid foundation. I've discovered additional foundational errors in modern climatology and published some of them to blogs. One is that the IPCC climate models are not falsifiable, thus lying outside science. I won't develop these ideas further in this posting.

Terry, here is where you

Terry, here is where you start to go wrong:

"With the air in place, the heat flux changes from ( PHot - PCold ) to Q' (W/square meter). By definition, the thermal conductivity k of the air is Q'/[(THot - TCold) * Gap]."

This is wrong in two ways. First note your dimensions are wrong - the distance 'Gap' should be dividing the temperature difference, not multiplying it, for thermal conductivity.

But more importantly, the presence of air does not remove the PHot -PCold heat flux. It adds a second flux Q' associated with the air's thermal conductivity k. And it adds a third flux (let's call it C) associated with convective flow (bulk motion of air) which in detail depends on the geometry and gravity of the system. And, if you had liquid water or another phase-change material present (as we do on Earth's surface) there is a fourth flux (let's call it L) associated with the evaporation and re-condensation of that liquid, the "latent heat" flux.

That is, heat flux from the warm surface to the cold atmosphere is (PHot - PCold) + k (THot - TCold)/Gap + C + L.

Now since all four effects are roughly linearizable in the THot - TCold temperature difference you could assign an "effective" thermal conductivity to the whole system. But note that PHot - PCold is independent of the "gap" distance, so that for very large dimensions (as we have in the real atmosphere) the normal 'k' term is far smaller than the others. Given that Gerlich and Tscheuschner devote many initial pages of their paper to thermal conductivity, this was pretty clear evidence of their ignorance of the basic magnitudes of the quantities relevant for discussion of climate.

And in particular, the effect of CO2 on 'k' is completely irrelevant. It is the effect of CO2 in "PCold" (increasing it due to the atmosphere's higher absorptivity and therefore emissivity) that has the most immediate effect in reducing PHot - PCold, and therefore decreasing heat flux from the surface, resulting in warming. And that change in atmospheric absorptivity due to higher CO2 is measurable by many different means - it is specifically that increase in back-radiation that a Pyrgeometer measures, for instance.

Your continued insistence on the importance of the distinction between a "photon flux" and a "heat flux" mystifies me. The photon flux is a microscopic representation of the transfer of energy, just as you would describe the flux of kinetic energy carried by molecules. "Heat", being a macroscopic quantity, is simply not well-defined on the microscopic scale, and it is the detailed energy flux that matters. UCAR, while using inappropriate terminology, got the basic physics correct. I hardly see that this is in any way significant to understanding of the issue.

Hi Arthur, Thanks for a nice

Hi Arthur,

Thanks for a nice article. I too, felt compelled to write about the nonsense in G&T's paper (at, though I think you did a better job than I did. Was yours the paper on arXiv that was removed? I also have to commend you on taking the time to respond in detail to all those posting comments.

While I don't work in atmospheric science, my research is in astrophysical radiation transfer, and it's pretty clear that the greenhouse effect follows from the equation of radiative transfer. One of the more puzzling (and infuriating) things about G&T's paper to me is that they write down the RTE and say that it governs the behavior of radiation, but then make absolutely no attempt at using it to investigate what it would tell you about whether the greenhouse effect exists or not.

I have also been thinking, in a recent discussion, about the relation between convective heat transport, the tropopause, and how the implied heat loss from the tropopause must imply that the atmosphere is radiating. I hadn't made the simple conclusion that the converse of course must imply an isothermal atmosphere. If there was no sink at the top of the atmosphere, convection would heat up the upper parts and lower the actual lapse rate to the point that convection would cease. Eventually, conduction would erase any temperature gradient. It's indeed freshman physics to know that a temperature gradient implies a heat flux, and if the atmosphere could not radiate away the heat, where would it go? Once you've admitted that the atmosphere must radiate, it's hard to argue that it doesn't radiate in both directions.

Patrik, thanks, your review

Patrik, thanks, your review there hit on several points I'd not paid attention to myself in reading G&T, so it's good to have.

I'd just point out that their "average temperature" argument is even worse than you imply. The 0.5C difference in their fictitious example is in the wrong direction! There is no way (as you note) to have a simple average be larger than the fourth-power average - yet that is the direction of the 33C discrepancy in the case of Earth.

Yeah, I missed that part. I

Yeah, I missed that part. I just noted the discrepancy between their "example" and their following conclusion that there is no room for warming, bizarre given that their example shows a discrepancy of only a fraction of a degree. I never reflected on the fact that it was actually going in the wrong direction for them.

Arthur: Thank you very much


Thank you very much for the excellent critique and comments and for correcting my error on the thermal conductivity formula. k is indeed Q'/[ (THot - TCold) / Gap ].

In the following remarks, I respond to the various elements of your critique and comments.

AS: "But more importantly, the presence of air does not remove the PHot -PCold heat flux. It adds a second flux Q' associated with the air's thermal conductivity k."

TO: With the air in the gap, I've assigned nil to PHot - PCold. This assignment is consistent with the finding from G&T's literature survey that, at atmospheric temperatures, neither the concentration of CO2 nor the concentration of water vapor has a discernable effect upon the thermal conductivity of air.

If PHot - PCold were not nil, the thermal conductivity would be increased with a resulting increase in the convective heat transfer coefficient h. An analytical advantage to taking the heat flux to be independent of PHot - PCold is that k is then a property of the air. The literature of convective heat transfer assumes this to be true. Thus, one gains the advantage of the wealth of data and models in this literature.

