Anthony Watts has kindly offered the Talkshop the exclusive on Ned Nikolov and Karl Zeller’s reply to the article by Willis Eschenbach published at WUWT, which we accept, gladly.
Reply to: ‘The Mystery of Equation 8’ by Willis Eschenbach
Ned Nikolov, Ph.D. and Karl Zeller, Ph.D.
February 07,2012
In a recent article entitled ‘The Mystery of Equation 8’ published at WUWT on January 23 2012, Mr. Willis Eschenbach claims to have uncovered serious mathematical and conceptual flaws with two principal equations in our paper ‘Unified Theory of Climate‘. In his ‘analysis’, Mr. Eschenbach makes several fundamental errors, the nature of which were so elementary that our initial reaction was to not respond. However, after 10 days of observing the online discussion, it became clear that a number of bloggers have fallen victim to the same confusion as Mr. Eschenbach. Hence, we decided to prepare this official reply in an effort to set the record straight. This will be the only time that we respond to such confused criticism, since we believe that the climate science community has much more serious issues to discuss.
Demystifying the Mysteries of Equations 7 and 8
We begin with the most amusing claim by Mr. Eschenbach, which he calls ‘the sting in the tale’. First, some background: in our original paper, we use 3 principal equations that form the backbone of our new ‘Greenhouse’ concept. For consistency, we use here the same formula numbering as adopted in the original paper. Equation (2) calculates the mean surface temperature (Tgb) of a standard Planetary Gray Body (PGB) with no atmosphere, i.e.
where So is the solar irradiance (W m-2), αgb = 0.12 is the PGB shortwave albedo, ϵ = 0.955 is PGB’s thermal emissivity, σ = 5.6704×10-8 W m-2 K-4 is the SB constant, and cs = 0.0001325 W m-2 is a small constant, the purpose of which is to ensure that Tgb = 2.725K when So = 0.0. The derivation and validation of this formula is discussed in more detail elsewhere. We redefine the ‘Greenhouse Effect’ as a near-surface Atmospheric Thermal Enhancement (ATE) measured by the non-dimensional ratio (NTE) of a planet’s actual mean near-surface temperature (Ts) to the temperature of an equivalent PGB at the same distance from the Sun, i.e. NTE = Ts / Tgb(where Tgb is computed by Eq. 2). We then use observed data on surface temperature and atmospheric pressure (Ps) for 8 celestial bodies to derive an empirical function relating NTE to Ps employing non-linear regression analysis. The result is our Eq. (7), which describes all planetary data points with a high degree of accuracy:
The key conceptual implication of Eq. (7) is that, across a broad range of atmospheric planetary conditions, the ATE factor is completely explained by variations in mean surface pressure. In Section 3.3 of our original paper, we specifically point out that NTE has no meaningful relationship with other variables such as total absorbed solar radiation by planets or the amount of greenhouse gases in their atmospheres. In other words, pressure is the only accurate predictor of NTE (i.e. ATE) we found. This fact appears to have completely escaped Mr. Eschenbach’s attention.
From Eq. (7) we derive our Equation 8 (the subject of Eschenbach’s analysis) in the following manner. First, we solve Eq. (7) for Ts, i.e
Secondly, we substitute Tgb for its actual expression from Eq. (2) to obtain:
Thirdly, we combine the fixed parameters 2/5, αgb, ϵ and σ in Eq. (7b) into a single constant, i.e.
Fourth, we use the newly computed constant along with the symbol NTE(Ps) representing the EXP term of Eq. (7b) to write our final Eq. (8):
Basically, Eq. (8) is Eq. (7b) expressed in a simplified and succinct form, where NTE(Ps) literally means the ATE factor as a function of pressure!
Let’s now look at how Mr. Eschenbach interprets Eq. (7) and its relationship to Eq. (8). He correctly identifies that Eq. (7) has 4 ‘tunable parameters’(the correct term is regression coefficients, but never mind this minor terminological inaccuracy for now). He then espouses:
Amusingly, the result of equation (7) is then used in another fitted (tuned) equation, number (8).
This is the first demonstration of misunderstanding in his analysis (with far reaching consequences as discussed below), where he fails to grasp that Eq. (8) follows simply and directly from Eq. (7) after a few straightforward algebraic rearrangements, and that it contains no additional tunable parameters! Instead, Mr. Eschenbach smugly informs our fellow bloggers that the constant 25.3966 is yet another tunable parameter, which he labels t5 (his Eq. 8sym)?! We point out that the fixed parameters used to produce this constant have been defined and set prior to carrying out the regression analysis that yielded Eq. (7). Indeed, it could not have been any other way, because these parameters are required to estimate the PGB temperatures (Tgb) used in the calculation of NTE values, which are subsequently regressed against observed pressure data. Thus, Eschenbach now leads the readers astray telling them that we use 5 tunable parameters instead of 4. Fascinating! Next, in a state of total confusion, he makes the following stunning proposition:
We can also substitute equation (7) into equation (8) in a
slightly different way, using the middle term in equation 7. This
yields:
Ts = t5 * Solar^0.25* Ts / Tgb (eqn 10
What middle term? This twisted line of reasoning is astounding, because it reveals an utter misunderstanding of basic algebra compounded with an inability to follow content, thus leaving the reader literally speechless! This error leads Eschenbach to his central false claim that our Eq. (8) simply meant Ts = Tgb * Ts / Tgb, and therefore reduces to Ts = Ts!? One can only stand in disbelief before such nonsense! This is what Mr. Eschenbach jubilantly calls ‘the sting in the tale‘. It is a big sting, alright, but in his tail, not ours! He proudly reiterates this ‘finding’ once again in the Conclusion section of his article leaving no doubt in reader’s mind about his analytical ‘skills’.
Blinded by a profound misunderstanding, Mr. Eschenbach pompously concludes in regard to the constant 25.3966 that what we have done is “estimate the Stefan-Boltzmann constant by a bizarre curve fitting method”. He further states: “And they did a decent job of that. Actually, pretty impressive considering the number of steps and parameters involved”. Wow! Hands down, such a conclusion could easily qualify for the Guinness Book of Records on Miscomprehension!
The rest of Eschenbach’s ‘revelations’ in regard to our Equations (7) and (8) are less flamboyant but equally amusing. He argues that the small constant cs in Eq. (2) is pointless while failing to understand the physical realism it brings to the new model (Eq. 8). Since the goal of our research was not just to derive a regression equation, but to develop a new physically viable model of the ‘Greenhouse Effect’, this constant is important in two ways: (a) it does not allow the PGB temperature to fall below 2.725K, the irreducible temperature of Deep Space, when So approaches zero; and (b) it enables Eq. (8) to predict increasing temperatures with rising pressure even in the absence of solar radiation. Indeed, if we set cs = 0.0, then Eq. (8) would always predict Ts = 0.0 when So = 0.0 regardless of pressure, which is physically unrealistic due to the presence of cosmic background radiation.
A major portion of Eschenbach’s criticism focuses on the ‘accusation’ that all we had done is just ‘curve fitting’ devoid of any physical meaning. In an Update to his article, Eschenbach attempts to prove that he can do a better job in fitting a curve through our planetary NTE values using an equation with fewer free parameters. His simplified version of our Eq. (8) has 3 regression parameters (instead of 4) and reads:
Figure 1. Absolute errors of predicted planetary mean surface temperatures by Eschenbach’s simplified equation and by N&Z’s Equation (8). Errors are assessed against the observed mean surface temperatures listed in Table 1 of Nikolov & Zeller’s original paper.
Note that his expression is in a sense more empirical than our Eq. (8), because the coefficient in front of So has been erroneously treated as a tunable (regression) parameter, hence distorting our PGB Eq. (2). Figure 1 compares the absolute deviations of predicted planetary surface temperatures from their true values (listed in Table 1 of our original paper) using Eschenbach’s regression equation and our Eq. (8). It is obvious to a naked eye that Eschenbach’s formula produces far less accurate results than our Eq. (8). This was also recently quantified statistically by Dan Hunt in an article published at the Tallbloke’s Talkshop. For example, Eschenbach’s equation predicts Earth’s mean temperature to be 295.2K, which is 7.9K higher that observed. This is not a small error, because the last time our Planet was 7.9K warmer than present some 40M years ago the earth surface was ice-free, and Antarctica was covered by subtropical vegetation! Of course, being a construction manager, Mr. Eschenbach likely has a limited understanding of Earth’s climate history and what a 7.9K warmer surface actually means. However, the fact that he claims aloud a superior accuracy of his simplified equation over ours is puzzling to say the least. His exact words were:
Curiously, my simplified version actually has a slightly lower RMS
error than the N&Z version, so I did indeed beat them at their own game. My
equation is not only simpler, it is more accurate
This statement blatantly contradicts the evidence. Mr. Eschenbach does not know that we have extensively experimented with exponential functions containing various numbers of free parameters many months before he became aware of our theory, and we have found that it takes a minimum of 4 parameters to accurately describe the highly non-linear relationship between NTE and surface pressure (Eq. 7). The basic implication of Eschenbach’s analysis is that one could indeed use a 3 parameter exponential function to predict planetary temperatures from solar irradiance and surface pressure but with far less accuracy. Truly enlightening!
By the way, curve fitting is an integral part of the classic science method. When dealing with an unknown process or phenomenon, taking measurements and using the data to fit curves is the only feasible approach to understand and develop a theory about the phenomenon. This method was extensively used throughout the 18th and 19th Century and a good part of the 20th Century to extract the so-called first principles in physics we currently employ to describe the World. However, arguing about curve fitting really misses the main point of our study.
Focusing on the Big Picture
What Mr. Eschenbach and a number of others have totally failed to grasp is the highly significant fact that the enhancement factor NTE (i.e. the Ts / Tgb ratio) is indeed closely related to pressure, and that no other variable can explain the interplanetary variation of NTE so completely. As Dr. Zeller pointed out in a recent blog post, given the simplicity of Eq. (8), it is a ‘miracle’ how accurately it predicts surface temperatures of planets spanning a vast range of environmental and atmospheric conditions throughout the solar system! This cannot be a coincidence! Rather it suggests the presence of a real physical mechanism behind the regression Equation (7) related to the thermal enhancement effect of pressure. This effect is physically similar (although different in magnitude) to the relative adiabatic heating observed in the atmosphere and described by the well-known Poisson formula derived from the Gas Law (see discussion in Section 3.3. and Fig. 6 in our original paper).
Even the mistaken analysis of Mr. Eschenbach could not manage to negate the above truth. He vigorously criticized our Eq. (8) using all sorts of faulty technical arguments only to arrive himself at a similar (albeit less accurate) equation that predicts planetary temperatures as a faction of the same two variables – solar insolation and pressure! His argument that one could arbitrarily use air density instead of pressure is groundless, because pressure as a force is the primary independent variable in the isobaric thermodynamic process of planetary atmospheres. Ground pressure depends solely on the mass of air column above a unit surface area and gravity, while air density is a function of temperature and pressure. In other words, density cannot exist without pressure. For a given pressure, the near-surface air density varies on a planetary scale in a fixed proportion with temperature, so that the product Density*Temperature = const. on average, i.e. higher temperature causes lower density while lower temperature brings about higher density according to the Charles/Gay-Lussac Law for an isobaric process.
We now draw attention to a key logical contradiction in Mr. Eschenbach’s approach. In the main text of his article, he makes the central claim that our Eq. (8) represented a mathematical nonsense, since according to his logic, it reduces to Ts = Ts (the TA-DA! moment). Yet, in the Update section, he uses data from Table 1 in our original paper to derive a very similar equation, which he calls a ‘simplified version’ of Eq. (8). So, according to Mr. Eschenbach, our Eq. (8) is numerically meaningless, while his equation based on the same data is mathematically sound. This raises the question, how poor do one’s reasoning skills have to be in order for one to contradict himself in such a ridiculous manner? We will let you be the judge …
Conclusion
We have shown in this reply that all criticism of our Equations (7) and (8) by Mr. Eschenbach is without merit. We emphasized the need for better understanding of and focusing on the big picture that our theory conveys. We propose to shift the discussion from meaningless argumentations about number of regression coefficients or number of significant digits of constants used, to how pressure as a force controls temperature and climate. In this regard, we would like to issue an appeal to all of you, who are capable of carrying out an intelligent discussion at a decent academic level to stop engaging in pseudoscientific, besides-the-point fruitless debates. We are here to discuss and offer a resolution to the current climate science debacle and welcome everyone who shares that goal. We are not here to promote or engage in endless circular talks or teach laymen ‘skeptics’ basic math and high-school level physics. Hence, we will no longer participate in dialogs of the kind that prompted this reply. We urge all sound thinking readers to do the same.
Thank you!
Tallbloke's Talkshop 
Any challenge to Eq. (8) would have to offer, IMO, a plausible and equally accurate way of deriving surface temperature(s). That would be quite a challenge, apparently!
Brian, yes! I told Leif to get back to me when he’s found a way of using the radiative theory to correctly calculate the same eight celestial body’s surface temperatures using an equally succinct set of equations.
No reply yet… 🙂
From 3.3 of the original paper:
“Such a similarity in responses suggests that both NTE and θ embody the effect of pressure-controlled adiabatic heating on air, even though the two mechanisms are not identical.”
and from the above:
“it suggests the presence of a real physical mechanism behind the regression Equation (7) related to the thermal enhancement effect of pressure. This effect is physically similar (although different in magnitude) to the relative adiabatic heating observed in the atmosphere.”
Those two extracts appear to suggest that N & Z have found a pressure induced thermal enhancement beyond that expected from pressure controlled adiabatic heating alone.
That would be interesting and novel.
Thanks!
May I hazard the guess that many people who’ve been commenting so exhaustively on that WUWT thread have been focussed on their physics to the exclusion of recognising the algebra used to reach the equations?
Ned and Karl, you really shouldn’t bother with the guy, he’s not worth your time. Now that you have thoroughly debunked his untutored meanderings, I am sure that most of the visitors to this blog are in eager anticipation of the next installment of your theory’s exposition.
“to predict increasing temperatures with rising pressure even in the absence of solar radiation”
Looking forward to part 2 to firm up on that.
My initial query is as to whether an atmosphere in gaseous form is possible at all without solar radiation to excite the molecules in the first place.
SW;
Note that N&Z do not postulate energy or heat ex nihilo. Radiation or some other source is assumed; it’s what happens to that energy, and how it translates into temperature (what they call “enhancement”, which I think is a poorly chosen English term) that the equations specify.
With no energy source (and assuming insufficient mass to initiate fusion), any gas will ultimately condense into a solid at cosmic background, 2.7K (except helium, which is still a liquid all the way down at <20 bar). So it seems what they have described and 'discovered' is how gas under pressure manages energy and temperature.
Stephen:
Neptune has pretty thick atmosphere despite the minimal w/m^2 of solar radiation it gets. I would suggest that not very far into that atmosphere, there is no penetration of solar radiation at all. This is a good confirmation of the thermal gradient in the pressure profile, since much lower down in the Neptunian atmosphere the temperatures are comparitively high.
Chris M says:
February 9, 2012 at 11:17 am
Ned and Karl, you really shouldn’t bother with the guy, he’s not worth your time>>>
Yes and no. Willis made a total and utter fool of himself with his Ts=Ts ta da! moment, and one can only hope that he’ll take a sheepish climb down from Mount Arrogance. This response from N&Z not only answers every issue that Willis raised, it exposes just how contrived his criticisms were in the first place. I agree that N&Z should not need to spend an additional second on dealing with him.
That said, Willis has a huge following that hang on his every word. Were he to claim that the sky is purple with pink poka dots, a surprising number of people would glance upward and exclaim, so THAT’s what purple with pink poka dots looks like! The CAGW meme has survived for years on exactly the misdirection and obfuscation evident in Willis’ criticisms.
Unfortunately, without the support of WUWT, N&Z may well be sentenced to obscurity. N&Z represent the final nails in the CAGW coffin, and Willis appears determined to throw them into the nearest landfill. If this response doesn’t get the climb down from Mount Arrogance from Willis, then it falls on Anthony Watts to reign in his “writer in residence”.
If Anthony fails in that regard, then the climate debate will continue to drag on for much longer than it should, greed driven researchers will continue to line their pockets while providing the evidence needed for power mad beauracrats to grasp at still more power, and the poor will struggle at the edge of starvation while the rest of us burn food instead of oil to “save” them. The damage done by the climate debate to real people is substantial, it is why I got involved, and it is why I am furious that with the means to end it once and for all staring us in the face, Willis and Co have instead contrived to extend it further.
Ts=Ts ta da my @@@
N&Z need not respond to Willis further in my opinion, they have nothing left to say to him that would make any difference. But if he fails to climb down from Mount Arrogance, then other people will need to take up the battle.
.
I wondered whether to create two threads for this. One for the science and one for the bitchin’ 🙂
On balance though, since the science is well treated in a reasonably studious atmosphere elsewhere on this site, I decided to let it mix-up here. All I ask is that people avoid ascribing motivation; keep speculative comment to the bare minimum; and try to keep a wider perspective and the enviable reputation for civility this site has in mind when commenting about matters other than the scientific content of this post.
I have to say that I disagree with the notion that N&Z shouldn’t engage (further) with Willis. Quite the contrary. Be the difference you want to see. Regardless of whether Willis’ understanding is flawed, the overriding popular issue sceptics have with climate scientists is their failure to engage – whether this be owing to an inability to put complex concepts in laymen’s terms or their inability to find the tolerance to do the same. Either way the scientist who “shows willing” is today perceived as the exception to the rule, and will ultimately be heard.
Three things to understand about Willis are that: a) he has an enormous following; b) he is exceptionally eloquent, off-the-cuff; c) his view CAN mature, and he is not without the capacity to correct himself publicly, in time.
In my view, engaging with Willis reasonably, correcting his rude misconceptions pleasantly (rather than matching his snark with snide, condescending or with vitriolic language) would be net-beneficial. Think what you want of him. Privately. How you engage with Willis, like it or not, is how you engage with a significant portion of the individuals you want to give as much consideration of your paper as you can garner.
This entire response could have been made with just as much clarity, correcting all of Willis’ misunderstandings no less succinctly and conclusively, but without leaving any hint of an impression that you repeatedly just called Eschenbach a complete wanker. IMO, that would have been far more shrewd. Isn’t it entirely sufficient to merely show him where he’s wrong? Do you have to also imply that he was stupid for being wrong? One approach has momentum, the other has none.
Urgh.. slow typist.. what davidmhoffer said!
Hoff says:
“Unfortunately, without the support of WUWT, N&Z may well be sentenced to obscurity. “
I anticipate that the pioneering work Ned and Karl have done here will soon lead to further discoveries. Once a wider pattern with more internally consistent evidence emerges, the shift in paradigm will become irresistable. The scientific truth trumps huffing, puffing, handwaving and hubris every time.
tallbloke;
I anticipate that the pioneering work Ned and Karl have done here will soon lead to further discoveries>>>>
I agree. But how long will it take for the CAGW meme to be buried and gone forever? How long must poor people struggle to put food on the table while we’re burning the food to save them? There is real harm done to real people every single day by the CAGW meme, and anything that prolongs it is criminal in my eyes.
That said, returning to the science (yeah, I noticed the comment about bi***ing, I get it) Willis can play with the math all he wants, but as I said to him in a thread on WUWT, even if he has a point right here or there (which he doesn’t), why throw the baby out with the bathwater?
1. N&Z have exposed the massive math error perpetrated by BOTH sides of the debate in terms of the misaplication of SB Law. This alone fundamentally changes the nature of the debate, and the science.
2. The Ideal Gas Law, as I’ve commented in other threads, can be used to model the atmosphere as “slices” of gas column stacked upon one another and when one does so, it becomes painfully obvious that PV=nRT requires that P and T vary directly with one another, even in an atmosphere which is not bounded by a container.
3. The Faint Sun Hypothesis comined with the observation that pterodactyls would not have been capable of flight unless the atmosphere was much denser at that time plus N&Z show that all those pieces fit. The Sun was fainter then, but temperatures were warmer, and we need no other explanation than the denser atmosphere and N&Z to understand how that was possible.
To me, these things stand alone. One can argue the fine points of both the math and the science all one wants, these things are pretty tough to challenge, and they are deal breakers for the CAGW meme.
And Willis should step up and say so.
Haven’t we seen this before? The pretty good correlation between rising CO2 levels and rising temperatures over a certain period. Causation not so good imo.
Now we see correlation between atmospheric pressure + solar irradiance and surface temp. on a planet using a blackbody (BB) approach. Does this imply causation as well? Perhaps atmospheric pressure is an indicator for the heat storage capacity of a planet or whatever.
For the cases where pressure is ~zero like our moon we can assume a behaviour more or less like a blackbody. Rocky planet / moon, not much influence from hot core or earthshine or whatever makes it a reasonable imitation of a BB. No surprise the formula works.
Planets with a sizeable atmospheric pressure also could have a sizeable heat storage capacity, like our earth or Venus.
So we need a physical process to show this theory is valid. The given manifestations of the effect in the original N&Z paper were star formation due collapsing interstellar clouds and the Chinook (Föhn) wind.
Both are DYNAMIC processes were potential energy is exchanged for kinetic energy, thus having no appearent relevance for a static atmosphere.
Question remains: what is the physical process we’re looking at?
Besides this the whole idea of a blackbody approach to a planet with an atmosphere is invalid imo.
I’ve been reading WUWT for a long time for two reasons; Anthony and Willis. I think what they bring to the table is a very strong ability to very capably articulate, in language alone, complicated science and then back it up with plausible mathematical reasoning. This is not to say they are always right. Actually I’m not qualified to make that judgement.
But, it is very important to me to have some sort of plausible language based reasoning as a basis before diving into the math in these discussions and I feel this is an enormous part of the success of WUWT. Having said that, I’ve also observed that many contributors who seem to have an exceptional grasp of the science are horrible at communicating. I can’t count the number of times I’ve abandoned threads where the discussion degrades into ad hominems where people are quite obviously talking past each other, failing to establish common definitions, and advancing arguments through opinion and hand waving.
I’d even go so far as to suggest that there is a general rule that says scientific competence is indirectly proportional to language skill. When the rule is contraindicated by anyone, that person stands out.
To Nikolov and Zeller I would suggest that it is critically important to continue to make your reasoned arguments with both the math and the language. You are standing out because you’ve managed to bridge the communication ‘divide’. If you hadn’t done so, your paper would be presently buried in some academic tome, seen only by the tiny percentage of geeks who read such things.
Together you and the geeks could relish in your delicious understanding but you would NOT change the world. Science, as wall decoration, is not a force. It’s only a curiosity.
Ben AW says:
Besides this the whole idea of a blackbody approach to a planet with an atmosphere is invalid imo.
Which is why N&Z apply it to a hypothetical Grey body Earth with no atmosphere at the same distance from the Sun (the Moon), and then compare the actual measured temperature on Earth and the Moon with it, as well as the temperature they calculate from their equation. This uses the grey body temperature as one of it’s inputs. They DO NOT MAKE A BLACKBODY APPROACH TO A PLANET WITH AN ATMOSPHERE.
And no Ben, it’s nothing like the co2 hypothesis. At all. It successfully calculates the empirically measured temperatures from first principles physics. For EIGHT CELESTIAL BODIES.
Perhaps atmospheric pressure is an indicator for the heat storage capacity of a planet or whatever.
The one is undoubtedly related to the other, but Gravity->Atmospheric mass->Pressure are the primary quantities. The theory shows that the composition of an atmosphere is a secondary consideration.
The Ts = Ts nonsense was a surprise to me, and I don’t think it was ever acknowledged as an error (correct me if I’m wrong).
It was such a silly and elementary mistake that it should have been quickly acknowledged and retracted, the fact it wasn’t was a black mark against WUWT. I’ve stopped reading articles by Willis.
I’d guess that 2 Ph.Ds must think they’re in a parallel universe to find themselves responding to such a criticism.
Hoff: “how long will it take for the CAGW meme to be buried and gone forever?”
Hard to call. A lot of people are heartily sick of it. It’s not just some academic argument that no one will notice if it drags on past it’s flush by date. As you pointed out, this is killing people.
tallbloke says:
February 9, 2012 at 2:26 pm
By using the moon N&Z DO use a BB (or GB) approach, since the moon IS a reasonable imitation of a GB.
“And no Ben, it’s nothing like the co2 hypothesis. At all. It successfully calculates the empirically measured temperatures from first principles physics. For EIGHT CELESTIAL BODIES.”
So far this theory IS the same as the CO2 hypothesis as there is only CORRELATION, no CAUSATION.
You have to come up with a working physical proces.
Star formation and Chinook appear to be the prime examples, but they are both examples of dynamic processes, no appearent relation with a static atmosphere.
BenWA says:
“So we need a physical process to show this theory is valid. The given manifestations of the effect in the original N&Z paper were star formation due collapsing interstellar clouds and the Chinook (Föhn) wind.
Both are DYNAMIC processes were potential energy is exchanged for kinetic energy, thus having no appearent relevance for a static atmosphere.
Question remains: what is the physical process we’re looking at?”
The physical process you are talking about is called the Ideal Gas Law. It has been discovered and tested more than 100 years ago! Pressure provides the FORCE, which is an essential component of the Kinetic Energy of the atmosphere and gives its temperature. There could be no kinetic energy and NO temperature without Pressure. Hence, changing the pressure, changes the force, which in turn changes the temperature of a gas operating otherwise under isobaric conditions such as a planet atmosphere. It’s that simple!
BenAW says:
February 9, 2012 at 3:21 pm
tallbloke says:
February 9, 2012 at 2:26 pm
Ben AW says:
“Besides this the whole idea of a blackbody approach to a planet with an atmosphere is invalid imo.”
Which is why N&Z apply it to a hypothetical Grey body Earth with no atmosphere at the same distance from the Sun (the Moon), and then compare the actual measured temperature on Earth and the Moon with it, as well as the temperature they calculate from their equation. This uses the grey body temperature as one of it’s inputs. They DO NOT MAKE A BLACKBODY APPROACH TO A PLANET WITH AN ATMOSPHERE.
By using the moon N&Z DO use a BB (or GB) approach, since the moon IS a reasonable imitation of a GB.
Exactly, and it doesn’t have an atmosphere, which was your original objection. The ‘Earth with no atmosphere’ would have no atmosphere either.
Having followed WUWT since the cliamtegate papers I am also concerned with the recent tone at WUWT. It is showing dangerous signs of adopting a “cult of personality”.
The primary tool of any cult is censorship of views that contradict the cult-head. In this regard, self imposed censorship is only likely to reinforce the cult. My advice is to read:
http://en.wikipedia.org/wiki/How_to_Win_Friends_and_Influence_People
davidmhoffer says:
February 9, 2012 at 12:18 pm
Simon Hopkinson says:
February 9, 2012 at 12:44 pm
Seconded!. All those in favour?
Paul Bahlin says:
February 9, 2012 at 2:26 pm
I’ve been reading WUWT for a long time for two reasons; Anthony and Willis. I think what they bring to the table is a very strong ability to very capably articulate, in language alone, complicated science and then back it up with plausible mathematical reasoning>>>
I agree with your semtiment, but there are limits to how much you can simplify science and still be articulating the concept accurately. At some point, one has to understand the math and the physics to judge the final details. The danger here, in my mind, is that Willis has tackled an issue that he clearly does NOT understand the math and physics of, and his written skills are so strong that we’re in danger of him wrongly discrediting quality science for the simple reason that many of his readers will not have the math or physics backgrounds required to see past his well articulated and seemingly reasonable arguments.
I’ve been advocating N&Z approach to SB Law for nearly two years now, and have corresponded with both Ira Glickstein and Joel Shore on the matter in private correspondence. I’m certain that they are both highly intelligent people with a firm grip and the basics of the math and physics, and just as certain that they’ve not grasped the big picture properly. If I can’t win the argument with them with all the gory math on the table, imagine trying to win the argument with Willis in the eyes of observers who haven’t the math and physics that Ira and Joel have to rely upon when making their judgment.
I agree with Simon Hopkinson that it is necessary to debate with those such as Willis Eschenbach who believe CO2 is a greenhouse gas.I found the reply to the Willis’s criticisms to be very enlightening. His analysis is well rebutted and he actually confirms what N and Z have found.
Willis is an eloquent opponant of CAGW. He can, as other have been, be convinced of the errors of the radiation approach and the value of the gas laws.
The need to re-establish the use of the gas laws in climate science is paramount and N and Z should be part of it.
Willis means well and is not stupid his however wrong about the physics.I would like him on our side.
Roger Clague says:
February 9, 2012 at 5:24 pm
I agree with Simon Hopkinson that it is necessary to debate with those such as Willis Eschenbach who believe CO2 is a greenhouse gas>>>
And right there is one of the issues that drives me around the bend because is makes the discussion so complicated. I agree with N&Z 100%. I also maintain that CO2 is, in fact, a GHG. How do I resolve these? Glad you asked.
CO2 does in fact absorb upward bound LW. We can measure that. It re-radiates LW. We can measure that too. Some of what it re-radiates winds up back down at the surface. We can measure that also. So why are these things true,and yet CO2 does NOT increase the temperature of the planet surface over all?
Because of Holder’s Inequality. Because of how we measure “average” temperature and give ourselves the illusion of “warming” when what we are really measuring is re-distribution of the energy flux.
CO2 works like a dam, preventing some portion of the upward bound LW from escaping directly to space. BUT… it STILL ESCAPES. If it didn’t, we’d all be cooked through and through by now. The point is that the LW escapes by a more cirquitous route than directly to space. Those photons bounce around, and they migrate sideways as well as up and down. They do indeed heat the surface below…which results in higher levels of convection which move energy from tropics toward poles (Stephen Wilde, please jump in!) and the LW escapes from there instead of directly, and after a few steps instead of just one. But the equilibrium temperature doesn’t change. Only how the photons escape, and from where changes.
No violation of the laws of thermodynamics occurs (despite Anthony’s contention to the contrary in the link he just posted).
In fact, I’d encourage Anthony (and everyone else) to think back to the article that Anthony ran some time ago about two Israeli statisticians who analyzed the temperature records, and found no evidence that increases in CO2 correlated to increases in temperature. What they found was that a change in CO2 caused a “ripple effect” that then settled back into the exact same equilibrium state there was before.
That study in my mind confirms N&Z. N&Z are pointing out that the change in CO2 concentration doesn’t change the equilibrium temperature, but that doesn’t mean there isn’t a “greenhouse” effect. There is. Doubling of CO2 is like throwing a rock into a lake. Lots of ripples, but when the ripples die out (LW finding new paths to space) the surface height of the lake is precisley the same as it was before. But some of the water flow is different.
Anthony Watts has put up a comments closed note on WUWT stating why he hasn’t stuck to the promise he gave Ned Nikolov before Willis’ equation 8 post went up, saying then that he would give them a right of reply at WUWT. I have changed very little in the paper as it was submitted to me, but to avoid any ugly connotations being put on a phrase I think was used innocently, I changed the phrase Anthony was mainly concerned about to the single word ‘resolution’ at their suggestion. Anthony was also made aware that Ned and Karl would be happy for him to publish the reply as it appears here. I haven’t removed any “angry passages”, because there aren’t any. There are a few pointed comments about Willis and his piece, but hey, he’s a big tough cowboy who dished out a lot worse to Ned and Karl than anything they’ve said in reply. In any case, we needn’t let the digs they’ve made distract or detract from the discussion of the science presented here.
“…, changing the pressure, changes the force, which in turn changes the temperature of a gas operating otherwise under isobaric conditions such as a planet atmosphere…”
Work = Force x Distance
You are talking about work being done by a force. However the distance is zero, as you are not talking about movement here. Therefore the work done is zero. Therefore it cannot change the temperature.
Adiabatic temperature changes occur because of the work done by the act of compression on the air by the force of pressure, not by static pressure in absence of compression.
Superb! Bravo! Drs Nikolov and Zeller I applaud you.
Doubting Rich;
You are talking about work being done by a force. However the distance is zero, as you are not talking about movement here. Therefore the work done is zero. Therefore it cannot change the temperature>>>
The distance is NOT zero. If you add additional gas to the atmosphere, the pressure increases, meaning that the “slices” if you will of atmosphere at the bottom of the stack must, in fact, compress. Hence, distance is not zero, and work in fact is done.
Hoff: Both Doubting Rich and you are missing the point here. You are going back to Ira’s argument about heat generated in the initial compression, which dissipates. This is a separate issue not relevant to N&Z’s theory. Their point is that the greater pressure (caused by mass and gravity acting on it) means also a greater density and more thermalisation per unit volume nearer the surface when external energy (Sunshine) is passing through it and back out of the system.
davidmhoffer says:
February 9, 2012 at 1:27 pm
“I agree. But how long will it take for the CAGW meme to be buried and gone forever? ”
1000 years?
– It’s a religion with a huge following of dedicated believers
– A huge number of people make a good living from it
– Many of the rich and powerful benefit greatly from it in terms of enhanced wealth, power and prestige.
A few technical papers questioning the basis of the greenhouse effect will have no detectable effect.
Many generations from now, our descendents will be giving thanks to St Mike and St Phil for having saved the planet, notwithstanding the evils of Beegoyle. The fact that CAGW has not yet happened will be proof of the effectiveness of the measures taken to date.
“CO2 does in fact absorb upward bound LW. We can measure that. It re-radiates LW. We can measure that too. Some of what it re-radiates winds up back down at the surface. We can measure that also. So why are these things true,and yet CO2 does NOT increase the temperature of the planet surface over all?”
While some of what’s absorbed will re-radiate back to the surface, a roughly equal amount will be re-radiating in the opposite direction, nullifying the net ‘flow’ of heat.
I don’t know what this means.
🙂
Nial
Being the first time I see a piece with the number of equations similar to the level of editorializing, I hereby announce I refuse to read any more of the [snip] work.
[ please don’t wind things up –Tim]
tallbloke says:
February 9, 2012 at 7:13 pm
Hoff: Both Doubting Rich and you are missing the point here. You are going back to Ira’s argument about heat generated in the initial compression, which dissipates. This is a separate issue not relevant to N&Z’s theory. Their point is that the greater pressure (caused by mass and gravity acting on it) means also a greater density and more thermalisation per unit volume nearer the surface when external energy (Sunshine) is passing through it and back out of the system.>>>>
Ooops!
