Guest Post by Willis Eschenbach (@weschenbach on X, blog at Skating Under The Ice)
Like Don Quixote suffering a coffee overdose, once again I mount my steed, take up my lance, and go tilting at windmills.
Here’s a thought experiment. Consider the Earth with no atmosphere and with the same surface albedo of 12.5% that it has now. How warm would it be?
In this condition, because there is no atmosphere, there are no heat losses from the surface by sensible or latent heat. For the same reason, there’s no reduction in incoming solar power as a result of reflection from clouds or solar radiation absorbed by the atmosphere. Solar radiation absorbed at the surface is radiated straight back to space. So we can calculate the temperature directly from the absorbed radiation using the Stefan-Boltzmann equation. This equation relates watts per square meter of surface radiation to the corresponding temperature of the radiating surface. I used the S/B equation with the average emissivity of the Earth, which is ~ 0.98, to calculate the surface temperature. All values are in watts per square meter (abbreviated variously as W/m2 or W/m2).
Figure 1. Total surface radiation absorption, Earth with no atmosphere, with the same albedo as the current Earth. Total absorbed solar radiation is the incoming 340 W/m2 minus the 43 W/m2 reflected solar radiation. Integer errors are due to rounding. All values are in watts per square meter (abbreviated as W/m2 or W/m2)
Minus two degrees C. What you might call totally chill. Just below freezing, in fact.
Now, over millions of years, let’s slowly add in an atmosphere and when it matches the modern atmosphere in all respects, let it percolate for another few million years.
After adding the atmosphere, there are lots of changes. Atmospheric absorption cuts down on the amount of solar radiation hitting the surface, which cools the surface. Of course, reduced surface radiation also reduces the amount reflected. However, this reduction in solar radiation at the surface is more than compensated for by the atmosphere adding in 340 W/m2 of downwelling longwave (thermal) radiation from the atmosphere to the surface (yellow arrow in Figure 2 below), which provides significant warming.
And back to the chill side, having an atmosphere allows for sensible and latent heat loss to the atmosphere, which cools the surface. In addition, with an atmosphere we get atmospheric absorption of sunlight, emergent phenomena like thunderstorms, and cloud radiative effects, all of which cool the surface.
It’s a mixed atmospheric bag that ends up with about 20°C less temperature change from the no-atmosphere to the with-atmosphere condition than you’d expect based on the large increase of ~ 212 W/m2 in absorbed radiation at the surface.
With that as prologue, here’s the surface radiation absorption with our current atmosphere to the same scale as Figure 1.
Figure 2. Total surface radiation absorption, Earth with an atmosphere. This 510 W/m2 is all the power absorbed by the surface. (Yeah, yeah, I know there’s geothermal heat. It’s on the order of tenths of one W/m2, so it’s always ignored for this level of analysis.) The yellow/black arrow is the downwelling longwave (thermal) radiation from the atmosphere to the surface.
OK. Some simple math.
The amount of radiation absorbed by the surface increased from 298 W/m2 with no atmosphere, to 510 W/m2 with an atmosphere, an increase of 212 W/m2.
Due to surface cooling from reduced solar hitting the surface as well as sensible and latent heat loss to the atmosphere, when the atmosphere was added, the temperature only went from -2°C to 18°C, an increase of 20°C.
This means that for each additional W/m2 absorbed by the surface, including all possible influences and feedbacks from clouds, water vapor, sensible and latent heat loss, etc., in the long term the temperature increased by 20°C / 212 W/m2 = 0.09°C per W/m2
If we use the IPCC canonical value of 3.7 W/m2 per doubling of CO2, this would mean that the equilibrium climate sensitivity at the surface is 0.35°C per doubling of CO2.
“But wait”, I hear you thinking. “Climate sensitivity is how much the temperature changes, not with downwelling longwave radiation at the surface, but how much temperature changes with the “greenhouse effect” radiation (GHE) from the atmosphere and the clouds, as measured at the top of the atmosphere (TOA)”.
And you’d be right. That’s the definition.
However, we can allow for this by understanding the relationship of surface downwelling longwave and downwelling “greenhouse radiation” from the atmosphere and clouds.
When we look at the current global correlation between the poorly-named atmospheric “greenhouse radiation” measured at the top of the atmosphere (TOA) and the surface downwelling longwave radiation, when the TOA-measured greenhouse radiation changes by 1 W/m2, due to internal feedbacks, the surface downwelling longwave radiation changes by 1.26 W/m2. Or vice versa. In either case, they move in synchrony.
Figure 3. Scatterplot, surface downwelling longwave radiation versus TOA-measured “greenhouse” radiation from the atmosphere and the clouds. At the monthly level, there is no temporal lag between the two. Current average GHE radiation is 158 W/m2.
Multiplying the surface sensitivity by 1.26 to convert to sensitivity to greenhouse gases increases the equilibrium climate sensitivity from the surface value of 0.35°C per doubling of CO2 calculated above, to a final figure of 0.44°C per CO2 doubling.
OK, that’s one way to get there. Interestingly, for verification of the sensitivity estimate, we can calculate the equilibrium climate sensitivity in a totally different manner. Consider the same thought experiment as above.
With no atmosphere, the GHE radiation is zero W/m2. Currently, the GHE radiation is 158 W/m2. That gives us 20°C / 158 W/m2 * 3.7 W/m2_per_CO2_doubling = 0.47°C per CO2 doubling … compared to the 0.44°C from the previous calculation using a different method, that’s excellent agreement. So to be conservative, let me call the warming on the order of half a degree C from a doubling of CO2.
This ~ half degree C of surface warming per doubling of CO2 represents a long-term equilibrium calculation, because it includes all known and unknown atmospheric factors and feedbacks involving water vapor, cloud radiative effects, latent and sensible heat losses, atmospheric absorption of solar radiation, all of that. The climate system during the Holocene is basically in a long-term (millennia) dynamic steady-state.
One advantage of using this method to calculate climate sensitivity is that the radiation numbers are large. As a result, small variations or uncertainties in them don’t change the answer much. For example, the current calculated ~ 2 W/m2 increase in “greenhouse radiation” since “pre-industrial” times is not significant because it is only ~ 1% of the change in downwelling longwave radiation from the no-atmosphere to the with-atmosphere condition. Basically, the answer is the same whether it’s included or not.
And while my estimate of the equilibrium climate sensitivity of ~ half-degree per CO2 doubling is well below the three degrees per doubling that the IPCC uses as the sensitivity, it’s not outside historical estimates.
