Earth's baseline black-body model – "a damn hard problem"

The Earth only has an absorbing area equal to a two dimensional disk, rather than the surface of a sphere.

By Robert G. Brown, Duke University (elevated from a WUWT comment)

I spent what little of last night that I semi-slept in a learning-dream state chewing over Caballero’s book and radiative transfer, and came to two insights. First, the baseline black-body model (that leads to T_b = 255K) is physically terrible, as a baseline. It treats the planet in question as a nonrotating superconductor of heat with no heat capacity. The reason it is terrible is that it is absolutely incorrect to ascribe 33K as even an estimate for the “greenhouse warming” relative to this baseline, as it is a completely nonphysical baseline; the 33K relative to it is both meaningless and mixes both heating and cooling effects that have absolutely nothing to do with the greenhouse effect. More on that later.

I also understand the greenhouse effect itself much better. I may write this up in my own words, since I don’t like some of Caballero’s notation and think that the presentation can be simplified and made more illustrative. I’m also thinking of using it to make a “build-a-model” kit, sort of like the “build-a-bear” stores in the malls.

Start with a nonrotating superconducting sphere, zero albedo, unit emissivity, perfect blackbody radiation from each point on the sphere. What’s the mean temperature?

Now make the non-rotating sphere perfectly non-conducting, so that every part of the surface has to be in radiative balance. What’s the average temperature now? This is a better model for the moon than the former, surely, although still not good enough. Let’s improve it.

Now make the surface have some thermalized heat capacity — make it heat superconducting, but only in the vertical direction and presume a mass shell of some thickness that has some reasonable specific heat. This changes nothing from the previous result, until we make the sphere rotate. Oooo, yet another average (surface) temperature, this time the spherical average of a distribution that depends on latitude, with the highest temperatures dayside near the equator sometime after “noon” (lagged because now it takes time to raise the temperature of each block as the insolation exceeds blackbody loss, and time for it to cool as the blackbody loss exceeds radiation, and the surface is never at a constant temperature anywhere but at the poles (no axial tilt, of course). This is probably a very decent model for the moon, once one adds back in an albedo (effectively scaling down the fraction of the incoming power that has to be thermally balanced).

One can for each of these changes actually compute the exact parametric temperature distribution as a function of spherical angle and radius, and (by integrating) compute the change in e.g. the average temperature from the superconducting perfect black body assumption. Going from superconducting planet to local detailed balance but otherwise perfectly insulating planet (nonrotating) simply drops the nightside temperature for exactly 1/2 the sphere to your choice of 3K or (easier to idealize) 0K after a very long time. This is bounded from below, independent of solar irradiance or albedo (or for that matter, emissivity). The dayside temperature, on the other hand, has a polar distribution with a pole facing the sun, and varies nonlinearly with irradiance, albedo, and (if you choose to vary it) emissivity.

That pesky T^4 makes everything complicated! I hesitate to even try to assign the sign of the change in average temperature going from the first model to the second! Every time I think that I have a good heuristic argument for saying that it should be lower, a little voice tells me — T^4 — better do the damn integral because the temperature at the separator has to go smoothly to zero from the dayside and there’s a lot of low-irradiance (and hence low temperature) area out there where the sun is at five o’clock, even for zero albedo and unit emissivity! The only easy part is to obtain the spherical average we can just take the dayside average and divide by two…