Yes!
I shouldn’t write science stuff while simulataneously responding to an RFP for some decidely non sciencey stuff.
Aplogies.
Hi all. I’m probably really wrong in how I understand the theory, but hopefully can clear it up in my mind.
So the N&Z theory equates long-term equilibrium temperature, right? As in, what the temp would be if all things were stable? So does the green house effect then act as a deviation from the equilibrium? As in, is the end temperature of the planet the sum of the N&Z equilibrium and the GHE deviation?
After all is said and done, you do have 4 coefficients and 8 data points, which is quite enough freedom to make most anything fit (but see below). I also don’t buy your claim that
is picked before you do your curve fitting, so it’s somehow different from the other 4 coefficients: you pick it in order to make your model fit your data better and it’s not some kind of physical constant, so yes it is a 5th coefficient. So you have 8 data points and five coefficients to drive a *non-linear* curve?
You’ve focused fire on Willis, who has stuck his statistical foot in his mouth a couple of times recently, but you ignore insightful commentary from WUWT, such as those by Robert Brown, which show that your equations fail fundamental unit analysis, which is extremely fundamental, and also:
“This explains how N&Z get a good fit to eight data points with only four parameters. All the “airless” planets have almost no atmosphere and their surface temperature compared to some arbitrary parametric baseline is a very weak function of the pressure — so weak that increasing the pressure by six orders of magnitude on the low end of things makes only a 10% or so change in
. The mechanism that keeps Mars, Earth and Venus warm, OTOH, appears to be totally different! The second term fits only these three planets — really only the last two, as 1.02 for Mars is a 2% shift and ignorable. So lessee, can I fit a two point monotonic difference function with a two parameter exponential that is basically “one” at the baseline/origin (Mars) and all pressures below! I believe I can! I bet I can do a really, really good job, too, with at most 2% total error to split three ways!”
Seriously!? You folks think that is a proper rebuttal above?
Let’s clarify, what Nikolov & Zeller have presented above is mostly a re-iteration of their original paper. The only rebuttal part is where Willis’s simplification is taken and graphed and that isn’t really a rebuttal but more in line of a “so there”.
Where Willis broke parts of the formula down and rationalized each component and it’s function, Ned and Karl have not analyzed Willis’s approach, but only focused on one of his end results. Yeah, Willis was a bit crude and over the top in his disgust at the approach and Willis should have kept his analysis to the math involved. So should Ned and Karl and his yea-sayers.
From my perspective, just because you derived a constant before using it in regression doesn’t make it an absolute constant. It is still derived and it’s derivation is based on inputs (observations in this case). That makes it a variable not a constant in my book and to me all variables are tunable parameters. As a constant, it is only constant in this iteration. A change in any of the observations will change it in the future. And no, I do NOT believe that our current observations are absolute forevermore.
My simplification of the intention. Take known observations, utilize the SB equation and derive a temperature/pressure profile for planets.
Is this accomplished? Yes.
Are the calculations accurate? Well, based on what we know, yes.
Do the calculations require this degree of multi-significant decimal accuracy? No. I’m sorry, but the 18K difference for mars (the widest variation) between Willis’s and your calculations is not enough for me to accept your tunings as required; not when we really know so little about mars.
Have Nikolov & Zeller proved they’ve developed a unified theory of climate? Not to me and apparently to many other folks too. Before I accept that, I would like to see provable predictions not modified parameters so that known observations can be matched.
Speaking of provable predictions; if the climate theory is unified, shouldn’t temperature based on atmospheric pressure be calculable locally universally?
Of course not. Are your researches funded from the private sector or through the public sector? If public money is funding your research, then I think it is in your d___ interest that you work on your public relations skills, including blogging. Telling us off and calling us less than pleasant names and implying that we are all idiots unworthy of teaching is a sure way for us peons and peasants to want and stop all funding of the arrogant.
Thanks for allowing this discussion here.
I believe N&Z have uncovered a correlation between pressure and temperature. I believe it is important and will eventually be used as the basis of a theory. Causation is right out the window right now and since the correlation is temperature vs pressure, no conservation of energy has been violated. Assigning causation is where we get stuck in the mud and where Anthony is similarly stuck in my opinion.
The N&Z paper can be used as a “then why” argument when sorting out the logic of the greenhouse effect, there it will be useful. If Anthony does not agree that the correlation exists, he should explain why. Arguing about conservation of energy is a straw man since pressure and temperature are static values. You only violate energy laws when you try to assign causation.
“They do indeed heat the surface below…which results in higher levels of convection which move energy from tropics toward poles (Stephen Wilde, please jump in!) and the LW escapes from there instead of directly, and after a few steps instead of just one. But the equilibrium temperature doesn’t change. Only how the photons escape, and from where changes.”
Thanks David.
To the extent that GHGs slow down the rate of energy flow from surface to space there is a speeding up of all the other energy transfer processes that serve to speed it up again just as much for a zero or near zero net effect on system energy content.
On a planet with an ambient temperature that sustains phase changes of materials such as the evaporation and condensation of water the process is greatly facilitated.
The circulation within the atmosphere simply reconfigures to negate or nearly negate the disruptive effect of any factor that seeks to disturb the lapse rate set by the gravitational field.
There is an energy redistribution but no net change in system energy content as long as the energy input, the mass of the atmosphere and the gravitational field remain the same.
That energy redistribution has a climate effect however. More GHGs will shift the climate zones but we have seen the zones shift by 1000 miles from solar and oceanic effects from MWP to LIA and LIA to date.
I’d be surprised if doubling CO2 were to shift the zones more than a mile or so. Someone needs to get down to working out the numbers for that. I can point in the right direction but I’m not a physicist or mathematician.
The best thing about the N & Z paper and the past work of Hans Jelbring and some others plus the well established Ideal Gas Laws is that they provide empirical evidence and a mechanism supporting the proposition that the effect of more GHGs (and other disruptive forcings) can never trump the effects of pressure and insolation.
There is much that falls into place when one realises that weather and climate simply represent changes in the rate of energy flow through a part of the system (the troposphere) and not any change in system energy content or equilibrium temperature.
I have submitted a layman’s summary to Rog for consideration here which is an update of an article of mine from 2008.
It is unfortunate that N&Z have been unable to simply and directly address and refute the apparent violation of conservation of energy described by Willis.
[Reply] This post deals with only with the errors in the EQ8 post at WUWT. I don’t think conservation of energy was mentioned in it?
The point that solar radiation is constantly heating up the system and various other mechanisms such as convection, radiation, evaporation, etc are actively removing the heat seems to be the dynamic that people overlook. I tend to think of it as pumping up a leaking tyre. The heat may get lost, but I keep generating more as I continue to apply pressure.
I’m struggling to understand the correction here:
NTE(Ps), according to N&Z’s comment above, includes a TS term:
NTE(PS) = Ts/Tgb
Evidently I’m making the same ‘mistake in basic algebra’ as WE, but I don’t see how that’s not the case. Does the symbology mean something I’m not understanding? A = B = C means all three things are equal, no?
If that is the case, then it’s obvious that equation (8) does include a Ts term on both sides which cancel out. So where am I going wrong?
Dale says:
February 9, 2012 at 7:28 pm
Hi all. I’m probably really wrong in how I understand the theory, but hopefully can clear it up in my mind.
So the N&Z theory equates long-term equilibrium temperature, right? As in, what the temp would be if all things were stable? So does the green house effect then act as a deviation from the equilibrium? As in, is the end temperature of the planet the sum of the N&Z equilibrium and the GHE deviation?
Hi Dale. One of the outcomes of N&Z’s theory is that albedo is a function of pressure and temperature. So theoretically, we’ll end up with a Miskolczi style constant optical depth. Of course, as natural variation occurs, there will be significant fluctuations, and untangling what the stuff inside the system does in reaction to solar variation, varying GCR intensity due to the passage of the solar system through local interstellar clouds etc is still a major task.
Over at WUWT A. Watts says;
“I also still have big problems with (my viewpoint) the theory apparently violating the law of conservation of energy.”
What is the comment from N. & Z. on that?
I agree with those here that comments on Willis’ apparent arrogance. I dont read his posts any more, either.
Why are everyone so bitchy about some discussions on some formula’s?
[Reply] If Anthony gets around to saying exactly how he thinks N&Z’s theory violates energy conservation, then N&Z will be able to address it.
As neither a “climate scientist” nor even meteorologist, but only a competent physicist with 40 years of experience in my craft, and what I consider to be the DEFINITIVE discovery for the correction of climate science (which has FAILED) to my credit, I must say there are only incompetent, angry “big heads” on BOTH SIDES of this intellectual showdown, between Eschenbach on one side and Nikolov and Zeller on the other.
1) Nikolov and Zeller: “We then use observed data on surface temperature and atmospheric pressure (Ps) for 8 celestial bodies to derive an empirical function relating NTE to Ps employing non-linear regression analysis.”
and Tallbloke: “It successfully calculates the empirically measured temperatures from first principles physics. For EIGHT CELESTIAL BODIES”
———————–
That is not so. As I responded to Stephen Wilde, on my blog: “His [Nikolov’s] function NTE is basically just an arbitrary mathematical description of the functional relationship he and Zeller found between surface temperature (divided by a constant, ‘universal gray body’ temperature) and surface pressure.
“NTE was thus specifically formed to fit the surface temperatures and pressures of the eight bodies he considered, so to brag that it fits the surface temperatures and pressures of all of those bodies is a logically empty boast, not science at all.” This criticism will never go away, whether N&K and their followers like it or not.
2) N&Z: “The rest of Eschenbach’s ‘revelations’ in regard to our Equations (7) and (8) are less flamboyant but equally amusing. He argues that the small constant cs in Eq. (2) is pointless while failing to understand the physical realism it brings to the new model (Eq. 8). Since the goal of our research was not just to derive a regression equation, but to develop a new physically viable model of the ‘Greenhouse Effect’, this constant is important in two ways: (a) it does not allow the PGB temperature to fall below 2.725K, the irreducible temperature of Deep Space, when So approaches zero; and (b) it enables Eq. (8) to predict increasing temperatures with rising pressure even in the absence of solar radiation. Indeed, if we set cs = 0.0, then Eq. (8) would always predict Ts = 0.0 when So = 0.0 regardless of pressure, which is physically unrealistic due to the presence of cosmic background radiation.”
————————-
If you want reality, get real. The constant cs is VERY small–13.25e-5, as N&K write it (and why didn’t they give it, as real scientists are trained early on to do, as 1.325e-4?)–while the smallest value of So, for any of the 8 bodies considered in N&K’s introductory paper, is given in their Table 1 as 1.51 (W/m^2) (and ranges as high as 9,126). In the real solar system, then, cs is indeed much too small to matter AT ALL. But more importantly: In the absence of solar irradiation, there simply would be no gaseous atmosphere (at 2.725K cosmic background temperature). So much for the “physical realism” of Nikolov and Zeller. I’m sorry, but they constantly show themselves to be at the level of not-particularly-bright high school students of physics, pretending to understand and explain the smallest details, but having no consistently trustworthy physical insight whatsoever.
3) N&Z (in reply to a comment by BenAW): “The physical process you are talking about is called the Ideal Gas Law. It has been discovered and tested more than 100 years ago! Pressure provides the FORCE, which is an essential component of the Kinetic Energy of the atmosphere and gives its temperature. There could be no kinetic energy and NO temperature without Pressure. Hence, changing the pressure, changes the force, which in turn changes the temperature of a gas operating otherwise under isobaric conditions such as a planet atmosphere. It’s that simple!”
———————–
Pressure does not provide the FORCE causing the temperature of the atmosphere, or of the troposphere in particular. It provides the heat-retaining STRUCTURE of the troposphere. That is, the pressure does not determine the temperature, but rather, (the form of) the vertical pressure distribution determines (the form of) the vertical temperature distribution, commonly known as the temperature lapse rate (but should better be called the “lapse rate structure”). In turn, the pressure distribution–in the governing hydrostatic condition (which was empirically uncovered, over many years of data-taking, codified in the Standard Atmosphere model, and the latter confirmed as the preferred, stable state of the troposphere by my Venus/Earth comparison)–is found from the simple requirement that the pressure at a given level is due to the weight of the atmosphere above that level.
As I put it, as simply as I could, in reply to “truthseeker” in the comments section of my “Venus: No Greenhouse Effect” blog post: “Heat energy is poured into the
atmosphere by the Sun like water into a glass, and that glass is simply wider (that is, the atmosphere is denser, and can hold more heat energy) the farther down it goes.”
So much for the heat-retaining STRUCTURE of the troposphere; but the actual temperature at a given pressure level is determined by that level’s position within the overall (lapse rate) structure, and the level of incident solar radiation. (With, of course, transient/local variations, commonly known as the weather.)
To Simon Hopkinson et al:
You are ascribing to WE an importance he does not possess in real life. The climate blogosphere is a bubble populated by a very small minority of the population of mainly Western countries, by people who are committed in one way or another to the debate, whether through adherence to or naive or deliberate distortion of scientific principles, and/or through political motivation, hoping to combat or contribute to the social engineering implicit in the CAGW meme.
Eschenbach may have a following on WUWT (a few of his fans have turned up in this thread) but that is of very little consequence in the grander scheme of things. To communicate science effectively to the wider public and powers-that-be, demonstration of scientific competence, usually meaning higher formal qualifications, is crucial. Anthony has credibility because of his background as a meteorologist. WE, as I have said before, is an enthusiastic amateur, who outside the perfervid climate blogosphere is readily recognized as such.
The days of the genius autodidacts of the 17th to 19th centuries are long over. In those days the education system was much less formalized, and proto-scientists with the time, dedication and (usually) ample personal financial resources could and did make landmark discoveries. Willis Eschenbach is no genius; he should not present himself to be qualified in technical areas in which he very clearly lacks sufficient insight or competence.
I’m glad N and Z published this short reply. Willis article at WUWT did look convincing, but I can see this was because of errors of omission. I don’t know whether the hypothesis is correct, but Willis’s rebutal can be ignored because it is a strawman.
Willis is not a supporter of AGW and has on many occasions made strident attacks on GCM’s, the IPCC and the cult of post normal science. Yet the idea of the GHG controlling temperature is so deeply ingrained in the minds of scholars – so deep that the man made bit is almost an irrelevance – that it will take more than a few papers by N and Z to change that. That is the way science progresses – or doesn’t progress – for generations. And then we reach a tipping point. Think plate tectonics, eugenics.
Not a very optimistic note, I know, but I like to call it as I see it.
Chris M>
Don’t be a dafty trousers. None of Eschenbach, Nikolov, Zeller, or even you or me, are right or wrong based on who they/we are. We’re right if we’re right, and wrong if we’re wrong. If Eschenbach’s wrong here, it won’t make any difference who he is, and similarly if he’s right, N&Z will still be wrong regardless of their job titles.
tallbloke says:
February 9, 2012 at 4:07 pm
By using the moon N&Z DO use a BB (or GB) approach, since the moon IS a reasonable imitation of a GB.
“Exactly, and it doesn’t have an atmosphere, which was your original objection. The ‘Earth with no atmosphere’ would have no atmosphere either”
I was under the impression that my English isn’t that bad for a foreigner, but I’ll try again.
The simple GB calc for the moon looks like:
TSI 1362 W/m^2, after reflection and emissivity 0,88*0,955*1362 = 1145 W/m^2
Distribute over half the sphere 1145/2 = 573 SB > 317K
Dark side is 0K (or 2,77K) so GB calc for moon gives ~160K.
(better would be to calculate SB for several lattitudes and average those)
Compare to 154,7K after all the calcs N&Z do, and the conclusion should be that no major difference exists. So comparing earth with the moon to arrive at Nte is the same as comparing earth with a GB.
Using the N&Z formula with pressure close to zero and arriving at the more or less correct GB temp for a planet without atmosphere shouldn’t come as a surprise.
This leaves the planets with a substantial atmosphere, where a correlation may be shown.
Assuming that pressure is the cause of this correlation is one step to far imo.
I think I have a simpler explanation, at least for planet earth.
Schrodinger’s Cat says:
February 9, 2012 at 8:00 pm
“The point that solar radiation is constantly heating up the system and various other mechanisms such as convection, radiation, evaporation, etc are actively removing the heat seems to be the dynamic that people overlook. I tend to think of it as pumping up a leaking tyre. The heat may get lost, but I keep generating more as I continue to apply pressure.
Correct (and I like your ‘leaky tyre’ analogy)!
Also, as the amount of radiation from the sun decreases during winter the heat from land and ocean stored during the summer makes are climate more clement than expected – just like a giant storage heater. Why would anyone expect Earth’s energy level ever to be in balance? It is always oscillating around the mean set by the atmospheric pressure.
Harry, thanks for posting here, your points are clear. Answering just to what you addressed to me, I agree I went too far, given that N&Z don’t have the underlying physical basis for two constants that they use. Nonetheless, until the radiative theorists are able to match their performance, it’s the best working hypothesis I’m aware of.
Ned Nikolov says:
February 9, 2012 at 3:35 pm
BenWA says:
“So we need a physical process to show this theory is valid. The given manifestations of the effect in the original N&Z paper were star formation due collapsing interstellar clouds and the Chinook (Föhn) wind.
Both are DYNAMIC processes were potential energy is exchanged for kinetic energy, thus having no appearent relevance for a static atmosphere.
Question remains: what is the physical process we’re looking at?”
The physical process you are talking about is called the Ideal Gas Law.
The current atmosphere has an average ENVIRONMENTAL lapse rate of ~6,5K/km according the ISA.
The lapse rate according the Ideal Gas Law on earth is 9,8K/km as in the Dry Adiabatic Lapse Rate.
This DALR is the result of a dynamic process, a parcel of air moving up or down in the atmosphere, without heat exchange with the surrounding air. No movement, no temp. change.
So it seems the temp distribution in our atmosphere isn’t according the Ideal Gas Law.
Since the atmosphere is warmed for a large part from the surface, the energy distribution in the atmosphere is a mix of kinetic and potential energy. In a steady, undisturbed atmosphere the sum of potential and kinetic energy at every altitude should be equal, decreasing temp and increasing potential energy with increasing altitude.
I still haven’t seen an explanation why the Chinook winds are a manifestation of the ATE.
Harry Dale Huffman;
Your criticisms of N&Z’s math may have some merit. But can we put that aside for a moment?
When I read what you just wrote, and think through the physics in my mind, the impression I get is that you and N&Z are describing the same things from different viewpoints and using different vocabularies.
I think the tragedy of N&Z is that everyone is going down the rat hole of the equations. Are the basic concepts that they present (and that you present) sound? Or not? For if they are sound, then SB Law, Holder’s Inequality, and PV=nRT combine to suggest that the composition of the atmosphere is a negligible matter when determining the equilibrium temperature of a planet.
If these concepts hold, then the debate should not be if N&Z (or you) are right or wrong because of their math. The debate should be about the correct mathematical approach to use. But the physics as main constructs either holds, or it doesn’t, and my read of it is that it holds.
“So it seems the temp distribution in our atmosphere isn’t according the Ideal Gas Law.”
Is that correct for the ENTIRE atmosphere from the surface of the Earth to the very top of the atmosphere (how would we define that anyway ?)
Logic suggests that the average vertical temperature distribution SHOULD be in accordance with the Ideal Gas Law otherwise there would be instability.
Is it just a matter of choosing the precise height at which radiation in equals radiation out?
If one were to take that point as the top of the atmosphere what is the environmental lapse rate from surface to that point ?
Does it on average match the dry adiabatic lapse rate or not ?
“When I read what you just wrote, and think through the physics in my mind, the impression I get is that you and N&Z are describing the same things from different viewpoints and using different vocabularies”
I think Harry is pretty clear that the Standard Atmosphere and the Adiabatic Lapse Rate is the whole story.
In contrast there seems to be some suggestion from N & Z that their ATE is distinct from and supplemental to that.
Either way my general proposals are unaffected but I would be pleased to be able to resolve the issue
TO: Harry Dale Huffman (February 9, 2012 at 9:09 pm)
Harry,
The atmosphere cannot hold much heat, because it has a negligibly small heat storage capacity. This is standard and indisputable physical fact. This makes you analogy with the holding glass not quite correct. There is no holding of energy, there is a temperature enhancement caused by the number of molecules per unit volume carrying specific amount of energy. The more molecules you have per volume (due to higher pressure), the higher the heat transfer to the sensor, hence the higher the palatable temperature that we measure.
The pressure is a FORCE per unit area (check the definition). So PV = Force per m-2 * Volume = Force*Distance = Joules. The kinetic energy (J) of the atmosphere, which gives its temperature, is a product IN PART of the force we call pressure. The atmospheric Volume, on the other hand, is controlled by the solar heating – more absorbed radiation causes higher volume (lesser air density), but the pressure near the surface is CONSTANT until one changes the atmospheric mass, since we have an isobaric thermodynamic process at the surface. So, the pressure force is INDEPENDENT of solar heating! The temperature of the atmosphere is a product of the pressure force AND solar heating. Changing EITHER one of those variables can change the temperature. More heating – higher temperature, higher pressure – also higher temperature … It’s pretty simple.
I invite the new visitors here to take a look at a different ‘curve fitting exercise’ we undertook here last year, and consider the reasons we are giving N&Z plenty of time and room at the Talkshop to expand on their ideas.
https://tallbloke.wordpress.com/2012/02/09/2011/02/21/tallbloke-and-tim-channon-a-cycles-analysis-approach-to-predicting-solar-activity/
CO2’s “backradiation” does not warm the atmosphere below DIRECTLY, a colder body of energy cannot warm a warmer body of energy. Thats like me saying holding an icecube in my hand will warm my hand.
I tend to believe N&Z’s paper over the current “mainstream” view for many reasons, but though, to note CO2 slows the release of LW which raises the emission height of the atmosphere, and of course warmer air is less dense than colder air which results in convective overturning…thats where I think the “Hockey Team” loses rationality…
Yes…….Think about it this way, almost ALL of the ocean waves, winds, cyclones, lightning storms, clouds, jet streams, etc, are induced by the GHE…and that is KINETIC energy, not thermal energy, but it was once thermal energy before compensation and transfer. It never remains in thermal form in a net sequence. We would not have much kinetic energy on earth without the GHE. Problem is people assume that all energy added to the system via CO2 increase will remain in thermal form for extended periods of time when in reality the system regulates internal thermal perturbation very quickly, as in, a matter of hours, not years. Quick equilibrium response time is asociated with low climate sensitivity for a reason.
Where’s Eschenbach’s response ?
[Reply] It might take a while to prepare, wherever he intends to post it. 🙂
Stephen Wilde (February 9, 2012 at 10:07 pm):
About the lapse rate and how it compares to ATE. The adiabatic lapse rate is a result of pressure, and so is ATE. However, ATE refers to the thermal effect of pressure just above a surface, while lapse rate refers to changing temperature in the FREE atmosphere when moving away from the surface. ATE would be comparable with decreasing temperature with increasing terrain height in the context of a wide spread mountain range.
Also, ATE measures the temperature enhancement with respect to an AIRLESS surface, while the lapse rate measures the temperature change as a function of declining pressure with altitude in the free atmosphere.
I hope this clarifies the difference!
This feeling is key to a lot of people’s discomfort with N&Z, not least Anthony and Willis, imho. I emphasise “feeling” because I think we have an unidentified rogue driving us at this point. I should know because I had it too. And had to simply take time out to bathe in the that maybe a temperature gradient corresponding to pressure gradient is simply, well, a law of nature, visible in the snow line on hills, the cloud undersides line, the extra heat of sub-sea-level Jericho compared with nearby Jerusalem.
But we do actually have some helpers to hand in the experimental department. Graeff actually measured it, again, right under our firkin’ noses. And Huffman’s figures of correspondences need to be wheeled out all the time until we get used to them.
Ned and Karl, I like your graph. Rog, I love bathing in the blog energy after I’ve been twisting my mind in pretzels with the wiki. David, I think that all is not lost. I would like you as a wiki contributor, especially when you feel a cache of expletives coming on. Just do it for your grandchildren.
Thank you everyone.
Lucy,
People who cannot distinguish between ‘feelings’ and physical facts should not claim using the scientific method. Anthony at WUWT plays that tune – that he ‘thinks’ or ‘feels’ that our theory violated the law of energy conservation, with no evidence to back it off. Going on ‘feelings’ is a very bad approach in science, especially when you have limited understanding to base your feelings on.
If you look up atmospheric pressure at different altitudes and also calculate the temperature at different altitudes based on an arbitrary surface temperature and a lapse rate of 6.5k/km then plot pressure vs lapsed temp you get a linear relationship, at least between 0 and 5000 metres.
Ned
Exactly. That’s why I flagged it up.
But feelings drive us all – and stay unconscious until we focus our awareness on them, as psychology says, “own” them. To say that people who cannot distinguish between feelings and physical facts should not claim using scientific method, while correct, is also a counsel of perfection which we can only try to measure up to.
Anthony has shown amazing levels of courtesy in most matters – but his achilles heel is handling new material. He is the most amazing foot soldier I could ever hope to meet, but he is a foot soldier rather than a scientific freethinker. And even Newton behaved badly on occasion.
1. Willis’s x = x was a stupid tautology to tout.
2. I think there’s something in this PV=nRT stuff, so I am happy that Venus’s temperature is more due to its pressure than its CO2.
3. N&Z have overfitted in terms of variables versus data points, and the form of their equation is not credible. We need them to use only bodies with atmospheres, and to be able to predict the temperature of one body dependent on fitting the others first.
4. Because N&Z have overfitted and do not have zero error, there is scope for GHGs to act as a second order effect (for example replacing the smaller of their exponential terms).
5. The concept that GHGs merely change the outward route of energy, and not the overall temperature, is an interesting one. I, that is we all, need to ponder that.
Rich.
@ N & Z
The clarification of equation 8 is one thing, but there is an incompleteness in your UCT study, as it has been presented so far. Continued argument on the maths, and derivation of factors and curve fitting will probably persist until some simple lab experiments are conducted, that show the theorized pressure enhancement effect is supported by convincing empirical data. (with and without GHG’s).
There is even a question of whether the data for the eight planetary bodies is reliable, and many have questioned what IS the average near-surface T? Is such a number meaningful?
There may also be an avenue for further elaboration, let’s call it planet 9…. Down a deep mine shaft subjected to higher atmospheric pressure and geothermal energy. (not much solar energy or GHE). Doug Hoyt and others discussed this in AussieDan’s thread, and Doug listed some interesting data on lapse rates etc.
[Reply] Watch out for the improved experiments we have planned, following further discussion of Konrad Hartmann’s experiment.
@Tallbloke: “I invite the new visitors here to take a look at a different ‘curve fitting exercise’ we undertook here last year, and consider the reasons we are giving N&Z plenty of time and room at the Talkshop to expand on their ideas.”
The linked article was fun and interesting, but I’m at a loss as to how it ties in to the current thread. As far as I can tell, nothing was actually learned by the exercise of creating a smoothed version of one signal by using 7 frequencies in a Fourier-Transform-like exercise. Yes, the fellow had some clever heuristics which I assume found more efficient frequencies than some algorithms, but other than people chiming in with a huge variety of earth and solar-system cycles to get a “close one”, I can’t see that anything was actually discovered.
As my quote from WUWT, above, points out: what N&Z have done is to take advantage of large ranges and small ranges to break their 8 samples into two categories and then match reasonably close, all with 5 parameters at their disposal. Also unaddressed are claims about N&Z’s units and whether they’ve carefully followed them through their calculations so that the resulting numbers have physical meaning. (Once you drop units, numbers are just numbers and you can mix-n-match as you wish.)
As I pointed out on the WUWT thread, if you put N&Z’s equation 7 in dimensionless form — easily done — two characteristic pressures emerge. Those two pressures are completely non-physical and absurd; they cannot possibly be linked to any physical process involved. Doing this also makes it very clear that what they are asserting is a single fit with wide explanatory power is really two distinct fits — one that fits only the small “planets” (moons) being fit and a second one that fits only Mars, Earth and Venus. It is hardly universal. It is meaningless.
I’m perfectly happy to go look up the dimensionless form I worked out on the WUWT thread if anybody cares — offhand I recall the two pressures involved being 200 something atmospheres and
atmospheres — yes, that’s right, 100,000 atmospheres is the characteristic pressure that lets them fit one cluster of planets, specifically the ones whose surface pressure is almost vacuum — but it was a week or two ago at this point and I could be misremembering.
I’m a physicist by trade and happy to debate whether or not a physically meaningful theory can possibly contain dimensioned parameters that are many, many orders of magnitude removed from the actual forces, pressures, and so on involved. The answer is “no”. Willis failed to note this at first, but most of the rest of his criticism of N&Z’s equation 7 is dead on the money. It means nothing, and has zero predictive value.
rgb
“related to the thermal enhancement effect of pressure” say what? A balloon in a room still has the same temperature as the room. What is the physical principle, you say make this theory work?
“I hope this clarifies the difference!”
Thank you, Ned. That does help. The differences are subtle but real.
I think both the points you make were always implicit in the Standard Atmosphere concept as Harry says but I can see some added value in separating them out and giving them a distinct identity.
So, although Harry is strictly correct, your more detailed approach is a useful step forward from the Standard Atmosphere as it has been to date.
It means that one can more readily introduce additional permutations of phenomena and then move on to link the Standard Atmosphere and Lapse Rate concepts to a broader theory of climate which you did imply from the outset by way of your original title.
For example, the concept of ‘thermal enhancement’ gives a starting point to discuss what happens next to the additional energy which builds up at the surface. In itself the Lapse Rate idea does not naturally lead on to that next step in the climate description though that has never prevented discussion of conduction convection and weather. However the Lapse Rate concept has never been itself regarded as the primary CAUSE of weather and climate. It is easier to see that a ‘thermal enhancement’ at the surface could be such a cause.
Mind you, I think I have already done the rest for you with the concept of variable atmospheric heights and variable horizontal climate zone shifting beneath the tropopause leading to the necessary changes in the rate of energy flow from surface to space as a negative response to any forcing process other than pressure and solar input.
The key is that, whatever the ATE is at the surface, that extra energy at or just above the surface operates the entire system by setting an inevitable baseline for the STRUCTURE within the atmosphere just as Harry emphasised.
To my mind that reconciles the different viewpoints of you and Harry and meshes in nicely with my own propositions.
Of course, you, Harry and others may disagree. C’est la vie 🙂
You all should really flesh out your equation for calculating surface pressure from the mass of the atmosphere alone. I’ve been playing with the numbers and it doesn’t work at all.
[Reply] You’ll be needing the value for the gravitational constant for the particular celestial body you are working on, and the surface area.
“…Mr. Eschenbach does not know that we have extensively experimented with exponential functions containing various numbers of free parameters many months before he became aware of our theory, and we have found that it takes a minimum of 4 parameters to accurately describe the highly non-linear relationship between NTE and surface pressure…”
Why doesn’t he know that? Because this finding wasn’t published anywhere? Because the details of these experiments weren’t included? Is there a statistical analysis to justify this? “Extensively experimented” over “many months”…seems like those results should’ve been available for Willis to see, no?
Lucy;
I’m flattered. Wow. Let me think about it.
Phil;
Try putting your hand 1 cm from a block of iron at -100 C. Now slide a 2 mm sheet of ice at -5 C between your hand and the block of iron. Is your hand going to be cooling off faster or slower than it was before? Slower? How is that? I maintain that nobody should be allowed to discuss the laws of thermodynamics until they’ve done at least one winter camping trip in which they were required to construct a shelter to stay alive in at -30 C with no tools other than warm mittens.
rgbatduke says:
February 9, 2012 at 11:34 pm
As I pointed out on the WUWT thread, if you put N&Z’s equation 7 in dimensionless form>>>
Why then you’d have a pointless equation from which to draw pointless conclusions.
Bob Fernley-Jones;
There is even a question of whether the data for the eight planetary bodies is reliable, and many have questioned what IS the average near-surface T? Is such a number meaningful>>>
Bingo. I don’t believe we even have a method for calculating this, let alone the data to plug into the method! Willis’ complaint that the laws of thermodynamics are being broken is based (from my recollection) on his contention that the equilibrium temperature of earth is 255K based on average insolation being 240 w/m2. Both numbers are bogus. I and others (not to mention N&Z) went out of our ways to show that averaging P to arrive at average T is a math blunder of gargantuan proportions. Not as big a math blunder as substituting one equation back into the equation it was derived from and arriving at Ts=Ts and trumpeting that as a flaw in the math mind you, but garagantuan none the less. couldn’t get his attention on it and any discussion with him about the laws of thermodynamics is pointless until he understands that.
Re: Anthony’s “feeling” that the laws of thermodynamics are being broken, I don’t regard that as a comment from Anthony based on his assessment of the science. Antyhony is a busy guy, and like all managers, he has to rely in part on his trusted advisors on issues that he hasn’t the skill set or time to consider in detail on his own. His trusted advisors include Willis and others who are negative to N&Z, and so he formulates his own gut feel on the issue accordingly. I think also that his refusal to publish N&Z’s rebuttal on WUWT is related to another gut feel that he has. A nagging gut feel that regardless of N&Z being right or wrong, Wllis’ has blown it big time on the issue, and by shunting the rebuttal over here, he spares Willis and WUWT the negative exposure that must result from Willis being taken down a peg or two. Or six.
dmh
Wayne2 says:
February 9, 2012 at 11:30 pm
@Tallbloke: “I invite the new visitors here to take a look at a different ‘curve fitting exercise’ we undertook here last year, and consider the reasons we are giving N&Z plenty of time and room at the Talkshop to expand on their ideas.”
The linked article was fun and interesting, but I’m at a loss as to how it ties in to the current thread.
It doesn’t tie in directly. It is another piece of a big jigsaw which isn’t joined up yet. The jigsaw is called “Human understanding of the solar system neighborhood”
dmh,
Anthony has allowed the publication of any number of rebuttals on his site, and he has both drawn attention to and linked to this “shunted” rebuttal and discussion.
Since you’ve done at least one recent guest post on Anthony’s site, I would think you were familiar enough with him and his website to give him more credit than that. Maybe he’ll share with you personally the tone and word-play he found unsuitable.
They are not due to ATE they are due to release of latent heat of evaporation as the air moves over a mountain barrier.