Figure 4. A large number of different estimates of the equilibrium climate sensitivity over the last half century, coded by color. Pale blue lines show the IPCC uncertainty values. My estimate of a half-degree per doubling is shown by the horizontal dotted black line.
Here are the authors, dates, and values of the best estimates shown in Figure 4 that are under 1 W/m2.
Author Year ECS Class
1 Specht et al. 2016 0.37 Theory & Reviews
2 Idso 1998 0.42 Theory & Reviews
3 Lindzen and Choi 2009 0.47 Observations
4 Harde 2017 0.65 Theory & Reviews
5 Lindzen and Choi 2011 0.72 Observations
6 Bates 2016 0.92 Observations
References are in the paper here.
In closing, in my post “Testing A Constructal Climate Model“, I described how the Constructal model estimates a climate sensitivity of 1.1°C per doubling of CO2. However, in that post I said:
Finally, this is a maximum sensitivity which does not include the various emergent thermoregulatory mechanisms that tend to oppose any heating or cooling. This means the actual sensitivity is lower than ~1.1°C per 2xCO2.
This latest result, of ~ half a degree warming per doubling of CO2, which includes not only emergent phenomena but all atmosphere-related phenomena, is in line with that assessment.
In related news, providing this method holds up, this means
“APOCALYPSE CANCELLED! SORRY, NO REFUNDS!”
It’s very unlikely that we will double the current CO2 level. Burning all total known reserves, not just the proven reserves, but all known reserves, will emit about 4,800 gigatonnes of CO2. This will raise the CO2 level in the atmosphere by ~ 280 ppmv. That’s far from doubling the current 420 ppmv atmospheric CO2 level.
This means that about a third of a degree of future warming lies in the ground in the form of fossil fuels.
Sadly, I fear the chance that this analysis will convince any true believers is small. They’re caught in the Upton Sinclair Trap. He famously said:
“It is difficult to get a man to understand something, when his salary depends on his not understanding it.”
It does seem recently, however, that more and more people are seeing through the climate grift. At least the US Government seems to be getting off the climate merry-go-round of endless failed predictions.
And to return to my analysis, what am I missing here? Where are my math mistakes or the holes in my logic? Why isn’t this a solid estimate of the equilibrium climate sensitivity, giving the same answer when calculated in two different ways?
Regards to all on a cloudy fall day,
w.
[UPDATE] In response to comments, a clarification.
A general comment for all, to clarify my position.
I do think that radiatively active gases affect the temperature. But I don’t think that small variations of a few watts per square meter in the resulting downwelling radiation change the temperature anywhere near as much as the conventional wisdom would have you alarmed to believe.
In addition to theoretical arguments and other evidence, my own climate model is able to do a very good job of emulating the real-world temperature using only albedo and the Ramanathan “greenhouse factor”, the percentage of upwelling surface radiation that is absorbed in the atmosphere.
Here is a more recent graphic from my ever-evolving Constructal climate model, showing how those two measurable environmental variables, albedo and greenhouse factor, are all you need to emulate the absolute temperature.
This also makes physical sense. Albedo controls how much energy is entering the system at any time. The greenhouse factor controls how much energy is leaving the system at any time. Any imbalance between those two will be reflected in a temperature change … just not as much as folks think.
This excellent goodness of fit of the Constructal climate model is further evidence that the greenhouse factor, the percentage of upwelling radiation absorbed by radiatively active gases in the atmosphere, does in fact affect the surface temperature.
Regards to everyone,
w.
As Is My Habit: I ask that when you comment, you QUOTE THE EXACT WORDS you are discussing. This is essential to prevent misunderstandings.
According to AI the difference in air pressure is the reason for the higher temperature at the bottom of a mountain than at the top.
If we imagine a mountain reaching from the bottom of the troposphere to the top of the troposphere the reason for the difference in temperature should also air pressure.
Air pressure is due to the weight of the atmosphere, while gravity provides the weight.
Clearly there is more energy at the Earth’s near surface than at the top of the troposphere. Absorbing and emitting energy by the radiative gases cannot create more energy. On the other hand, the Gravitational Potential Energy can be a source of energy.
Regarding the average temperature of Earth and, given the temperature gradient of the atmosphere, the average should be found around halfway to the top, not at the bottom.
Just goes to show that AI might as well stand for Absolute Idiocy.
John Tyndall, as well as being a brilliant experimenter, was also a keen alpinist, and measurement ground temperatures at altitude, as well as “air temperatures”. I’ll throw a bit of clickbait at you, and suggest you go to https://archive.org/details/heatamodemotion05tyndgoog, and read Tyndall’s book.
I’ll leave it to you.
Willis, your ‘thought experiment’ starts with a picture of what looks like Sol illuminating the lunar surface. That implies that you are starting with a body the size of Earth, but not only lacking an atmosphere and clouds, but also lacking water. That is an important omission because the directionality of specular reflectance from water, particularly at high angles of incidence, is much greater than for terrestrial materials and especially for lunar-like materials that are dominated by regolith.
Even CERES does not provide us with good estimates of the out-going light lost to space currently because of the geometry; it only measures light reflected off Earth up to a latitude of 82 degrees.
More importantly, because of how specular reflection works, a sensor has to have the telescope in the same plane as the source (sun) and the normal to the surface (point of incidence for a ray); it also has to look at the same angle as the angle of incidence! Miss it by a few degrees and the sensor will only record stray diffuse light. That means the telescope has to be steerable, not fixed at right angles to the orbit of the satellite. Thus, almost all the specular reflection is missed! All that one gets over the oceans is the diffuse back-scattered light, which is minimal compared to the specular reflection, especially in the deep, open ocean. That means, the estimate for the forward-scattered light is biased low for high angles of incidence.
All the above basically means is that the estimate for reflected energy lost to space is a lower-bound. It is clearly higher. The question is, how much higher?
I love this place!
Thanks, Clyde! 🙂
You are welcome, and thank you!
Clyde, one thing I think I know, is that the surface cooled from a molten condition to what it is now, over the last four and a half billion years.
Another thing I have personally observed is that night time temperatures drop, and winter is colder than summer.
I see no reason to disagree with Baron Fourier who opined that the Earth loses all the heat it receives from the Sun, plus a little interior heat. Observation, measurements, and theory seem to back us up.
Adding CO2 to air does not “make the Earth hotter”. Anyone who thinks so is obviously ignorant and gullible in this regard.
Keep in mind the SB T^4 relationship. It tells us that heat loss was at a much faster rate during the molten phase. It is the rate that is critical for the net behavior.