I’m not even happy with the sign for the rotating sphere, as this depends on the interplay between the time required to heat the thermal ballast given the difference between insolation and outgoing radiation and the rate of rotation. Rotate at infinite speed and you are back at the superconducting sphere. Rotate at zero speed and you’re at the static nonconducting sphere. Rotate in between and — damn — now by varying only the magnitude of the thermal ballast (which determines the thermalization time) you can arrange for even a rapidly rotating sphere to behave like the static nonconducting sphere and a slowly rotating sphere to behave like a superconducting sphere (zero heat capacity and very large heat capacity, respectively). Worse, you’ve changed the geometry of the axial poles (presumed to lie untilted w.r.t. the ecliptic still). Where before the entire day-night terminator was smoothly approaching T = 0 from the day side, now this is true only at the poles! The integral of the polar area (for a given polar angle d\theta) is much smaller than the integral of the equatorial angle, and on top of that one now has a smeared out set of steady state temperatures that are all functions of azimuthal angle \phi and polar angle \theta, one that changes nonlinearly as you crank any of: Insolation, albedo, emissivity, \omega (angular velocity of rotation) and heat capacity of the surface.

And we haven’t even got an atmosphere yet. Or water. But at least up to this point, one can solve for the temperature distribution T(\theta,\phi,\alpha,S,\epsilon,c) exactly, I think.

Furthermore, one can actually model something like water pretty well in this way. In fact, if we imagine covering the planet not with air but with a layer of water with a blackbody on the bottom and a thin layer of perfectly transparent saran wrap on top to prevent pesky old evaporation, the water becomes a contribution to the thermal ballast. It takes a lot longer to raise or lower the temperature of a layer of water a meter deep (given an imbalance between incoming radiation) than it does to raise or lower the temperature of maybe the top centimeter or two of rock or dirt or sand. A lot longer.

Once one has a good feel for this, one could decorate the model with oceans and land bodies (but still prohibit lateral energy transfer and assume immediate vertical equilibration). One could let the water have the right albedo and freeze when it hits the right temperature. Then things get tough.

You have to add an atmosphere. Damn. You also have to let the ocean itself convect, and have density, and variable depth. And all of this on a rotating sphere where things (air masses) moving up deflect antispinward (relative to the surface), things moving down deflect spinward, things moving north deflect spinward (they’re going to fast) in the northern hemisphere, things moving south deflect antispinward, as a function of angle and speed and rotational velocity. Friggin’ coriolis force, deflects naval artillery and so on. And now we’re going to differentially heat the damn thing so that turbulence occurs everywhere on all available length scales, where we don’t even have some simple symmetry to the differential heating any more because we might as well have let a five year old throw paint at the sphere to mark out where the land masses are versus the oceans, and or better yet given him some Tonka trucks and let him play in the spherical sandbox until he had a nice irregular surface and then filled the surface with water until it was 70% submerged or something.

Ow, my aching head. And note well — we still haven’t turned on a Greenhouse Effect! And I now have nothing like a heuristic for radiant emission cooling even in the ideal case, because it is quite literally distilled, fractionated by temperature and height even without CO_2 per se present at all. Clouds. Air with a nontrivial short wavelength scattering cross-section. Energy transfer galore.

And then, before we mess with CO_2, we have to take quantum mechanics and the incident spectrum into account, and start to look at the hitherto ignored details of the ground, air, and water. The air needs a lapse rate, which will vary with humidity and albedo and ground temperature and… The molecules in the air recoil when the scatter incoming photons, and if a collision with another air molecule occurs in the right time interval they will mutually absorb some or all of the energy instead of elastically scattering it, heating the air. It can also absorb one wavelength and emit a cascade of photons at a different wavelength (depending on its spectrum).

Finally, one has to add in the GHGs, notably CO_2 (water is already there). They have the effect increasing the outgoing radiance from the (higher temperature) surface in some bands, and transferring some of it to CO_2 where it is trapped until it diffuses to the top of the CO_2 column, where it is emitted at a cooler temperature. The total power going out is thus split up, with that pesky blackbody spectrum modulated so that different frequencies have different effective temperatures, in a way that is locally modulated by — nearly everything. The lapse rate. Moisture content. Clouds. Bulk transport of heat up or down via convection. Bulk transport of heat up or down via caged radiation in parts of the spectrum. And don’t forget sideways! Everything is now circulating, wind and surface evaporation are coupled, the equilibration time for the ocean has stretched from “commensurate with the rotational period” for shallow seas to a thousand years or more so that the ocean is never at equilibrium, it is always tugging surface temperatures one way or the other with substantial thermal ballast, heat deposited not today but over the last week, month, year, decade, century, millennium.