Take a parcel of air which is absolutely dry. Move it up a mountain range and it will cool at the dry adiabatic lapse rate. When it crosses the summit it will begin to fall back down to its original altitude. If it is dry, it will heat back up to the same temperature on the other side of the mountain range as it had at the same altitude on the assent.
No heating on descent above its original heat content. It is simple exchange of potential energy for thermal kinetic energy.
Now replace that parcel of air with one that is near saturation. It rises up the upslope side of the mountain, and this orographic lifting causes it to cool at the wet adiabatic lapse rate, (or some rate between the dry and wet adiabatic rate depending on its moisture content. IF it reaches saturation and starts to rain all the latent heat of vaporization released as the water condenses is added to the parcels heat content. As the rain falls out it leaves behind air that has not cooled as fast (or as much) as it would have if dry. That now drier air crosses the summit and begins to fall on the lee side of the mountain, gaining temperature at or near the dry adiabatic lapse rate. As a result on descent to its original altitude it warms to a higher temperature that its original on the other side of the mountain. If it not only condenses out moisture as liquid water but also reaches the freezing level and forms snow, you also have the latent heat of fusion added to the air.
Down slope winds only warm if they lose moisture on the upslope side of the mountains, creating as chinook or santa anna type wind, if they do not lose moisture you have a cold down slope wind (bora wind). Same exact path for the air parcel but different thermodynamics.
Larry
I admit to some confusion regarding the source of the experimental data. If atmospheric and/or surface/near-surface temperatures [as observed from space] are not adequately described by radiative physics, then how were these temperatures determined for these heavenly bodies, (if I may use that phrase) ?
That is, if radiative physics does not solely determine the observed temperature, can you use radiative physics to reliably measure the same temperature [and the pressures?] ? As far as I am aware, no lander has ever been sent to Mercury or Triton, so these, at least, must be measured by remote sensing. This appears to suggest using data collected according to a theory being used as evidence to disprove the same theory.
Michael Jankowski;
Since you’ve done at least one recent guest post on Anthony’s site, I would think you were familiar enough with him and his website to give him more credit than that. Maybe he’ll share with you personally the tone and word-play he found unsuitable>>>
I’m pretty certain I know what the unsuitable phrase was and tallbloke has already stipulated to the changes that were made. I’ve considered expressing my ire on the matter to Anthony directly, but have chosen not to because a direct email from me to him on the matter will likely only harden his position. On the other hand, I’m guessing that he’s reading this entire thread and I would not be surprised if Willis is as well despite his self imposed ban in protest of the Joel Shore ban. I’m guessing they’re both thinking over what they are reading, and in time they’ll either engage in a positive fashion on N&Z… or set the climate debate backward several years by not doing so.
I think that Harry Huffman and N&Z are saying exactly the same thing (and mathematically shown through different methods), that the S-B equation has been improperly applied to all the planets and moons in our solar system.
Furthermore, they have shown that atmospheric mass, not albedo, or composition, determines the temperature via the ideal gas law (solar radiation staying constant of course).
Are we in agreement here?
I still do not see the point of that Cs = 0.0001325 constant added to S0 given that the experimental uncertainty in the measured value of S0 is at least 1000 times greater than that.
[co-mod: pedantic correctness. A general formula, where the term is the radiation from the cold sink, almost nothing for most of our planets. If they leave it out complaints, leave it in complaints… –Tim]
I’d like to take a stab (yet again) at putting Willis’ contention that N&Z violate the 2nd law of thermodynamics. In brief, Willis’ argument is that if one averages insolation for both the curvature of the earth and the rotation of the earth plus the albedo, one gets an “average” of 240 w/m2 which yields a blackbody temperature via SB Law of 255K. He then concludes that since the “average” earth surface temperature is 288K, that this can be explained by GHG’s, but not by N&Z.
I see this as being rather simple, but explaining it in writing is not as easy as one might think. I pointed out that taking an average of two numbers that do not vary linearly with each other cannot produce a meaningful average. This is called Holder’s Inequality. Joel Shore was quick to jump in and advise that if Holder’s Inequality was taken into account, the surface temperature of the earth would be even higher than 288K, leaving an even larger discrepancy, not a smaller one, and thus violate the 2nd law of thermodynamics by even a larger margin.
I responsed by pointing out that the problem is larger still. While applying Holder’s Inequality to the observed temperature record raises the “average” surface temperature by only a few degrees, doing the same with the insolation drops the “average” block body temperature of earth by over 100 degrees. On the surface, it looks like I am beating myself to death with my own numbers. I’m not.
Consider what ERBE shows us. http://eos.atmos.washington.edu/erbe/
We know that in the tropics, insolation peaks at about 1000 w/m2 at noon. But on an annualized basis (see ERBE absorbed shortwave radiation), it is more like 350 w/m2. Via SB Law… that’s only about 280K. The tropics are warmer than that, a lot warmer! Must be GHG’s. And it is. But let’s take a gander at higher latitudes, referring to the same ERBE chart.
In the temperate zones, we’re only about 180 w/m2. That’s only 237 K!
Onto the Arctic zones at more like 80 w/m2 is only 194 K. Frigid.
If we used ONLY those three numbers (which I pretty much picked for convenience, didn’t do the math in advance, so I don’t know where this is going to wind up) and “averaged” them:
(350+180+80)/3= 203 w/m2
SB Law for 203 w/m2 = 245K
Now let’s average those temps.
(280+237+194)/3 = 237 K. Ooops, I’ve misplaced 8 degrees!
SB Law for 237 K = 179 w/m2. Ooops, I’ve misplaced 24 w/m2!
That’s Holder’s Inequality in action.
Now let’s take a look at ERBE but this time refer to Net Radiation. From that graphic we see that the tropics absorb about 80 w/m2 MORE than they emit. Now we have the pieces of the puzzle coming together.
Since the tropics absorb 80 w/m2 more than they emit, we now have the reason why they are warmer than the blackbody calculation of 280K. With an energy imbalance like that, the tropics HAVE to heat up ABOVE their blackbody temperature calculated from “average” insolation. Is it GHG’s that do it? Of course it is!
But…
The tropics don’t heat up forever, they still hit an equilibrium temperature at some point, so where do the extra 80 w/m2 go to?
Why the temperate zones and Arctic zones. Look at the ERBE graphic. The temperate zones emit about 30 w/m2 more than they absorb, and the Arctic zones more like 150. Energy is moved via radiance, conductance, convection, whatever from tropics to poles. Adjust for relative area, and we’re back to an energy balance. But the “average” blackbody calculation is clearly well below 255 K and the “average” observed temperature is much higher than the blackbody calc, not because of any violation of the laws of thermodynamics, but because of arithmetic and the folly of averaging things that do not vary linearly with one another.
So let’s now ask ourselves, what would happen if there were no GHG’s and no conduction or convection? Would the surface temperature change?
At any given latitude, yes. As an average…
The tropics would have to get hotter. They would have to increase in temperature to radiate as much energy as they receive, since they now have no way to ship 80 w/m2 to the higher latitudes. And the higher latitudes would DECREASE in temperature since they now are warmed ONLY by insolation. What would the new “average” surface temperature be?
It would, if calculated as the average of the 4th root and then converted back to T, be unchanged. If one simply averaged the observed temperatures, then the folly of Holder’s Inequality that I demonstrated above would come to the fore, no “match” to the “average” insolation could be derived from those numbers, and it would appear on the surface that conservation of energy had been breached.
Except it wasn’t. The watts in (as a total) didn’t change and the watts out (as a total) didn’t change. The only thing that changed is WHERE they went out, and at what temperature. Holder’s Inequality did the rest, creating a fictitious violation of the 2nd law of thermodynamics.
Ok dmh,
Just keep guessing, using your gut, and pretending ulterior motives must exist.
That’s more like the kind of BS that sets the “climate debate backward.” As I noted, Anthony created a post and provided a link to this rebuttal. It’s how I got here. If he wanted to keep silent on the matter, he could have. He didn’t. If you want to attack people for not being open, for true censorship, for trying to cover the tracks of themselves/peers, and for truly setting the “climate debate backward,” there’s plenty of low-hanging fruit out there. You don’t need to guess or use your gut for those.
According the N+Z’s formula, the satellites of Jupiter (with the possible exception of Europa) should all have the same temperature (they all have the same S0). So why don’t they?
Ryan says:
February 9, 2012 at 11:44 pm
“You all should really flesh out your equation for calculating surface pressure from the mass of the atmosphere alone. I’ve been playing with the numbers and it doesn’t work at all.”
This is an example of the type of uneducated comment that drives a scientist nuts on a blog! – if you are not sue what pressure is and how it depends on atmospheric mass AND gravity, just Google it! This question is below basic physics really, and saying that we have to flesh it out before discussing anything else is absurd. Also, if you go back and read our original paper, the formula for calculating pressure from atmos, mass and gravity is right there on page 6, Section 3.1. Please, do you basic homework before splashing an opinion like this … Thank you!
Great post by N&Z. I will stop my nit picking with regard to their ignoring the effect of water in Earth’s atmosphere.
A couple of physicists armed with a few equations do a better job of explaining observations than a horde of statisticians calling themselves “Climate Scientists”.
Tomorrow I look forward to meeting Nicola Scafetta from the Duke University Free Electron Laser Laboratory (world’s brightest gamma ray source) to hear at first hand what his work with the ACRIM satellite implies for climate change to 2100:
It is totally awesome to find physicists speaking up in public on climate issues. Don’t forget Kirkby and his CLOUD experiment. The squishy scientists can’t cope with this kind of onslaught.
For the record, I usually agree with Willis Eschenbach but he is dead wrong on this issue.
I have for many years been arguing that our atmosphere is not static.
The atmosphere is constantly being pulled by the sun and the moon sometimes working in unison sometimes working against each other.
The diurnal/atmospheric bulge is a well noted and observed phenomen. The bulging of the atmosphere in this manner is like flexing the walls of a car tyre or squeezing a balloon.
When you fill a tyre with air, the temperature will rise. It will relatively quickly drop back to prevailing ambient temperatures. However, if you promptly drive on the tyre the flexing of the tyre wall will maintain the high temperature. Ditto, blowing up a balloon and continuing to squeeze it.
I do not know how large a graviational effect is being exerted on the atmosphere by the celestrial bodies (mainly the sun and moon) but it is undeniably the case that some work is being effected (witness the diurnal/atmospheric bulge) and the resultant effect of this is to put some heat into the atmosphere.
It may be that the ideal gas law is sufficient alone to explain matters. However, it may be that the continuous graviational work being done by the sun and moon plays a part.
If one looks at Io one can see an extreme example of the effects of gravitaional pull where Io is pulled between Jupiter and the other Galean moons resulting in Io being the most geologically active body in the solar system. I know that that is an extreme example, but it shows the effect of graviational pull. Fortunally, our atmosphere is not exposed to the same amount of gravitational pull, but the gravitaional pull exerted by the sun and moon is not de minimus either.
Just a point to throw into the overall mix.
PS. I was upset by the tone of Willis’s posts when commenting on this paper. His tone was completely innecessary and, no matter what he thinks of the contention set out in the paper, not at all helpful
I am disappointed that WUWT is not carrying this reply. I consider that decision to be misguided.
@ B_Happy
Seems you must have all of the surface temperatures of Jupiter’s moons… I didn’t realize such data had been gathered by probes or landers to date. Could you please either share or provide an open science link to the values? Surface pressure too if you also have those vaslues, they would have been measured in tandem.
Hi again. Thanks for the reply!
I used F=Gm1m2/r^2 and then divided by the surface area of the earth. Where m1 was the Me and m2 was mass atmosphere. The pressure I arrived at was a good thousand times lower than observed.
Could be a math error (my excell skills have declined over time).
But, I think the overall argument would be greatly strengthened by explicit derivation of surface pressure from first principles.
[co-mod: good reply, not winding up blood pressure, often questions can be both daft and in context of the asker not daft, so this eventually is the kind of thing answered in a genuine FAQ, right now we are all standing in the house with walls not yet complete, oops, looks like rain –Tim]
Regarding this theory’s calculation of the Tsb for the planets it’s unclear to me why the appropriate model should be a planet with zero heat capacity. Regarding the application of the Gas Law is done incorrectly, the pressure is determined by the atmospheric mass and the gravity of the planet, the temperature is determined by the radiation incident on the surface, the third parameter of the equation of state, the density, is determined from the first two. Regarding Ned’s statement that the adiabatic lapse rate is determined by pressure, this is incorrect it depends on the Cp of the atmosphere and the gravity of the planet. Applying the Gas Law as the equation of state for Venus is problematic too since the lower atmosphere is supercritical. The pressure dependence found by this study (even given the inappropriate model of Tsb is not surprising since it basically arises from Mars, Earth & Venus, where the differing GHE is due to pressure broadening of the spectral lines of the GHGs.
[Reply] This is argument by assertion, which is not supported by the latest modeling of Venus’ atmosphere.
“A Discrete Ordinate, Multiple Scattering, Radiative Transfer Model of the Venus
Atmosphere from 0.1 to 260 mm,” C. Lee and M.I. Richardson, J Atm Sci (June 2011) 1323-1339.
Click to access LeeAndRichardson11.pdf
From the conclusion:
“We suggest that the lower atmosphere con-
vective adjustment may be better parameterized sepa-
rately from the radiative forcing and that an additional
IR cooling term be included in the parameterization.”
@ Ned Nikolov once again
Using Ps=gMat/As
I get 1.14e13 Pa, which is about ten million times more than observed.
I know this sucks, but if you would just correct the math I would be eternally grateful.
Tallbloke, CC N&Z
Roger, I guess it was you that appended a comment on my: February 9, 11:18 pm:
Well that is very encouraging, but who is “we”, and will N & Z include such empirical data as an essential lead-in element prior to their supportive maths, to produce a truly convincing paper?
Hi Ned
I asked this question before on another blog, but here goes again. As I understand it most planetary pressures and temperatures are derived spectroscopically or radiometrically. Which means that they are derived using SB distributions. If this is the case, then your curves will always be logarithmic in line with SB irrespective of the actual true T or P that actually exists there. Thoughts ?
Regards
Simple Newtonian equations with normal maths and geometry are used for satellite and space exploration, complex maths and Einstinian gravity equations are not used.
If a simple equation is predictive over a huge variance of diverse planetary bodies, it has to be close to the basic parameters that are in play. No other theory or equations that I am aware of come close to fitting, well done and thank you, it may be proved you are not totally right but you are surely close to the truth.
Reblogged this on Xylance's Blog.
Ryan, ok, still hung huh? Here’s two versions. One is the mass to give std. atm. pressure by the 1976 US Std. Atm. The other is using NASA fact sheets values for the mass.
9.80665 * 5.27015E+18 / (4*π*6371008²) = 101325 Pa
9.80665 * 5.1E+18 / (4*π*6371008²) = 98054 Pa
Anyone have an answer for my question at February 9, 2012 at 8:10 pm? Am I stuck in a moderation queue or something?
[co-mod: can’t see it in moderation, spam or trash, sorry –Tim]
Wayne@5:37
The data for the Jovian satellites comes from the Galileo spacecraft which orbited Jupiter for several years. There are no landers on the moons, nor on Mercury, Titan or Triton for that matter so the measurements must be spectroscopic. The basic data are summarised here:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/galileanfact_table.html
The original data must be somewhere on NASA’s site – you could always e-mail them and ask.
None of the moons have any atmosphere, except a very tenuous one on Europa, so the temperatures only constitute a test of the ability of equation (2) to be generalised to objects other than Mercury and our Moon. Note than Europa, the only one with even a trace of atmosphere, is actually the coldest.
Roger
Let’s assume the rough edges of this paper are sorted out, that the results are correct and the authors decide to communicate their findings in a less abrasive manner.
What happens next?
I would liken Climate science to that of a supertanker. Not only is it difficult to change direction but before that can happen the bridge actually needs to receive instructions and then act on them.
Unfortunately I don’t hear anyone on the bridge listening for new instructions, let alone being in any mood to take any notice of them.
So how can we communicate with the bridge AND make them take notice? Its all very well people producing papers-and I concentrate on the historcal precedence side-but ‘we’ all seem to have a singular lack of success in producing influential papers. After all, those are the only ones that ultimately count.
tonyb
Black coal on the ground doesn’t assume a different electromagnetic spectrum, by its composition, as the energy around it interacts with single atoms and molecules, its behaviour also depends on the amount of energy per quantum (photon) available.
Solid, liquid or gas, mass cannot retain more photons then the energy balance around it allows. Hence, Co2 cannot add heat by its composition to the atmosphere.
I thought is was akin to the universal nature of things. Now that there are other perspectives on how the climate works, the planetary harmonics, solar isolation, galactic energy flows, a complex coupled atmosphere/ocean system, are being seen in a new light.
Not to mention Nikolav & Zeller knockout, United Theory Of Climate hypotheses. A killer punch to AGW, if there ever was going to be one.
Who would think, the force of pressure was the enclosure regulating energy flow through the atmosphere? Seems better than having a roof over my head, there’s blue sky above now. I wonder if Baron Fourier owned a greenhouse?
———————————————————————————————————————
The pressure of the atmosphere and bodies of water, has the general effect to render the distribution of heat more uniform. In the ocean and in the lakes, the coldest particles, or rather those whose density is the greatest, are continually tending downwards, and the motion of heat depending on this cause is much more rapid than that which takes place in solid masses in consequence of their connecting power. The mathematical examination of this effect would require exact and numerous observations. These would enable us to understand how this internal motion prevents the internal heat of the globe from becoming sensible in deep waters.
General Remarks on the Temperature of the Terrestrial Globe and the Planetary Spaces; by Baron Fourier.
—————————————————————————————————————-
If anyone doubts the heat derived from pressure in planetary atmospheres look at Jupiter which emits more heat than it receives from the sun. The Jovian atmosphere is hydrogen/helium.
I cannot see how the 1st law of thermodynamics is violated by the N&Z paper. Their energy from pressure is created by the work done by the pressure on the atmosphere.
Since the GHG theory violates the 2nd law we need another mechanism to explain the extra heat at the surface compared to the SB calculated one. Adiabatic compressive heat does the job without any violations of known laws.
[co-mod: I am suspicious of the Jupiter excess heat, put down in hand waving standard to unknown cause and associated with failure of AGW to explain actual Jupiter data. However, at 1 bar and 5.2AU distance equates to the same temperature as Earth and with a lapse rate just like here. N&Z have ignored Jupiter because it has no known definite surface, surface pressure, atmospheric mass, surface gravity, therefore no maths. We have correlation only.
Unknown: heat still leaking out from original planet formation or has a heat generating core or some other magic or just perhaps the data is wrong –Tim]
Stephen Wilde says:
February 9, 2012 at 10:01 pm
“So it seems the temp distribution in our atmosphere isn’t according the Ideal Gas Law.”
“Is that correct for the ENTIRE atmosphere from the surface of the Earth to the very top of the atmosphere (how would we define that anyway ?)”
No, lets stick to the troposphere, about 80% of atmospheric mass. Above the tropopause the atmosphere gets rapidly so thin that the “normal” processes like conduction and convection have very minor influence, and radiation takes over probably.
“Logic suggests that the average vertical temperature distribution SHOULD be in accordance with the Ideal Gas Law otherwise there would be instability.”
Why? The environmental lapse rate is ~6,5K/km and that is stable for dry air.
If the ELR is < ~5K/km the atmosphere is stable for both dry and wet air.
Is it just a matter of choosing the precise height at which radiation in equals radiation out?
Radiation in and out has to equal outside the atmosphere (TOA) otherwise you have warming or cooling. What happens INSIDE the atmosphere is weather.
If one were to take that point as the top of the atmosphere what is the environmental lapse rate from surface to that point ?
Don't follow.
Does it on average match the dry adiabatic lapse rate or not
NOT.
hotrod (larry L) says:
February 10, 2012 at 12:58 am
I still haven’t seen an explanation why the Chinook winds are a manifestation of the ATE.
“They are not due to ATE they are due to release of latent heat of evaporation as the air moves over a mountain barrier.”
That’s what I try them to realise, but to no avail sofar. Still this is in their paper:
“The thermal effect of pressure is vividly demonstrated on a cosmic scale in the process of star formation, where gravity-induced rise of gas pressure boosts the temperature of an interstellar cloud to the threshold of nuclear fusion. At a planetary level, the effect is manifest in Chinook winds, where adiabatically heated downslope airflow raises the local temperature by 20C-30C in a matter of hours.”
See also the following: https://tallbloke.wordpress.com/2012/02/02/ausie-dan-encircling-the-dragon-2/#comment-16382
and follow the link. All basic meteorology /climatology, but the classic way 😉
Hi Dr Nikolov
I followed the whole ‘NZ affair’ only from afar, until the Willis post deletion meltdown, at which time I got interested. But then of course, I realised that an accessible summary of the whole story was not available (would like to know of it, if available).
How does your basic pressure-derived temperature rise mechanism accomodate ‘large’ temperature changes in the different climatic zones over millenia, like ice sheet advances, and the like?
REALITY CHECK:
– earths surface is ~70% oceans, 3000m deep or more.
– heat capacity of the atmosphere is the same as that of ~3,2m of ocean
– oceans volume is ~1.300.000.000.000.000 m^3 (may have missed a zero somewhere 😉 )
– every cubic metre of the oceans has a temp of ~275K or even higher at the surface.
GHE effect claims that after heating by the sun, earths temp is 255K
N&Z claim that earth without atmosphere is at 155K.
Both claim that their effect causes the earth to warm to our pleasant ~288K average temp.
I claim that before the sun starts to shine, the oceans are ALREADY at 275K, and together solar heating, GHE and ATE warm the earth from 275K to 288K, a mere 13K.
My bet is solidly on solar to achieve this.
Shub,
Milankovitch cycles affect the distribution of insolation, and predispose the Earth towards glaciation/deglaciation. Once in a glacial period, evaporation and precipitation is low, so less mass of water in the atmosphere. Less mass means colder according to N&Z’s theory.
Ben AW:
I claim that before the sun starts to shine, the oceans are ALREADY at 275K, and together solar heating, GHE and ATE warm the earth from 275K to 288K, a mere 13K.
Ah, groundhog day again… 🙂
So how well does your theory hold up when we apply it to Venus?
Look you doubters, let me put it more simply than I usually do. N&Z are rock’n’roll versus the sheer stodge perpetrated by most of the climate change “community”. Their theory, whether ultimately proven or (partly) disproven, is a breath of fresh air that was sorely needed. It is inspiring to see the vehemence, honesty and humour with which Ned and Karl prosecute their case. Most of us may be OWGs (sorry Lucy, I know there are exceptions) but we don’t have to act like it! As Noddy Holder of Slade sang all those decades ago, “Cum on Feel the Noize”. =)
Dave says:
February 10, 2012 at 10:23 am
“Anyone have an answer for my question at February 9, 2012 at 8:10 pm? Am I stuck in a moderation queue or something?”
You are right in that if you substitute Ts/Tgb for Nte in Eq.8 you will end up with Ts/Tgb=Ts/Tgb. But what you have missed is that the Nte(Ps) in Eq.8 is the value calculated from Eq.7. N & V have described the derivation of Eq.7 in some detail.
Regarding Eq.7, the note I made in the earlier AusieDan post on Feb.4 at 07:09 is perhaps worth repeating here (with a couple of edits for clarity):
“Which brings me back to my comment about the importance of the expression for surface pressure: Ps=(g*Mat)/As. In this, where Mat is the mass of the atmosphere in kg, and As is in m^2, the top line (g*Mat) becomes a force in Newtons, thus Ps is in N/m^2, or Pascals. Note that on a planet with a given value of g and a fixed surface area, we can say: Ps=(Mat*C), where the constant C=g/As.
The N & Z Eq.7 says that: Nte(Ps)=EXP((0.233001*Ps^0.0651203)+(0.0015393*Ps^0.385232)). in this, using Ps as the defining parameter makes the expression applicable to all planets & moons studied.
But, for a given planet we can now substitute (Mat*C) for Ps to get:
Nte(Ma)=EXP((0.233001*(Mat*C)^0.0651203)+(0.0015393*(Mat*C)^0.385232))……………..Eq.7m.
The implication is simply that on any given planet, Nte is a function of the mass of the atmosphere alone, and nothing but the mass. Ps is really a derived parameter.”
I suggest that Eq.7m shifts the emphasis away from pressure as the primary determinant of temperature distribution within the atmosphere of a given planet.
The maths is beyond me, but I have one comment for davidmhoffer, (Feb. 9, 6:39): You draw an analogy between the effect of CO2 and a dam, and state that all it does is to change the course of the energy flux. Maybe you are right. But in real life, a dam certainly raises the level of the river which is barricaded by it. Once the higher level is obtained, the current flows at the same speed as before. This is to me just what the CO2 thesis claims: Temperature rises, the transfer to space nevertheless goes on. Maybe I got it wrong?
tallbloke says:
February 10, 2012 at 11:35 am
Ben AW:
I claim that before the sun starts to shine, the oceans are ALREADY at 275K, and together solar heating, GHE and ATE warm the earth from 275K to 288K, a mere 13K.
Ah, groundhog day again…
So how well does your theory hold up when we apply it to Venus?
Not sure why I should be worried about the weather on Venus.
Are you saying that the temperature of the oceans is NOT at ~275K?
ATE effect on earth is supposed to be ~133K. Adding that to 275K gives 408K.
Do you know a place on earth were these temps occur in the atmosphere?
Do you already have an explanation about those Chinook winds that so wonderfully
manifested the ATE. Or do you finally realise that they are just a well understood manifestation of the DALR and WALR, using the Ideal Gas Law as the ATE was supposed to do?
“In his ‘analysis’, Mr. Eschenbach makes several fundamental errors, the nature of which were so elementary that our initial reaction was to not respond.”
Classic. Pot calls Kettle black. Dumb and Dumber.
My initial reaction to the ATE theory is that its errors are so elementary it wasn’t worth a response. I stand by that reaction.
[Reply] Try to get beyond the first couple of sentences Dave. Thanks. TB.
Tonyb;
So how can we communicate with the bridge AND make them take notice?>>>>
Sometimes you have to stand in a skiff right in front of the supertanker with a megaphone and scream as loud as you can, hoping that they’ll notice you and change course before running you over. (and that’s what the alarmists are doing right now. running over any dissent, determined to ground the tanker which represents our global economy).
Which is why I am so ticked with WUWT. No one has a bigger megaphone than Anthony.
“BenAW says:
February 10, 2012 at 11:02 am”
Sorry Ben but you missed the point completely. Responding in full would take us too far off topic.
richard verney says:
February 10, 2012 at 5:09 am
There’s a fundamental problem in comparing the atmosphere to a car tire or balloon. The former is an open container the latter are closed. There’s a HUGE difference the most fundamental of which is which is the free variable in the fundamental gas law. In a tire if you heat the air the pressure rises because the volume is constrained by the closed container. If you heat the atmosphere the volume expands while the pressure remains the same.
That distinction between open and closed vessels and the ideal gas law is what the authors continually fail to understand. If you heat an atmosphere the pressure will not increase. If you cool an atmosphere the pressure will not decrease. The inverse must also be true i.e. if you increase the pressure the temperature will not increase and if you decrease the pressure the temperature will not increase. This is because the atmosphere is not a closed container. Volume is the free variable in the open container. The authors insist that temperature is the free variable and this is just fundamentally wrong. That is NOT how it works in an open container where pressure is a function of mass and gravity with no dependence on temperature.
ThomasU said:
“a dam certainly raises the level of the river which is barricaded by it”
Not if there is an alternative route around the dam it doesn’t and in the case of the atmosphere a change in the height of the tropopause and a latitudinal shift of the climate zones provides just such an alternative exit route.
Dave Springer said:
“My initial reaction to the ATE theory is that its errors are so elementary it wasn’t worth a response. I stand by that reaction.”
Dave, could you just give us a bit of a clue ? At worst N & Z are just rediscovering the Gas Laws, at best they have a valuable extension or reinterpretation of them. Do you dispute the Gas Laws ?
I see that Dave Springer’s elucidation has cross posted my question to him.
I don’t think the objection is valid where there is an external source of energy input because higher pressure at the surface creates greater molecular density at the surface so that more of the energy flowing through is thermalised at the surface than at higher less dense levels producing the highest temperature at the surface.
Davidmhoffer ran through the equations very well in an earlier thread and volume is indeed the only free variable as Dave Springer notes but that means that changes in volume can prevent temperature changes from any causation other than changes in atmospheric mass, the gravitational field or solar energy input.
All forms of energy input will increase the total volume of the atmosphere but more solar input will both increase atmospheric volume AND increase temperature at the surface because more energy is passing through the system.
Anything else that heats the atmosphere (excluding a stronger gravitational field or greater atmospheric mass) only effects a redistribution of energy passing through and does not affect total energy involved and so is negated by a change in atmospheric volume whereas a change in solar input is not so negated.
I don’t think N & Z say that temperature is a free variable at all. They say that temperature is fixed by gravity and atmospheric mass at any given level of solar input.
Dave Springer says:
February 10, 2012 at 1:53 pm
That distinction between open and closed vessels and the ideal gas law is what the authors continually fail to understand. If you heat an atmosphere the pressure will not increase. If you cool an atmosphere the pressure will not decrease. The inverse must also be true i.e. if you increase the pressure the temperature will not increase and if you decrease the pressure the temperature will not decrease.
Hi Dave. Your misunderstanding of N&Z’s proposition now becomes clear. You are thinking that all they are discussing is the application of Charles’ law. They’re not.
You are considering a static system. they recognise that the real situation is dynamic. It is the dynamic throughput of solar energy acting in concert with the structure of the atmosphere caused by gravity acting on mass creating a gradient of pressure which brings about the near surface thermal enhancement they refer to.
Stephen Wilde says:
February 10, 2012 at 2:16 pm
Anything else that heats the atmosphere (excluding a stronger gravitational field or greater atmospheric mass) only effects a redistribution of energy passing through
Whoah! watch what you stick in parentheses as an afterthought. Gravity does not heat anything. Nor does mass. Gravity acting on atmospheric mass create a pressure profile which when illuminated by solar radiation brings about a thermal enhancement nearer the surface. We’re talking about things which affect the distribution of energy here, not the creation of it.
Ben AW says:
GHE effect claims that after heating by the sun, earths temp is 255K
N&Z claim that earth without atmosphere is at 155K.
Both claim that their effect causes the earth to warm to our pleasant ~288K average temp.
I claim that before the sun starts to shine, the oceans are ALREADY at 275K
You can claim nonsense all you like. The sun don’t shine, everything is at 2.7K
PV=nRT
P(ressure) is a function of the weight of the atmosphere which is a function of the mass of the atmosphere and gravity. Unless a change in composition of the atmosphere changes the mass of the atmosphere, P is fixed. In the context of the climate debate, substituting 300 ppm of O2 with CO2 results in a change in mass so small as to be negligible.
n is the number of moles in the atmosphere. Given that the discussion regards composition, not total number of moles, this can be assumed to be fixed. In the context of the climate debate, we are not adding moles to the atmosphere as for every molecule of CO2 we add, one molecule of O2 is removed, and hence, n is fixed.
R is a constant. ’nuff said.
T(emperature) is a function of the insolation and is fixed according to SB Law. Unless a change in the composition of the atmosphere results in a change to the amount of insolation absorbed, then T cannot change. What can change is the distribution of T with GHG’s, convection, conduction etc spreading the energy flux about the planet such that the tropics are cooler than they otherwise would be, and the temperate and arctic zones warmer than they otherwise would be. Depending on how one calculates “average” temperature, Holder’s Inequality may well result in the illusion of warming when in fact the radiative balance hasn’t changed.
Since P, n, R, & T cannot change, only V can change.
The atmosphere may not be bounded by a container, but that is why we get the result we do. If the atmosphere were bounded by a container, then V would not be able to change, forcing one of the other variables (P and/or T) to change. Since the atmosphere is NOT bounded by a container, and all other variables are fixed, V must change due to a change in atmospheric composition. T cannot change.
tallbloke says:
February 10, 2012 at 2:29 pm
Stephen Wilde says:
February 10, 2012 at 2:16 pm
Anything else that heats the atmosphere (excluding a stronger gravitational field or greater atmospheric mass) only effects a redistribution of energy passing through
Whoah! watch what you stick in parentheses as an afterthought. Gravity does not heat anything>>>
No…. but if you were to increase gravity you would:
a) get a Nobel prize for figuring out how to do that.
b) cause an increase in temperature since P(ressure) would increase.
Similarily re mass. No mass doesn’t heat anything, but adding mass adds weight adds pressure….
tallbloke (to BenAW);
I claim that before the sun starts to shine, the oceans are ALREADY at 275K
You can claim nonsense all you like. The sun don’t shine, everything is at 2.7K>>>
Yes, but that wasn’t Ben’s point. The ocean surface never reaches the peak blackbody temperature that would otherwise be associated with peak insolation, and it never reaches 2.7K either despite having zero insolation for 12 hours at a time. The heat capacity of the ocean plus GHG’s plus convection plus conduction plus secret Green Peace submarines shining lights on Argo buoys to make them provide false readings result in the temperature of the ocean (or anything else for that matter) to fluctuate above and below an equilibrium point. This exacerbates Holder’s Inequality and our entire discussion of “equilibrium temperature”.
dmh
PS – in retrospect, my shot at Green Peace was out of line. I have no way of knowing if they use spot lights or something else to mess up the Argo Buoys.
Davidmhoffer said to me
‘Which is why I am so ticked with WUWT. No one has a bigger megaphone than Anthony.’
I don’t want to divert attention away from the fascinating and erudite analysis of this paper, but unless we can idenify,collate and present this sort of papers to people that matter we are always going to get run down by the IPCC ‘superanker,’ either deliberately or because they are just not expecting anything to get in their way.
I agree that no one has a bigger megaphone than Anthony and as such it is a shame in some ways that this thread has been diverted to Rogers excellent blog. However, the question also needs to be asked that IF this thread was at WUWT would that give the carbon zealots a very good excuse to ignore it,because I doubt his credibility is too high with them? That may be unfair but that is likely to be the reality.
I suspect there are 20 or so key papers out there that need to be collected together, put into context and then repeatedly presented to the powers that be- and that includes policy makers as well as scientists. In fact the former are more important than the latter.