Not sure what you mean. I believe the present rate of cooling is around one to four millionths of a Kelvin per annum. Slow but sure. I’m pretty sure that any reduction in the rate, caused by changing the composition of the atmosphere, is unlikely to be noticeable.
Is that what you meant?
No. I meant that because of ‘T^4’ a molten Earth will radiate to space, thus cooling, more rapidly than what it is currently doing. I was not considering any changes in the atmosphere other than temperature.
Clyde, I agree that rate of cooling has slowed, as you say. I’m not sure what you meant by “net behaviour”, or why the rate of cooling is “critical”.
No offence intended, I’m just not sure what you are trying to say.
What I’m saying is that if the rate of cooling (flux) it greater than the rate of heating, then the Earth will cool over time. That was the state of the Earth when the surface was molten. If the two rates are equal, then the Earth is in equilibrium, and a small change in any of the parameters can reverse the thermal state. That is what I meant by “critical.”
I agree. At present, the Earth loses 44TW or so. As Fourier said, the Earth lose all the heat it receives from the Sun to outer space, plus a little internal heat – about 44 TW at the moment.
All anthropogenic heat is lost to space. Gone. Vanished. No local “conservation of energy” to be seen!
You can see why I can’t help laughing at the frantically wriggling pseudoscientific CO2 obsessed doom-mongers.
Most AGW advocates don’t even recognize that the Earth radiates away heat even during the day! it’s why the daytime temperature curve is not a true sine wave, the sine wave from the sun insolation is mixed with an exponential decay signal, even during the day.
Think most people don’t understand that the cooling you mention is a reduction of the TOTAL heat content of the Earth.
Most think only of the surface temperatures and its variations.
One thing I didn’t see you mention is the radiative decay in the mantle. Supposedly equals about halve the total energy loss of the Earth.
Willis wrote:
“solar radiation [energy, i.e. capacity to do work] hitting the surface”
What a bizarre statement, Willis. Does the capacity to do something “hit” things? Does your capacity to go fishing “hit” you in the stomach? That would be a very odd thing to see.
And before you lie again that these are somehow not your own words (see “However, you have falsely interpolated “[energy]” and “[being available to do work at]” in the middle of a quote of mine, making it appear as if I said it” which you said on June 25th), here is where you did, in point of fact, indisputably write them. You wrote “radiation is energy” here:
https://wattsupwiththat.com/2025/05/29/not-all-that-sensitive/#comment-4078770
And you wrote “energy is the capacity to do work” here:
https://wattsupwiththat.com/2024/05/13/modeling-the-mysteries/#comment-3909732
(I’m treating “capacity” and “being available” as synonyms in this context, it doesn’t matter which one you use)
So no, those syllogisms are not in any way “falsely interpolated”. That was simply another one of your damned lies, wasn’t it?
Willis may think that the “capacity to do work” implies that “work” always occurs, because he believes that adding CO2 to air makes thermometers hotter.
However, the energy emitted by ice at 300 W/m2, obviously has the “capacity to do work”. Adding this energy to something like hot soup (or coffee) seems to do “reverse work”<g>, resulting in a lower temperature.
Willis waffles, implying much, but endeavouring not to commit himself to anything specific. Any attempt to pin Willis down can result in a torrent of abuse from Willis, accusations of lying, threats of “banning”, and so.
The vague untestable declaration is Willis’ stock in trade, backed up lordly assumptions that he can disregard the laws a of physics by saying “it’s close enough that it doesn’t matter in practice”, or words to that effect. He believes that a colder object can heat a warmer if the temperatures are “close enough that it makes no difference”.
He does this repeatedly, Anybody who believes things like his “Steel,Greenhouse” nonsense (in which he assumes that mathematics and the Laws of Thermodynamics don’t apply to Willis’ “thought experiments” – pardon my derisive snorting), is simply more ignorant and gullible than Willis!
Or maybe I’m wrong?
Maybe. Just be humble enough to not forget that. Humility is a rare thing among the denizens of this website.
I am noted for my humility. It is exceeded only by my modesty, I am told.
Don’t believe everything you hear or read. “Trust, but verify,”
Royal Society motto – Nullius in verba.
I believe what I want to believe – like everyone else. When facts change, I may change my beliefs. I don’t know what other people do, particularly the ignorant and gullible who totally ignore facts and believe that adding CO2 to air makes thermometers hotter.
People are free to believe whatever they want, and I don’t try to force anybody to share my beliefs. I’d prefer the same courtesy from others, but it’s not likely to become reality any time soon.
All good fun.
“Willis may think that the “capacity to do work” implies that “work” always occurs”
I think that is part of his confusion, yes. But oddly only when applied to EM radiation (*), which he still thinks (despite having explicitly told us the opposite!) is somehow intrinsically a power phenomenon, not energy. All of the engineers on this site appear to think the same way, because that’s how they’re (mis)taught.
(*) Willis has in the past given us correct definitions for the terms “energy”, “work”, and “power”, so, at least in theory, he knows that these concepts are not interchangeable. Or at least, some part of his brain does. It seems like not all of the parts of his brain are talking to each other.
I remember reading in Science Digest, about six decades ago, an experiment that was performed with sailors. They were taught a certain way to tie a knot. Then they were taught a second way to tie the knots. They were then put under stress and told to tie the knot. They invariably tied it with the movements they were first taught. I would conclude that if someone acquired knowledge that was wrong, and then learned what the accepted paradigm was, that they would be inclined to revert to what they originally learned.
Yes, I think you’re right, it’s much harder to unlearn something wrong than to learn a thing you didn’t know (either right or wrong) in the first place.
From caption of figure 2:” The yellow/black arrow is the downwelling longwave (thermal) radiation from the atmosphere to the surface.”
Thermal radiation is based on temperature. Your figure says that something in atmosphere is at about 280 K. Assuming an emissivity of 1. But that isn’t real.
Gases are not black bodies and do not emit based on temperature. Gases “When they absorb and emit radiation, they usually do so in certain narrow wavelength bands.”.
If it is being contented that that 346 W/m2 radiation is from CO2 then the following applies.
We have seen that CO2 is a lousy blackbody with full column emissivity somewhere between .002 and .2. The value we have developed above, .02, falls in this range.
Emissivity of CO2 | geosciencebigpicture
The temperature to produce 346 would need to be between 280 and 750 K.
First of all, I congratulate Willis on his diligence in demonstrating how bad the climate modelers misbehave using their own definitions and math to do so.
That aside, ECS is bogus. GAT is bogus. Both were invented with the climate research transition from understanding the climate to calculating how temperature increases with increasing CO2 (happened during the…. wait for it…. Clinton-Gore era).