Yessir, a damn hard problem. Anybody who calls this settled science is out of their ever-loving mind. Note well that I still haven’t included solar magnetism or any serious modulation of solar irradiance, or even the axial tilt of the earth, which once again completely changes everything, because now the timescales at the poles become annual, and the north pole and south pole are not at all alike! Consider the enormous difference in their thermal ballast and oceanic heat transport and atmospheric heat transport!

A hard problem. But perhaps I’ll try to tackle it, if I have time, at least through the first few steps outlined above. At the very least I’d like to have a better idea of the direction of some of the first few build-a-bear steps on the average temperature (while the term “average temperature” has some meaning, that is before making the system chaotic).

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Myrrh
January 14, 2012 6:19 am

davidmhoffer says:
January 13, 2012 at 9:47 pm
Myrrh;
Shrug. >>>
Gee, you stole my response to you. Thread after thread you ask for proof of this thing or that thing and when it is offered to you, your response is, yeah but I want proof. 2+2=4 and Myrrh hollers, yeah, but I want proof. Well, here’s two pospsicle sticks Myrrh and here’s two more popsicsle sticks and if we put them together and count….one, two, three, four…to which the inevitable rebuttal from Myrrh arrives…. yeah, but I want proof. To which I reply with my new stock answer to your serial idiocy. Shrug.
But… you’ve never come up with any proof! Most of the time what I get is the arrogant response from y’all to go read books on physics! Hello, is anybody in? I’m arguing about the physics in those books..
Prove that ‘the heat we feel from the Sun comes from visible light’ of the nonsense Ira gave and yet you say you’ve given proof? I’m not interested in the blackbody arguments, far too much maths for me find time following, what does interest me is the sleight of hand produced in support of AGW which has very subtley created an impossible, imaginary, world, which you all then argue about as if it is real..!
And to do this I’ve noticed a pattern of taking laws out of context, of giving the properties of one thing to another, of missing out rebuttals from the past to continue emphasising errors as if they’re not – Arrehnius the classic example here.* My call, if I was allowed to make it here, is for you all to go back to basics.. Until you get that right, have some grip on the reality of the world around us, you’ll continue arguing about this fantasy world created by AGW pushers and ever so often you’ll come out with ‘gosh, we found that carbon dioxide wasn’t well-mixed at all, but lumpy’, or similar surprise when you finally get some real data which you could have extrapolated if knowing that CO2 is heavier than air and the atmosphere around us wasn’t empty space with molecules zipping around at gazillion miles an hour bouncing off each other in elastic collisions and so throughly mixing, and even, adding Brownian motion to that to prove carbon dioxide will sponaneously diffuse into empty space oblivious that Brownian motion presupposes a fluid medium.., etc. Do you understand what I’m being so sarky about here? Nice to see that conduction and convection is finally making an appearance…
And, I’m fed up with being told that ‘experiments’ prove that greenhouse gas warming is a reality, but when I ask for these to be produced they never are. Where does Tyndall, who was experimenter of high reknown, prove that? I haven’t been able to find it in his writings. Maybe I missed it, I’m willing to stand corrected if so.
I’ll say it as clearly as I can, what I’ve been finding is very subtle tweaks to the physics of the real world which give an erroneous impression of the real world, added together they have created a world which doesn’t exist, and that’s what you’re arguing about.
As the man says here: “Latour insists that the apparent errors in atmospheric physics made by climatologists are because they work in a ‘generalist’ field of science, unlike most ‘hard’ sciences such as physics, chemistry, biology, engineering and medicine where detailed and in-depth specialization is essential so that products and services actually work.” http://johnosullivan.livejournal.com/43659.html
Which is how I came to see the tweaks, through following both sides arguing and the applied scientists won hands down on logical physics. My conclusion though is that certain key erroneous memes about the physical world have been deliberately introduced to create this climate of confusion about the physics, and it takes someone with a very thorough grounding in real science to do this and come up with ‘experiments’ that apparently ‘prove’ these memes, see Anthony’s deconstruction of Gore’s experiment. Attention! Magicians at work.