In that respect I agree with Lucys suggestions of a sceptics Wiki but I think the scope of it needs to be drastically smaller than she envisages and be presented proactively rather than people find it on the internet.
Always value your opinion, but isn’;t it time you went back into the fray…?
all the best
tonyb
Restrict yourself to just a small set of boundaries, say a 1 meter high column of air with an area of 1 square meter, bounded on the bottom by the earth’s surface and open to the atmosphere on the top, you have a 1 cubic meter chunk of air, right?
Now the ideal gas law ( PV=nrT) is an energy balance, Joules on both sides. The neat thing is that you can think of this column as having a constant energy; pressure at its top will always be one atmosphere and the volume, by definition is constant. The left side of the equation can’t change.
If you attempt to add energy to this column by any surface phenomenon you want to pick, the volume’s energy can’t change so on the right side, two things have to change; molecules exit and T goes up to maintain the energy. At night the reverse happens; energy is trying to exit the column at the surface so molecules come back in and T goes down.
No CO2 is required. No radiation imbalance is created. Indeed, if you pick an imaginary gas with total radiation transparency it still works. Everything else going on around this column is just weather and that little column, replicated all over the planet is the fundamental equilibrium set point that every perturbation is destined to return to.
I don’t see the big mystery to this. Gravity is not creating energy and it’s not a perpetual motion machine, but clearly surface pressure from an atmosphere can be responsible for surface T in the presence of an energy source that modulates n.
BTW, that last bit about ‘in the presence of an energy source’ seems to be overlooked in lots of comments where folks argue that pressure can’t create temperature. This is true of course if there’s no energy because T eventually reaches 3K irrespective of pressure in that case. But, with energy present, n is modulated and T has to change to maintain the state of the gas.
Rog, I put those items in parentheses because increasing either would increase pressure and thus temperature. I needed to mention them so as to distinguish all other factors that fail to alter temperature such as more GHGs.
davidmhoffer got the point.
[Reply] Sure, just don’t want certain people who wilfully misinterpret saying “told you it breaks energy conservation”.
“Everything else going on around this column is just weather and that little column, replicated all over the planet is the fundamental equilibrium set point that every perturbation is destined to return to.”
Exactly, people are starting to get it. And in essence it is very simple.
Stephen Wilde;
Exactly, people are starting to get it. And in essence it is very simple.>>>
Actually, it is rather simple. The arguments over the math of N&Z have been very distracting from the big picture.
What we need, I think, is a succinct summary of:
SB Law
Holder’s Inequality
Ideal Gas Law
and how they all fit together. I don’t think a mathematical model predicting the temperature of various bodies based on their insolation and surface pressure is ever going to be produced that satisfies all the critics, even if it was 100% correct. It is just an awful complicated task.
Understanding the basics of SB Law, Holder’s Inequality, and the Ideal Gas Law and how they work together however, is a simpler task. Once one understands those basics, it seems to me that the CAGW meme is dead.
Phil. says:
February 10, 2012 at 6:22 am
Regarding this theory’s calculation of the Tsb for the planets it’s unclear to me why the appropriate model should be a planet with zero heat capacity. Regarding the application of the Gas Law (this) is done incorrectly, the pressure is determined by the atmospheric mass and the gravity of the planet, the temperature is determined by the radiation incident on the surface, the third parameter of the equation of state, the density, is determined from the first two. Regarding Ned’s statement that the adiabatic lapse rate is determined by pressure, this is incorrect it depends on the Cp of the atmosphere and the gravity of the planet. Applying the Gas Law as the equation of state for Venus is problematic too since the lower atmosphere is supercritical. The pressure dependence found by this study (even given the inappropriate model of Tsb is not surprising since it basically arises from Mars, Earth & Venus, where the differing GHE is due to pressure broadening of the spectral lines of the GHGs.
[Reply] This is argument by assertion, which is not supported by the latest modeling of Venus’ atmosphere.
“A Discrete Ordinate, Multiple Scattering, Radiative Transfer Model of the Venus
Atmosphere from 0.1 to 260 mm,” C. Lee and M.I. Richardson, J Atm Sci (June 2011) 1323-1339.
Click to access LeeAndRichardson11.pdf
From the conclusion:
“We suggest that the lower atmosphere con-
vective adjustment may be better parameterized sepa-
rately from the radiative forcing and that an additional
IR cooling term be included in the parameterization.”
So why don’t you address the other points, I note that in the paper you reference their model uses the pressure broadened GHG spectra just as I pointed out above.
John Marshall says:
February 10, 2012 at 10:55 am
I cannot see how the 1st law of thermodynamics is violated by the N&Z paper. Their energy from pressure is created by the work done by the pressure on the atmosphere.
In order for pressure to do work on the atmosphere there must be a change in volume, according to N&Z that change must sustain a temperature differential of 133ºC. I don’t see any indication of such a change in volume.
“This exacerbates Holder’s Inequality and our entire discussion of “equilibrium temperature”.”
Which is why I have taken to referring to system energy content rather than equilibrium temperature.
System energy is exactly where the focus should be. Temperature is nothing more than a man made proxy for energy isn’t it?
The introduction of Holder’s Inequality by davidmhoffer has been very helpful to my mind since I was not previously aware of it.
I had problems getting it across that despite a bit of extra surface warming from more energy in the air for whatever reason the increased rate of energy flow to space would prevent a warming of the system overall.
Combining the concept of Holder’s Inequality with a change in terminology to system energy content rather than equilibrium temperature deals with that problem nicely.
I think it is an aspect of the debate that many AGW proponents will struggle with jiust as I did at first so it is an important issue to get across.
I think we can summarise as follows:
i) The SB Law is not applicable to a planetary body with any sort of atmosphere. If one must try to apply it then it must be applied outside the atmosphere just as Harry Huffman says.
ii) When there is any sort of atmosphere then the Ideal Gas Law applies and governs the temperature of every molecule in the atmosphere, not just GHGs. In the process, radiative physics is sidelined so as to become unnecessary.
iii) Then apply Holder’s Inequality to explain why there can be more energy at the surface from some other cause such as more GHGs whilst NOT increasing total system energy content which is actually fixed by surface pressure and solar energy input.
iv) Recognise that there will be a climate/weather consequence from the changed rate of energy flow from surface to space but demonstrate that it will be miniscule compared to variability caused naturally by sun and oceans.
davidmhoffer says:
February 10, 2012 at 2:35 pm
Nice refresher, David. Thank you.
I do notice how both your comments and mine are gradually becoming clearer and more specific with greater verbal economy.
With the addition of Holder’s Inequality I think the issues are pretty much nailed.
When the gas laws are taught they usually involve gas in a container. The atmosphere does not have a container. But there is another difference too. The container in the gas law tutorial is not usually several miles tall so we ignore the mass of the gas and the effect of gravity.
The downward pressure of the column of air compresses the air towards the ground – the surface that is being heated by the solar radiation. So, at the lowest level of the atmosphere we have heating taking place raising the kinetic energy of the air molecules.
The consequence of atmospheric mass and gravity means that there are a lot more molecules close to the ground than elsewhere. This, I think, is the enhancer. There is more kinetic energy (equals temperature) in this layer of air because (a) it is closest to the ground and (b) it contains a lot more air molecules per unit volume.
Now, what about expansion and convection because as discussed above, there is no container wall to maintain the pressure? Some of that must, and does occur, but the weight of the air continues to bear down and the greatest density of molecules will always be at the bottom of the pile due to the weight of the column. The mass of air in this column doesn’t change much, so in effect, the pressure doesn’t either. It is the high concentration of molecules with high kinetic energy that creates the higher temperature.
So the enhancement of temperature at the surface is due to the kinetic energy gradient. Some energetic gas molecules do reach higher altitudes where the molecular concentration per unit volume is much less, the kinetic enery is less and the air is cooler.
Schrodinger’s Cat,
Another nice summary especially the phrase ‘ kinetic energy gradient’.
The more easily that different people can translate this into their own words the faster it can take hold.
I feel that good progress is being made here.
Phil. says (February 10, 2012 at 6:22 am)
Regarding this theory’s calculation of the Tsb for the planets it’s unclear to me why the appropriate model should be a planet with zero heat capacity. Regarding the application of the Gas Law is done incorrectly, the pressure is determined by the atmospheric mass and the gravity of the planet, the temperature is determined by the radiation incident on the surface, the third parameter of the equation of state, the density, is determined from the first two. Regarding Ned’s statement that the adiabatic lapse rate is determined by pressure, this is incorrect it depends on the Cp of the atmosphere and the gravity of the planet. Applying the Gas Law as the equation of state for Venus is problematic too since the lower atmosphere is supercritical. The pressure dependence found by this study (even given the inappropriate model of Tsb is not surprising since it basically arises from Mars, Earth & Venus, where the differing GHE is due to pressure broadening of the spectral lines of the GHGs.
I’d like to make a few clarification to your points:
1) Our theory does not claim that pressure in itself (i.e. in isolation) brings an absolute amount of energy to the system. What we say is that pressure brings a relative enhancement to the thermal environment through its physical characteristic called FORCE. The absolute kinetic energy (and temperature) of a gas is a product of the pressure FORCE * Gas VOLUME. On a planetary scale, the atmospheric volume is completely controlled by solar heating. Solar radiation is the active component here. Because of that, the absolute temperature of a planet appears to follow closely the solar insolation. For example, Titan, due to it’s higher surface pressure, has a larger NTE factor (relative thermal enhancement) than Earth (1.92 vs. 1.86). However, Titan’s surface is MUCH colder (93.7K) than Earth’s surface (287.6K), because Titan receives about 10 times less solar radiation than Earth. However, if Earth were moved the the orbit of Titan (with no change in the overall pressure), then (according to our model in Eq. 8) its the surface will be at 91K, or 2.7K colder than Titan!
2) You are correct that numerically, the adiabatic lapse rate (which is the backbone for the environmental lapse rate) is given by dT/dz = -g/Cp (gravity divided by the specific heat of air at constant pressure). However, this formula conceals the effect of pressure in the following way. The adiabatic lapse rate is a product of two other rates – the temperature change with pressure and the pressure change with height, i.e. dT/dz = (dT/dP)*(dP/dz). In turn, dT/dP is derived from the Gas Law, where dT/dP = 1/(ρ*Cp) and ρ is air density, while the other rate is based on the assumption for hydrostatic equilibrium, which yields dP/dz = -g*ρ. In other words, it is the vertical pressure gradient that is ultimately responsible for the existence of the lapse rate in the troposphere. If we had dP/dz = 0, there would be no lapse rate, and the atmosphere would be isothermal in the vertical.
3) Our model for calculating the planetary gray-body temperature is CORRECT, and the Moon temperature measurements prove that (see our Reply Part 1). The standard application of the SB equation to a sphere is mathematically wrong, and as a result of that, the emission temperatures calculated from it are NOT physically compatible with any measured palatable temperatures on the surface of an airless body. Emission temperatures are a mathematical construct, not a physical reality!
You have two energy types who must sum to a constant, gravitational potential energy which increases with height above the surface and a kinetic energy gradient that decreases with height above the surface.
They exactly compensate for each other with the sum of Ke and Pe being always equal at any height. If you loft a ball high into the air, it exchanges energy of motion as it leaves your hand for gravitational potential energy as it rises in altitude. As the altitude increases (increasing its potential energy) its velocity and kinetic energy decrease by the same amount. The sum of the ball’s energy is always the same regardless of altitude, only the form that energy is stored in changes.
At high altitude you also have low volumetric specific heat (less mass per volume) so it takes less energy to heat that volume to a given temperature. Temperature is not energy – it a meaningless value unless you know how much of a substance and what type of substance is at that temperature. Then and only then can you assign and energy content.
A volume which is a near vacuum at 1,000,000 degrees holds very little energy.
At the surface, a similar volume contains much more atmospheric mass, and thus more heat capacity. It holds more energy per volume in the form of both pressure and kinetic heat energy.
The basic concept is as simple as the beginning science class discussion about the kinetic energy and potential energy of a ball as it drops from a height. As it drops it loses gravitational potential energy which is converted into an equal amount of kinetic energy of motion as it falls. In a vacuum they would be identical inverse quantities.
What is disregarded in that process discussion of the class room, is some of that kinetic energy of motion is dissipated at frictional heating. It is so trivial as it can be ignored for the examples used in a basic science class demonstration. It is NOT trivial for a body falling from 60000 ft altitude and it does not matter if that body is a physical solid object like a re-entry vehicle or the same mass of air descending the same distance. It also does not matter at what rate it falls, the same energy will have to be dissipated regardless if it is a free fall at 20,000 ft/second or a gentle descent on a parachute, or the diffusion of gas molecules changing altitude.
All that gravitational potential energy must be eventually converted to heat and or pressure as the ideal gas laws explain.
Larry
Davidmhoffer summarised the argument that Willis put forward regarding the violation of the 2nd law. I think this summary is incorrect.
Willis did a thought experiment in which there was no ghg in the atmosphere, and then allowed the pressure hypothesis to increase the surface temperature. He said, since there was no ghg, then the upper atmosphere cannot radiate energy into space. This led to the outcome that the only radiating surface was the physical surface of the planet. If that were now warmer due to the pressure, then he concludes that the planet would then be radiating more energy than it receives, which obviously don’t add up.
I think the flaw in the argument is the assumption that the atmosphere cannot radiate unless it containst ghg. I’m not convinced of that at all, although Willis seemed pretty certain.
Here’s my detailed criticism of N&Z equation 7 above, based on pure dimensional analysis. N&Z assert that:
fits certain planetary data (hardly “all” planetary data as they claim). Note well that this is a dimensionless expression. Let’s rewrite it:
(to show that it is really the product of two exponentials, one of which is nearly flat and the other of which is extremely sharp) and put the arguments of this formula in manifestly dimensionless form.
That is, the numbers “0.233” and “0.00154” are not pure numbers, they are dimensioned numbers. Furthermore, they must have some very odd dimensions indeed to match the exponents of the asserted surface pressures. But the most interesting thing is the values of these dimensioned characteristic pressures.
in atmospheres. Individuals are invited to confirm that the characteristic pressures in these two exponentials are
atmospheres and 
atmospheres.
Comments:
* First, the characteristic dimensioned pressures
and 
that are hidden in the N&Z’s equation 7 are absurd. There is no possible way that either one is even faintly physically relevant to atmospheric dynamics in a series of planets where the highest surface pressure present is 
atmospheres (Venus). All of the other planets in this “fit” have surface pressures less than or much less than 1 atmosphere.
* Second, by writing the product out, one can easily see how the “fit” works. Three of the planets being fit have no atmosphere, so
is 1. They all constitute a single point as far as the fit is concerned and cannot possibly not be fit by a product of exponentials that are 1 when 
. They do not constitute any sort of constraint on the parameters of the fit for these forms. One is left with five data points that have to be fit with four free parameters. It is hardly surprising that they can succeed with this, but it is still interesting to look at how they succeed.
If the moderator would be so good as to insert the figure I generated here:
you can see exactly how it works. Basically, the first five points are fit with the first exponential — that is the moon through Mars, where three of the points are “free” as noted above. So this is really a two parameter, two point fit. Gosh, it works. The last three points — Earth, Triton, and Venus — are more or less entirely fit with the second exponential only. Again three points with two parameters — nothing impressive there as well. The first exponential has conveniently become an irrelevant near constant in the meantime.
Just thought you’d like to know.
rgb
If my above summary is correct (and the N&Z theory valid) I would pose a simple proof would be to determine that the sum of the three components of energy in a gas atmosphere always sum to a constant with altitude.
You have energy content due to heat (temperature, mass and specific heat)
You have energy content due to pressure (liter atmospheres of that same mass of gas at that altitude)
You have the energy content of that mass of gas due to gravitational potential energy above the planet surface at a given altitude.
Conservation of energy and the perfect gas laws tell me that those three values should always sum to a constant for a given mass of gas, in a given gravitational field at all altitudes above the surface.
I need to leave for work and do not have time to mess with the numbers, but I suspect some of you are far better qualified to carry out those computations than I anyway.
Larry
Roy Martin says (February 10, 2012 at 11:58 am):
I suggest that Eq.7m shifts the emphasis away from pressure as the primary determinant of temperature distribution within the atmosphere of a given planet.
Roy, your line of thought is correct! With respect to ATE, pressure is the required variable ONLY if one compares ATEs across planets. For any individual planet, it is the atmospheric mass that effectively controls ATE. Thinking in those terms, DOES INDEED helps resolve the confusion with the pressure-controlled lapse rate with the atmosphere of a given planet.
Thank you making this important distinction!
“For any individual planet, it is the atmospheric mass that effectively controls ATE. Thinking in those terms, DOES INDEED helps resolve the confusion with the pressure-controlled lapse rate with the atmosphere of a given planet. ”
So, would it be right to say:
i) The gravitational field determines the slope of the lapse rate.
ii) The solar input determines the height of the atmosphere
iii) The atmospheric mass determines the temperature at the surface.
rgbatduke says:
February 10, 2012 at 6:17 pm
I’m not sure that many of us are overly concerned about the equations.
What matters most is the concepts in relation to the basic laws of physics. Either they make sense in light of observations or they don’t.
Get the concepts right so that they fit observations without offending the laws of physics and the equations can be refined subsequently.
In any event I suspect that Ned or Karl can deal with Robert’s comments appropriately.
Shub Niggurath says:
February 10, 2012 at 11:23 am
Hi Dr Nikolov
I followed the whole ‘NZ affair’ only from afar, until the Willis post deletion meltdown, at which time I got interested. But then of course, I realised that an accessible summary of the whole story was not available (would like to know of it, if available).
How does your basic pressure-derived temperature rise mechanism accomodate ‘large’ temperature changes in the different climatic zones over millenia, like ice sheet advances, and the like?
==============================================
Albedo changes, therfore insolation changes. Over long term insolation changes.
Stephen Wilde says (February 10, 2012 at 6:56 pm):
So, would it be right to say:
i) The gravitational field determines the slope of the lapse rate.
ii) The solar input determines the height of the atmosphere
iii) The atmospheric mass determines the temperature at the surface
To your questions:
i) No, that would be inaccurate statement, because the adiabatic lapse rate depends equally on g and Cp. Also, on Earth, the actual (environmental) lapse rate depends on water vapor. The presence of evaporation and convection reduces the adiabatic lapse rate from 9.8C/km to about 5.5C – 6.0C/km.
ii) Yes, that’s correct. This is the reason why the troposphere is 15-17 km deep in the tropics, and only about 6-7 km near the poles.
iii) To be correct, this statement should read: The atmospheric mass determines the temperature at the surface for any given planet and amount of solar radiation received. Atmospheric mass alone cannot produce temperature. It need radiation and gravity to do that.
@ Stephen Wilde, February 10, 2012 at 3:41 pm:
“Everything else going on around this column is just weather and that little column, replicated all over the planet is the fundamental equilibrium set point that every perturbation is destined to return to.”
Exactly, people are starting to get it. And in essence it is very simple.
(My bold)
I’d say that it is this simplicity which has people so at sixes and sevenses.
They are so used to everything being extremely complicated and esoteric that they look for the complications they think have to be there.
So they tie themselves in knots, trying to find the esoteric which only the cognoscenti can understand, and not finding any, make them up or reject this thesis out of hand.
Regrettable, but their loss.
Simon Hopkinson says:
February 9, 2012 at 12:44 pm
I agree with that. Willis Eschenbach will usually respond to a simply and clearly worded correction. I found reading this rebuttal worthwhile, but it should be abbreviated, all snark removed, and introduced with a sentence such as “We believe that you misunderstood … Let us explain thus because other readers may be similarly confused”. Willis Eschenbach does himself a disservice with his arrogant tone, in my opinion, but that’s no reason you should engage in similar self-harm.
Ned Nikolov says:
February 10, 2012 at 7:52 pm
“…The atmospheric mass determines the temperature at the surface for any given planet and amount of solar radiation received. Atmospheric mass alone cannot produce temperature. It need radiation and gravity to do that.”
Thanks Ned, this seems close to getting the idea into a single sentence!
Does this sentence work?
” The long term mean temperature at the surface of any given planet depends on the weight of it’s atmosphere and it’s distance from the sun.”
Of the many good comments above, I liked this one the best:
Harry Dale Huffman says:
February 9, 2012 at 9:09 pm
I make no claim about the overall merits of WE vs N&Z, but there is a serious problem with a derivation that depends on a nonlinear function with 4 free parameters computed from 8 data points. It is intriguing and may be useful, but the perils of overfitting must be remembered.
“The discrete set of vibration frequencies of a molecule is called its spectrum; this is both a la Kirchhoff’s Law its absorption spectrum and its emissions spectrum. If the impinging radiation had to have exactly the wavelength of the discrete spectral lines there would not be much interaction between the radiation an the molecules.
The spectrum is modified by the motion of the molecules. The Doppler effect is the modification of the perceived frequency of radiation due to the motion of the molecule. If the molecule is traveling in opposite direction from the incoming radiation the perceived frequency of the radiation is greater. Thus if radiation were slightly lower frequency than a vibration frequency of a molecule the Doppler effect could bring about a coincidence with the vibration frequency of the molecule. If a molecule were traveling in the same direction as incoming radiation the Doppler effect lowers its perceived frequency and thus could result in the absorption of radiation of a slightly higher frequency.
In effect the lines of the absorption spectrum are broadened by the Doppler effect. They are also broadened by collision frequency within a gas.”
http://www.applet-magic.com/absorptionspectra.htm
The atmospere on Venus is 70 times earth What is the absorption spectra of H2O (@100ppm) and CO2, and H2SO4 etc.
Click to access sagawa09_pressure_jqsrt.pdf
[Reply] TFP: Have you mistaken this venue for the spectrum line knitters circle? Spectra certainly need broadening, along with perspectives 🙂
Thanks Ned.
As regards iii) I was taking it as a given that radiation and gravity were present but I’m happy with your suggested alternative wording.
As regards i) I think it would be helpful to your readers to firm up on that a bit.
I was trying to get at the essential ingredient contributed by the gravitational field. I know that other factors create an environmental lapse rate which differs from the dry adiabatic lapse rate.
A weak gravitational field would seem to cause a dry adiabatic lapse rate nearer to the horizontal for a given atmospheric mass whereas a strong gravitational field would cause a lapse rate nearer to the vertical for a given atmospheric mass.
Hence my focus on the slope of the dry adiabatic lapse rate.
Whatever the atmospheric mass the gravitational field would then determine the slope of the dry adiabatic lapse rate for that particular atmospheric mass wouldn’t it ?
I’m not sure that many of us are overly concerned about the equations.
What matters most is the concepts in relation to the basic laws of physics. Either they make sense in light of observations or they don’t.
Get the concepts right so that they fit observations without offending the laws of physics and the equations can be refined subsequently.
Sadly, what I’ve just shown is that the equations make no sense at all in terms of the basic laws of physics. Seriously, show me where a characteristic pressure of 54,000 atmospheres makes sense in the description of planets where the largest surface pressure represented is less than 100 atmospheres (and where only three of the pressures are significantly distinct from 0 atmospheres). Show me where a characteristic pressure of 200 atmospheres makes any sense at all trying to describe phenomena associated with the surface pressure on Mars or Europa or Triton.
I’ve also shown — as did Willis — that there is nothing miraculous about this fit. Look at the log-log version of the fit (since it is impossible to resolve the details when the surface pressures span 15 or 16 orders of magnitude). I put it here:
You will notice that their curve doesn’t even fit the bottom three data points — the moon and mercury are completely missed, and Europa is well off the curve. They are thus “fitting” five monotonic data points with the product of two exponentials with four free parameters. The data range is so great that you cannot really see how far the points are from the curve are even so. If you look at the first (linear scale) plot you can clearly see that the Earth, Triton and Venus aren’t well fit — Venus is over the green curve and Triton and the Earth split the difference. Those errors are hard to see on the log-log plot. If you look at the log-log plot you see that it just doesn’t fit the bottom three points and sort-of fits Mars and Triton.
If you look at which exponential is predominantly fitting which part of the data, all you can do is conclude that the physics that dominates the surface temperature relative to greybody for the five light planets is completely different — I mean astoundingly different — from the physics that dominates the surface temperature for the Earth, Triton, and Venus.
At the end of the day, the N&Z curve doesn’t mean a thing. You might as well have just plotted the data and said “look, planets with a higher surface pressure are in general warmer compared to ones with a lower surface pressure” and had precisely the same informational content. N&Z equation 7 provides zero insight into why that is so — neither the characteristic pressures nor the particular exponents that they chose have any physical meaning. Why the 0.065 power (which is close to but not identical to 1/15)? Does
look like plausible physics to you (with 
measured in atmospheres, or bar if you prefer — at these scales it doesn’t matter)? The sole virtue of the huge exponent is that it makes the first exponential function nearly a straight line between the Earth and Venus, so that it becomes a nearly irrelevant factor in the independent fit of the last three points. By the same token, the second exponential is nearly basically equal to 1 for the first five points being fit.
So we take the product of a function that is 1 for small P but that varies monotonically for large P with a function that varies rapidly for small P but that is similarly monotonic and nearly constant for large P, and is it surprising that you can fit data — badly — with two nearly independent monotonic trends in widely different pressure regimes? Of course not.
rgb
thefordprefect says:
February 10, 2012 at 9:01 pm
I’m curious — do O2 and N2 have lines that get smeared out at Venusian pressures and temperatures so that they become “greenhouse gases”? Ditto general gases at e.g. Jovian or Saturnine (gas giant) pressures? Venus’ atmosphere seems likely to be more or less opaque at all wavelengths, so that all its cooling has to occur in the greenhouse layer of its atmosphere, but that’s where all the absorption has to occur as well.
Not that I care that much — Venus is clearly completely different from most other planets, the Earth in particular, in its climatological dynamics. That’s why it needed a term “all its own” in N&Z’s fit, and why the term it got has a nonphysical reference pressure in it and a double exponential form that makes little sense.
rgb
rgbatduke said:
“At the end of the day, the N&Z curve doesn’t mean a thing. You might as well have just plotted the data and said “look, planets with a higher surface pressure are in general warmer compared to ones with a lower surface pressure” and had precisely the same informational content. N&Z equation 7 provides zero insight into why that is so ”
Well, given that Venus has 95% CO2 against Earths 0.04% CO2 yet both show a similar temperature at the same atmospheric pressure subject to an adjustment for distance from the sun how does your pet theory of radiative physics dependent on GHG quantities deal with that observation ?
Apart from that I’m sure Ned and Karl have a suitable response to your more detailed points. Maybe it will be clarified in Part 2.
Tenuc says (February 10, 2012 at 8:49 pm)
Does this sentence work?
” The long term mean temperature at the surface of any given planet depends on the weight of it’s atmosphere and it’s distance from the sun.”
Yes, very close! I would suggest the following:
The long-term mean temperature at the surface of any given planet depends on its insolation and the average weight of its atmosphere above a unit area.
The term ‘insolation’ refers to the solar irradiance on top of the atmosphere, and is more accurate than ‘distance from the sun’, because when Sun’s luminosity changes such as a result of stellar evolution, the irradiance for each planet will also change for the same distance. The Sun’s brightness (radiant output) has been increasing at rate of 10% per 1.1 billion years.
N2 O2 do not radiate, They can transfer energy to molecules that can radiate GHGs
During the day near the equator the actual radiation hitting the ground from the sun is of the order of 1000w/m^2
You suggest that this + gravity heats the atmosphere and gives you your solar/gravity/atmospherical temperature
Southern Great Plains:
From this referenced document the LWIR MEASURED is 300+w/m^2 during the day (note that the peak TSI is filtered from these measurements (The AERI-ER measures downward infrared
radiance from 3.3 to 25 um (400 to 3000 cm-1) with a spectral resolution of 0.482 cm^-1)
From this referenced document the LWIR MEASURED is 200+w/m^2 during the night
Click to access LongWaveIrradianceMeas.pdf
In the arctic
From this referenced document the LWIR MEASURED is 140w/m^2 during the night and day
Click to access Marty2003_IPASRCII_JGR.pdf
You say you have allowed for the day time 1000W (and distributed it round the globe) to produce your theory – but what about the nighght time 200W/m^2 (this is constant and does not need distributing. The level falls to 140w/m^2 above the arctic circle but it is still there day and night.
This is a large error if indeed it is missed. If you do not believe in GHE where does this night time radiation come from?
My previous post pointed out a couple (out of many) research papers that suggest at 70 atmospheres the spectral line broadening of GHG absorbtion and re-radiation would be great. Couple this with temperature (motion) induced doppler broadening the trace gas h2o in venusian atmosphere, the CO2, The H2SO4, the SO2 must have a phenomenal effect on the rate that energy can leave the venusian atmosphere
rgbatduke;
Sadly, what I’ve just shown is that the equations make no sense at all in terms of the basic laws of physics.>>>
What frustrates me about discussions between academics is that they seem to have a prediliction for responses like “they made mistakes x, y and z, and so their work is refuted”.
Excuse me, but this debate is far too important for that sort of bickering. This isn’t about their work being right, or their work being wrong. It is about the portions of the work that they got right, and helping to build upon those portions. Let us start with their initial premise which is founded upon:
SB Law
Holder’s Inequality
PV=nRT
They’ve explained those concepts, and they’ve been repeated many times from many perspectives in this and other threads.
So…do those three things fit together the way N&Z claim?
If not, why not?
If yes, then a more valuable discussion regarding their math would be how to proceed from those three concepts to arrive at the proper math. Just pointing out an objection to the math they came up with is pointless in my mind. Isolate the parts that are right, and build upon them.
When the inspector discovers that the ceiling light receptacles have all been installed upside down, you don’t tackle the problem by ripping down the whole building.
Well said Hoff.
I wanted to extend the discussion regarding Willis’ contention that an “average” 240 w/m2 that resulted in a surface temperature of 288K was impossible without GHG’s, or else breaking the laws of thermodynamics. The following is a simple model that requires no calculus to follow, ir reasonably accurate, and demonstrates both Holder’s Inequality and how easily 240 w/m2 can, in fact, arrive at an “average” temperature much higher than the SB Law “average” would imply.
240 w/m2 via SB Law = 255 K.
So, let us assume a body with 0 heat capacity (so that we get an instant temperature response) and rather than a smooth curve, we’ll use a “step” function in one hour increments for insolation (because if we use a curve, I have to recall calculus long since forgotten plus we lose all the readers who don’t have a calculus background in the first place). The step function that I used is contrived to illustrate a point, but is a reasonable approximation for the tropics. I’ve started at midnight, hence the first six and last six values being zero.
Insolation SB Law T
w/m2 degrees K
0 0
0 0
0 0
0 0
0 0
0 0
100 204.9
150 226.8
350 280.3
650 327.2
800 344.6
850 349.9
850 349.9
800 344.6
650 327.2
350 280.3
150 226.8
100 204.9
0 0
0 0
0 0
0 0
0 0
0 0
This gives us the following:
average w/m2 = 241.7
“average” T = 289.0 K
I referenced 240 w/m2 above, so for the purists, 241.7 w/m2 via SB Law gives 255.5 K
And there you have it. A surface temperature driven by an “average” of 241.7 w/m2 gives an “average” blackbody temperature of 289 K, a full 33.5 K above the supposed blackbody temperature.
No GHG’s were harmed or used in any fashion in demonstrating the falsehood that insolation of 240 w/m2 cannot produce a surface temperature that is, as an “average” higher than 255K. Laws of thermodynamics were similarly unharmed.
tonybclimatereason (February 10, 2012 at 3:06 pm) wrote:
“I agree that no one has a bigger megaphone than Anthony and as such it is a shame in some ways that this thread has been diverted to Rogers excellent blog.”
On the other hand, that diversion led me here for the first time and I am totally impressed with the discussion here. I have learned a great deal and will be regularly following this blog in the future.
So we have contradictory maths and associated derivations according to at least three authors:
• N & Z
• Willis
• Robert Brown
Against my principles, I had a quick look over at RC, and I was surprised that a site search for Nikolov drew a blank.
Whatever, the controversy over the maths is I think something that won’t go away. Those that refuse to consider the theory, will likely attack the maths ad nauseam and achieve success where they want it. The final paper surely needs to be reconstructed such that there is less dependence on the maths.
thefordprefect;
This is a large error if indeed it is missed. If you do not believe in GHE where does this night time radiation come from?>>>
GHE could not possibly account for all of the effects that you reffered to. GHE is one of many factors that result in the number to which you refer. Others are heat capacity, convection, conduction, and so on.
Bob Fernley-Jones;
Against my principles, I had a quick look over at RC, and I was surprised that a site search for Nikolov drew a blank.>>>
They’re terrified of it. Even if they were to try and knock it down, by acknowledging it, they’d have to come to grips with both Holder’s Inequality and PV=nRT. They can’t knock it down without those factors coming into play, so they pretend that it doesn’t exist, and hope that it doesn’t get enough traction elsewhere to become a threat.
And, sadly, they are being aided and abbeted on that by the loudest megaphone in the debate.
davidmhoffer says: February 11, 2012 at 12:16 am
GHE could not possibly account for all of the effects that you reffered to. GHE is one of many factors that result in the number to which you refer. Others are heat capacity, convection, conduction, and so on.
========
1kW/m^2 is tsi less the cloud reflection.
all the others are measured with devices only sensitive to LWIR (other than one which was only used at night to remove the effect of SW solar) – heat capacity, convection, conduction are not relevant in this unless you can explain how these methods of heat transfer can be collected via a radiation measuring device.
The night LWIR received by these UPWARD pointing devices can only come from GHGs. (plus a insignificant amount from rotational “vibration” of O2 N2 molecules).
Where is this visible in any of N-Zs calculations?
Please explain where this night time IR is coming from if not from a GHG.
Thanks
[co-mod: Sure it is there. Now show the data for DOWNWARD pointing devices. Hint, nightside temperature inversions are normal including over the sea. I think you will find this is atmospheric coupling which is cooling when conduction and scour are failing. Is it forward or reverse at night? There is much more.
–Tim]
All,
I received private correspondence from Joel Shore pointing out to me that I had the wrong average temperature in my step model upthread. He blamed it on me dividing by 24. I checked my spreadsheet, and he’s right, for the wrong reason. In fact, I did divide by 24, by I also inadvertantly included subtotals with the grand total, doubling the total before I divided by 24. So, the correct numbers should have been:
Insolation: 241.7 w/m2
“average” T = 144.5K
So, while Joel is correct that I screwed up the math, as I commented before, take the stuff that is right and build upon it.