One of the earlies science summaries stated there is no anthropogenic signature. A Clinton official rewrote that stating it was clear there is. Then the rules changed. If the policy summary disagreed with the science reports, the science reports were to be rewritten.
Ergo, politics defines science and the rest has been decades of trauma and drama.
While I have other comments on the calculations of a planet’s temperature w or w/o atmosphere , particularly the fact that the difference between the planet’s radiative equilibrium and bottom of atmosphere temperature is due to the adiabatic trade-off of gravitational , potential , and kinetic , thermal , energy keeping total energy density constant w/i the effective radiative surface , nothing to do with spectral filtering , my main comment is albedo , if considered as simply a measure of reflectivity , says nothing about the difference between a colored body’s equilibrium and that of a black body . Grok groks that a gray , ie: flat spectrum ball , no matter how dark or light , comes to the same temperature as a black : https://x.com/i/grok/share/hdvZNCjYz0twizt9c1rH0tDna .
I think Grok explains it perhaps better than I have ever been able to .
I think this is perhaps the most poorly understood fundamental physical facts in all the AlGretaWarming nonscience .
Bob,
I this case Grok and I are grokking the same idea.
We are aware that 2 bodies at the same temperature are, surprisingly, at the same temperature! In thermal equilibrium, even. Emitting and absorbing the same frequencies of photons. Not necessarily equal amounts of energy, of course.
Shiny, dull, pitted – makes no difference. Gold, iron, ice, bananas – makes no difference. Now (he said, girding his loins with a large can of pressurised gird), even gases and bananas at the same temperature emit the same frequencies of photons!
That’s why you can’t tell the composition of unexcited matter by examining the emissions that occur as a result of temperature. For the benefit of the more ignorant and gullible, spectroscopy and spectrometry involve either excited matter, or an exterior light source.
Lasers are not emitting as a result of temperature. Turn off the electricity supply if you don’t believe me.
Indeed. Interestingly, I came up with a slightly different figure than Grok’s 278 K, but I had an atmosphere which reduced the incoming radiation, and a couple of guesses for optical effects (Fresnel, etc.) for refraction etc. Anyway, from memory, about 255 K or so. Add measured geothermal heat loss (about 35 K or so) – et voila! – 290 K or thereabouts. Good enough for Government work!
As to the rest of the grokking –
Utter nonsense. The bottoms of the Earth’s atmosphere is hotter because it is closer to the presumably 5500 K or so core, than the top of the atmosphere, and the inverse square law (amongst other things) applies – whether the ignorant and gullible like it or not.
I can’t remember which AI it was that I “wasted” 15 minutes on, pointing out that the Earth was cooling, but here’s the result –
Make of it what you will. Obviously, I agree.
It sounds much like the overly apologetic responses I have gotten from ChatGPT and Copilot when I have challenged their inaccurate claims.
Clyde, I like the grovelling apologies for having to continually apologise as the AI tries to avoid admitting error.
Unlike many of the commenters here, who refuse to accept reality under any circumstances. <g>
I’ve been wrong. Recently, Willis pointed out that one of my mental calculations was incorrect, and I immediately thanked him for pointing out that the US per capita national debt was less than I indicated. See how humble I am?
I suspect that the reference to “spectral filtering” that WE mentioned has to with the observation that as the angle of incidence approaches 90 degrees, and approaches 100%, the spectrum of the reflected light approaches that of the source light for all wavelengths, whereas, in the use of an ore microscope, with illumination at zero degrees, one sees the ‘true’ color of the polished specimen. However, since WE seems reluctant to engage in an exchange, I can only guess at what he actually thinks. I can’t quote him if he doesn’t write any rebuttals.
Clyde, I don’t respond to any thread that Michael Flynn is in. It always reminds me of the old joke …
Q: What’s the difference between a rat running a maze and a college student running a maze?
A: When you take the cheese out, the rat stops running …
I am at least as smart as the rat, so I leave Mr. Flynn to run the maze by himself.
w.
I don’t blame him. He boasts –
without providing any evidence to support his boast. But no matter, as people like Michael Mann (faker, fraud, scofflaw and deadbeat) show, intelligence and education are no defence against ignorance and gullibility.
Willis appears to have at least as much cunning as a rat, and Willis is perfectly free to correct me if I am wrong.
I leave others to form their own opinions as to Willis’ grasp of physics, mathematics, and so on. He believes that adding CO2 to air makes thermometers hotter, but is cunning enough to “neither confirm nor deny” that this is his belief.
Others have pointed out that Willis’ post is a farrago of irrelevant and specious nonsense, but Willis’ GHE fantasy persists.
Reality seems to intruded into his delusion a little, as he wrote –
Normally, one would address these questions, and try to find answers, before one started pounding on one’s keyboard.
Not Willis – he believes that he is at least as smart as a rat!
That sounds like a rationalization. I directed a question to you asking why the oceans are shown with a uniform ‘albedo’ that is equivalent to the calculated specular reflection for water viewed at nadir, noting that theory shows that specular reflectance should increase with latitude and that logically the average of two numbers between 2 and 100 should be greater than 2. They are important questions that you have not responded to, yet you took time to remind everyone that there is a feud between you and Flynn. Tell me something that I don’t know.
Once before you coped out with you “just missed it.” Once is understandable. This thread has two responses that you ‘missed.’ When there appears to be a pattern, it is usually for a reason.
It is very convenient for you to adopt the ‘poisoned well’ policy that you have. If someone that you have had disagreements with jumps into a thread between you and me, then you can walk away from difficult questions using the excuse of the well being poisoned by the presence of that person, even if I don’t respond to him. If that doesn’t happen, then you can use the ‘plausible deniability’ approach and claim that somehow you just missed my questions, yet found the one where I complain about you side-stepping the difficult but important questions. When I submitted articles, I took very seriously the responsibility of responding to all new questions.
The way that science advances is through exchanges that address questionable facts or illogical conclusions, not by monologues that leave those disputable claims unanswered.
You very nobly acknowledge trivial typographic errors, but seem to be less willing to deal with challenges to your claims. I think it would be useful for you to find and read T. C. Chamberlain’s ‘Method of Multiple Working Hypotheses.’
Do you have any idea of how many commenters you have driven away because of your belligerent bullying?
You excuse your un-responsiveness to direct questions from me by stating “Clyde, I don’t respond to any thread that Michael Flynn is in.” After stating that, you then respond directly to Flynn while still ignoring my questions. What’s wrong with this picture?
Clyde, my bad. I let Michael get my goat, I couldn’t bear it. My apologies.