Typical is that introduced into classrooms some time ago, to show that carbon dioxide was well mixed and diffused through the atmosphere rapidly to be that, opening a bottle of scent. That this says nothing about carbon dioxide is not the message got by the children, but now they argue pro AGW by saying carbon dioxide can do this and can’t separate out from the atmosphere in layers, etc. .. Do you understand the point I’m making here? They can no longer understand the basics of the world around them.
This has now been so thoroughly confused that I think the easiest way would be to go back to basics – perhaps taking each of those memes and examining the tweaks to physics creating them.
We need more applied scientists..
Where does the meme come from that radiation in the atmosphere is in all directions? There’s a distinct difference between that travelling direct from the Sun in concentrated force to reach us, the great heat from the Sun reaching us in straight lines in eight minutes, and that given off by the much colder Earth from the variety of parts into the atmosphere.
As Tyndall said in: On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption and Conduction
“The solar heat possesses… the power of crossing an atmosphere; but, when the heat is absorbed by the planet, it is so changed in quality that the rays emanating from the planet cannot get with the same freedom back into space. Thus, the atmosphere admits of the entrance of the solar heat, but checks its exit; and the result is a tendency to accumulate heat at the surface of the planet.” -Tyndall
What’s he mean by “so changed in quality”? No, he didn’t mean that shortwave becomes longwave .., he’s talking about heat from the Sun, thermal infrared, and not light, visible, he knew the difference even if y’all arguing AGW KT meme that shortwave heats land and oceans, don’t.
……….
Pierre R Latour says:
January 13, 2012 at 7:18 am
GHG Theory 33C Effect Whatchamacallit
GHG Theory was invented to explain a so-called 33C atmospheric greenhouse gas global warming effect. In 1981 James Hanson stated the average thermal T at Earth’s surface is 15C (ok) and Earth radiates to space at -18C (ok). Then he declared the difference 15 – (-18) = 33C (arithmetic ok) is the famous greenhouse gas effect. This is not ok because there is no physics to connect these two dissimilar numbers. The 33C are whatchamacallits. This greenhouse gas effect does not exist.
I see this from a different slant, there is a physics to connect them.. These figures were sleight of handed to give the impression that there was such a thing as ‘greenhouse gas global warming’. There is no Water Cycle in this, in the KT97 and ilk.
These come from:
Earth with atmosphere as we have it, 15°C
Earth without atmosphere, -18°C
Earth with atmosphere but without water, 67°C
Hidden by simply removing it from the AGW energy budget which now is ubiquitously taught to represent the real world, let me present to you, drum roll, the Water Cycle.
This cools the Earth by 52°C, to get it down to the 15°C
The main greenhouse gas cools the Earth, ergo, greenhouse gases cool the Earth. There is no greenhouse gas warming, it’s a trick, in the slip between cup and lip the water has disappeared.
Carbon dioxide is fully part of that cycle – all pure clean rain is carbonic acid. Water vapour and carbon dioxide have irresistible attraction for each other, what carbon dioxide doesn’t come down to Earth by displacing the molecules of oxygen and nitrogen in the fluid gaseous ocean around us because heavier than air, will come down in the rain, water vapour hoovering in whatever is around – how then can carbon dioxide ‘accumulate for hundreds and thousands of years in the atmosphere’?
Getting rid of the Water Cycle they can pretend that convection etc. doesn’t exist, with no convection no atmosphere necessary, all can now be reduced to the one dimensional imaginary empty space of the basic imaginary ideal gas volumeless world where dot molecules travel unimpeded at great speeds bouncing off each other with no attraction and so becoming thoroughly mixed, and only radiation necessary as the means of transferring heat. So trace CO2 the greenhouse culprit who raises the temp of the Earth from -18°C to 15°C.
Supermolecule defying gravity! He wears his knickers on the outside.
And I’m continually told that the ‘greenhouse gases warm the Earth’ is real and proved by experiments ‘somewhere over there’ but never fetched for perusal and the argument should be only how much it warms the Earth..
So, David, effin’ prove it.
* I’ll fetch something I found interesting about this.