This is, in fact, an excellent demonstration of Holder’s Inequality. While it went the opposite direction that I thought at first blush, the fact of the matter is that 240 w/m2 does NOT in fact result in a an “average” surface temperature of 255K. Not even close.
I’ll jump into how “average” surface temp gets to 288K via Holder inthe AM.
Bob Fernley-Jones says (February 11, 2012 at 12:11 am):
So we have contradictory maths and associated derivations according to at least three authors:
• N & Z
• Willis
• Robert Brown
Whatever, the controversy over the maths is I think something that won’t go away. Those that refuse to consider the theory, will likely attack the maths ad nauseam and achieve success where they want it. The final paper surely needs to be reconstructed such that there is less dependence on the maths.
What contradictory math? The fact that some folks have ‘opinions’ that are mute, does not mean that math is contradictory. The math is very simple and clear! I have intentionally not replied to Dr. Brown, because he has no point and fails, like Willis, to see the big picture, which is blatantly obvious. Please, read the section in our paper above called “Focusing on the Big Picture”, because I do not plan to repeat again what we already explained in plain English!
And please do not cite Willis as if he is some kind of authority figure. He is math illiterate, and we have proven it crystal clear in our reply to his essay here…. What’s amazing to me is how easily adult folks get distracted (like children), because someone had expressed some groundless opinion and their whole attention shifts towards trying to ‘reconcile’ his/her fractionated opinion with the main theme … Try to not loose sight of the ‘new forest’ for the little trees and ants in it! … 🙂
About the RC website – I agree that they are strangely silent about the discussions on this blog and others.
However, here is a little real-life story that might explain their lack of response….
Gavin Schmidt and Kevin Trenberth came to see our poster at the WCRP Open Science Conference in Denver on Oct. 24 last year, where we presented our results publicly for the first time. They were amused by the title “Unified Theory of Climate”. With a smile on their faces they commented that this was quite an ambitious title, and asked me what kind of a new theory we claim to have. I responded “Well, it’s a new concept about the GH effect”. … “Oh really!”, they exclaimed, “What’s new about it?”. … “Have you heard about the Gas Law?”, I asked. “Yeah, we know about the Gas Law”, said Gavin with an even bigger smile, “What about it?” …”Well”, I said, “We provide evidence using planetary data that the GH effect is in fact a Pressure-induced Thermal Enhancement that’s independent of atmospheric composition” … Their smiles vanished in an instant! Gavin’s jaw literally dropped, he made a big long face, then they said something like “Well, good luck with that”, and quickly moved away… I though this was an interesting reaction … 🙂
Ned,
I pointed out that there are at least three different versions of the maths floating around, and to expand on that, IMO this is a serious problem POLITICALLY, and maybe even if you try for publication in a peer reviewed journal. (oh, and I’m on your side BTW). I agree with you about Willis’ incompetence, and could give you some additional examples, however that is not relevant to my concern, and what I think should be yours. The point is that Willis is a generator of very high traffic at WUWT, and he has a big following there. (which I suspect is why Anthony is so supportive of him, and influenced, by his “expert advice”). There is also WUWT’s rising star; Robert Brown, whom might influence other physicists, but covertly may not agree with Willis.
IMO, much though you like your mathematical derivations, I don’t think that you can win the political war unless you have more convincing empirical data from lab tests.
Did you see my suggestion that maybe there is a potential “ninth planet” if you look at geothermal energy at higher atmospheric pressure down deep mines? Lucy Skywalker probably has collated most stuff on it including lapse rates.
Dave Springer says:
February 10, 2012 at 1:53 pm
////////////////////////////////////////////////////////
The atmosphere is not comparable with an open vessel. The atmosphere is restrained by gravity. If for example, the Earth was the same size but had just 100th of the mass, we would not now have an atmosphere. The fact that we do have an atmosphere is proof that it is restrained and therefore not wholly analagous to an open system.
The atmosphere is constantly being flexed due to the interaction with other celestrial bodies, including being pushed from the bottom up with the ebb and flow of the tides. This flexing of the atmosphere (the flexing taking place within the broad bounds imposed by the gravitational restraint) inevitably inputs heat into the atmosphere. Whether the effect is large or not, is entirely a different matter.
,
“I don’t think that you can win the political war unless you have more convincing empirical data from lab tests.”
The political war can be ‘won’ by emphasising the settled science of the Gas Laws such that the composition of the atmosphere becomes irrelevant to surface temperature.
As soon as one can involve Oxygen, Nitrogen and indeed the water in the oceans in the process of setting system energy content then all GHGs let alone our pitiful contribution become irrelevant.
One doesn’t even have to discredit the so called radiative theory of GHGs to achieve that. Just put it into perspective as a complete irrelevance whether it is correct or not.
Politicians are starting to see the impracticalities of the economics of reducing fossil fuel dependence before the alternative energy production methods have matured sufficiently. Lots of them will soon see more votes in strangling the AGW approach than impoverishing their citizens.
Political fashions come and go and AGW is past the peak.
Ned Nikolov says:
February 10, 2012 at 5:47 pm
2) You are correct that numerically, the adiabatic lapse rate (which is the backbone for the environmental lapse rate) is given by dT/dz = -g/Cp (gravity divided by the specific heat of air at constant pressure). However, this formula conceals the effect of pressure in the following way. The adiabatic lapse rate is a product of two other rates – the temperature change with pressure and the pressure change with height, i.e. dT/dz = (dT/dP)*(dP/dz). In turn, dT/dP is derived from the Gas Law, where dT/dP = 1/(ρ*Cp) and ρ is air density, while the other rate is based on the assumption for hydrostatic equilibrium, which yields dP/dz = -g*ρ. In other words, it is the vertical pressure gradient that is ultimately responsible for the existence of the lapse rate in the troposphere. If we had dP/dz = 0, there would be no lapse rate, and the atmosphere would be isothermal in the vertical.
No ρ(z)*T(z) would be constant, if the atmosphere were isothermal then you have a constant density with height, not very likely in a gravitational field. More likely a declining density with height with a corresponding increase in temperature with height, i.e. an atmosphere heated from above.
3) Our model for calculating the planetary gray-body temperature is CORRECT,
For a planet with no surface heat capacity.
and the Moon temperature measurements prove that (see our Reply Part 1).
Even the moon shows that your model isn’t a very good one for a real planet.
Your model gives the lowest average surface temperature for a radiationally heated planet.
The standard application of the SB equation to a sphere is mathematically wrong,
No it’s correct for a radiationally heated planet with a uniform temperature which gives the highest average surface temperature, a much better model for the Earth than yours, reality lies between the two.
and as a result of that, the emission temperatures calculated from it are NOT physically compatible with any measured palatable temperatures on the surface of an airless body. Emission temperatures are a mathematical construct, not a physical reality!
No more so than those calculated using your model, unless the planet has zero surface heat capacity of course.
Davidmhoffer:
With respect to your reference of the ideal gas law, PV=nRT . Take a insulated column of gas, with temperature T, far away from gravitating bodies and accelerate it to one g. The whole column would have the same number of moles, n, but will stratify by compression with different number of moles of gas in each equal volume stratum, with the greatest density per compressed volume at the bottom of the column and the least at the top. A volume of gas at the bottom will have a higher temperature due to compression than a like volume at the top of the column. The acceleration redistributes the kinetic energy towards the bottom of the column by moving gas molecules toward the bottom. The total volume of the column is unchanged due to the kinetic energy of the gas molecules, just the densities are changed in the strata along the column and thus the number of moles of gas per stratum increase toward the bottom of the column. Does the ratio P / n in PV / n = RT increase for equal volume strata along the column of gas? Since the equal volumes would have increasing number of moles of gas with increasing pressure, the pressure in a stratum would have to increase faster than the number of moles of gas in a stratum if the temperature is to increase. It would seem that the temperature increase would be due to the accelerating force on the column, as it would be due to gravity in the case of a planet atmosphere. The lapse rate then is due to compressive work by gravity with convection from any input heat energy doing work expanding and raising gas against gravity. If the column was an open system with only accelerated or gravitational energy input, the gas would radiate and cool until it liquified removing the lapse rate.
“The atmosphere is restrained by gravity”
Of course it is, but it is only restrained and not constrained so volume changes readily with any change in energy content.
It’s the big picture that matters, not the minutiae of the equations.
AGW theory relies on hiding the significance for system energy content of Oxygen, Nitrogen and water in the form of both vapour and liquid and a denial of the implications of the Gas Laws.
All else is chaff. It has taken hold for political reasons rather than scientific reasons. When the western world was prosperous an indulgence in the emotional pull of being strongly environmentally concerned was very powerful. Now, not so much, if at all. A new sense of perspective is required with a more practical balance between development and environmental awareness.
Especially when one observes that it is the developed nations that are kinder to their local environments and that the environmental damage and resource wastage involved in current designs of wind and solar power paraphernalia is worse than that of efficiently produced energy from fossil fuels or nuclear power.
It is no coincidence that only the so called ‘rich’ nations developed that pathology.
We are probably pushing at an open door.
Anyway, back to the science.
thefordprefect;
Please explain where this night time IR is coming from if not from a GHG.>>>
It does come from a GHG. So what?
There are a variety of mechanisms that move energy about the planet. GHG’s are amongst them. Yes, you can measure given IR and conclude that it was emitted by GHG’s. The question is not if the IR was emitted by GHG’s. The question is, if the GHG’s were not present, what would be different?
The answer is that unless the absence of the GHG’s changes the amount of energy absorbed in the first place, then the amount of energy emitted doesn’t change either. That being the case, T doesn’t change. What changes is where and how the energy escapes to space. If there is less IR emitted from GHG’s, then to establish equilibrium, there most be more emitted by something else. Its like one of those long balloon the clowns use to make animal shapes with. Squeeze it in the middle, the ends get longer. Squeeze is at one end, the other end gets longer. Squeeze it ANYWHERE and the air just moves to someplace else in the balloon. But the amount of air in the balloon stays exactly the same.
Again, would the absence of GHG’s (or doubling them for that matter) change the amount of energy absorbed by the system in the first place? Unless you can show that the answer to that is “yes” then there is no possible way for T to change.
“If you do not believe in GHE where does this night time radiation come from?”
Warm water, warm ground, warm water vapour, warm Oxygen and Nitrogen conducting to and from the ground and to each other. And yes a miniscule fraction from non condensing GHGs (which are also emitting energy straight out to space faster than could be achieved by other mechanisms).
Conduction, convection, evaporation and lateral winds around the world.
Open your eyes and your mind.
Get used to it. N & Z and many others are right. Perfect mathematical precision will follow in due course assuming they aren’t already there.
Bob Fernley-Jones says (February 11, 2012 at 3:56 am):
I get your point! However, we are talking here science and math, not politics. The laws of math and physics cannot be bent by politics … It’s unwise to think that way!
Here is the simple fact: We have found, using empirical data across a broad range of planetary environments, that there is a very tight relationship between the RELATIVE thermal enhancement NTE and pressure. We have derived an EMPIRICAL relationship that is highly significant due to of its close resemblance in shape to the Poisson formula (Fig. 5 in our original paper) and because of its general theoretical support by the Gas Law. This relationship incorporates the effect of cloud albedo and a number of other climate factors operating in the context of the ENTIRE planet. Hence, it is not something that one would expect to observe in a laboratory. In that sense, it is a new higher-order relationship rooted in the Gas Law, but not yet fully understood in terms of “first principles“! …
The fact that the regression coefficients cannot be easily cast into known quantities of the Gas Law (known from simple Lab observations) does not mean that the relationship is meaningless! It’s VERY REAL because: (1) it’s based on ACTUAL planetary data; and (2) there are no other variables that can describe the atmospheric thermal effect as accurately as Eq. 7 be it GH gases, radiative fluxes or whatever, none! … A tight relationship as the one displayed in Fig. 5 of our first paper CANNOT happen by accident.. It has solid underlying physics that we may not understand in all the details yet (since it’s on a planetary scale), but this does not mean and should not be interpreted as a reason to discard it … There is currently no other single mechanism in climate science that can describe so beautifully and with such precision the average surface temperature on so many diverse celestial bodies! The present GH concept does not even come close to that!
So, discussing how many coefficients or exponents there are in the regression equation and trying to explain them with known laboratory concepts is simply missing the point! And the point is that there IS a strong relationship! That is why I maintain that Dr. Brown’s analysis is completely irrelevant. The inability to explain the constants with known to him simple physical quantities does NOT negate the relationship itself …
About ‘leaders’ like Willis, it’s truly pathetic! Why should we pay attention in a science debate to people with absolutely no science education, who demonstrate total ignorance about basic math, and on top of that have a huge ego. How can those types of people solve anything that eventually boils down to science? … When you are building a house, would you call a climate scientist to draw your plans and execute the construction? I suppose, not! Then why would you rely on a construction manager to solve the climate issue? It makes no sense, doesn’t?
🙂
Ned Nikolov;
What contradictory math? The fact that some folks have ‘opinions’ that are mute, does not mean that math is contradictory. The math is very simple and clear!>>>>
Stephen Wilde and Bob Fernley-Jones and others are giving you good solid advice on this Ned. The math is NOT simple for the vast bulk of people who are reading your articles and comments. There is a limit to how simple you can make the math and the explanation without actually presenting the physics properly, I understand that. But it isn’t a few elite physicists that need to be convinced. It is the average person who has bothered to take an interest in the climate debate.
Dismissing Willis out of hand because you’ve thoroughly debunked him is winning the battle at the expense of the war. Winning the war requires, not convincing Willis that he is wrong, but convincing the thousands of readers who hang on his every word that he is wrong. There are only two ways to do that:
1. debunk each and every mistake he makes, until he caves and admits his mistakes, or
2. debunk each and every mistake he makes until even his most ardent supporters abandon his position.
These require that your rebuttals be factual and accurate, but also, to the extent possible, understandable by the layman. Substitute Robert Brown for Willis, same answer. etc etc.
Ned Nikolov;
I get your point! However, we are talking here science and math, not politics. The laws of math and physics cannot be bent by politics … It’s unwise to think that way!>>>
Sorry Ned, but the reality is that you are wrong. Politics bends math, physics, economics, and reality itself. History is replete with examples of exactly that. If you do not learn the lessons that history has to offer, you are condemned by your own hand to repeat the history.
It matters not that Willis is a construction manager. The only thing that matters is that there are an awful lot of people who believe you are wrong because he said so. Pointing out that he is a construction manager has no more value in winning the argument with him than Phil Jones insisting you are wrong because you aren’t a climate scientist, you’re only a physicist.
As one of the many lay people who have been following this debate from its inception, I found the following exchange illuminating. I am quoting in full because I think it is important:
“Ned Nikolov says, February 10, 2012 at 10:01 pm:
Tenuc says (February 10, 2012 at 8:49 pm):
Does this sentence work?
” The long term mean temperature at the surface of any given planet depends on the weight of it’s atmosphere and it’s distance from the sun.”
Yes, very close! I would suggest the following:
The long-term mean temperature at the surface of any given planet depends on its insolation and the average weight of its atmosphere above a unit area.
The term ‘insolation’ refers to the solar irradiance on top of the atmosphere, and is more accurate than ‘distance from the sun’, because when Sun’s luminosity changes such as a result of stellar evolution, the irradiance for each planet will also change for the same distance. The Sun’s brightness (radiant output) has been increasing at rate of 10% per 1.1 billion years.”
Could any of the physicists populating this thread tell me and all other lay people why this statement is unacceptable, wrong, to be rejected – and why?
Because to me, it makes eminent sense.
David,
We said this in the conclusion of our reply, and I’ll repeat it again:
“We are here to discuss and offer a resolution to the current climate science debacle and welcome everyone who shares that goal. We are not here to promote or engage in endless circular talks or teach laymen ‘skeptics’ basic math and high-school level physics. Hence, we will no longer participate in dialogs of the kind that prompted this reply. We urge all sound thinking readers to do the same.”
So, we will not waste any more time with characters such as Willis and his ‘followers’. You are welcome to do it if you’d like, but that’s not our game, sorry! Enough on this topic, please …
Ned
It occurs me that in essence what you are saying in simple terms is that the gas laws should not be used in the ideal gas form and that your pressure induced enhancement is essentially the adjustment that should be made for non-ideality. Or is it something else that can be attributed to pressure. Rgds Terry
Ned Nikolov;
So, we will not waste any more time with characters such as Willis and his ‘followers’. You are welcome to do it if you’d like, but that’s not our game, sorry! Enough on this topic, please …>>>
Yes Ned, you said that. But you didn’t do what you said. 200+ comments downthread you are still making disparaging remarks about Willis and others. If you want to be done with this topic, then be done with it, and stop taking pot shots at him. If you take pot shots at him, be prepared to defend them. If you don’t want to contend with cirticism regarding how you are dealing with him, then stop taking pot shots.
And I, and others ARE in fact dealing with him because we are trying to win the war and we recognize that he is one of the most important writers there is for the skeptic side on earth. We don’t want to beat him to death, we want to bring him, and his “followers” on side. We want to win the war and bury the CAGW meme for good.
If you don’t want to deal with the guy, then don’t. But don’t make it harder for the rest of us (who are supporting you) to take up that task on your behalf.
Ned Nikolov @ February 11, 2:14 am
Ned,
Further to various comments above on POLITICS, and the reality of its importance in science…… for instance, the emphasis on funding of “climate research” and the bias in the media etc. The semantics of the word POLITICAL includes religiosity and other fringe stuff like various alleged Armageddon future scenarios caused by mankind. (and a propensity for many people to gorge on such alleged impending disasters, and the ability of loud minorities to have great influence). I regard the catastrophic AGW alarmists as belonging to a church, and it is interesting that in history, various scientific innovators did fall victims to the Christian Church. There is so much stuff that I could elaborate, such as in the Climategate 1 & 2 Emails, but please concentrate on producing a paper that can be comprehended by policy makers. (including politicians) I think that requires convincing empirical lab results.
It might surprise you that me, a retired managerial engineer in my seventies, whilst I think I still retain a good scientific analytical mind, have made no attempt to follow your maths. It is enough for me to think that your big picture is credible, whilst eagerly awaiting your part 2. There is really no hope that the people who actually matter in the war will have a slightest clue about your maths, and will happily accept contrary claims from the church “disproving” your maths. I respect your scientific purism, but frankly I think it seems to be naïve in the reality of the political world out there. (and I’m on your side)
PLEASE DO NOT IGNORE THE POLITICS, OR POSSIBLE DIFFICULTY TO PASS PEER REVIEW ON THE MATHS. (depending on the referees, and sorry for shouting)
I know you may find this a hurtful suggestion, but I strongly think you should use your maths as a supporting thing to less disputable lab work.
Just some thoughts…
Beer–Lambert–Bouguer law in the atmosphere:
http://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law
Nikolov & Zeller Unified Theory of Climate equation 7 (substituted):
(tau in this case is not the exact form of optical thickness and Ts and Tgb could easily be radation but to the fourth power, as Fs/Fgb so it would then belong under the radical below)
I see very little difference in the general form of the equations between the two. I suppose Dr. Robert Brown,
supposedlya physicist from the department at Duke University, would have little problem at also tearing apart the Beer–Lambert–Bouguer law in like manner as he just attempted to N&Z’s equation 7 being with the same form.I don’t know… the more I look into it, the more those two terms in Nte do seem to be optical in nature. The only correction I might see is k1 & k3 just might need the proper units to make these two terms optical thicknesses much as the Beer–Lambert law states. If this the case the Nte would have to take on the fourth power to become a member of the flux term:
![\large Ts=\frac{2}{5} \sqrt[4]{\left [ \frac{(1-\alpha _{gb})}{\epsilon \sigma } \right ](S_0 + c_s) N_{TE}}](https://s0.wp.com/latex.php?latex=%5Clarge+Ts%3D%5Cfrac%7B2%7D%7B5%7D+%5Csqrt%5B4%5D%7B%5Cleft+%5B+%5Cfrac%7B%281-%5Calpha+_%7Bgb%7D%29%7D%7B%5Cepsilon+%5Csigma+%7D+%5Cright+%5D%28S_0+%2B+c_s%29+N_%7BTE%7D%7D&bg=f9f9f9&fg=333333&s=0&c=20201002)
… or something similar. One difference is the air mass term is embedded within the Ps pressure terms themselves. It will be interesting to see the final form this relationship might take.
davidmhoffer says:
February 10, 2012 at 11:38 pm
I sometimes come across obscure papers (obscure to me) in my research work. The below linked paper will be of interest to you.
The paper is heavy with calculus, but there is no avoiding that when calculating the planets greenhouse effect.
This paper disects, from go to whoa, the work of authors that the IPCC relies on for their greenhouse effect hypothesis, namely Ramaswamy, Trenberth, Schneider & Mass, and Budyko.
http://arxiv.org/abs/1002.0883
Not paywalled. Enjoy it, I’m sure you will.
regards
p.s. the authors have a 2nd comprehensive paper that I can link to if you’re interested.
Ned Nikolov says:
February 11, 2012 at 5:00 am
“I get your point! However, we are talking here science and math, not politics. The laws of math and physics cannot be bent by politics … It’s unwise to think that way!”
May I suggest that NNs’ phase would be less confrontational by changing “cannot” to “should not” because science and maths have always been bent by politicians to suit their agendas. I am reminded of Lysenkoism.
From 1934 to 1940, under Lysenko’s admonitions and with Stalin’s approval, many geneticists were executed (including Isaak Agol, Solomon Levit, Grigorii Levitskii, Georgii Karpechenko and Georgii Nadson) or sent to labor camps. The famous Soviet geneticist Nikolai Vavilov was arrested in 1940 and died in prison in 1943.
http://www.skepdic.com/lysenko.html
http://en.wikipedia.org/wiki/Lysenkoism#Repercussions
Just a thought.
Back near the start of this thread I commented that I decided to ‘let the politics, the science and the bitchin’ mix up together rather than separating them (which would have been a moderation headache anyway). On the whole this has turned out well, with scientific discussion predominating, and most political comment has been kept general and non-personal.
Ned has mostly been answering science points and we thank him for his willingness to spend time here giving freely of his science expertise. By the same token, he needs to take to heart the expertise offered to him in a genuine and friendly way by contributors such as David Hoffer on this thread and David Socrates on others wrt matters pertaining to the social aspects of science.
There has been a clash of strong personalities, and misunderstandings have arisen due not only to misinterpretation of scientific content, but also because of the fact that those strong personalities use styles and humour foreign to each other. People who consider these matters more deeply make allowances for those differences, but the majority do not, and deep division can be engendered unnecessarily.
There is the wider picture to consider, not only in Ned and Karl’s theory, which they rightly emphasise, but also across the breadth of the community, with it’s many different strands of approach to a wide variety of subject matter. Finding the way to successfully communicate the concepts and fit Ned and Karl’s findings into that wider picture is as important a challenge as their upcoming more narrowly focussed quest to get their technical papers through peer review and into the scientific literature.
It’s a big task that requires a team effort, and alienating potential peer reviewers by, for example, making injudicious jokes about their nationality won’t help. Those reviewers will in all likelihood ask exactly the sort of questions Robert Brown has about the physics underlying the constants used to generate the regression curve. So whether or not the importance of such concerns should be downgraded by weighing them against the explanatory power of the bigger picture, Ned and Karl will need to have an answer ready which will satisfy them.
Whatever the stance adopted by other blogs, here at the Talkshop we are happy to provide a venue for the ongoing social and layman-technical side of discussion and a point of publication for Ned and Karl’s ‘for general release’ papers.
All I ask is that that discussion is courteous, measured and considerate of the wider community.
Roll on ‘Reply to Comments on the UTC part 2’ !
I think it might be as well to split the issue into two:
i) It seems to me that the Ideal Gas Law does a pretty good job of explaining why a planet with an atmosphere is warmer than one without. AGW theory is demolished by that alone because the Ideal Gas Law involves every molecule in the atmosphere whether a GHG or not so the AGW reliance on GHGs becomes irrelevant in quantitative terms. The fact is that all that Oxygen and Nitrogen do reach an ambient temperature at the surface which is similar to that of the surface and bleating about their lack of radiative absorption capability does nothing to change that fact. They would still reach that ambient temperature with no GHGs in the air at all due to their contact with the irradiated surface and subsequent convection with planetwide lateral winds on a rotating planet under a single sun.
ii) Then there is the separate issue of Ned and Karl’s ATE. I am inclined to accept their contention that they have added something useful to the long established concepts of the Standard Atmosphere and the Adiabatic Lapse Rate as implicit in the Ideal Gas Law. As I said above, their act of more clearly identifying and describing that thermal enhancement at the surface opens the way to a more intuitive linkage to the wider range of climate phenomena.
What I see happening here is that those who do not accept ii) are evading the implications of i).
Whether or not N & Z can establish that they have progressed the basic science there is still a severe challenge to AGW theory just by virtue of the Gas Laws which seem to have been ignored by that so called consensus for the past 20 years.
How does Robert Brown, for one, justify his ignoring of the Gas Laws ?
http://gravatar.com/davidmhoffer
GHE could not possibly account for all of the effects that you reffered to. GHE is one of many factors that result in the number to which you refer. Others are heat capacity, convection, conduction, and so on.
================================
It does appear in a non GHG world that at night, sans insolation, all the mass of atmosphere containing specific heat could only lose that heat via conduction to the ground, then radiation. Any ideas on how to compare, for instance, how long does it take the non ghg specific heat at 1000m to conduct it energy to the ground, and for that energy ( the portion which does not inturn conduct back to the atmosphere) to radiate to space, verses GHG energy at 1000 m radiating same energy.
davidmhoffer says:
February 11, 2012 at 5:10 am
—————————————–
Well put David. Ned and Carl are in a post normal world, weather the wish it or not. Nothing is more post normal then CAGW, with thousands of politicians and billions of dollars , and POWER galore, all riding on CAGW. They, or their champions, will have to, in an egoless manner, answer the same questions over and over, always working to avoid snark. (When bucking a trend of prejudice it takes the even minded patience of a Jackie Robinson to make headway), Right or wrong, the only way to keep focus on the science, is to stick to it only, and remove all ego. Not easy, but very admirable if achieved.
davidmhoffer says:
February 11, 2012 at 6:58 am
(to Ned Nikolov)
“If you don’t want to contend with criticism regarding how you are dealing with him, then stop taking pot shots.
And I, and others ARE in fact dealing with him because we are trying to win the war and we recognize that he is one of the most important writers there is for the skeptic side on earth.”
The fact is dmh, that your dominant presence on TB’s blog is similar to WE’s on WUWT, and you and Willis probably share much the same cultural and social background. Could that be why you are empathising with him? I agree with a lot of what you say on other issues, but you should not presume to tell Ned how to deal with this issue and risk insulting him in the process.
It gets back to what I said about the climate blogosphere bubble. If you genuinely believe that WE is so important in the scheme of things, which has me gob-smacked, my suggestion is that you should step back and try to take in a wider perspective. The best thing we CAGW opponents can do imo is to support people like Ned and Karl, not alienate them. Ultimately the scientific truth must prevail, because as Stephen Wilde said the meme is already fading. Reality bites and the politicians, acting in self-interest as they always do, will not ignore an increasingly annoyed populace.
So Dr Nikolov, if you have been offended, please do not disengage from your interaction here. I am grateful for it, as I would think are many others. The climate debacle cannot be resolved without genuine scientists like yourself who are committed to establishing the truth. Many thanks!
I do not know enough physics to follow NZ but I find their willingness to defend their theory in layman’s language impressive. As a maths graduate myself, I find Dr. Nikolov’s comments about Willis Eschenbach far too harsh. He may not have retained as much maths as Dr. Nikolov and, like us all, he is certainly open to making mistakes but he is far from being “total ignoran[t] about basic math.”
Perhaps if Dr. Nicolov was not so rude about Mr. Eschenbach, Anthony Watts would have hosted NZ on WUWT rather than offer it to this site. Had Anthony done so, Mr. Eschenbach would have been obliged either to admit his mistake or to explain why he was not mistaken. Having followed this thread and, in the absence of any attempted rebuttal by Mr. Eschenbach, I accept that NZ have produced an original and feasible theory. Because there has been no response from Mr. Eschenbach I will now, unfortunately, view all his postings with suspicion.
[Reply] Mr. Eschenbach won’t be replying here. Whether he will elsewhere is up to him. I suspect he may have ‘moved on’, but time will tell.
I’m not so sure that we’re in a post normal world. I’m reminded of Columbus who had to go on bended knee to plead for funding (with the politicians of the day, royalty) to go on his voyage to prove that the earth wasn’t flat. While this was widely suspected at the time it was not proven by anyone. He subsequently ‘proved’ it (to the satisfaction of the funders) by only getting half way round.
He discovered India was actually in the Caribbean basin. Who knew?
Any science that ever ‘moved’ the world had political roots, some of it even proved lethal to the scientists involved. All of it had rocky beginnings. It’s the nature of the beast. The only difference today is that all the sausage making has gone public.
Baa Humbug;
Wow, that is some paper!
I was going to build a step function type model this morning to show how Holder’s Inequality plus heat capacity plus a couple of other factors arrive at a global temperature of 288K without the need for GHG’s, but I got distracted by the paper linked to by Baa Humbug upthread. Here is the direct link:
Click to access 1002.0883.pdf
How this paper failed to get more attention than it has is beyond me. N&Z, I recommend you have a look! Actually, I recommend everyone have a look, though I have to say that Baa Humbug is right about the math in this paper, it is daunting.
That said, they use ,multiple mathematical approaches to calculate the effective equilibrium temperature of the earth, and come up with 288K. But I like the money quote from their summary the best:
“However, for realistic empirical
data, also these results do not support the existence of the so-called greenhouse effect.
Nevertheless, with exception of the non-existing effect of the infrared radiation reflected back by
the atmosphere, Dines-type two-layer energy balance models are still the basis for global annual
mean Earth’s energy budgets as recently published by Trenberth et al. [27].
Based on our findings we may conclude that it is time to acknowledge that the principles
on which global energy balance climate models like that of Schneider and Mass [2] or that of
Dines [58] are based have serious physical shortcomings and should not further use to study
feedback mechanisms, transient climate response, and the so-called atmospheric greenhouse
effect.”
To All
I agree with Tallbloke’s comments and general appeal. I apologize if some of my remarks may have left the wrong impression, but I made them in a lighthearted way and with absolutely no intent to offend anyone personally. The truth is that I enjoy this blog the most for its higher level of rationality and commonsense compared to others…. I do understand the importance of politics and its oftentimes unjustified ‘power’ over science. In the long run, however, politics have to align with reality simply because the latter puts solid boundaries on the former … For example, I think it’s quite possible that the current GH concept and its supporting multi-billion Dollar political machine might disintegrate on their own over the next 10-20 years even without a sensible new theory such as ours, simply because the climate will get colder as a result of declining solar magnetic activity and the resulting increase in global cloud cover… The Earth has been warming for about 350 years and we are now at the peak of one of those cycles (there have been about 10 of them in the last 10,500 years). Global temperature varies with an amplitude of 1.0 – 1.4C between peaks and troughs of these cycles. This may not seem much, but it’s enough to cause significant disruption in crop production and food supply. So, we are now headed towards the downward slope in one of those cycles after experiencing a plateau in global temperature over the past 12 years… So, the physical climate system will eventually force our thinking onto the right path weather we enjoy it or not …. 🙂
Ned, you’re right too. We can argue about how many photons can dance on the top of a co2 molecule forever, but Mother Nature will tell us more about what really drives the climate system soon enough!
Ned Nikolov
In my article ‘the long slow thaw’ I compared the reconstructions of Dr Mann and Hubert Lamb and carried out my own to the year 1538
As I continually say, and you seem to agree, the world has been warming for around 350/370 years. This needs to be explained by climate science but never seems to be addressed.
However, there are some parts of the world that have been operating in a counter cyclical fashion and have been cooling for a statistically meaningful length of time of at least 30 years, and some areas since around 1880. They also need to be explained. The IPCC and the Met office completely ignore them
I am enjoying the discussion which, as you say, is at a high level
tonyb
I wanted to avoid talking about the politics but maybe some comments might help.
People employ different learning strategies and we see them all displayed in the comments. These include paraphrasing what has already being said, checking detail (nit-picking), aggressive challenging, etc. Most of the commenters are genuinely concerned with the learning process and because they are grappling with a new idea that clashes with the old mindset, it is inevitable that many comments or questions are irrelevent or just wrong.
However each reply has to be patient, courteous and display an effort to give an even better explanation than the last time. Here is the reason – especially on a site like WUWT, for every comment there may be hundreds or perhaps thousands of onlookers ranging from experts to journalists, politicians and amateurs. They are keen to learn from others. They will follow every thread and form their judgements based on the quality of the replies.
When you are on a project to change the world’s understanding of climate science, you need to have regard for the wider audience. You also need to get the agenda setting or influential commenters on your side. That is important, because they have the power to shut you down. I would suggest that the exercise so far has failed, but with some effort, the losses can be retrieved. I wish you luck.
tonybclimatereason says:
February 11, 2012 at 4:40 pm
In fact there is a paper that addresses this.
On the recovery from the Little Ice Age. Syun-Ichi Akasofu
ABSTRACT:
A number of published papers and openly available data on sea level changes, glacier retreat, freezing/break-up dates of rivers, sea ice retreat, tree-ring observations, ice cores and changes of the cosmic-ray intensity, from the year 1000 to the present, are studied to examine how the Earth has recovered from the Little Ice Age (LIA). We learn that the recovery from the LIA has proceeded continuously, roughly in a linear manner, from 1800-1850 to the present. The rate of the recovery in terms of temperature is about 0.5°C/100 years and thus it has important implications for understanding the present global warming. It is suggested on the basis of a much longer period covering that the Earth is still in the process of recovery from the LIA; there is no sign to indicate the end of the recovery before 1900. Cosmic-ray intensity data show that solar activity was related to both the LIA and its recovery. The multi-decadal oscillation of a period of 50 to 60 years was superposed on the linear change; it peaked in 1940 and 2000, causing the halting of warming temporarily after 2000. These changes are natural changes, and in order to determine the contribution of the manmade greenhouse effect, there is an urgent need to identify them correctly and accurately and remove them.