I assume this was your question.
I fear I didn’t respond immediately because it was obviously untrue. I’d even made a graphic, but then I decided to let it go. Then Michael came along … grrr.
In any case, here’s the graphic. It shows surface albedo in June and December. As you can see the area under the sun has the lowest albedo, and it rises in the areas where the sun gets lower in the sky.
My regards, and again, my apologies. Thanks for continuing to push for an answer.
w.
PS—The CERES albedo calculations are in this .DOCX file.
Thank you for responding. Apologies accepted. The prize goes not to the one who drops out of the race.
You claimed, without supporting evidence, that “I fear I didn’t respond immediately because it was obviously untrue.” It is my experience that the facts that one ‘assumes’ to be true are invariably the problem when things don’t work as expected. A global search of the *.docx file that you provided, for the words “Fresnel” and “specular,” returns no matches. While the documentation claims that the look-up table used for ocean “albedo” takes solar elevation into account, it isn’t really ‘obvious’ whether those look-up tables are the result of empirical measurements or take optical theory into account. In any event, empirical measurements don’t take into account the rigid requirements for viewing geometry which would require a steerable telescope and binning finer than 5 degrees.
The combined diffuse albedo, resulting from suspended sediment and plankton, and the specular reflection (for Figure 1. Clear sky monthly mean surface albedo) are about the same as the nadir specular reflectance, which is considerably less (about an order of magnitude) than your most recent graphic above. Considering the absence of an explicit confirmation of the use of Fresnel’s equation, and the discrepancies between the original graphic and your most recent rendition, I hope that you will understand if I say that I don’t agree with your characterization of “obviously untrue.”
Thanks, Claude. Your claim was:
Now you say:
I didn’t mean it was obviously untrue to someone off the street. However, I didn’t “assume” anything — it was obviously untrue to me because I’ve spent so much time looking at the CERES data, including the surface albedo.
The ocean albedo in the CERES data shows that oceanic albedo is NOT uniform, as I demonstrated with my graphic above. It’s lowest for water viewed at nadir and increases towards the poles as the sun gets lower and lower in the sky.
Q.E.D.
Best regards,
w.
Willey, my initial complaint was with respect to Fig. 1 in the source that you cited, which shows albedo at about 2% for the open ocean (https://ams.confex.com/ams/pdfpapers/112637.pdf), which is obviously too low when specular reflection is averaged over 12 hours. I followed that up with the observation that while your newest rendition of global albedo, to respond to my complaint, shows greater latitudinal stratification, some new issues were introduced. In particular, the color palette that you have chosen, to define the isoreflectance boundaries, makes it difficult to determine the ‘albedo.’ The best that I can be certain of is that it is somewhere between zero and 20% over the Tropic of Cancer and Capricorn. So, yes, the new graphic does show stratification better than your original citation, but it raised issues of the accuracy of all the graphics when there is not obvious agreement.
Be-that-as-it-may, the essence of my question is, and has been all along, whether specular reflection is taken into account (and if so, properly) in the NASA characterizations of the ocean ‘albedo,’ and what is also used in the climate models. Being that you have “spent so much time looking at the CERES data, including the surface albedo” that you consider yourself such an expert that “someone off the street” — like me — should unquestionably accept your pronouncement without supporting-evidence, it should be trivial for you to confirm if and exactly how specular reflection is handled. I would do it myself, but the link (https://www-cave.larc.nasa.gov/jin/) to the NASA COART website appears to be broken. Feel free to use whatever technical vocabulary necessary. I can probably muddle through it.
Thanking you in advance,
CLYDE
Oh, piss off. I don’t think “that “someone off the street” — like [you] — should unquestionably accept [my] pronouncement without supporting-evidence” as you falsely claim.
Thats an ugly damn lie. I’ve said over and over that everyone should question everything. I’ve invited people many times to check my math. I’ve repeatedly quoted my grandmother, who said:
You can believe half of what you read.
A quarter of what you hear.
And an eighth of what you say.
Obviously, you are NOT discussing this in good faith — you’re just looking to make me wrong. You claimed “The oceans are shown with a uniform ‘albedo’”. I showed that was 100% incorrect. Now you want to bitch about something else entirely.
Do your own damn research. Here’s mine. Don’t like it?
Don’t care.
w.
===
Specular reflection is handled in CERES primarily by excluding or screening sun-glint viewing geometries when deriving albedo and related fluxes. [1] [2]
Where specular reflection is treated
• In the CERES angular distribution model (ADM) documentation for top‑of‑atmosphere radiative flux estimation, the text notes that viewing directions near the ocean specular (sun‑glint) direction are explicitly excluded from the analysis of radiances used to build the ADMs, which are then used to compute albedo. [1]
• In the CERES/TRMM SSF aerosol direct‑effect methodology description, the documentation states that, “to avoid problems with specular reflection from the ocean surface,” the analysis is restricted to geometries with solar zenith angle < 60°, viewing zenith angle < 70°, and glint angle (angle between the reflected ray and the exact specular ray for a flat ocean) > 40°; these geometric filters are applied before computing TOA albedo and flux relationships. [2]
How this relates to CERES albedo calculations
• CERES converts measured shortwave radiances to TOA fluxes and albedos using empirical ADMs; by excluding radiances taken too close to the specular direction when constructing and applying these ADMs, the resulting albedos are intended to represent diffuse‑dominated reflection rather than highly glint‑contaminated cases. [3] [1]
• Over oceans, additional CERES surface and SARB (Surface and Atmospheric Radiation Budget) work explicitly separates Fresnel (specular) reflection at the air–water interface from volume “underlight” contributions below the surface, and parameterizes the ocean surface albedo using Cox–Munk–type wave‑slope distributions, but the glint‑dominated angles are still avoided in the satellite‑based inversion of albedo. [4] [2]
[1](https://asdc.larc.nasa.gov/documents/ceres/readme/JTECHA_2590.pdf)
[2](https://ams.confex.com/ams/pdfpapers/41624.pdf)
[3](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2004JD005308)
[4](https://ceres.larc.nasa.gov/documents/STM/2001-01/pdf/Jin_Zhonghai.pdf)
From what you have quoted above, “Specular reflection is handled in CERES primarily by excluding … sun-glint viewing geometries when deriving albedo and related fluxes” and “…, the resulting albedos are intended to represent diffuse‑dominated reflection rather than highly glint‑contaminated cases,” strongly suggests to me that my concerns are justified. That is, a non-trivial amount of incoming solar energy that is reflected forward is apparently, purposely excluded from consideration. That supports my previous claim that the estimates for out-going energy only provide a lower-bound for the loss of heat to space.