January 14, 2012 7:33 am

That in turn results in an increased average T for the exact some P absorbed. No change in energy balance need occur to account for some of the the increase in T.
(Boldface my addition.) Sure, with the addition, since we now have multiple mechanisms in place. This doesn’t mean that differential radiation atmospheric effect (not really “greenhouse”) warming or cooling doesn’t also take place, only that there are multiple channels and one cannot attribute all warming observed to differential radiation rate local warming in the naive picture, one has to mentally split it up into warming (and cooling) caused by other processes. Even though balance is still purely radiative in the end, transport matters, and (like albedo) might well matter more than small changes in local differential forcing. Regardless, the mere existence of the channel implies that “greenhouse warming” per se is a smaller fraction of the total observed warming than unity.
The really interesting thing is the modulation of mixing. One has to assume that the big oscillations all mix, but they also drive extremes, or at least modulate the mixing. If mixing leads to relative warming, and oscillations modulate mixing, oscillations modulate relative warming and relative cooling. Q.E.D. All that remains is to consider magnitudes.
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January 14, 2012 7:40 am

When writing my first post last night, I realized an answer to question of whether the greenhouse effect is a real phenomenon. This answer is a resounding YES!
Absolutely, which is why I try not to let it pass when people assert otherwise. The radiation data are absolute proof of it. The question isn’t “is there a GHG effect that contributes to the warming”, it is “what are the feedbacks, and what are the other mechanisms that also contribute to warming among which total observed warming (or cooling) must be split up”.
Short version, what are the feedbacks. A difficult question to answer, either empirically or theoretically — theories depend on assumptions, most of the untestable or difficult to test in the short run. Empirically one has to understand all of the dynamics, not just simplified idealized pictures of the dynamics, in order to “measure” it. “Catastrophe” is based on assumptions of large feedback. “Reality” seems to be empirically lowering the upper bound on the feedback quite systematically. It also strongly suggests that the models are leaving out important physics and feedbacks, notably solar modulation of albedo and possibly mixing.
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Joel Shore
January 14, 2012 8:14 am

Joe says:

That last sentence leads me to an interesting yet disturbing aside. Ever notice how Alaska and the Arctic are the showcase for global warming because their temperatures are increasing two or three times faster than the average global increase? For that to be true, and I do not doubt that the measured temperature rise is true, someplace else on the earth’s surface of equal area must be decreasing in temperature in order for the average world-wide temperature increase to be only 1 degree. Where is that place?

No…There can just be places that are rising somewhat less rapidly than average. In particular, one important thing to realize is that the arctic is a fairly small part of the global area: In particular, only 13.4% of the Earth’s surface lies north of 60 deg N latitude (and, of course, another 13.4% lies south of 60 deg S) and fully half of the Earth’s surface lies in what one might call the tropics between 30deg N and 30deg S latitude.
To show you a concrete example: Let us say (to make the numbers simple) that the Earth has warmed an average of 1 deg. Let us also assume that the arctic region north of 60 deg N has warmed at 2.5 times this rate, and the rest of the world outside the tropics have warmed at exactly the average rate. Then, how fast would the tropics (30deg S to 30 deg N) have had to warm? They would have had to warm ~0.6 deg.

davidmhoffer
January 14, 2012 8:15 am

Myrrh;
I’m not interested in the blackbody arguments, far too much maths for me >>>
Shrug.