The above is from my own pdf copy. Would you like me to locate the full paper on line for you?
regards
Tony B: I can’t find the URL, but I saw an interesting animation of a reconstruction of the geomagnetic field from the mid 1500’s. It seems to me that there was a shift in magnetic field strength from Africa to South America over the period. Glancing at the country by country seasonal temperature maps liberated from the CRU, it occurred to me that those countervailing examples may correlate with these centennial shifts in geomagnetism. It’s another layer of complexity in the climate jigsaw.
The ~974yr cycle of angular momentum within the solar system may be correlated with the up and down see-saw between Roman warmth: dark ages cold : Medieval warmth: Little Ice Age and Modern warm period. As Ned says,1.5K or so isn’t much in absolute terms, a mere 0.5%. Given that the Sun is known to fluctuate around 0.1% over the 11 year cycle, I can easily see a 0.2% fluctuation over hundreds of years being possible. There are viable amplification mechanisms involving cloud albedo too, so I think explaining the magnitude of climate change with solar variation is well within our grasp.
Yes please if anyone can find/link to that article.
I was however thinking of the warming in a broader context, in as much our temperature snapshots from Hadley in 1850 and Giss in 1880 show an upward trend, but it is merely the end portion of the warming trend and not the start of it.
Having spoken to a politician recently who was still utterly convinced by the hockey stick warming since 1900 they could not (would not?) comprehend the idea that they were just looking at a tiny portion of the larger picture.
Within my article that I linked to above is a composite of all the temperature data sets including BEST and my own extension to 1538. The gradual warming trend- set against a background of peaks and troughs is clear to see.
Sorry to divert your other discussions here, but it is rare to hear scientists comment on this 350 year warming as Ned did above.
tonyb
Open access paper
http://www.scirp.org/journal/PaperInformation.aspx?paperID=3217&JournalID=69
On the recovery from the Little Ice Age
Syun-Ichi Akasofu
Baa Humbug
Excellent, thank you.
tonyb
Tony B: Leif is better organised than me, he just emailed me the info.
This paper http://www.terrapub.co.jp/journals/EPS/pdf/2008/6009/60090937.pdf
explains how the geomag models are constructed.
Movies are available here http://earthref.org/ERDA/431/ for the past
several thousand years. The zip file [132 Mb] contains four movies.
The ‘Br’ movie is the one I was talking about
Tall bloke
Thank you. I will read them over the next few days
Tonyb
Ned Nikolov says, February 10, 2012 at 10:01 pm:
“…Yes, very close! I would suggest the following:
The long-term mean temperature at the surface of any given planet depends on its insolation and the average weight of its atmosphere above a unit area.
Thanks Ned, this will be a useful ‘sound byte’ to use when confronting the true believers in CAGW and their addiction to the anti-CO2 meme… 🙂
If Willis knows this was the piece refused ‘publication’ at WUWT, how come he is keeping quiet about it?
Tenuc
One clarification to the statement:
“The long-term mean temperature at the surface of any given planet depends on its insolation and the average weight of its atmosphere above a unit area.”
Insolation and pressure explain about 99.6% of the surface temperature. There is, however, a 0.4% fraction of the absolute mean surface temperature, the change of which depends on the variation of global cloud cover controlled by solar magnetic activity. On Earth, this amounts to 1.2K global temperature change. This fraction may vary a bit among planets as a function of the NTE factor. Why is this fraction important, though?
The 0.7K warming observed over the past 130 years, which began as a trend in the 17th Century and amounts to a total of 1.2K over the past 360 years is due entirely to a decrease in global cloud cover driven by rising solar activity. The Sun’s activity (measured by the number of group sun spots at peak solar cycle) reached a maximum in late 1990s, and has been declining ever since. This caused a sharp increase in low-level clouds in 2001, which led to a leveling-off of the temperature trend (canceling the warming) over the past 11 years (see Fig. 7 in our original paper). So, the climate change we’ve been talking about so much, which gave birth to the AGW concept, is NOT related to changes of atmospheric mass or insolation, but to cloud dynamics.
I am making this clarification, because several bloggers tried to attribute our modern climate change to variations in atmospheric mass without apparently paying attention to Section 4C in our first paper. We are NOT claiming that global warming over the past 360 years has been caused by a change in atmospheric mass or pressure! Pressure changes occur on a time scale from tens of thousands to tens of millions of years, not centuries or millennia! Earth’s atmospheric pressure has been stable for the past 1.8 million years. See Fig. 10 in our original paper for the hierarchy of forcings (drivers) of climate we propose in the context of the UTC.
Ned Nikolov @ February 11, 2:57 am
I was highly amused by your account about a face to face meeting with Gavin Schmidt and Kevin Trenberth at the WCRP Open Science Conference in Denver on Oct. 24 last year.
Hey look I’ve been a really brave boy, and whilst risking an outbreak of hives, I visited Tamino’s website. (not that guy prancing through the forest in Mozart’s “The Magic Flute”, but Grant Foster @ “Open Mind”). I did a site search for Nikolov and also N & Z, and scanned the recent post-articles for relevance, but was again very surprised to draw a blank.
I might pluck –up courage to visit some other CAGW sites, but if you have ever experienced allergic hives, you may understand my caution in taking it slowly.
Hello Ned, you said, “So, the climate change we’ve been talking about so much, which gave birth to the AGW concept, is NOT related to changes of atmospheric mass or insolation, but to cloud dynamics.”
It is my understanding that cloud dynamics are very much related to cloud microphysical properties and that aerosol play a pivotal role in their formation and behaviour. I read somewhere that biomass burning produced smaller than normal type aerosol and this changed the precipitation rate and increased cloud lifetime for that region. If our atmosphere was shown to be progressively dustier and smokier wouldn’t this have a marked affect on cloud dynamics and maybe result in changes of equal significance to radiation driven changes?
Could aerosol increases be responsible for increasing cloud cover and therefore cooling in some regions. You seem to be saying it is all down to the amount of cloud cover that dictates temperature, and that this is dependent only on solar activity, is that correct.
davidmhoffer says:
February 11, 2012 at 2:39 pm
“How this paper failed to get more attention than it has is beyond me. N&Z, I recommend you have a look! Actually, I recommend everyone have a look, though I have to say that Baa Humbug is right about the math in this paper, it is daunting.”
Click to access 1002.0883.pdf
It does appear to be a very robust rebuttal of current CAGW theories.
Upthread I posted a “step” temperature curve that purported to show higher than 255K from 240 w/m2. I messed up my spreadsheet and Joel Shore called me out on it. I’m a bit embarrased, because when I first read through N&Z, I started doing some back of the envelope calcs and did it right. A couple of weeks go by, I set out to do it again…and forgot exactly what I did. Thanks to Joel Shore for calling out my error.
What I did show was an insolation model that arrived at an average of 241.7 w/m2 and an average blackbody temperature via SB Law of 144.5K. This speaks to a major portion of N&Z’s work. By simply averaging insolation and calculating blackbody temperature from that, we arrive at 255K as the equilibrium temperature of earth. But, assuming an earth of zero heat capcity, and simply by breaking it up into 24 hour periods, we discover the impact of Holder’s Inequality.
POINT: The theoretical blackbody temperature of earth is no where near 255K. It is at least 100 degrees LESS than that!
But the problem with this way of looking at things is that the earth does not have a heat capacity of zero. I was clued into looking at things from this perspective by BenAW, who has pointed out many times that when the sun comes up, the ocean isn’t at zero degrees, it is at 275 degrees (or so). The temperature of a body with a large heat capacity exposed to a fluctuating heat source doesn’t reach either the peak temperature suggested by a straight blackbody calculation, nor does it fall to zero when the heat source is absent (unless a very long time passes with no heat source. The temperature fluctuates around a mid point. The energy flux required to maintain that mid point (as an average) when combined with Holder’s Inequality, results in a much higher surface temperature witht he exact same “average” energy flux.
The following is illustrative. This “step” curve is NOT realistic. I simply fiddled with the numbers to come up with a step curve that fluctuated around a mid point and wound up with an “average” of close to 241.7 w/m2 (from my first example) and an “average” temperature of more than 144.5 K. Starting again from midnight:
w/m2 degK
121.2 215
121.2 215
110.3 210
110.3 210
100.1 205
100.1 205
110.3 210
132.8 220
172.9 235
279.6 265
374.1 285
459.3 300
523.6 310
558.2 315
558.2 315
459.3 300
324.3 275
259.1 260
188.1 240
158.7 230
158.7 230
145.3 225
132.8 220
132.8 220
average w/m2 = 241.3
“average” T = 246.5 degK.
[
add by co-mod –Tim]
POINT: Assuming some heat capacity that results in the planet fluctuating between 220K and 315K (rather than between zero and 350K as in my first example) we see that the same “average” 241 w/m2 can easily maintain a surface temperature 120 degrees HIGHER than would be possible with a blackbody of zero heat capacity.
No GHG’s or laws of thermodynamics were harmed in this process. Math bungling may well have been possible.
Hoff says:
I was clued into looking at things from this perspective by BenAW, who has pointed out many times that when the sun comes up, the ocean isn’t at zero degrees, it is at 275 degrees (or so).
Ahhhh, so that’s what he meant. I need to apologise to him next time he calls by for saying he was talking nonsense. What I’ve been saying to Ben AW which I think is relevant here, is that without the presence of the atmospheric mass and the pressure it generates, and the pressure/temperature gradient in the ocean, the ocean wouldn’t be there anyway. But because it is, and because of the peculiar properties of water and it’s thermal mobility, energy is moved very efficiently from equator towards high latitudes. Your numerical example is a very powerful simple exposition of the effect of Holder’s inequality. This is really important stuff and I think we’ll make a new post for it soon using your examples.
PS – there is a part 3 coming when I have a moment. The original goal was to show a BB temp higher than 255K that was the result of 240 w/m2. I think I’ve shown rather conclusively that the 255K number is completely ficitious in the first place. Meaningless in all respects. BUT…the fact remains that when one consider’s Holder’s Inequality, no matter how you mix up the insolation curve, you CANNOT get to higher than 255K from 240 w/m2.
Except that you can!
Not, however, from simple blackbody calcs that assume a heat capcity of zero. One must add than in. Then one must ALSO add in the effects of convection and conduction that cool the tropics and warm the temperate and arctic zones.
My maths skills being bungle prone, that may take a while.
In the meantime though, I’ll leave this little Aha! moment that resulted from some of my initial attempts for people to ponder.
Starting with ERBE data to come up with some realistic starting point, I noticed that the tropics absorbe about 80 w/m2 more than the emitt. The difference is accounted for by conduction and convection moving that 80 w/m2 to the temperate and artic zones.
But is it not interesting that the tropics, where GHG’s are strongest (by several orders of magnitude compared to the poles) radiate at a BB temperature LESS than the incoming w/m2? I thought GHG’s caused a dramatic INCREASE in surface temperature? But the tropics exhibit a DECREASED surface temperature?
I already figured out the answer, (I think) but thought I’d leave that one for the GHG’s increase surface temperature zealots to ponder.
Note: I’ve added a pair of plots to David’s data table couple of posts above.
It’s a big task that requires a team effort, and alienating potential peer reviewers by, for example, making injudicious jokes about their nationality won’t help. Those reviewers will in all likelihood ask exactly the sort of questions Robert Brown has about the physics underlying the constants used to generate the regression curve. So whether or not the importance of such concerns should be downgraded by weighing them against the explanatory power of the bigger picture, Ned and Karl will need to have an answer ready which will satisfy them.
Well said, and I agree. As I said in the reply immediately preceding this one, Tallbloke, I would reject the paper out of hand as it is written right now, not out of any sort of hostility towards them or their work, but because the fit is statistically meaningless — five data points, four parameters, two physically distinct nonlinear regimes — and because the implicit physical quantities “hidden” in their dimensionless functions have absurd values.
Any competent referee of the paper would almost certainly have the same objections — would certainly have them if they were brought to their attention.
I would like to suggest that readers of this thread go read Richard Feynman’s famous “Cargo Cult Science” talk, not to accuse N&Z of cargo cult science but to if anything encourage them to meet Feynman’s not unreasonable standards by drawing attention themselves to places where their results do not make sense — or better yet, do not attempt to publish them until they do make sense. And by “make sense” I do not mean the way the term is used by the lay public, satisfies some verbal heuristic argument. Physics has higher standards than that. It needs to make algebraic sense. I’d rather see a fit with a much larger error that has a halfway decent justification and physical constants that are plausible for the phenonmena being studied than Equation 7 of Nikolov and Zeller.
rgb
davidmhoffer says:
February 12, 2012 at 3:34 pm
“The original goal was to show a BB temp higher than 255K that was the result of 240 w/m2. I think I’ve shown rather conclusively that the 255K number is completely ficitious in the first place. Meaningless in all respects. BUT…the fact remains that when one consider’s Holder’s Inequality, no matter how you mix up the insolation curve, you CANNOT get to higher than 255K from 240 w/m2.
Except that you can!
Not, however, from simple blackbody calcs that assume a heat capcity of zero. ”
David, glad someone is finally getting the message.
Took only a month or so 😉
A. C. Osborn (February 12, 2012 at 12:57 pm):
Yes, very interesting paper indeed!
Click to access 1002.0883.pdf
I was not aware of it. Thank you, Osborn…
It indirectly supports our premise that the 255K emission temperature is a pure mathematical construct with no physical relevance. Interestingly, they do not discuss the Holder’s inequality suggesting that the authors are apparently unaware of it… If they were, they would have realized right the way that one cannot write an energy balance equation for the ENTIRE planet that relates average temperature to average energy fluxes!
In the context of the planet as a whole, it is ONLY physically feasible to talk in terms of either mean fluxes to mean temperatures, but never combining the two in a single equation, because such equation has no meaning in the context of the planet!In the context of the planet as a whole, it is ONLY feasible to talk in terms of either mean fluxes OR mean temperatures, but never combining the two in a single equation, because such an equation has no physical meaning due to Holder’s inequality! [see correction below –Tim]Hi Ben AW. First of all, please accept my apology for using the word ‘nonsense’ in your direction the other day, it wasn’t polite, and I was wrong to use it.
Secondly, It’s not true that we haven’t understood what you’ve been saying. There are comments I made in reply to you on the previous N&Z thread saying you may well be right, and previous posts I’ve made here at the talkshop which talk about the oceans high heat capacity and extremely long retention times. The top 2m of the ocean has the same heat capacity as the entire atmosphere above it. There is enough energy stored in the ocean to keep the atmosphere warm for a very long time even if cloud albedo were to rise dramatically.
So, please contribute your thoughts as to how the ocean gets Earth above the 255K level without the need for any heating effect from the alleged radiative greenhouse effect.
Correcting couple typos in the last sentence of my previous post:
In the context of the planet as a whole, it is ONLY feasible to talk in terms of either mean fluxes OR mean temperatures, but never combining the two in a single equation, because such an equation has no physical meaning due to Holder’s inequality!
What contradictory math? The fact that some folks have ‘opinions’ that are mute, does not mean that math is contradictory. The math is very simple and clear! I have intentionally not replied to Dr. Brown, because he has no point and fails, like Willis, to see the big picture, which is blatantly obvious. Please, read the section in our paper above called “Focusing on the Big Picture”, because I do not plan to repeat again what we already explained in plain English!
Dear Dr. Nikolov,
What, precisely, is your “big picture” if equation 7 is shown to be nonsense? What part of:
is “simple and clear math” (with
measured in atmospheres or bar)? What part of completely failing to fit the bottom three values eludes you? What part of fitting the five remaining data points with four free parameters provides a “big picture” worthy of publication?
So far your paper can be thus summarized:
You define a single function,
, for all the planets on your list (and yes, I read the derivation elsewhere, which is pretty much due to other researchers, except that you’ve added the completely arbitrary (heuristic) fudge factor 
).
Physically, you ignore all sorts of details expected to be important, such as what the albedo of the planets in question really are, what their emissivity really is, whether or not they have an axial tilt. Those things seem to me like they might be important, but fine, you get to state your assumptions.
You then take the average surface temperature of 8 planetary objects, divide it by this “one size fits all”
and get a table of data you call 
. You ignore the fact that this data spans fourteen or fifteen orders of magnitude in surface pressure and factors of 2 in e.g. albedo and emissivity. You ignore the fact that the first two entries are basically in a hard vacuum and the third is not far behind. You fit a product of two exponentials with physically absurd pressure scales to the upper five points, which happens to pass somewhat near these bottom three, and then assert in plain English that it is a miracle that this four parameter fit explains the five points of data so well, glossing over the fact that it really isn’t that close to at least one of them (and ignoring the fact that you have no measure of goodness of fit, so a “good fit” is whatever you want to claim that it is).
The fit has two utterly meaningless physical constants in it, as well as utterly meaningless exponents. It is not only not a physically derived result, it is clearly not under any circumstances derivable. You would have done just as well to have fit the data with a cubic spline. Then it would have been a perfect fit, and you could claim an even bigger miracle. The coefficients of the fit would have been just precisely as meaningful either way, right?
So I’m struggling to see just what your “big picture” is, and how it is worthy of publication. Is it “The Greenhouse Effect Monotonically Scales With Surface Pressure in a Way That Is Different For Near Vacuum Planets Compared To Planets With A Greenhouse Effect”? Surely you are aware that every planetary climatologist or ordinary physicist in existence can see that as well as you can, without a physically meaningless “miracle” fit being asserted or a claim that you’ve actually “done” something in this paper.
Where, sir(s), is the Beef?
Where do you explain anything?
Where does anything you assert in reference to equation 7 make sense?
So by all means, start a top-level article to defend your [snip] result, and do so by refusing to do so when I point out perfectly reasonable and very thoroughly worked out objections. That way you can be praised by everybody on the list who does not actually understand any physics. But one would think that you might, eventually, want to convince physicists and physical climatologists, and in order to do that you will sooner or later have to answer my objections.
rgb
[Reply] Keep the tone polite please. It’s more likely to obtain a reply, and will be more in line with the standards of discourse expected here. Thanks – TB.
Ned, David Hoffer and I have been having an email convo about Holders inequality and the way the oceans spread heat polewards which we hope to turn into an article for the talkshop soon. With more input from Ben AW and you, I think we’ll be able to show that the Earth can have an average surface temperature of more than 255K before we need any assistance from either the controversial Loschmidt effect (still a paradox after more than 120 years) or ‘back radiation’.
Robert Brown;
As I said in the reply immediately preceding this one, Tallbloke, I would reject the paper out of hand as it is written right now.>>>
As I said in other comments, this is a blog. I’m not interested in academic standards and if they would fairly accept or reject this paper. What I’m interested in, and what I think most people who participate in the discussion who are not researchers themselves, is improved understanding. I have reservations about some portions of N&Z. But they nailed solid the misaplication of SB Law, Holder’s Inequality, and the logic behind PV=nRT.
What I’m interested in from learned people such as yourelf is not what you think is wrong with N&Z. I’m interested in what you think is right, and how to build upon it to arrive at a more accurate understanding of the climate and our effect on it.
Tallbloke (February 12, 2012 at 11:38 pm):
“There is enough energy stored in the ocean to keep the atmosphere warm for a very long time even if cloud albedo were to rise dramatically.
Rog, this statement is not supported by the empirical observations. Satellite data show that the global surface temperature responds to changes in cloud albedo with a lag of 12-24 months. Even small changes (less than 0.5%) in global cloud cover show up in the surface temperature record within a year to 2 years (see Fig. 7 in our original paper)… Satellite observations also suggest that Earth loses heat (cools down) much faster than climate models predict. These two types of evidence indicate that oceans cannot buffer much global temperature changes …
In regard to previous comments about the ocean surface temperature – there would be NO liquid oceans without the thermal enhancement provided by the atmosphere! The ATE is the reason for the ocean temperature, not the other way around! Reduction of surface pressure to about 30% of the current value (i.e. to ~30 kPa), due to slowing down of tectonic activity and mantle degassing, is the most likely cause for the Snowball Earth events that occurred in the distant past, when oceans became frozen down to the equator.
tallbloke;
Ned, David Hoffer and I have been having an email convo about Holders inequality and the way the oceans spread heat polewards which we hope to turn into an article for the talkshop soon. With more input from Ben AW and you>>>
please feel free to provide them with my email address. Stephen Wilde too.
I ran into a conundrum showing how conduction/convection raise temps beyond 255K. I think I’ve got the matter figured out concept wise, I just have no clue how to handle it mathematically.
Hoff: Better to have an open barnstorming discussion on the blog. There’s too much going on behind the scenes in email as it is. I can’t keep up, and I’m having smtp problems anyway.
I’ll start a thread on this stuff outlining the general issues and we can take it from there.
Ned: Think potential temperature, at a depth of 5000m. The pressure effect isn’t only in the atmosphere. Also, the lags you note are just one of the timescales the ocean operates on, and represent the interaction of only a tiny fraction of it’s retained energy. When I said “keep the atmosphere warm” I meant “above freezing” which is well above 255K.
About poleward heat transport – keep in mind that research has shown that about 85-90% of that transport is atmospheric currents and only 10-15% through ocean currents.
The atmosphere is by far the dominant medium for equator-to-pole heat transport!
Ned, what I’ve read is that ocean transport dominates from equator to mid latitudes, and atmospheric transport from there to the poles. I’ll try to find the reference for you. Please find a reference for the research you are referring to as well. Thanks.
Update: looks like you’re closer than me!
Click to access arnaud_john__partition.pdf
The Partitioning of Poleward Heat Transport between the Atmosphere and Ocean
ARNAUD CZAJA
Department of Physics, Imperial College, London, United Kingdom
JOHN MARSHALL
Department of Earth, Atmosphere and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
(Manuscript received 28 February 2005, in final form 28 September 2005)
ABSTRACT
Observations of the poleward heat transport of the earth (H ) suggest that the atmosphere is the primary
transporting agent poleward of 30°, that oceanic (HO) and atmospheric (HA) contributions are comparable
in the tropical belt, and that ocean transport dominates in the deep Tropics.
Ned Nikolov says:
February 13, 2012 at 12:32 am
About poleward heat transport – keep in mind that research has shown that about 85-90% of that transport is atmospheric currents and only 10-15% through ocean currents.
The atmosphere is by far the dominant medium for equator-to-pole heat transport>>>
Ned,
I’m not all that concerned with the means of transport for my current purposes. I built a couple of simple models upthread to demonstrate the insanity of trying to calculate an equilibrium temperature based on an “average” of 240 w/m2.
If I try and construct a two part model, one area very warm and the other very cold, both fluctuating in temperature due to insolation that is intermittant and variable due to earth rotation, I can show that any process that moves energy from hot area to cold area drives the average temperature closer and closer to 255K for an average insolation of 240 w/m2. Holder’s Inequality acts exactly like a “limit” even when the areas are out of proportion. For example, my “warm area” has three times the area of my “cold area”, and I move 50 w/m2 from warm to add 150 w/m2 to the cold area, the exact same limit is reached, 255K.
Except that’s not what I’m trying to actually model. That gives me a model for surface temperature on an airless planet. What I’m actually trying to model is the “equilibrium plane”. For our only available apparatus (planet Earth), 255K occurs “on average” at 14,000 feet altitude. I understand the lapse rate and how you’ve figured PV=nRT into describing what that should be. What I’m looking for is a mean to understand this strictly from SB Law, which gets real tricky real fast. At that equilibrium plane I’ve got upward bound LW plus downward bound LW plus heat capacity plus conduction and convection….
Ned, While the atmosphere transports most of the heat, we need to remember that according to NASA’s energy budget, only around 16% of TOA insolation is absorbed directly in the atmosphere. Just over half is absorbed by land and ocean. So ~40% of the energy disappears into the ocean, then reappears later to warm the air (mostly by convection and the latent heat of condensation). Only after that does the air transport the heat anywhere.
Robert Brown (February 12, 2012 at 11:41 pm):
Dr. Brown, I believe you’ll find the answers to your questions in our upcoming Reply Part 2.
Thank you for engaging in this discussion.
Keep an eye on what Konrad is doing on his own with his own resources
davidmhoffer says: February 12, 2012 at 11:57 pm
What I’m interested in from learned people such as yourelf is not what you think is wrong with N&Z. I’m interested in what you think is right, and how to build upon it to arrive at a more accurate understanding of the climate and our effect on it.
============
well the full stops seem to be followed by capital letters %-)
You surely cannot be serious. Peer review accepts +ve and -ve reviews as they should. You want just correct points!!! This is not review.
Lets consider another paper – If the basic physics is wrong but magically you can create a curve fit to your results how can you point out the good bits
Back to N&Z
Equation 2 seems to sum TSI and Cs then spread it round the globe. However Cs is already global so should not be so spread it must be constant over the surface. Inconsequential but physically wrong.
I do not see where the continuous downwelling radiation is handled in the equations. Like Cs this is day and night 200 watts so should not be spread equatorially although it does taper off polewards.
the 200Watts was measured here SGP Central Facility, Ponca City, OK 36° 36′ 18.0″ N, 97° 29′ 6.0″ W Altitude: 320 meters
Eq 3 uses ap= Earth’s planetary albedo (≈0.3).
Eq 2 uses agb=Earth’s albedo without atmosphere (≈0.125),
Why the difference both assume atmosphereless planet?
How does the effect of clouds at night get accounted for when all nz’s parameters have not changed therefore no additional retention of heat? But GHE creates a slower cooling rate under the clouds?
Convection is a slow (compared to radiation) and unreliable process. – Where do temperature inversions appear in the equations. where is time in all of this – How long does it take for a photon from the ground to reach TOA? How long for convection to reach TOA?
Convection causes a parcel to rise but why is there very little manifestation of this (apart from the first 1k of air – its still got an awful long way to go)
I was looking forward to having breakfast with Robert Brown yesterday. He did not show up and he has ignored my recent emails. Now that I have had time to read the exchange between him and N&K, my guess is that he is ticked off at me but does not want to hurt my feelings. Don’t worry Robert, I still hold you in the highest regard; thank you again for all the help you gave me during my 12 years in the Duke university physics department.
My take on this spat is that both Robert and N&K have thrown some light on the issue of planetary surface temperatures using gas equations, Stephan-Boltzman etc. Absolutely no need for Radiative Transfer Equations or trace gasses such as CO2. Elsewhere I have pointed out that N&K’s theory does not cover the effect of water vapor in Earth’s atmosphere or sulphuric acid in Venus’ atmosphere but N&K never claimed their theory was complete.
If one is convinced (as I am) that the major determinants of planetary surface temperatures are TSI and atmospheric mass, it does not preclude the idea that there may be many minor factors such as water vapor, CO2, cosmic rays etc. that also have an influence.
The good news is that Nicola Scafetta did turn up for breakfast yesterday and made a convincing explanation of a “minor” factor that may be several times more important than CO2. If Nicola is vindicated, the implications will be huge for science and for politics too.
Gallopingcamel (February 13, 2012 at 4:29 am):
I’m familiar with the work of Nicola Scafetta! He has found some very interesting correlations between cycles of Earth surface temperature and certain orbital frequencies of Jupiter and Saturn. His results imply that Earth’s cloud cover and albedo are influenced in a complex way by other celestial bodies besides Sun and the cosmic rays… This is where the future of climate science will be – discovering the subtle effects of Sun’s magnetic field, and the magnetic/gravitational fields of other planets on Earth’s cloud albedo. These influences are small compared to pressure effects or orbital changes, but since they operate on a ‘human’ time scale (decades to centuries) and can cause 1.0C – 1.4C fluctuations in the mean global temperature, they are most important/relevant to our lives and civilization.
I cannot help but see an interesting connection / analogy between Scafetta’s research and ours (N&Z). Both studies focus on new and unknown mechanisms, and use correlations and empirical relationships to quantify them. Scafetta’s work is already published in the peer-reviewed literature, and no one has objected that he did not explain the highly significant correlations he found via ‘first principles‘. The lack of physical ‘first principals’ is very typical when studying new phenomena, and is part of the standard scientific inquiry. I’m mentioning this in regard to Dr. Brown’s criticism of our work, where he argues against the physical significance of our Eq. 7 simply because he could not explain values of the regression coefficients through known laboratory-derived physical constants. Such a critique is unwarranted for the above reasons …
davidmhoffer @ February 11, 1:58 am
Oh, that is interesting. If I read you correctly, he has visited here whilst knowing that he is banned from commenting, as a consequence of his unruly past habits as determined by the moderators here?
I guess it is not a stretch of the imagination that perhaps Willis and Anthony Watts, may also imbibe. (and Robert Brown provably so, although surprisingly, Tim Folkerts and some “other suspects” seem to be absent)
Further my comment just above:
Why do I find the absence of the usual suspects surprising?
Because they have been alerted to this thread by non-other than Anthony Watts at WUWT.
Tim: Thanks for the heads-up. Konrad’s experimental-empirical work is important. This is another step along the road. I hope to do some high pressure tests once we get some sunshine in the UK!
Serge: What we’d like to see is some balanced viewpoints, which acknowledge the strengths as well as criticising the perceived weaknesses. Your complaints are misplaced, because they represent work to be tackled once the basic premises are established.
GC: How I wish I could have been at Breakfast with you and Nicola. We have been working on the same questions here for the last two years. Nicola has actually acknowledged our work and linked the Talkshop in the references section of one of his papers.
Ned: I hope you find the time to read some of the earlier work done here, as Nicola Scafetta drew on some of it, and has encouraged me to try to get some of my own original research published.
Bob FJ: It is a matter of regret to me that a rift developed between myself and some prominent members of the layman climate science community. Please don’t worsen the situation by stirring the pot too vigorously. Thanks.
At the risk of making an overused Gandhi quote even more tired:
First they ignore you (Anthony and the general Totschweigentaktik still prevailing).
Then they mock you (Willis Eschenbach).
Then they fight you (Robert Brown).
Then you win! (?)
Well the jury is still very much out on the last, but it’s a very healthy sign that the physicists, who are traditionally the smartest of scientists, are now starting to duke it out. Post-post-normal science = back-to-normal science? Let’s hope so.
tallbloke says:
February 12, 2012 at 11:38 pm
Hi Ben AW. First of all, please accept my apology for using the word ‘nonsense’ in your direction the other day, it wasn’t polite, and I was wrong to use it.
Accepted.
So, please contribute your thoughts as to how the ocean gets Earth above the 255K level without the need for any heating effect from the alleged radiative greenhouse effect
I don’t know how to be more explicit than I have been but here is another try.
The whole idea of comparing waterplanet earth to a BB of GB is total nonsense.
But since you’re still in “BB mode” try this:
a normal BB in space without radiation falling on it, immediately goes to 0K (2,77344564K if you insist)
Earth is a “BB” that is already at ~275K without any radiation falling on it (oceans bulk temp).
Switch on the sun, and the whole system starts at a base temp of 275K.
All the sun has to do, is keep a very shallow top layer of the oceans + the atmosphere at our present pleasant temperatures.
I’m pretty much convinced that starting from here we can explain most of the climate using simple processes like conduction, convection etc. Back to good old meteorology.
This implies that the 255K of the GHE and the 155K of N&Z are meaningless, since planet earth is already warmer than this before we start considering the effect of the sun.
Regarding N&Z I feel that a lot of the confusion stems from a solid misunderstanding of the adiabatic lapse rate. (Did I mention the Chinook winds already ?)
See https://tallbloke.wordpress.com/2012/01/25/hans-jelbring-an-alternative-derivation-of-the-static-dry-adiabatic-temperature-lapse-rate/#comment-15299
Ben AW: Thanks, we can start disagreeing agreeably again now. 🙂
“Earth is a “BB” that is already at ~275K without any radiation falling on it (oceans bulk temp).”
How does it get from 2.75K to 275K?
The work done in heating several squintillion litres of seawater from 2.75 to 275K is considerably more than that done in moving a decimal point a couple of places on a calculator.
If you mean that’s the temperature the bulk of the ocean stays at overnight after 3.5 billion years of being warmed by the Sun every day, we can move forward.
Chris M: It will be healthy for the sceptical side of the climate blogosphere to have a robust debate about the merits of competing theories. If WUWT has chosen to take the ‘Radiative GHG Content’ position against the Talkshop’s ‘Gravity, Mass and Sunshine’ position that’s fine. 🙂
It might be that ultimately a better synthesis of the two will develop and prevail. Or a winning coup-de-grace may be delivered from either side. Seems to me that the new post from Doug Proctor has tilted the odds in our favour today.
May the chips fall where they may and the best theory win the day.
Ned has thanked Robert Brown for his contribution to our debate here. I hope one day soon when the dust has settled Ned will be thanked for his contribution to debate there too.
tallbloke;
How does it get from 2.75K to 275K?>>>>
To BenAW’s point, it doesn’t matter. All that matters is that at dawn we have an initial condition of about 275K. What happened over the course of 3 billion years to get it there in the first place is immaterial. that’s the starting point at first light.
But I don’t think we can explain it from there with back of the envelope BB calcs. To push the temp beyond the putative BB temp, we need a grey body calc with emissitvity and absortivity (that the right word?) that are “unbalanced”.
I’be neen trying to figure out how to articulate this properly. In electronics there is something called a “spitter cirquit”. It is a clever arrangement of diodes and capacitors that, when exposed to an alternating current, charges up to produce an output voltage 3 times the input voltage. You can build them in series to arrive at a voltage hundreds of times the input. It is used commonly in things like camera flashes where you need hundreds of volts to fire the flash, but you need to do it with a couple of 1.5 volt batteries. Tim Channon will know what I am talking about.
I think we have a similar concept at work here. I’ve got the “spitter cirquit” in my head screaming at me these last several days, now I have to sit down and get a grip on the radiative/conductive analogy to it.
David, I wish I could get a copy of the full paper, but this might be part of the answer:
Omigosh, that’s it. The ocean is a diode.
I was looking at Doug Proctor’s figure 5 and thought to myself, a couple of resistors and a diode and an off again on again power source, and I could mimic that curve.
A diode simpy conducts really well one way, not so well the other. That’s what the oceans do. SW comes in and gets absorbed by the oceans to considerable depths. Then the energy has to fight itz way beack out by a variety of processes that are nowhere near as efficient. So, the warming pulse builds up heat quickly, sun shuts off at night, but the cooling pulse is way slower, just as Doug Proctor shows in Figure 5.