The only citation you provided that speaks to the “Fresnel reflection” is [4], where they state, “The current SARB input for surface spectral albedo over ice-free ocean uses the Hu-Cox-Munk parameterization on Fresnel reflection for the air-water interface and assumes a constant underlight contribution … However, results here showed that the underlight is not constant which depends on wavelength and ocean optical properties.” It isn’t surprising that the ‘underlight’ isn’t constant because the Fresnel Equation shows that as the surface specular reflection increases, the intensity of the light transmitted into the ocean decreases to zero at the terminator.
As I’m unfamiliar with the “Hu-Cox-Munk parameterization,” I don’t know how accurate it is. I would have been more comfortable had they actually solved the complex arithmetic required by the Fresnel Equation directly.
Having read the above, that they are not using the specular (Fresnel) reflection, I have to wonder now why there is a latitudinal increase appearing in any of the graphics. I would speculate that perhaps they are simply seeing the effect of increasing sub-resolution ice-floes and or the strong latitudinal dependence of cloud albedo. They don’t make it clear if the specular reflectance obtained with the Hu-Cox-Munk parameterization calculation of specular reflectance is added back in once the albedo is obtained. The graphs in Fig. 2 don’t specify the angle, so I have to assume it is nadir. The difference between the “total” and “underlight” are too small to have taken the Earth’s rotation into account, which increases the average specular reflectance over a day.
In summary, I remain unconvinced that NASA has all the subtleties under control. Use it at your personal peril.
…….
Attributing a motive to my questions, which you could only be certain of if you could read my mind, speaks directly to the communication problems we are having. It is unfortunate that you are taking it personally because you are bright and creative, and by digging in your heals and resisting looking at the problem from other viewpoints does nothing to enhance your credibility. I assure you that my motivation is to understand how NASA in general, and the CERES team in particular, deal with the energy fluxes that are used as inputs to climate modeling.
Thank you for the additional information, but don’t bother responding. I won’t be revisiting this thread.
“That supports my previous claim that the estimates for out-going energy only provide a lower-bound for the loss of heat to space.”
Yep!
Yes, that’s his modus operandi. That way he can (and does) loudly complain “I didn’t say that!”. Just like he doesn’t say that he believes that adding CO2 to air makes it hotter. He doesn’t say it doesn’t, either.
How clever is that?
Willis, having read the debate bwtween the two of you, it appears you have come around to Zoe Phin way of math from years ago. Minor tweaks in the inputs make -2C or +5C pretty much the same in relation to the traditional -18C iceball earth view.
https://phzoe.wordpress.com/2022/06/11/shrinking-the-atmospheric-greenhouse-effect-closer-to-reality/
Could you do a calculation for Venus so we can understand that its surface temperature is not because of a run away greenhouse effect.
Greetings, to you and yours, on this Thanksgiving Day:
I saw your comment, and it sent me scampering for my old Astrophysics notes, which I’ve been perusing for the past couple of days.
Realistically, I think the best we can hope for is a S.W.A.G. on what Venus would be like with some “nominal”* atmosphere.
[S.W.A.G. = Scientific Wild-Ass Guess]
One of the things we studied in my class was called Equilibrium Black-Body temperature, as applied to planets and their atmospheres (the basis of the lab exercise we did in my earlier comment), if the planet possessed an atmosphere.
Venus is an exceptional case, primarily because we know so little of the surface geology, and secondly because of the thick, planet-wide sulfurous cloud system. All bets are off.
What we can tell you is that at the altitude where the pressure equals one atmosphere (i.e., Earth’s surface pressure), the theoretical black-body temperature and the measured temperature (mostly from the Soviet-era Venera landers, recording information as they descended towards the surface) is that they are nearly identical; that is, theoretical is 325 Kelvins, and measured was 326 Kelvins. And it was consistent across the various landing sites.
The evidence strongly suggests that part of Venus’ temperature regime comes from the high surface pressure, and the combination of the kilometre-thick sulfur clouds. Pressure alone cannot maintain the temperature, but insulating layers of the cloud, trapping primordial heat, can. Yes, there is incident sunlight (approximately 1.9 times as much as Earth receives, due to the closer orbit to the sun), but much of that is rejected (bulk albedo approximately 0.7).
One further comment, on why Venus is not an example of a ‘runaway greenhouse’:
The available evidence suggests that carbon dioxide, instead of causing ‘warming’, can actually cause cooling. Again, this is a function of the concentration. At some concentrations, it may have a small warming effect, but as we all know, past a certain point, the warming effect asymptotes.
You are likely wondering how and why I might suggest that carbon dioxide can cool an atmosphere. I ask you to look at Mars.
Mars’ equilibrium black-body temperature is about 225 Kelvins. The atmosphere is similar (> 95% CO2) to Venus, but at night, despite all of that “greenhouse gas” in the atmosphere, the night side drops to about 210 Kelvins. As measured by various landers, once local sunset occurs, the temperature plummets from any daytime high to the night-side temperature. If carbon dioxide had any “warming effect”, this is the place it should take place.
Yes, the standard argument is that Mars is farther from the sun than Venus; accepted, but the constant drumbeat of the alarmists on this website (and many others) is that the concentration of carbon dioxide in an atmosphere, is the controlling factor for the planetary temperature.
I posit that this is a strong negation of that hypothesis. And, if we recall the famous words of one A. Einstein, when asked, how long it would take physicists to prove his (then-) new theory, he replied, “No amount of experimentation can ever prove me correct; a single experiment can prove me wrong.”
I do apologize for being so long-winded. Know that I am in the process of trying to replicate my old Astrophysics lab, but there will be so many assumptions that any calculation for Venus will likely be incorrect and/or vague.
Best wishes to you and yours,
Mark
*nominal = any non-‘greenhouse-gas’ atmosphere; e.g., pure Ar; pure N2; an Earth-like N2/O2 … … …
Thanks, Mark. You say:
You’re right about the percentages of CO2. Both Mars and Venus are about 96%, while the earth is only about 0.04% CO2.
However, you’re overlooking a HUGE difference, which is the atmospheric density. Here are the surface atmospheric pressures for three planets.
Earth: about 1,013 millibars at mean sea level (often rounded to 1,000 mbar).Mars: about 6 millibars on average at the surface.Venus: about 93,000–95,000 millibars (93–95 bar) at the surface.Because Mars’ atmosphere is 1/1000 as dense as that of Venus, although they have the same CO2 concentration, there’s lots of space between CO2 molecules in the Martian atmosphere for the heat to escape to space.