Joel Shore
January 14, 2012 8:50 am

davidmhoffer says:

I’m sorry that you can’t follow the logic nor the physics and so understand neither my explanation of the matter currently being discussed, nor how it differs from isolated and specific instances of radiation balance. The GHE is of course a real change in energy transfer that can be measured and verified. The notion that the GHE breaks the laws of thermodynamics isn’t correct. What is ALSO not correct is that one can determine if the earth is gaining or losing energy by averaging T instead of T^4. what is further not correct is that a change in CO2 levels results in an energy imbalance rather than an energy redistribution that results in a higher average T without changing average T^4 and average P. If you cannot understand these dead simple issues, then I have little choice but to relegate you to the Myrrh bin. Shrug.

The point is that I understand this well enough to know that it is a fairly small effect. Let’s take a concrete example: Suppose we have a world that is half at 268 K and half at 308 K…That’s a distribution that likely has a larger standard deviation than temperatures on the Earth (particularly when you consider, as I have noted, that half the world is in the tropics, defined by 30 deg N to 30 deg S and 70% is ocean where temperature variability is much lower than on land).
Let us further suppose that the entire world warms by an average of 1 K but that the warming is twice as large (1.33 K) for the colder half as for the warmer half (0.67 K). Then, if we look at taking the fourth root of the average of T^4 rather than just averaging T, how much will we conclude the world has warmed? The answer is that we would conclude the world has warmed 0.93 K rather than 1 K.
Heck, even if we assume that ALL of the warming occurs in the colder half (so it warms 2 K) and none in the warmer half, then the method of averaging T^4 and taking the fourth root gives us the result that the world has warmed 0.80 K.

The point was to understand what the actual theoretical average black body temperature of the earth is when properly calculated so that we can COMPARE to the observed temperatures and determine how much should be allocated to insolation and how much to GHE. REALLY JOEL? YOU DIDN’T GET THAT?

And, the answer, as I have demonstrated above, will be that most of the rise is due to the increase in the amount of power being radiated and only a fairly small fraction is due to the temperature becoming more uniform on the Earth.
So, at the end of the day, what you have shown is what we already know: That a single number like average temperature is an imperfect metric. We already knew that the average is only an average and that actual warming will generally be greater in cold regions than warm regions, considerably greater over the continents (where people live) and less over the oceans, etc., etc. Characterizing a whole distribution by one number always necessarily results in a large loss of information.
And, as for the main focus of what we have been discussing here, the magnitude of the natural greenhouse effect, we know the following: The Earth would be about 33 K colder without the greenhouse effect because the surface would be emitting ~240 W/m^2 rather than ~390 W/m^2. To the extent that such a world without a greenhouse effect has a broader temperature distribution, this could make the 33 K number even larger although I would argue that this is somewhat of a “false effect”, i.e., it is due just to a redistribution of the energy that the surface would be emitting without a change in the actual amount emitted.
In general, I think that you are making a mountain out of a molehill, although less so in your latest post than in your previous one ( http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-863072 ) where you were just totally off the rails.