[Terry, I have taken the liberty of editing the rest of your comment because this statement is fundamentally wrong, and the rest of your discussion depends on it. See the Policy link at top for a discussion of why I am doing this... - moderator]


Terry, you cannot just

Terry, you cannot just "assign nil to PHot -PCold". Those photon flows do not cease just because you've added some air. What happens in the limit where the air density gets very small?

Furthermore, the two heat flow terms have a completely different functional dependence on system parameters.

If "Gap" is very small, then Q' becomes very large, since it is inversely proportional to "Gap". The relative size of the "PHot - PCold" and the "k (THot -TCold/Gap)" terms differs by a factor of 10^6 when you change "Gap" from km (Earth's atmosphere) to mm (in the lab). That is an observational, verifiable difference.

G&T's discussion of thermal conductivity was just that, a discussion of thermal conductivity. It completely left out the radiative component. For short distances, the radiative component of heat transfer is relatively small. Nevertheless, even in engineering applications it is measurable and of some interest - there are whole books on the subject, for example "Radiative heat transfer", by Michael F. Modest (Elsevier, 2003 second edition).

I think you've hit upon a

I think you've hit upon a point that might be cause for the severe confusion here. As an astrophysicist, I come to the problem from a field where the scales and densities are such that radiation dominates energy transport in the vast majority of cases. Convection is important in a few situations (stellar structure and possibly AGN accretion disks) and conduction almost never (neutron stars might be an exception). On Earth, on the other hand, radiation is much less important, so it makes sense that people used to dealing with terrestrial thermodynamic systems almost never deal with radiation and will have less intuition for how energy transport by radiation works. I, on the other hand, probably have a tendency to think in radiation terms even when I shouldn't. (For example, when thinking of the greenhouse effect, I never reflected until recently on the fact that heat is transported by convection in the troposphere. I should have known better, because in stars it's generally assumed that convection, if it operates, is so efficient that it will always lock the temperature gradient at the adiabatic rate.)

It would be interesting to know what fraction of the energy transport outward from the surface is in terms of convection vs radiation. Clearly there's everyday evidence that both radiation (i.e. frost on clear nights) and convection (thermals, cumulus clouds) operate. Does anyone have any data on this?

Ah, you need to take a look

Ah, you need to take a look at the Kiehl-Trenberth diagram:

Net average heat flow from surface to atmosphere for Earth is 23 W/m^2 by radiation, 17 W/m^2 by convection, and 80 W/m^2 via latent heat flow (conduction is, as I suggested, negligible on the real Earth). There's an additional 40 W/m^2 of radiation that leaves Earth and goes directly into space - that number would be higher on clear nights, as you note. So total net radiative cooling of Earth's surface (the PHot - PCold term discussed above) averages to 63 W/m^2, or a little under 40% of the total heat flow.

Arthur: Do you have a

Do you have a response to the note from Gerhard Kramm about the notational disagreements? Smith and the basic rules of calculus.pdf

Especially on his comments about the use of your notation in turbulence?

Søren - I discussed Kramm's

Søren - I discussed Kramm's confusion more specifically in this earlier post. I have corresponded with him at length and I can find no point on which he will stick, he seems to keep changing the subject (generally reverting to ad hominems - for example calling us communists in an email exchange just a few days ago). I'm not particularly interested in trying to fix his brain, but if you have a specific question on the notation, feel free to ask. In particular, the surface area element "dx" he seems to complain about in my paper is converted to standard spherical coordinates (r^2 sin(theta)d theta d phi) to solve the various equations presented, it's quite straightforward.

Thanks for the quick reply

Thanks for the quick reply Arthur.
I did already read that post as wells as Kramms pdf I linked to. It seems like he is confusing your definitions.
I just asked aobut the turbulence stuff because I am a little bit rusty in that but I am going to look at this soon.

I agree that the surface integral issue is quite straight forward.

I have another question that might be off topic, but however:
I have seen the rebuttal paper to Gerlich and Tscheuschner, I would like to know if it was accepted for publication or if it will be?

Thanks for your time,
Søren R. Jensen

Actually I don't even

Actually I don't even remember a turbulence argument. I don't particularly want to reread it - if you do have a specific question from it let me know.

Not sure what version of the rebuttal you saw, but yes a version should be published in coming months. Haven't heard a date though yet.

I have now studied both the

I have now studied both the article and Kramms pdf-document closer.

I was also quite confused because you state right under equation 6 that the effective quantities you define by equation 7 and 8 are planetal averages. Reading your comment "Why are some people so easy confused" solved it for me however. While equation (7) is a true average for for T^4 the same does not hold for equation 8. But I fully understand what you mean in the context.
If one plugs in definitions (7) and (8) to equation 9 one recovers equation 6, just as expected.
It is vital to realise what you state "effective radiative temperature in this discussion, the particularly useful value corresponds to the uniform temperature that would given the same Stefan-Boltzmann emissions as the given temperature distribution under uniform emissivity" if one wants to understand this.

I think the confusion could have been avoided if you had used another expression after equation 6. If one makes standard averages as Kramm does (and the text kind of suggests) then equation 9 does not hold.

Best regards
Søren Rosdahl Jensen

Yes, the epsilon_eff is a

Yes, the epsilon_eff is a weighted average, not a straight average - but then T_eff is not exactly a weighted average or a straight average, it's a power-law average so I'm not sure there's any one term that would work better than the generic "average". My intent was more for the equations to speak for themselves, but obviously the wording could have been a little clearer around there. Still, you'd think after explaining it several times Kramm would have realized oh yeah, that makes sense. No such luck (as far as I can tell anyway).