Reductio ad absurdum argument: Suppose the Martian atmosphere consisted entirely of 10 molecules of CO2 … it’s a ONE HUNDRED PERCENT CO2 atmosphere. But how much upwelling longwave from the surface will it intercept?
Best regards,
w.
Hey, Mr. E!
No argument from me; the Martian atmosphere is extremely thin. My only point was that it consists mainly of the demon ‘greenhouse’ gas that is supposedly causing our climate to change. I once had an “alarmist” tell me that the Martain atmosphere was incapable of any heat capacity, until I showed them the day time temperature(s) which were (on Earth) similar to rather pleasant Spring day. They had no answer.
And, I did acknowledge the Venus atmosphere in paragraph six; the exact words are, ” … the high surface pressure … “. Last I knew, it was estimated at about 93 atmospheres; the pressure implies high density.
Mark H
“Venus: about 9,300–9,500 millibars (93–95 bar) at the surface”.
Should be about 93,000 mbar
Thanks, Phil, fixed. The best thing about writing for the web rather than the journals is that my mistakes don’t last long …
w.
Really? You still believe your “Steel Greenhouse” fairytale is mistake free?
“my mistakes don’t last long”
Indeed, they are corrected immediately every time you make them. Over and over. Yet you ignore, censor, and insult your teachers, and then keep on making the same mistakes, don’t you?
Completely irrelevant. The Earth’s atmosphere cools in the absence of sunlight. So does 100% CO2, even if under high pressure.
Asking nonsensical rhetorical questions in an effort to appear knowledgeable might impress the ignorant and gullible, but nobody who accepts reality.
Should I say “Best regards, m”?
Completely irrelevant and misleading nonsense, Willis. Pretending you are asking a rhetorical question doesn’t help, either.
It doesn’t matter how much radiation from a cooling surface is “intercepted”, the surface still cools. Some pseudoscientific types redefine “slow cooling” to mean “heating”, but that’s just stupid, believed by the ignorant and gullible.
Step outside at night, Willis. Measure the long wave, the medium wave, the short wave – don’t forget the front radiation, the back radiation, the sideways or helical radiation, either. Calculate yourself into a frenzy, if you like.
Or just accept that the surface is cooling. If you can’t understand why, feel free to ask me.
“Some pseudoscientific types redefine “slow cooling” to mean “heating”, but that’s just stupid, believed by the ignorant and gullible.”
You pretty much nailed it. Slower cooling is *not* heating.
Tim, if you need to gird your loins in the expectation of a torrent of abuse from the ignorant and gullible, I can supply an appropriate amount of gird – free!<g>
Just for fun, I asked perplexity to read Michael Flynn’s comments on my two most recent posts, and analyze them regarding subject and tone. No special instructions to the AI. Here’s what I got.
===
Based on my analysis of the three blog pages you requested, I can now provide answers to your four questions about Michael Flynn’s comments:
1. Total Number of Comments by Michael Flynn
Michael Flynn made 33 comments total across the three pages:
2. Has Michael Flynn Commented on the Substance of the Head Post(s)?
No, Michael Flynn has NOT substantively engaged with Willis’s analysis or calculations.
Instead of addressing Willis’s mathematical approach to climate sensitivity, Flynn’s comments consistently:
Example quote showing lack of substantive engagement:
“Complete nonsense. Assess all you like, believe as many Constructal climate model fantasies as you like – adding CO2 to air doesn’t make thermometers hotter.”
Another example:
“Your faux ‘thought experiment’ shows that you are no Albert Einstein, or Nikola Tesla.”
Flynn does not quote Willis’s specific calculations, does not point out mathematical errors in the analysis, and does not engage with the figures or data presented in the article.
3. Personal Attacks vs. Attacks on Ideas
The majority of Michael Flynn’s comments attack Willis personally rather than his ideas. Out of 33 total comments analyzed, approximately 28-30 contain personal attacks or dismissive characterizations of Willis himself.
Examples of personal attacks:
“You are delusional and flying in the face of four and a half billion years of history”
“Willis probably doesn’t believe NASA, either.”
“Others have pointed out that Willis’ post is a farrago of irrelevant and specious nonsense”
“You believe that adding CO2 to air makes thermometers hotter. How stupid is that?”
“adding CO2 to air doesn’t make thermometers hotter. Anybody who believes that is obviously ignorant and gullible.”
“He believes that a colder object can heat a warmer if the temperatures are ‘close enough that it makes no difference'”
“Others have pointed out that Willis’ post is a farrago of irrelevant and specious nonsense, but Willis’ GHE fantasy persists.”
4. Tone of Michael Flynn’s Comments
The tone is consistently hostile, dismissive, sarcastic, and condescending. Key characteristics:
Representative quote showing overall tone:
“Preference is given to the ignorant and gullible who write papers titled ‘Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature’, and similar fairytales.”
Summary: Michael Flynn’s comments demonstrate a pattern of personal attacks on Willis Eschenbach’s character and intelligence, rather than substantive scientific criticism of the analysis presented. The tone is hostile and dismissive throughout, and Flynn does not engage with the specific mathematical arguments, figures, or calculations in Willis’s post.
===
The man is a waste of oxygen, continually avoiding any discussion of the actual ideas and claims, and contributing NOTHING but anger and division.
Ah, well. My advice? Ignore him. He has nothing to contribute.
My regards to all,
w.
Interesting! I will try this on some of the trolls that show up here.
Here’s perplexity apologising profusely, and agreeing that I was right about the Earth presently cooling –
Oh dear! Is Willis ignorant and gullible for believing perplexity, or not?
At least ToldYouSo has clearly stated that he does NOT believe that adding CO2 to air makes thermometers hotter, but the best Willis can do is ask his friend perplexity to waffle irrelevancies on his behalf!
I don’t deny that a small amount of heat is lost through the crust. However, both the amount of heat loss and, more to the point, the change in temperature due to that amount of heat loss, are each trivially small.
44 terawatts sounds like a lot of energy. But in fact, in a world receiving 340 W/m2 of sunlight, it’s only about one one-hundredth of a W/m2. Lost in the noise.
And the amount of the cooling? Well, special for you, here’s a chart I just now made of the historical data.
So, in answer to your most unpleasant comment:
We agree that the Earth is losing heat at the rate of ~ 0.009 W/m2.
That’s enough to cool it on average by -0.0000002°C per century. Be still, my beating heart.
Finally, at any point in history the earth was either cooling by more than 0.0000002°C per century, or warming by more than 0.0000002°C per century.