With that in mind, we do indeed get a temperature well above 255K. The system still behaves like a limit, but instead of the limit being the “average” which would drive it to 255K, the limit is now the peak input, which is way higher.
Insolation varies from 0 to 1000 w/m2 in the tropics. If the warming cycle is very efficient it all goes in. But if the cooling cycles is inneficient (once again, exactly as Doug Proctor shows it) it takes longer, much longer, for that heat to find its way back out. If the next shot of warming starts before the cooling entirely dissipates, the new high the next day will be incrementally higher than the day before.
The temperature must continue to climb in this fashion until the inneficient cooling process is at such a high temperature than, inneficient thought it may be, it finally catches up to the short but high efficient warming pulse to establish equilibrium.
BUT…with an unbalanced function like that, the equilibrium temperature will be ABOVE the average temperature.
Wee hours of the AM here, I’m going back to bed, will try and put together an illustrative math model in the AM. Grab any daily temperature record and look at the curves though. The night time cooling curve is very gentle compared the daily warming curve. As a consequence, the limit to be approached is peak insolation, NOT average insolation!
Hoff: Sounds good! I think this idea fits too:
Another part of the answer is in the N&Z theory. The distribution of solar energy as it moves dynamically through the system is such that temperature is enhanced in the near surface atmosphere to the detriment of temperatures at higher altitudes. This makes the conduction of heat from ocean to air slower than it would otherwise be. So heat accumulates in the ocean until it is in thermal equilibrium with the air above it. This gets us above the 255K BB calc and explains most if not all of the misnamed ‘GHE’.
Maybe the ‘supercritical’ extremely dense and highly pressurized co2 fog near the surface of Venus acts as it’s ‘ocean’…
I’ve raised the issue of the error in N&Z of using as a model for all the planets of a zero heat capacity object, both here and at WUWT. Ned refuses to even address the point, Ben has raised the point in a different way raising the heat capacity of the oceans. However, the data that Ned himself posted for the moon shows his model doesn’t work even for a rock surface. The fit for their derived parameter is of no consequence when the first step is in error. The method Ned uses greatly over estimates the ‘enhancement’ for all the planets. The conventional approach gives an upper bound for the average temperature and therefore a lower bound for the ‘enhancement’, Ned’s approach yields a lower bound for the average which is far less realistic for Earth and Venus than uniformity.
“The distribution of solar energy as it moves dynamically through the system is such that temperature is enhanced in the near surface atmosphere relative to higher altitudes. This makes the conduction of heat from ocean to air slower than it would otherwise be. So heat accumulates in the ocean until it is in thermal equilibrium with the air above it.”
That is similar to the AGW contention that downwelling IR makes the ocean skin warmer and so heats up the oceans by making the flow of energy from ocean to air slower than it otherwise would be. We need to distinguish between those two propositions.
I can accept that pressure could achieve that outcome but not so called downward IR because downward IR would just cause more evaporation whereas the energy flow through the system and hence ocean temperature would already have come into balance with the surface pressure so that without a change in pressure there would be no change in ocean temperature.
I don’t believe there is any downward IR anyway. All that is recorded by the sensors is the warmer air near the surface and directly in front of the sensor. Any IR comes from that warm air near the surface and not from up in the sky.
Furthermore the evidence from Earth and Venus is that anything other than pressure is irrelevant.
Phil: You raise two issues.
On the first, Ned has been working with a NASA scientist on the Diviner data and the N&Z grey body calc is within 6K of the integrated empirical data.
On the second, the grey body calc for Earth gives nearly the same result (to within a couple of Kelvin) because an airless Earth wouldn’t have an ocean either.
[co-mod: Phil, try these backlinks Ned 6th Jan and same date a search will find more.
Try google (or bing or whatever) like this
site:tallbloke.wordpress.com search_text
–Tim]
tallbloke says:
February 13, 2012 at 10:37 am
Ben AW: Thanks, we can start disagreeing agreeably again now.
“Earth is a “BB” that is already at ~275K without any radiation falling on it (oceans bulk temp).”
How does it get from 2.75K to 275K?
If you mean that’s the temperature the bulk of the ocean stays at overnight after 3.5 billion years of being warmed by the Sun every day, we can move forward
I assume the bulk of the oceans do NOT interact with either the atmosphere nor the hot core.
They just sit there being oceans. (forget about upwelling etc etc for the moment, these are disruptions of the big picture)
The oceans temperature came either from their creation, billions of years ago (remember the hot core?) or a later warming event, like the braking up of Pangea, with some of Earths internal heat escaping, or a major meteorite crash or whatever.
Point is, only the surface layer (few hundred meters) is DIRECTLY influenced by solar and cools during the night, having enough heat capacity to have a relatively steady temp over a 24 hr period.
I assume the depth of the thermocline will vary slightly over a day, and will certainly vary over the seasons.
Ben AW: I think the oceans have a large degree of thermal inertia, which may enable an oscillation at the length of Milankovitch cycles. I don’t accept your “they just got created that way” argument though.
What about all the paleo evidence for thermohaline overturning, internal tides, meridional circulation, coriolis forces, and all the rest of their motions? If there was no overturning, the whole of the deep ocean would be anoxic, and no fish could live in the deep.
No. The thermal oceans have the temperature/depth profile they do, and are teeming with life because they are dynamic, not because they are static and stagnant. Sorry, I don’t buy it.
Tallbloke the point I raised regarding heat capacity applies for a rocky planet , the existance of an ocean is not relevant. Ned’s calculation does not agree with Diviner, the temperature on the dark side of the moon does not get close to 3K, Ned’s model assumption. Ned’s basic assumption is unrealistic, far more so than the conventional one of uniformity. Why doesn’t Ned do the calculation using a realistic value for surface heat capacity, his enhancement parameter will be smaller and his compensation for the error by excessive pressure terms will be less.
davidmhoffer says: February 13, 2012 at 11:40 am
;
“spitter cirquit”. I assume you mean voltage multiplier as this takes AC and gives you higher voltage DC out
Remember that using R and D in this sort of circuit need to be used sensibly since there is no loss what goes in is still in till it comes out!.
Free simulator:
http://www.linear.com/designtools/software/
Phil: The point is that they are not striving to make a perfect model of surface temperature, but to do a calculation using a relatively simple equation which gets the right answer for the average temperature of the grey body. Which it does to within 6K. This is substantially better than the classic misapplication of S-B, which get the wrong answer, ~100K out.
Get real please.
On your second point, it might make a very small difference, but I doubt it would make Robert Brown happy. That issue will be dealt with in N&Z’s ‘Reply to comments on the UTC part 2’ which will be published here at the Talkshop when they are good and ready.
[snip]
Quote what Tim said and give the timestamp link to when and where he said it, and then try again.
Thanks – TB.
Tallbloke, I’m not going to be able to do that from my phone so you’ll have to wait. Regarding your comparison of the conventional and Ned’s model, it’s inappropriate because they are doing different things. The conventional model addresses the influence of radiatively active gases in the atmosphere (the filtering effect of the atmosphere) whereas Ned is trying to model the effect of having an atmosphere. By neglecting surface heat capacity in his model he makes a significant error. By Holders inequality it’s not possible to get the right average temperature by using the correct integrated flux and the wrong temperature distribution.
[Reply]
1) I stepped through Tim’s comments to this thread and he has said nothing about Holder’s Inequality, so whatever your reply to him is, put it on the thread where he said whatever it is you are replying to, not here.
2) You were discussing Diviner data, which measured the Moon’s surface temperatures, not Earth’s, so stop wriggling.
3) By neglecting heat capacity Ned’s calc comes out 6K low, whereas the classic misapplication of the S-B equation comes out 100K high. You should be able to work out which is better.
4) Whatever the ‘conventional model’ is trying to do, it is wrong because it’s application of the S-B equation is demonstrably incorrect. As you said earlier, if a model fails at the first step, everything afterwards will be wrong too. If the ‘conventional modelers’ want to provide some other rationale for a ghg free atmosphere leading to a 255K Earth surface, tell them to bring it on.
thefordprefect;
spitter cirquit”. I assume you mean voltage multiplier as this takes AC and gives you higher voltage DC out>>>
Yes, same thing.
thefordprefect;
Remember that using R and D in this sort of circuit need to be used sensibly since there is no loss what goes in is still in till it comes out!.>>>
see next comment. the spitter gave me the idea, but a much simpler cirquit is a better description of the actual use case.
tallbloke says:
February 13, 2012 at 1:11 pm
Ben AW: I think the oceans have a large degree of thermal inertia, which may enable an oscillation at the length of Milankovitch cycles. I don’t accept your “they just got created that way” argument though.
What about all the paleo evidence for thermohaline overturning, internal tides, meridional circulation, coriolis forces, and all the rest of their motions? If there was no overturning, the whole of the deep ocean would be anoxic, and no fish could live in the deep.
No. The thermal oceans have the temperature/depth profile they do, and are teeming with life because they are dynamic, not because they are static and stagnant. Sorry, I don’t buy it.
Of course these things are real. Lets stick to the basics first, and worry about secondary effects later.
If it makes you happy, fine, the oceans have accumulated their present profile over billions of years.
See: http://er.jsc.nasa.gov/seh/Ocean_Planet/activities/ts2ssac4.pdf
second page
Also: http://earthguide.ucsd.edu/earthguide/diagrams/woce/
Pacific ocean
Only the top layer of the oceans is DIRECTLY heated by solar, with a nice fall of the temp. towards the poles. Around the polar circles the cold deep ocean “surfaces”.
The “band” of warm water extending from equator to both poles buffers the incoming solar over the day.
This is the basic picture. Continents, ocean currents, upwelling etc. etc just disrupt this basic picture.
OK, here’s the brief explanation before I run off to engage in income generation:
Consider a capacitor in parallel with an AC voltage.
Assume an AC voltage with a peak of 200 volts and an “effective” voltage of 120 volts. (engineering class was too long ago and not enough time to figure out the right numbers at the moment so all you EE’s out there just live with it I’m illustrating a concept not a perfectly valid physical model).
“Average” voltage across the capacitor is zero.
Slap a diode in series with the capacitor.
The voltage across the capacitor will build to peak voltage, which is 200 volts.
Now make it real world and put a resistor in parallel with the diode.
If the value of the resistor is infinity, the voltage reaches a limit of 200 volts.
If we adjust the resistor value downward, the voltage that the capacitor reaches goes downward as well.
The warmists would have us believe that the maximum voltage the capacitor can reach is 120 volts. In their model, there is another resistor in the cirquit, in series with the diode. This “charge” resistance exactly equals the resistance of the “discharge” resistor. If that were the case, then the voltage across the capacitor would in fact reach exactly 120 volts as a maximum.
But as soon as those two resistances change such that the “charge” resistance is lower than the “discharge” resistance, the voltage across the capacitor will increases above 120. The higher the resistance of the discharge resistor, the closer to the peak voltage of 200 volts the capacitor will get.
SW goes into the system with nearly no resistance at all.
LW comes out of the system fighting high resistance every step of the way.
Heat capacity is equivelant to capacitance.
Insolation is just like an AC voltage except that it is a half wave with a flat line between half waves.
This is what BenAW was alluding to.
This is why surface temperature can get above 255K with nary a GHG in sight.
Observational evidence to support this is in Figure 5 of Doug Proctor’s article, and in his detailed explanations.
I’m an idiot.
the resistor in my comment above goes in parallel with the DIODE not the cap.
[Fixed… Maybe 🙂 ]
Ben AW: I think the reason I’m fighting you is because although your model might be sufficient for your understanding of the overall ‘big picture’ energy balance, it conflicts with my understanding of the solar cycle in relation to ENSO, and other oceanic oscillations. So maybe we can compromise. If you can agree with me that the dynamic aspects of the oceans are vital to our understanding of shorter term climatic variation and not mere ‘secondary effects’, I’ll agree we can put them aside for the sake of the elegant simplicity of your particular Gedanken experiment.
Agreed?
Close David but the diode should be on the input side so that charging is only half the time, the average voltage will not be zero. There will be a charging half-cycle and a discharging half-cycle, N&Z’s model has a zero capacity.
I was looking forward to having breakfast with Robert Brown yesterday. He did not show up and he has ignored my recent emails. Now that I have had time to read the exchange between him and N&K, my guess is that he is ticked off at me but does not want to hurt my feelings. Don’t worry Robert, I still hold you in the highest regard; thank you again for all the help you gave me during my 12 years in the Duke university physics department.
Dearest Camel,
I didn’t reply to your emails because I could not go on Saturday, and you phrased your invitation in such a way that I didn’t feel a need to decline, only accept. I am not in any way ticked off at you, only insanely busy. I’m teaching a double load of recitation sections this spring — six of them — and have a lot of family stuff on my plate as well. Perhaps another time I will be less busy, although (did I mention that I’m CTO of a small startup as well, and it may be getting ready to take off and consume the little sleep that I get now) I can’t see any time soon — maybe lunch on a Monday or Wednesday.
I would have enjoyed meeting Dr. Scafetta although it is certainly true that I have somewhat similar reservations about his work as I have Nikolov and Zeller’s. However, I can think of a number of ways for various coincidences between planetary periods and local climate fluctuations to occur, both as “coincidences” — similar periods but no causal relationship — and as highly indirect causal influences. One of the first things I read about in my initial foray into the climate was the apparent coincidence of solar variation and climate variation, which led through a discussion of Mauder minima, Gleissberg cycles, the Sun’s erratic orbit around the center of mass of the solar system, and much more. Even as I’m still critical of its “numerological” character — Scafetta has IIRC compared his work to early heuristics concerning the tides, but the comparison is not apropos in an era when we know physics well enough to do far, far better — at least in the case of his work I can observe the coincidence and imagine at least one or two plausible explanatory causal chains, chains that I think it was his responsibility to investigate and quantify before publishing.
I guess it is not a stretch of the imagination that perhaps Willis and Anthony Watts, may also imbibe. (and Robert Brown provably so, although surprisingly, Tim Folkerts and some “other suspects” seem to be absent)
I’m curious, just what is it that I “imbibe” other than the beer I spent all night last night making (it’s the only time I can run my personal brewing operation, see “overcommitted and too damn busy” above:-)? If this is yet another form of dim ad hominem to avoid having to make a substantive comment on Nikolov and Zeller’s absurd equation 7, why not have a beer instead and save the blogosphere from yet another zero information content remark.
I cannot help but see an interesting connection / analogy between Scafetta’s research and ours (N&Z). Both studies focus on new and unknown mechanisms, and use correlations and empirical relationships to quantify them. Scafetta’s work is already published in the peer-reviewed literature, and no one has objected that he did not explain the highly significant correlations he found via ‘first principles‘. The lack of physical ‘first principals’ is very typical when studying new phenomena, and is part of the standard scientific inquiry. I’m mentioning this in regard to Dr. Brown’s criticism of our work, where he argues against the physical significance of our Eq. 7 simply because he could not explain values of the regression coefficients through known laboratory-derived physical constants. Such a critique is unwarranted for the above reasons …
Actually, I’m certain that a lot of people have objected — myself among them — but as noted just above, because the Sun is itself a complex system with chaotic internal dynamics — instantly visible in a plot of the Solar cycle over the Holocene, for example, as captured in radiometric proxies — and because Jupiter and Saturn are both powerful drivers of the Sun’s erratic internal orbit around the center of mass of the solar system, an orbit which doubtless drives internal resonances that can be lagged as much as 100,000 years, one can at least imagine a causal process with an effect on the Earth’s climate, and with resonance phenomena the physical forces involved need not be very large if they have a very long time to operate. With that said, I think that pointing out the numerical coincidence without analyzing the causality associated with it does little to advance our knowledge, especially when there are decadal oscillations already known to have an effect on our climate that are have similar periods. That is, there are confounding explanations that cannot readily be separated from the data.
I’d be happy to work through the usual “correlation is not causality” argument with you, and why this really does matter in general epistemology lest we use statistics to prove that smoking causes pregnancy (example from one of my favorite statistics books) or other nonsense. This kind of “numerology” is rife in the medical profession, where it is used to “prove” that high voltage power lines, or cell phones, or failing to eat your oatmeal, all cause cancer. It isn’t terribly good science there (as it is an open invitation to cherrypick and engage in confirmation bias and other forms of Feynman’s “Cargo Cult Science”) and it only ends up being decent science if it is rapidly followed by a quantitative and consistent causal analysis that includes a full disclosure discussion of the possibly confounding causes and where the observation fails. I’m awaiting this in the case of Scafetta’s paper, but I’m not holding my breath.
However, the difference between Scafetta’s reported coincidence and your Equation 7 is that there is no possible way that your Equation 7 can have the slightest bit of physical meaning. You have obscured this — quite possibly from yourselves — by writing it in a way that hides its internal dimensional scaling and the scale pressures involved — but I’ve helped you (or rather forced you) to confront it.
[MEGA SNIP]
[Reply]
1) Hi Robert. I won’t tolerate accusations of dishonesty here, since Ned Nikolov stated earlier that he and Karl Zeller will address your points in their upcoming ‘Reply to comments on the UTC part 2’. The policy here is that everything from the offending remark onwards goes in the bit bucket. Think of it as aversion therapy. As a special favour, since it was such a humongous snip, I saved it in a text file. Let me know if you want it emailing. I might put our new menu system to the test with a new sub-page for ‘Rants’. 🙂
2) N&Z know what your objections are, so you don’t need to club them over the head with them in 14 foot long comments. I won’t allow you to dominate with such lengthy bombastic diatribe either, so cool it if you want to get your (hopefully shorter) comments posted here in future. Thanks – TB.
PS. Why not simply wait until they publish ‘Reply to comments on the UTC part 2’ and then see what pertains? Just a thought.
Phil: I thought capacitors did the charging and diodes blocked two way traffic?
Anyway, you still don’t understand N&Z’s ‘model’. They calculate the grey body temperature, and the actual temperature as derived from the surface pressure and the TOA insolation.
The ATE factor is then the ratio of these two numbers. Theirs is the more realistic model, because without an atmosphere and its consequent pressure, there is no ocean to spread heat around.
Now, the conventional modelers say that Earth with no ghg’s would be 255K at the surface. This is arguable, though from N&Z’s point of view, it a fruitless argument anyway. This is because according to their theory, the surface temperature is a result of atmospheric mass and TOA insolation, and albedo is a result of temperature and pressure.
Phil,
Yeah, yeah, I’m trying to get to work and the last time I drew a cirquit was a different millenium.
I sent rog a drawing, such as it is.
there are two resistors. One in series with the diode that limits the charge rate, and one in parallel with the whole thing that limits discharge rate.
If the charge and discharge rates are equal, the maximum voltage across the cap is the effective voltage which is 120. That’s the model that the radiative xfer models use, and that is why they get 255K as a max.
If the charge resistance is zero, and the discharge resistance is infinity, the cap will charge to 200V. That’s unrealistic of course. But given a “low” charge resistance and a “high” discharge resistance, the voltage that the capacitor reaches is somewhere above 120 but below 200.
Or, in climate terms where resistance to incoming SW is very very low, but resistance to out going LW is very high:
The temperature that results is above the effective BB of 255K, but below the peak of whatever 1000 w/m2 comes out to. If someone wants to suggest 288K as a good approximation, I’d be willing to accept that.
David, the voltage is the analog of the energy flux, I guess the level of charge in the capacitor is the analog of T? To be accurate the discharge rate would need to be proportional to charge^4. I don’t know if this simple a circuit can be a true analog, maybe with op-amps?
Phil. says:
February 13, 2012 at 3:51 pm
David, the voltage is the analog of the energy flux, I guess the level of charge in the capacitor is the analog of T? To be accurate the discharge rate would need to be proportional to charge^4. I don’t know if this simple a circuit can be a true analog, maybe with op-amps>>>
If Rog or Tim can post the drawing I sent them, it will be a lot more clear. Actually, the drawing I sent them is missing a diode on the discharge side, I’ll fix it when I have a moment. But essentially:
SW = charge voltage. Resistance to SW is LOW.
LW = discharge voltage. Resistance to LW is HIGH
Capacitance = heat capacity
Voltage across capacitor = Temperature.
No need for op amps.
In an AC cirquit, V(effective) = RMS = Root Mean Square
In an Insolation circquit, P(effective) = 4th-root Mean 4th-power
The two are 100% analagous, just one uses square root and the other 4th root. Other than that the equations for both are identical and so are the concepts. Take a look at the top graphic in Figure 5 of Doug Proctor’s paper. What that is showing you is that R to SW is LOW and R to LW is high. If I configured this cirquit with resistances, voltages and capcitances of the right order of magnitude, I’d get a voltage curve exactly like that one.
tallbloke says:
February 13, 2012 at 3:03 pm
Ben AW: I think the reason I’m fighting you is because although your model might be sufficient for your understanding of the overall ‘big picture’ energy balance, it conflicts with my understanding of the solar cycle in relation to ENSO, and other oceanic oscillations. So maybe we can compromise. If you can agree with me that the dynamic aspects of the oceans are vital to our understanding of shorter term climatic variation and not mere ‘secondary effects’, I’ll agree we can put them aside for the sake of the elegant simplicity of your particular Gedanken experiment.
Agreed?
Of course, I assumed it would be blazingly obvious that this is not the complete picture.
Do you accept that the oceans have a temp of ~275K and that this is above any BB or GB approach, making these numbers meaningless for waterplanet earth?
And that this kills the whole GHE, because their model assumes a deficit of 33K AFTER the sun has
heated the earth?
So lets get this in a post and move on from there. Imo this finding should make even a politician or journalist understand the enormous mistake in the GHE theory.
Ben AW: I suspect their counterargument is that the back radiation warms the near surface air, and this slows down oceanic cooling, and that is why the ocean is at 275K rather than frozen at 255K.
How do you reply to them?
tallbloke says:
February 13, 2012 at 4:32 pm
Ben AW: I suspect their counterargument is that the back radiation warms the near surface air, and this slows down oceanic cooling, and that is why the ocean is at 275K rather than frozen at 255K.
How do you reply to them?
Backradiation in the GHE is supposed to increase the surface temps from 255K to 288K (33K difference)
Adding 33K to 275K gives 308K as average earth temp. Not even close.
1) Hi Robert. I won’t tolerate accusations of dishonesty here, since Ned Nikolov stated earlier that he and Karl Zeller will address your points in their upcoming ‘Reply to comments on the UTC part 2′.
It’s your blog, censor as you like. I was utterly respectful in those accusations — if there was any irritation that showed through it was strictly due to the fact that it is dead on topic for this thread and yet N&Z refuse to address it on thread. Or am I mistaken, and is this not all about “Reply to: ‘The Mystery of Equation 8’ by Willis Eschenbach” which — note well — contains Equation 7 as its sole “interesting” input. Equation 8 is after all just a rewriting of Equation 7 with the substitution of an uninteresting if oversimplified description of
?
Why, exactly, do we need yet another thread for them to reply in?
2) N&Z know what your objections are, so you don’t need to club them over the head with them in 14 foot long comments. I won’t allow you to dominate with such lengthy
Excellent! Then perhaps they can reply to them instead of starting a thread in which they wish to claim that Willis was completely wrong in his criticism of Equation 7/8 and then ignoring the only post in it that shows that Willis was completely correct in his criticism of Equation 7/8, only his criticism wasn’t strong enough. Or starting yet another thread just to reply to them. Or stating that they don’t need to reply to them, because this thread and their paper are about something else entirely, something that presumably survives the death of their “miracle equation” (their words, not mine).
bombastic diatribe either, so cool it if you want to get your (hopefully shorter) comments posted here in future. Thanks – TB.
Two remarks — one is the post was long because I was replying to three different posts above and avoiding the posting of a fourth. It’s more efficient for me that way — I’m in a hurry and am really too busy to be participating at all, but it strikes me that preventing questionable science — for surely Equation 7 is questionable, given my very specific and thoroughly supported questions — from being taken too seriously is a worthwhile cause. Including when I do it. Let he who has never made an error in a printed paper cast the first stone — I certainly have, and as a consequence I rather welcome it when people point out my errors. Even students catch me in errors.
Second, I am busy and I am a physicist. I’m not a climate scientist, and if anything I am a skeptic (probably technically a “non-catastrophic lukewarmist” if skepticism has to come in flavors these days). All I care about in my replies and the issues I’m pursuing is whether the science and the math/statistics are done well, or at least plausibly. If you want to boot all of the physicists who are actually critical of mistakes like Equation 7, it’s your call, but think about the probable consequences.
Finally, I will apologize on general principles since I was not trying to offend anyone with my post. I do admit that I have gotten frustrated by the manifest fact that the authors of the paper refuse to actually reply to and address the very, very simple points that I raise, supported by both computations and figures, and instead say that I’m missing some sort of “big picture”.
Perhaps I am — I’m completely uninterested in a “big picture” supported by hand waving, heuristics, the production of arbitrary curves with impossible dimensioned numbers and exponents that don’t quite fit even the highly idealized data. But this thread isn’t about the big picture, it is about equation 7/8! If they want to address the “big picture” (again), perhaps that might be a good new toplevel post, as long as that picture doesn’t rely on a still-undefended Equation 7/8.
It doesn’t have to be Nikolov or Zeller. I’d be thrilled to hear you personally or anyone explain how 54,000 bar can reasonably appear in and dominate the fit of five out of the eight planets with atmospheric surface pressures ranging from “zero” to a tiny fraction of a bar or atmosphere. It does seem as though defending equation 8 requires an actual explanation of this here and now not in the future and yet another thread on equation 8. We’re up to four or five threads that I know of so far — top posts on the original paper here and on WUWT, criticism on WUWT, this rebuttal here — do we really need to shoot for number 5 or number 6 to hear an actual explanation?
PS. Why not simply wait until they publish ‘Reply to comments on the UTC part 2′ and then see what pertains? Just a thought.
If I notice, I will. That doesn’t stop me from being frustrated here and now. If I had just said (as Willis did) “Look, your fit isn’t physically motivated and statistically it isn’t that impressive to fit 8 points with four parameters, look, I can do it too” that would be one thing. I did not just do this, I went far beyond this, both here and on the WUWT thread. Just for my second post on this thread I spent several hours doing the arithmetic, writing code, building the plots, inserting their own data from their table of planetary temperatures and pressures to be sure that I was using the same numbers they used. Their sole reply is that I’m missing the big picture. What big picture? I’m addressing Equation 8, the topic of this thread. Do I need to make that a top post on the blog myself to get their focused attention? Nothing else that they can say in defense of Equation 8 matters in the least until they address my quantitative and specific objections, and no big picture arguments can be taken seriously with the guts (Equation 8) kicked out.
rgb
[Reply] Well, according to you anyway. I’ll happily wait to see what Ned and Karl have to say in ‘Reply to comments on the UTC part 2′. They’ve blown Willis’ math away here on this thread, and they intend to deal with your objections in their next paper. I think it’s quite legitimate, given the length, detail and repetition of your points by you, that they choose to keep their powder dry until they set everything down that they want to in one place on a new headline post.
Thank you again for your learned input, and spare us any further “utterly respectful accusations” if you don’t mind. Thanks – TB.
PS. Friendly advice: When in a hurry, type less, because less is more when people read to the end. 😉
tallbloke says:
February 13, 2012 at 4:32 pm
Backradiation is invented to explain the missing 33K in the GHE.
Imo it’s not a physical reality.
See: http://principia-scientific.org/publications/New_Concise_Experiment_on_Backradiation.pdf
If my theory holds, I doubt an AGW’er will have much to ask, after seeing that they missed a 275K base in their assumptions.
If the sun is capable to keeping a BB earth 255K above it’s base temp of 0K, why wouldn’t it be capable of keeping our waterplanet 15K above it’s basetemp of 275K?
tallbloke says:
February 13, 2012 at 3:23 pm
Anyway, you still don’t understand N&Z’s ‘model’. They calculate the grey body temperature, and the actual temperature as derived from the surface pressure and the TOA insolation.
I think I understand it fairly well actually.
They calculate the grey body temperature for a rocky, atmosphere-less, planet with zero surface heat capacity (this gives the minimum average temperature for a given input flux).
They then calculate the ‘actual average temperature’ for those planets with an atmosphere from the surface pressure and near surface gas density using the ideal gas equation of state. (This assumes that the gas density is better known than the surface temperature which seems a questionable assumption to me, only applicable to 4 of the planets anyway, the application of the ideal gas law to the super-critical atmosphere of Venus is questionable too).
They then fit the ratio of those two temperatures to an arbitrary curve with P as the variable (see Brown’s critique of that process with which I agree).
[Reply] Read their papers Phil. I challenge you to find any reliance on density in their equations.
The ATE factor is then the ratio of these two numbers. Theirs is the more realistic model, because without an atmosphere and its consequent pressure, there is no ocean to spread heat around.
The assumption of zero heat capacity is unrealistic as indicated by the temperature distribution on the moon. That the Earth has an ocean makes it a poorer model since the heat capacity of the ocean is a major factor.
[Reply] Which part of ‘there would be no ocean without the atmospheric mass and pressure’ do you not understand? Are you aware of how small the energy distribution difference is between their lunar GB calc assuming no heat capacity and the diviner measurements? They get the actual average surface temperature correct to within 6K. The method used by ‘conventional models’ was 100K+ too hot. I don’t think they need to take any lessons in heat distribution from you or them.
Now, the conventional modelers say that Earth with no ghg’s would be 255K at the surface. This is arguable, though from N&Z’s point of view, it a fruitless argument anyway.
It is a fruitless argument because it’s an apples and oranges comparison. The Conventional view models an earth with an atmosphere and ocean and surface heat capacity and tries to remove the effect of GHGs. The N&Z approach attempts to model a rocky planet without an atmosphere or ocean and no surface heat capacity, in the case of Earth this leaves the effect of atmosphere, GHE, ocean and surface heat capacity out, so the rather large deficit due to these missing terms is assumed to be a fitted function of pressure. For the other planets with an atmosphere the term due to the ocean is absent. If you want to follow this approach then you’d have to account for the surface heat capacity as there’s no reason to assume that it’s a function of pressure. Even then you have two effects of the pressure of the atmosphere due to its heat capacity and GHE (filtering effect) both of which are functions of pressure so how do you disentangle them?
[Reply] What ‘term due to the oceans’. I challenge you to identify in their equations. No more posts from you until you find it or admit you are wrong about that and density.
This is because according to their theory, the surface temperature is a result of atmospheric mass and TOA insolation, and albedo is a result of temperature and pressure.
Their theory assumes constant albedo, if they want it to be a function of P then their constant 25.3966 should in fact be a function of P!
[Reply] Their theory does nothing of the sort. It uses the empirically measured lunar grey body albedo to obtain the grey body temperature for all rocky planets, from which they calculate ATE as a ratio between that and the actual surface temperature derived from atmospheric mass and distance from the Sun. Do us a favour and read their papers before you come back to admit you were wrong.
[Reply] Read their papers Phil. I challenge you to find any reliance on density in their equations.
Answer to Tallbloke the Ideal Gas Law is:
P=ρRT where ρ is the gas density
They say in their paper:
“This can be written in terms of the average air density ρ (kg m-3) as
ρTs =const.=Ps M/R (6)”
The whole of section 3.1 deals with this and the Ts in Table 1 is calculated using density!
Satisfied? I take it the ban is lifted and an apology will be forthcoming?
[Reply] Read it again Phil. Eq 7 shows that Ts/Tgb is equivalent to their exponential function which involves pressure only. the discussion is about Eq 8 which is Eq 7 transposed. So their theory does not rely on density as I said, and you are the one who needs to admit you’re wrong (no apology needed). You are not banned, but you won’t be having further comments published until after you step up and do the right thing.
You said:
This is because according to their theory, the surface temperature is a result of atmospheric mass and TOA insolation, and albedo is a result of temperature and pressure.
When I pointed out that they actually use a constant albedo and if their theory in fact uses an albedo which is a function of pressure then that should be included in their equation (8), you remarked:
“[Reply] Their theory does nothing of the sort. It uses the empirically measured lunar grey body albedo to obtain the grey body temperature for all rocky planets, from which they calculate ATE as a ratio between that and the actual surface temperature derived from atmospheric mass and distance from the Sun. Do us a favour and read their papers before you come back to admit you were wrong.”
I have read the papers, and my remark is correct.
[Reply] Their theory doesn’t use an albedo which is a function of pressure. An atmospheric albedo which is a function of pressure (and temperature) is a logical outcome derived from their theory. So once again Phil, man up and admit you are incorrect.
rgbatduke;
Excellent! Then perhaps they can reply to them instead of starting a thread in which they wish to claim that Willis was completely wrong in his criticism of Equation 7/8 and then ignoring the only post in it that shows that Willis was completely correct in his criticism of Equation 7/8, only his criticism wasn’t strong enough.>>>
I read Willis’ criticism and if you consider substituting an equation into the equation it was derived from to arrive at a variable that equals itself as correct criticism… I don’t even have words to describe that.
Your first comments at WUWT in regardf to calculating surface temperature properly were informative and valuable. Unfortunately I for one have seen nothing informative or of value from you since.
[…] SB Law of 255K), these figures have very little practical value. If you go to the links, I have two additional comments that illustrated this. The first one shows a very simple “step” function […]
Robert Brown @ February 13, 3:12 pm
I guess you are fairly new to blogging, but you may have to accept the fact that many threads wander into fringe areas around the lead article, and even off-topic. The exchange I was having with David Hoffer concerned some unusual and interesting aspects of how the N&Z hypothesis was being addressed or not addressed in various areas of the blogosphere. (was on-topic)
I’m sorry if you felt an ad hominem innuendo in my use of the word imbibe. Where I come from, the word has several meanings in addition to your wrong interpretation.
Bob, don’t worry about it. Robert was looking for any handy peg to hang his shirtiness on. 🙂
Bob, don’t worry about it. Robert was looking for any handy peg to hang his shirtiness on. 🙂
Actually, I didn’t understand what he was trying to say to, or about, me (or Anthony or Willis or whoever). I still don’t. I wasn’t really accusing you of ad hominem; rather asking what you meant. That’s why I put the smiley face at the end of the sentence.
rgb
Robert, I think Bob just meant the use of the word in the old fashioned sense of ‘partake of’ but ‘drinking in’ the written word rather than one of the many beverages available. By the way, I’m trying a Belgian dark beer brew kit for the first time, and considering using some molasses instead of some of the glucose. I don’t really know what quantity gives me ‘measure for measure’ though. Any experience to share?
rgb said:
“It isn’t terribly good science there (as it is an open invitation to cherrypick and engage in confirmation bias and other forms of Feynman’s “Cargo Cult Science”) and it only ends up being decent science if it is rapidly followed by a quantitative and consistent causal analysis that includes a full disclosure discussion of the possibly confounding causes and where the observation fails. I’m awaiting this in the case of Scafetta’s paper, but I’m not holding my breath.”
Nicola Scafetta is working with models but he is well aware that the correlations they show need to be backed up by plausible mechanisms if they are to be taken seriously. He sees that as “the hard part”. He already has some ideas that make sense to me. You would probably be a much tougher audience so why not ask Nicola to sample some of your home brew. That might take the sharp edge off criticism.
While it is desirable that causal analysis should “rapidly follow” it took over 30 years for Wegener’s “Continental Drift” hypothesis to be vindicated.
I think it is fair to say that the same applies to N&K, although their analysis did start with a series of physics equations which they boiled down to the dimensionless one you don’t like.
“So their theory does not rely on density as I said”
It’s here in this post:
“For a given pressure, the near-surface air density varies on a planetary scale in a fixed proportion with temperature, so that the product Density*Temperature = const. on average, i.e. higher temperature causes lower density while lower temperature brings about higher density according to the Charles/Gay-Lussac Law for an isobaric process.”
rgb,
You mentioned the possiblity of getting together today or Wednesday. Unfortunately I am teaching in Tennessee through to February 20 with no days off. Thanks to a certain university cancelling my contract, I no longer have any courses scheduled in North Carolina. It may be time to retire. For real this time.
It was a thrill to find Dukies such as you and Nicola getting involved in climate science issues. It would have been a blast to be a participant in some small way. I was hoping that the Physics department was showing the spirit to resist being engulfed by the Nicholas School of the Environment.
I’m trying hard to understand Dr. Brown’s objection to equation 7. As I understand it, he’s saying essentially that the equation was empirically derived (a best-fit regression), instead of being derived by a logical progression of real-world observations. I can understand that logic and it’s what I initially wondered about when reading N&Z’s first paper. I agree it would be much more satisfying to see an argument that derived an equation from first-principles if-then sort of logic.
However, I’m lost regarding the argument that if certain parts of an equation imply non-real results, then the formula must be wrong. For example, people that look at demographics will say that the replacement rate for a given society must be 1.9 children per female or higher in order to have a stable population. Dr. Brown seems to be arguing that since there is no such thing as a real-world 9/10 child, this statistic is meaningless. I’m not claiming that is what he’s saying; it’s just all that I can gather from what I’m reading; i.e. since we don’t have any observable planetary bodies with an atmosphere at 54,000 bar, then N&Z’s result must obviously be wrong.
Can somebody help me here? I believe Dr. Brown is trying to say something important to math-challenged people like me, but I’m not getting it.
ALL,
Am I getting irrational in my septuagenarianisticalific afflictions, when I expound the following?
I can see that the mathematical derivations of N&Z will be variously critiqued by those that step forward to oppose the new theory. (which is a normal part of science). This then boils down to acceptance of the arguments from whomever one might alternatively prefer as an authority. (camp or consensus culture annat)….. He said, she said, we said, they said, and I like her because she has [self snip] !!!
So, whilst the N&Z mathematical derivations may be “difficult”, it does not mean that they don’t work, even if why it is so, is not fully understood. However, if their hypothesis is correct it should be possible to obtain a series of correlating data with a range of parameters in the lab. If this is successful in outcome, then it should precede the maths in any paper, which should then be offered as a possible mathematical solution.
Of course, see earlier threads where low budget Konrad is still exploring such data.
And, I wonder if deep mineshafts with geothermal energy source might also reveal another piece of supporting empirical data.
Nick Stokes says:
February 14, 2012 at 2:15 am
Tallbloke said:
“So their theory does not rely on density as I said”
It’s here in this post:
“For a given pressure, the near-surface air density varies on a planetary scale in a fixed proportion with temperature, so that the product Density*Temperature = const. on average, i.e. higher temperature causes lower density while lower temperature brings about higher density according to the Charles/Gay-Lussac Law for an isobaric process.”
Yes Nick, but this is additional explanation. They do not need to rely on density because Eq 7 shows that Ts/Tgb is equivalent to their exponential function which involves pressure only. This is why there are two ‘equals’ signs in Eq 7. Immediately above Eq 8 they say
“Equation (7) allows us to derive a simple yet robust formula for predicting a planet’s mean surface
temperature as a function of only two variables – TOA solar irradiance and mean atmospheric surface pressure, i.e. [Eq 8]”
No doubt accurate density measurements for Earth could have assisted them in calibrating their pressure function, but density is not required for the other celestial bodies they then go on to calculate surface temperatures for. This is an important distinction.
I had to point this out to Willis Eschenbach on the demonstration of his own ignorance in the post this present discussion addresses. I’m somewhat shocked to see you making the same elementary error. I thought WUWT troll ‘Phil’ was being disingenuous with his comment here and willfully misinterpreting N&Z in an attempt to cast doubt on their work. Seeing you make the same mistake has me wondering if a lot of the argument over N&Z’s work is a result of people simply failing to read what they wrote.
Having said that, I had to correct Willis Eschenbach on his claim that they were using the atmospheric albedos inside equation 2 and thus ‘tunaeable parameters’ as well. Not that he accepted that he had made a ‘mistake’ even after I pointed it out. Phil has also parroted a variation of this error. N&Z use a single empirically measured grey body albedo (our Moon’s) in their Tgb for all rocky planets in Eq 2, which seems reasonable to me. I think he Willis-fully Hash’n’baulk’ed the theory and then trash talked it. Whatever his reasons, it ain’t science so far as I can see.
Robert Brown says Willis’ criticisms of Eq’s 7 and 8 are correct, despite N&Z’s elegant demolition of his faulty algebra in the headline post here. This and his errors on the Loschmidt effect in hs criticism of Hans Jelbring’s paper leads me to doubt the value of his other criticisms too.
Then there is Ira Glickstein’s misdirection of discussion of N&Z’s theory with the spurious discussion of the heat of initial compression, which is simply irrelevant to the discussion of the dynamic throughput of solar energy in an atmosphere subject to a gravitational field.
All in all, WUWT hasn’t handled discussion of Nikolov and Zeller’s theory at all well, to put it kindly.
No doubt accurate density measurements for Earth could have assisted them in calibrating their pressure function, but density is not required for the other celestial bodies they then go on to calculate surface temperatures for. This is an important distinction.
For what it is worth, density and pressure are not independent variables. The pressure at any given height is
. Atmospheric pressure has to support the weight of all of the atmosphere above any given height. Any fluid, atmosphere or not, in (even approximate) hydrostatic equilibrium must satisfy the relation:
(for
positive “up”). If one knows the thermal profile of the atmosphere (and assume that it e.g. an ideal gas) it is a straightforward mathematical exercise, although one that may or may not be easy to do analytically, to convert a function in one variable to a function in the other.
[Reply] True but irrelevant to my point, which is that having calibrated their EQ8, Which they could have done with temperature rather than density, they are able to correctly calculate the surface temperatures of the other celestial bodies using only their pressure function and the TOA insolation. Furthermore the pressure at any given height can be calculated by using the mass and the gravitational constant rather than the density.
This is related to why Nikolov and Zeller need two distinct exponential forms to fit the planetary data. The physics that describes the surface temperature of the extreme low pressure/density planets is different from the physics that describes/predicts the surface temperature of the four planets on their list with substantial atmospheres. In particular, the last four planets have atmospheres that consist of optically thick greenhouse gases. The first four planets have atmospheres that are optically thin. These are two completely different regimes, so the functional form of the surface warming changes. If you like, the exosphere begins at the surface of the first four planets — they lack meaningful convective transport and have only a tiny split between the direct radiation temperature from the surface and the radiation temperature of the extremely diffuse atmospheric gas.
[Reply] Yes, I agree it’s quite remarkable that their equation holds good across such a diverse set of temperature and pressure regimes.
Robert Brown says Willis’ criticisms of Eq’s 7 and 8 are correct, despite N&Z’s elegant demolition of his faulty algebra in the headline post here. This and his errors on the Loschmidt effect in hs criticism of Hans Jelbring’s paper leads me to doubt the value of his other criticisms too.
Willis is correct when he asserts that taking some data (
), normalizing it with a computed number 
to form 
, fitting the 
data to a mathematical form 
that is neither derived nor heuristically justified, and then multiplying out the normalization to get:
is hardly a “derivation”.
If I have data points
and a smooth function 
, and I use this function to convert the data to 
, empirically fit the data to a smooth function 
, and then assert that:
this is an identity, not a derivation.
If I define
, fit 
, then assert 
I haven’t “derived” anything at all. If I fit 
with a functional form that is not justified by any physical argument that has enough free parameters, I can find alternative descriptions of 
that are all equally meaningful, given that 
(lack of meaning is conserved).
[Reply] All very snarky, but not what Wilis said at all.
As for my “errors” concerning the Loschmidt effect in my criticism of Jelbring’s paper, Jelbring’s paper does not refer to any such effect. It quotes a single textbook that derives the DALR for an atmosphere in which there are parcels in convective motion. It asserts without proof that this lapse rate applies to an isolated ideal gas that is not being driven and is in true static equilibrium, even though an ideal gas (being ideal) has the thermal conductivity of an ideal gas and it is the work of a few seconds to see that the DALR atmosphere is not a state of maximum entropy. It then concludes that the atmosphere in question will have a lapse rate and hence be warmer at the bottom than at the top.
I do not question that dynamical atmospheres have a lapse rate. I do not question that the lapse rate is important in determining surface temperatures. I question — indeed, I categorically reject — the assertion that a lapsed atmosphere is a state of true thermodynamic equilibrium for an isolated ideal gas. I offer considerable proof that this is so, including the straight-up observation that if it were true it would violate the second law of thermodynamics.
[Reply] What you fail to appreciate here Robert is that there is a 120 year old paradox here which has not been resolved. If you had taken the trouble to read the Loschmidt thread on this site you’d be better informed, and if you had any science sensibility, a good deal less categorical too.
Whether or not you ultimately agree with my proofs, with the explicit statement of the author of a textbook on physical climatology on the thread (Caballero) that I am correct, with the statistical mechanical computation cited on the thread that concludes that I am correct, whether or not you take note that the DALR is always derived in the context of slowly moving parcels of air in a dynamical atmosphere and that any sort of additional mixing e.g. turbulence destroys it and restores isothermal equilbrium (as does conduction, but much more slowly) — it is difficult to assert that Jelbring dealt with any of this in his paper. He takes a well-known result of atmospheric dynamics, moves it out of context, and makes an entirely circular argument that it applies to the static case as well. It does not. The actual dynamics even of moving air parcels is “adiabatic” only to the extent that you neglect conduction, but an ideal gas has an ideal, easily computed, thermal conductivity that is not zero. Most textbooks point that out when they derive the DALR. Caballero’s certainly does.
[Reply] See the Loschmidt thread for where Caballero gets it right, where he gets it wrong, and where he gets it muddled. It would also have behooved you to have taken a bit more notice of WUWT commenter ‘Trick’ on your impossibly long thread. He tried to alert you to another equally eminent Author and textbook which sits on the other side of the paradox. You ignored him of course.
To conclude — I am certain that you are aware that your “argument” that I am not to be believed because I once stated something that you disagree with and that is disproved by something I’ve never heard of and therefore I must be wrong now is a textbook case of logical fallacy. This makes it all the more ironic when you conclude by stating:
All in all, WUWT hasn’t handled discussion of Nikolov and Zeller’s theory at all well, to put it kindly.
If by this you mean that Anthony hasn’t (to my knowledge) stepped into the discussion to defend a theory that he’s fond of not by addressing specific algebraic points of concern, the actual physics of the theory, but by http://en.wikipedia.org/wiki/Poisoning_the_well, I suppose you are correct.
[Reply] Anthony is not so much at fault as those who took advantage of the fact that he’s too busy to keep an eye on what they’re up to.
In the meantime, I’m perfectly happy to wait for Nikolov and Zeller’s actual derivation of equation 7 to continue the discussion, aside from answering specific questions about my specific objection to equation 7 in the comments above.
rgb
Dan in Nevada;
I’m trying hard to understand Dr. Brown’s objection to equation 7. As I understand it, he’s saying essentially that the equation was empirically derived >>>
His complaint relates to the number of free parameters which have been assigned as constants by N&Z. Essentially, N&Z have come up with an equation that successfully calculates the surface temperature of various planets from their insolation and their surface pressure. But, did they come up with an equation that is right simply because of the variables and constants they chose? We cannot say for certain because we don’t have enough data points (planets) to compare to. It could be that for a broader number of use cases, their formula will break down.
N&Z believe that their formula will hold up for any planet that one can get the data for.
RB believs they have fooled themselves by developing a complicated equation that is right for the 8 planets we do have data for, but will have no predictive value for a broader set of planets.
Can somebody help me here? I believe Dr. Brown is trying to say something important to math-challenged people like me, but I’m not getting it.
Sure. The point is that one can learn, or estimate, a lot about any physical quantity from a knowledge of its dimensions, its units. This is particularly true for exponential functions. Take exponential decay, for example, which describes things as disparate as the population of radioactive atoms. The idea there is that every decay event is independent, and occurs with the same probability per unit time.
Suppose the probability of a single atom decaying in some small time interval
is 
. This is easy to understand — think of it as rolling dice once a second, and if snake eyes comes up then the decay happens, but in a way that works for smaller and smaller intervals so that the probability per unit time is constant in the limit of very small times.
Then the number of decays we expect in a population of
atoms in that small time 
is just the probability of decay per atom times the number of atoms:
Physicists usually start thinking about finite times
, but they want to be able to use calculus to find the result so they assume things like “
is really big” and “
can be made arbitrarily small” so that the discretization error associated with turning this expression into a continuous expression can be ignored. Note that these assumptions won’t work at all well for 
atoms and very short times, because an atom can’t fractionally decay — either it does or it doesn’t. This sort of process is called “coarse graining” the derivatives — choosing intervals large compared to the place where discrete events matter, get small enough to use calculus.
If we coarse grain our decay problem we get:
and we do basic calculus. Don’t worry about understanding it if you’ve never had calculus, but if you have had calculus you should recognize this:
and exponentiating both sides and defining
is the number of particles one has at time 
, one gets:
There are some very general things about this derivation — the exponential function is the function that is directly proportional to its own derivative, and exponentials in physics therefore must describe this sort of differential relationship. However, this sort of relationship is common as dirt in science — physics and chemistry in particular — and statistics in general, making exponential functions very important. This particular example is exponential decay, but very similar reasoning applies to e.g. compound interest investments and exponential growth, trigonometry (the sine and cosine functions are parts of a complex exponential), oscillations and waves and ever so much more.
Physicists learn early on that when one introduces functions like an exponential into a theory — in particular any nonlinear function that has a power series expansion, such as
— the arguments of the exponential must be dimensionless. This is easy to understand. Suppose that 
in this expression were a length and had units of length. Length squared is an area. Length cubed is volume. Length to the 28th power is God knows what. Then the expansion for 
would have us adding a pure number (1) to a length to an area to a volume… which is nonsense. I don’t know what it could possible mean to add a liter to a meter.
That means that in our example above,
must be dimensionless! We know that the units of 
are units of time, say seconds, so the units of 
must be inverse time! There is really no choice here. It cannot be otherwise. Even if we didn’t know where 
came from (you can see above that it has units of “probability per second” and since “probability” has no dimensions this is inverse seconds) we would know its units because we know 
must be dimensionless.
This suggests that instead of using
at all, it might be better to use the time implicit in it: 
. This time is called the “exponential decay time” and we can write:
as a manifestly dimensionless form to describe the number of still-undecayed radioactive atoms as a function of time. Writing it with the
was OK, but it hid the true dimensions and characteristic time associated with the process from us. The second form is much more revealing, because now we can interpret the time that has appeared.
The point of this is that
isn’t a random number. It has a physical meaning. It has to be connected to a physical process — the one responsible for the decay occurring. This time has to appear naturally when considering the units and sizes of the actual components of the system in question.
To understand this, one has to learn a bit about Fermi estimation. Enrico Fermi was famous for his ability to take a physical process and, by considering the units and “reasonable” dimensions of the system in question, produce remarkably accurate estimates of the physics involved, although the idea applies to many things. I’ll include this link:
http://en.wikipedia.org/wiki/Fermi_problem
and quote from it: “Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes. (Performing the Fermi calculation first is preferable because the intermediate estimates might otherwise be biased by knowledge of the calculated answer.)” In other words, Fermi estimates are invaluable as sanity checks. They reveal results that, however much we are biased to believe in them, are in the end unbelievable. You can learn a lot more about Fermi estimation online — it is literally a part of most introductory physics courses. I’ll offer a single example of Fermi estimation and dimensional analysis here. It is not inapropos to my objection.
Students often are asked to compute the moment of intertia of things like spheres, rods, cylinders, grandfather clock pendula, in physics courses. Doing so involves formulating and evaluating an often-complicated integral and perhaps using something like the parallel axis theorem. It is easy to make purely algebraic errors. How can a student tell if their end answer makes sense, at least enough sense that it might be correct? By checking its units and making sure that the answer satisfies Fermi! The former requires that they look at the size and mass involved. The units of a moment of inertia are
— mass times length squared. The units of the algebraic answer had better contain the mass of the object, to the first power, and its characteristic size to the second power, or it is wrong out of hand. Then one can look at everything else. Most moments of inertia about the center of mass of an object have the form 
where 
is a pure (dimensionless) number between 0 and 1. It cannot be negative, and I can’t think offhand of a case where it could be greater than 1 if 
is the maximum radius of the system relative to its center of mass. If a student somehow ends up with 
in their answer, even if it otherwise has the right units, they probably divided instead of multiplied somewhere, or made some other error in their algebra or arithmetic.
That’s it — in physics the arguments of exponentials must be dimensionless or they are nonsense. If a dimensioned variable appears in the exponential there must be a similarly dimensioned variable that cancels its units. Finally, in order for the expression to make sense, the actual dimensioned variable that provides the “characteristic” length, or time, or pressure, in the expression has to be physically reasonable. It is this characteristic pressure that dominates the exponential behavior. It is the signpost towards the important physics, and vice versa. Like
in the previous example, we should be very worried if it is much more than order unity away from the range of mundane values we expect for the actual physical quantities we are trying to describe.
All I did is take Nikolov and Zeller’s empirical equation 7 and put it in manifestly dimensionless form. This is unique — there is no other way to do it, any more than there is for the radioactive decay example above. This reveals that their coefficients are actually dimensioned pressures
, the characteristic pressures 
where 
has an argument of order unity, where the “shape” of the exponential is important. I argue that it is unreasonable for a characteristic pressure of 54,000 atmospheres to describe the actual physics of a gas at a pressure of 
atmospheres or even less. It can’t even reasonably describe a gas in the pressure range from 1 to 100 atmospheres. The second characteristic pressure that appears is 202 bar/atmospheres (at this level of Fermi-estimate description the difference doesn’t matter). This isn’t as bad as the 54,000, but it is still worrisome. It is still a “
answer, given that the largest pressure being fit is 92 atmospheres.
The last area of concern in their result is the very, very odd exponents that appear within the exponentials. One of them is
. Again, in physics, one expects there to be very ordinary relationships between connected quantities in a physical theory, especially when one is considering an idealized theory like an ideal gas (or a normal gas far away from critical points where its behavior is expected to be “nearly” ideal). 
has fairly straightforward exponents — they are all 1!
It’s true that other exponents can appear — an ideal gas that is confined to a container and adiabatically expanding follows a different curve, one where
a constant. This means that the exponent 0.385 in the second term is not inconceivable — it is difficult for me to see how it could arise from any simple dimensional analysis of the problem — it is close to but not equal to 
for an ideal diatomic gas, but the atmospheric gases of the planets in question do not all have the same 
— Mars is mostly triatomic CO_2 and the Earth is mostly diatomic N_2 and O_2, for example, and Triton is a complicated brew of all sorts of non-diatomic molecules.
However, the particular exponents of exponents and characteristic pressures in the second term of the fit depends in detail on the values of the first exponential term with its unphysical 54000 and 0.064. If one simply fit (say) the last four planets all by themselves, one might get a functional form that wouldn’t make Fermi (or me, channelling his and Feynman’s ghosts in this discussion) from running screaming from the room — or rather, gently saying “no, that cannot be a physically meaningful description of the phenomena”.
Hopefully this explains why Nikolov and Zeller’s empirical fit almost certainly is not physically meaningful as it stands, in terms even a non-math lay person can understand. There are many ways one might fit radioactive decay data with combinations of functional forms, but only one of them is going to be rationally derivable and it will contain a characteristic time that is directly characteristic of the physics of the process, not e.g. the age of the Universe or the period of the Earth around the Sun. At 54000 bar and the surface temperatures in question, the atmospheres would no longer be gases in the case of all of the colder planets. I don’t know the coexistence curves offhand for the components of Venus’ atmosphere, but I’m guessing even its atmosphere would liquify at this pressure and its ambient temperatures.
rgb
His complaint relates to the number of free parameters which have been assigned as constants by N&Z. Essentially, N&Z have come up with an equation that successfully calculates the surface temperature of various planets from their insolation and their surface pressure. But, did they come up with an equation that is right simply because of the variables and constants they chose? We cannot say for certain because we don’t have enough data points (planets) to compare to. It could be that for a broader number of use cases, their formula will break down.
N&Z believe that their formula will hold up for any planet that one can get the data for.
RB believs they have fooled themselves by developing a complicated equation that is right for the 8 planets we do have data for, but will have no predictive value for a broader set of planets.
This is also true, but does not actually answer Dan’s question. I just did that above. The problem with fitting eight points of data with four free parameters was actually originally raised by Willis. All I did here is refine it and plot the actual fit against the actual data so one can see that it is not, in fact, a good fit of all eight points, but rather fits four points well and four points poorly, three at one end and one at the other. Where “poorly”, in an arbitrary nonlinear functional fit to data without without error bars, with no
or objective measure of quality of fit even theoretically possible, is in the eye of the beholder, to be sure.
As for predictive value: Suppose one simply connected the data points with a cubic spline, with any number of parameters you like. If one supposes that there is a monotonic increasing function that describes the data, then this spline might well have predictive value of that monotonic increasing function, as might a line you just draw with a pencil so that it passes smoothly through all of the points. However, there isn’t any physics in the interpolating spline, the line you draw with your pencil, or in Nikolov and Zeller’s equation 7. The coefficients of the spline are not simply related to the actual physical processes that govern and establish the hypothetical relationship, and one gets zero physical insight or knowledge from knowing them. The four parameters of Nikolov and Zeller’s fit are manifestly not related to the actual physical processes that govern the surface temperatures, and one gets zero physical insight or knowledge from knowing them, even though they, too, might have just as much predictive power as a spline. Would they fit surface temperatures on the gas giants? Highly doubtful. Do they fit surface temperatures on the moon as they are now? Only if you are generous about what constitutes “a fit”.
There is a lovely paper written by a couple of Greek guys who are analyzing e.g rainfall that I have squirrelled away somewhere that illustrates the problem of taking a small finite section of data and extrapolating it vs interpolating it. Interpolation is generally “easy” — lots of functions will fit/interpolate any small data set, especially when one is willing to use any nonlinear function with any form to do so without regard for any sort of justification or reason to think it is a correct or relevant form. They illustrate this by taking IIRC a cosine function plus white noise and then analyzing how fits to this function might well proceed. If you take a very small interval and fit it, your best fit will be a linear function, and you are tempted to say “Aha, I’ve discovered that
is linearly dependent on 
” and then use that to predict the end of the world, if 
exceeding some threshold will bring it about. This argument is, in fact, familiar to us all in CAGW “science”. Of course, eventually one gets more data, and — Aha! — now the data turns up. In fact, it looks a lot like the true dependence of 
on 
is quadratic! Eureka! Surely now we can use it to predict our catastrophe.
Only we, gifted with God-knowledge, know that this is an illusion. They only learn of their error when they get still more data and their quadratic function fails to extrapolate and they now have to add e.g. a cubic terms, or perhaps some bright lad then tries to fit an exponential to it, fails, and tries — just saying, you know — an exponential with its argument itself a nonlinear exponential function, all with adjustable parameters. Well, the function is still smooth — there are an infinity of smooth nonlinear functions that correspond within the fit domain, all with the same first
terms in their power series expansion (for example) and all of which differ completely beyond this point. Even the cosine could be modulated with e.g. a long time exponential decay (or other modulating function) and you couldn’t fit it or observe it until you had tracked many cycles of oscillation and identified the apparent cosine.
This is why simply fitting arbitrary functional forms to a small data set, however successful it might be at interpolating the data, however predictive it might be of new data within the interpolated domain, is not useful or meaningful. One can always perform such fits many different ways, and I haven’t even gotten to overcomplete bases yet where even the fit in terms of a given set of functions is not necessarily unique. All of this is well known in functional analysis. In order for the results of a fit to be anything other than heuristic and descriptive, the numbers in the fit and the functions themselves have to have some physical basis. Willis pointed out the problem of fitting from the infinitely large set of all possible nonlinear functions — hell, one might well find a one parameter fit out of that set — without any sort of physical argument supporting it or criterion for judging goodness of fit and a claimed “derivation” of equation 8 that was really just restating the definition of the function empirically fit via equation 7. I pointed out that it is worse than that — the fit they obtained does contain hidden physics (whether they like it or not) [snip].
[Reply] Now you’re getting the hang of it! Leave the insult to the end so you don’t lose so much of the post. 🙂
rgb
Robert Brown (February 14, 2012 at 3:10 pm):
Dr. Brown,
I do not quite understand why is all that twisted reasoning, when the reality of our derivation is simple and can be summarized in the following commonsense points:
1) We define the ‘Greenhouse Effect’ as a ratio of the actual surface temperature to the planet’s equivalent gray-body temperature, since such a ratio expresses the integrated thermal effect of the atmosphere in a single non-dimensional number (non-dimensional numbers as you know are widely used in fluid dynamics to describe turbulence and other phenomena). This definition also has a physical meaning one can call relative Atmospheric Thermal Enhancement (ATE).
2) Our gray-body temperature model is not arbitrary, but based on proper integration of the SB law over a sphere and uses values for regolith albedo and emissivity that are representative of values measured for Moon and Mercury. Even the average albedo of the earth surface (0.12) is very close to that of the Moon’s rocky surface (0.11). The data suggest that short-wave substrate albedo and emissivity of airless planets are quite conservative quantities, i.e. A ~ 0.11, and e ~ 0.95.
3) Our analysis revealed that mean surface total pressure (Ps) is the only parameter that nearly completely explains the ATE values for all 8 planets. No other parameters such as ‘greenhouse-gas’ concentrations or their partial pressures, or the actual absorbed radiation by planets (accounting for observed albedos) came even close to describing the ATE variation. Hence, the derivation of Eq. 7. Again, NTE(Ps) was derived using non-linear regression!
4) Eq. 8 is simply a solution of Eq. 7 for the surface temperature (Ts). This is a legitimate and simple (high-school level) math, and it’s really puzzling to me why it prompts any questions at all. Willis made a silly algebraic error of substituting Eq. 7 into itself, thus arriving at the non-nonsensical and false conclusion that Ts = Tgb * (Ts / Tgb). This is a demonstration of his ignorance in math, not a deep thought!
With respect to your comment that pressure and density are not independent variables – we never claimed that they were! However, at the surface, the mean atmos. pressure is only a function of the average weight of atmospheric column above a unit surface area and gravity. Surface air density, on the other hand, depends on surface pressure and temperature. Hence, the mean pressure at the surface is independent of near-surface temperature and density! That is because the average thermodynamic process at the surface is isobaric in nature.
In summary, the tight exponential relationship between NTE and pressure is real, and the fact that it is described by a function, which coefficients cannot be easily interpreted in terms of known physical quantities, does not invalidate that relationship! This is because it is a higher-order emergent relationship, which summarizes the net effect of countless atmospheric processes including the formation of clouds and cloud albedo. This relationship might not be precisely reproducible in a lab, simply because it may require a planetary scale to manifest. However, a lab experiment should be able to validate the overall shape of the curve defining the thermal enhancement effect of pressure over an airless surface. BTY, this shape is already supported by the response function of relative adiabatic heating defined by Poisson’s formula (Fig. 6 in our paper).
davidmhoffer says (February 14, 2012 at 3:58 pm):
RB believs they have fooled themselves by developing a complicated equation that is right for the 8 planets we do have data for, but will have no predictive value for a broader set of planets.
I think you right about Dr. Brown’s belief. However, if those planets span a really broad range of conditions as they do, it is very unlikely that this relationship will break. The tightness of the relationship suggest that this is NOT an accident, but a real physical phenomenon … Read my comments in the previous post addressing Brown’s arguments…
This whole conversation about regression coefficients is really meaningless, as it reveals a lack of understanding about the fact that we are dealing with a HIGHER-ORDER EMERGENT RELATIONSHIP that is rooted in the Gas Law, but embeds complexities that are beyond the simple gas law equation and not necessarily observable in a lab such as the cloud dynamics and cloud albedo. In a sense we are dealing with an interplanetary manifestation of the Gas Law, which maybe a higher-level fractal expression of the simple gas law equation … For those, who are not familiar with fractal structures, please see
http://en.wikipedia.org/wiki/Fractal
http://en.wikipedia.org/wiki/Fractal_dimension
Fractals as an organizational principle in Nature occur not only in physical structures, but in the hierarchy of processes as well.
Ned,
I had the oddest thought. What would the result be if you were to derive all your equations and constants, but limit yourself to only three planets for doing so? Say Earth, Venus, and Mars. If you did that, and made it clear that ONLY data from those three were used, then we’d have the use case that RB demands. An equation that is built upon a very small set of data, and then it either extrapolates to other planets… or doesn’t.
RB,
Am I on the right track here? Would you choose three different panets?
dmh
PS – btw RB, I got a lot of value out of your last two comments, thanks. I’m not saying that I agree 100%, just that there’s a lot of value to be had in a constructive discussion of the issues which is what I saw in your last two comments. thanks!
Please could Robert explain the physical basis of the imaginary number ‘i’ (or ‘j’ in engineering) the product of which when multiplied by itself is minus 1, which is used extensively in electronics design and control engineering?
Presumably any competent Duke physicist at the time of the invention of this imaginary quantity which defies the laws of mathematics would have rejected it out of hand for being “absurd nonsense” and therefore of no possible use?
Thanks. 😉
Wiki ref: http://en.wikipedia.org/wiki/Imaginary_number
davidmhoffer says (February 14, 2012 at 7:14 pm):
I had the oddest thought. What would the result be if you were to derive all your equations and constants, but limit yourself to only three planets for doing so? Say Earth, Venus, and Mars. If you did that, and made it clear that ONLY data from those three were used, then we’d have the use case that RB demands. An equation that is built upon a very small set of data, and then it either extrapolates to other planets… or doesn’t.
David,
We have already done this! In fact, the regression constants in our Eq.7 were derived from a plot of ln(Ts/Tgb) vs. ln(Ps) that did NOT include Titan, Moon and Mercury (we have not explicitly stated this in the paper). You can reduce the number of points (planets) and still get a very similar response function as long as the planets included in the regression span more or less the the whole environmental range. I think using Venus, Earth, Triton ans Europa will produce a function that very closely predicts the mean temperatures of Mars, Titan, Moon and Mercury. Try it …
davidmhoffer said:
“N&Z believe that their formula will hold up for any planet that one can get the data for.
RB believes they have fooled themselves by developing a complicated equation that is right for the 8 planets we do have data for, but will have no predictive value for a broader set of planets.”
I think that helpful summary from davidmhoffer is right.
So, we can tell from the Gas Laws and observations that planets with atmospheres are very different from those without.
We can see from Venus and Earth that despite their very different atmospheres there is an observed match (approximately) between temperatures on both Earth and Venus at the same atmospheric pressure after adjusting for distance from the sun.
N & Z are doing their best to ascertain whether the same relationship applies on other planets within the solar system and so far it is looking good although the precision of the data is weak.
In the process N & Z have put forward some equations that fit the observations but to my mind it is early days because we just don’t have enough planets or enough variations between planets or accurate enough data to provide absolute proof. N & Z acknowledge those limitations but aver that what they do have is enough to demonstrate a surprising similarity from one planet to another regardless of the vast differences in their atmospheric compositions.
Then rgb comes along and from an ivory tower says that because it isn’t all perfect and that therefore it cannot (yet) be shown to be an absolute proof applicable always and everywhere then it has no significance or value at all.
Well, excuse me, but I think that given the Gas Laws and the observations we do have then it is perfectly reasonable and indeed valuable for N & Z to announce that they have created a formula that could extend the Gas Laws as observed on Earth to other planets and thereby say something useful about the climates on all planets everywhere.
My personal opinion is that in due course they will be found to be correct and that for every planet with an atmosphere it is atmospheric mass, planetary gravity and solar input that ultimately defines every aspect of the atmospheric circulation and that nothing else affects total system energy content. All other factors simply redistribute energy differently within the system.
I have no doubt that any planet which fails to configure its atmosphere according to atmospheric mass, planetary gravity and solar input will simply have no atmosphere. Either it will have boiled off into space or be frozen and congealed on the surface.
However given the wide range of ‘successful’ planetary atmospheres already found within the solar system it is clear that planets without any atmosphere at all are extraordinarily rare so that one must assume that the relationships which N & Z are endeavouring to describe are very robust.
rgb’s time would be better spent accepting that N & Z are attempting something novel here and doing the best possible with the data currently available.
My understanding of Equation 7 is (a) that it is empirically derived (b) unfortunately I don’t know what “exp” means so I cannot check myself (c) there are four six-figure numbers measured / calculated / tuned from this empirical fit that produces the curve with all the planets on it.
My question is, how many planets are needed to define this curve requiring those four very precise numbers extracted from the curve-fit? My first thought was, this is a logarithmic curve that is defined from just three fixed points. But here I am not so sure.
How many planets are surplus to definition requirements, and therefore constitute hard evidence?
Is it possible to rescale the graph so that a straight line appears, using logarithmic scales? Seems this would help a lot to convince, if it is possible. P=1000W 🙂