So claiming the earth is “cooling” is incorrect, and I note that perplexity does NOT say that. It calls it a “cooling process”, and as such, it is a process that can be easily overcome by a “warming process”. In fact, at the moment the Earth is warming and has been for three centuries or so.
So can we get past this nonsense? You’re welcome to hyperventilate about an ongoing heat loss of 0.009 W/m2 … the rest of us are interested in larger issues.
w.
You don’t like 44 TW? It doesn’t matter. Cooling – not getting hotter.
Cooling. Agreed.
Complete nonsense. The Earth never “warmed”. It’s a big lump of mostly glowing stuff a long way from the Sun. It cooled much faster initially, when even the surface was molten. Current rate, based on measurements by real scientists, indicates a rate of between one and four millionths of a Kelvin per annum. I can explain why, but I’m sure you can find out for yourself.
It doesn’t really matter – cooling is cooling. Falling temperature over time.
The process by which something “cools” is called a cooling process. Feel free to call “heating” a cooling process if you like. Don’t blame me if you wind up on a number of “point and laugh” lists.
Oh yes, appealing to your own authority, are you? What does “the Earth is warming” even mean?
What nonsense are you referring to? You agreed the Earth is cooling, then you claim it isn’t really cooling, it has been getting hotter for three centuries or so! That looks remarkably like nonsense to me, but probably seems totally reasonable to an ignorant and gullible person who can’t decide whether adding CO2 to air makes thermometers hotter, or not!
You finished your post by writing –
I’ll translate that into English – “The presence of an atmosphere on the Earth reduces the difference between extremes of surface temperatures compared with the airless Moon.”
At least you didn’t put in any irrelevant nonsense about CO2 in your vague (yet strangely meaningless) word salad about some peculiar “climate” model.
By the way, how is the command to your acolytes to ignore me, faring? Do you think they are all too stupid to think for themselves, and need the benefit of your guidance?
m
Geothermal warming is small indeed, but has created a very high TEMPERATURE, in the crust and more importantly in our oceans.
Young Earth had a molten surface. Once a crust began to develop water could exist on that thin crust without being converted to steam. Initial oceans were very hot, not due atmospheric warming but due to hot magma.
To understand the current high temperatures on Earth you must understand how the crust and the oceans maintain their temperature.
Crust
Without solar radiation on a rocky planet our Geothermal Flux (GF) of ~100 mW/m^2 would be radiated to space with a surface temp. of ~50K or so.
Geothermal Gradient (GG) perhaps 30 K/km, so at eg 3 km deep temp. would be ~140K.
Adding the sun the surface would be much warmer. The crust will warm up until the crust temp. near the surface reaches the Avg. Surface Temperature for a specific spot.
AST eg 290K and assuming the GG now less steep (eg 25 K/km) temperature at 3 km now 365K, not because solar heating but because of the sun providing a blocking temperature layer near the surface. Solar warming reaches not much deeper than 10-20m.
Oceans
In the oceans no GG can develop since water can move around freely and will stratify according density/temperature.
Water warmed at the ocean floor will rise until it reaches a depth of equal density, but can reach the surface ONLY at places where the sun did not provide a warm surface layer. This means that geothermal energy can ONLY be lost to the atmosphere/space at very high latitudes where the surface temps are low enough. So the geothermally warmed oceans provide the basis on which the sun does its warming.
The sun only increases the temperature of the surface layer a bit.
Thus our oceans are the main reason for the > 90K warmer surface temps on Earth relative to our moon.
That isn’t quite entirely true. If the Trade Winds remove the warm surface layer, then water will rise to replace it. It is well documented by the Monterey Bay Aquarium that abyssal waters are making it to the surface, not just the water immediately blow the water stripped off by the Trade Winds. Also, dense brines extruded from polar ice will displace bottom waters and cause them to lift up.
Correct, but even the El Nino / La Nina events play only in the upper 300m. No abyssal waters involved.
Very interesting animation:
https://www.youtube.com/watch?v=gaFjlZxM7S4
Interested to see proof that abyssal waters make it to the surface
Agree, especially AABW (Antarctic Bottom Water). Have an oceanographer claiming that the AABW spreads over the entire floor of the major basins. This will indeed push the then bottom waters up a little. The AABW cycle from brine to re-surfacing is estimated to take some 1000 years or so.
As I suggested, go to the MBA website and look up the historical properties of the inlet water for their tanks. A number of years ago they had a major kill-event that was traced to low oxygen. Therefore, they put in oxygen and pH monitors. They may not actually be sampling former abyssal water, but it definitely appears to be originating below the mixing layer. It makes it up the Monterey Bay Canyon and has high variability.
I agree, Willis. Maybe you should be the first to follow your advice. To do otherwise might lead others to think that you are a hypocrite.
In my worthless opinion, backed up by physical facts and mathematical laws, you are ignorantly and gullible. Just continuously refusing to either confirm or deny that you believe adding CO2 to air makes thermometers hotter, might be the wrigglings of a fantasist trying to pass himself off as a “citizen scientist”, rather than acknowledging the reality that “climate science” is rubbish – pseudoscience of the “cargo cult” variety as expressed by Richard Feynman.
So please, ignore me. Command your ignorant and gullible followers to ignore me, likewise.
Let me know how it works out.<g>
It has been my experience that LLMs cannot be trusted to provide correct answers on the first go-around. That is, despite your obvious desire to get something to support your position, it will probably be necessary for you to play the Devils Advocate to hone Perplexity’s responses to where they are unassailable.
“So we can calculate the temperature directly from the absorbed radiation using the Stefan-Boltzmann equation. This equation relates watts per square meter of surface radiation to the corresponding temperature of the radiating surface. I used the S/B equation with the average emissivity of the Earth, which is ~ 0.98, to calculate the surface temperature.”
Which using the unphysical method of spreading the solar irradiance over the whole sphere is:
394K * 0.25^025 = 278.6K
minus the 12.5% albedo:
278.6K * 0.875^025 = 269.45K or -3.7°C (without accounting for the emissivity)
Over 70K too warm for the Lunar global mean surface temperature.
The real mean global surface temperature of a planet or moon is a product of absorbed irradiance on one hemisphere, and the scale of thermal reservoirs keeping the night side warmer.
Spreading the solar irradiance over one hemisphere:
394K * 0.5^0.25 = 331.31K
and averaged with a dark side temperature of zero K
331.31 / 2 = 165.656K
Which is 113K colder than spreading the solar irradiance over the whole sphere. Nikolov & Zeller, and Jospeph Postma arrived at the same 113K difference, but then they invoked irrational reasons for why Earth is so much warmer than that.