Joe Postma
January 14, 2012 9:24 am

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Tim Folkerts says:
January 13, 2012 at 8:10 pm
Joe Postma says: January 13, 2012 at 5:41 pm …
Joe, I would prefer sticking to my planet-in-a-nebula case. Stars have many complicating factors (they DO have gravitational heating, they have nuclear energy, the plasma is good at absorbing/emitting radiation so they don;t need polyatomic molecules to radiate, … )
You never addressed my conclusion –> the planet-in-a-nebula will cool slower than the naked planet. Can you argue in this simple case that I am wrong? (BTW, I am pretty sure I can argue that even your protostar situation leads to a warmer star if there is a surrounding cocoon of GHG, so even that doesn’t support your conclusions.)
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I can understand the desire to turn the argument around back into the standard GHE paradigm…that the molecules in the cloud cause heating. But that’s not what happens or what we address. I wanted to present the astrophysical theory because it had been presented to me by a colleague who IS an expert on that particular issue; he thought I would be interested in the information.
The center of the gas cloud is where the heat is being generated; this is just like the Earth where the heat is generated by the action of sunlight upon the ground, at a temperature potential of up to +121C, at the bottom of the atmosphere.
In astrophysics, that heat finds a vector to leave the gas via the mechanism I have explained above – if it behaved the opposite way, that of increasing the internal temperature, it would do the exact opposite thing it is needed to do, which is assist the cloud in collapsing by damping the thermal build-up. Otherwise the cloud would be prevented from collapsing.
The heat is generated internally, by collapse, or by sunlight, and this is what sets the internal temperature and amount of energy; THAT energy is then modulated and distributed by the gases, and there is no mechanism (in astrophysics) by which the gases would amplify said preexisting energy; if they did, then stars shouldn’t be able to form.
Anyway I don’t think you and I can get much further on this issue, as it is quite a new and unique angle to look at the situation from. I will discuss at length this physics more with the colleague who does work in this field, and will write about the findings in an upcoming paper.

January 14, 2012 9:27 am

Robert Brown says:
January 13, 2012 at 10:08 am
“Anything with a temperature radiates…in the case of non-spectral gases like N2 or O2, the radiation will arise from inter-molecular collisions. Perhaps we haven’t explored the spectrum at far enough wavelengths to see this emission; perhaps this emission is what helps constitute the entire profile of the “black-body” output curve of the Earth as seen from space in any case.”

These emissions are so weak by orders of magnitude in the Earth’s atmosphere that they are negligible. We do see O2 emissions from O2 at ‘far enough wavelengths’, they’re in the microwave range and they’re what MSU uses to measure the atmospheric temperature but their contribution to the energy balance is minuscule.
To clarify this a bit, if one looks at the actual spectrum associated with the cold top of atmosphere, one doesn’t see “CO_2 lines”, one sees pretty much a BB curve, but at a colder temperature in the general IR window. There is clearly a reduction of ground level IR at T_s and its replacement by atmospheric IR at T_a. That’s the physical reality of actual measurements. This is why I have very carefully avoided giving any impression that I “deny” that the “greenhouse effect” or “atmospheric warming effect” in general terms exists.
However, the data tells us something else as well. It is not CO_2 emissions lines. It is well-thermalized emissions from a colder radiator. It clearly does not come from CO_2, which is 0.03% of the atmosphere, recall. It comes from all of the air, well mixed.

It’s the CO2 emission band with the lines thermally and pressure broadened and the resolution of the spectrometer causing the lines to merge. It does not come from well mixed air!

Joe Postma
January 14, 2012 9:29 am

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davidmhoffer says:
January 13, 2012 at 10:38 pm
3. In other words, the warming occurs the least where it could do potential harm and the most where it can only improve conditions.
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Wow!

January 14, 2012 10:09 am

But… you’ve never come up with any proof! Most of the time what I get is the arrogant response from y’all to go read books on physics! Hello, is anybody in? I’m arguing about the physics in those books..
The proof isn’t theoretical, although you do have to understand at least the idea that as far as the Earth as a whole is concerned, the fundamental issue is how hot the Earth has to be in order for radiation in to equal radiation out.
At that point, one goes up into space, measures the radiation coming out as a function of wavelength (or frequency, if you prefer) and goes “wow, the fact that the atmosphere is experimentally observed to take up some of the total heat delivered and radiate it at cooler temperatures than the surface means that the surface temperature is somewhat higher than it would be if it were an ideal black body.
That’s all. Forget any discussion of mechanism. To understand that, you’d have to actually work through and learn to understand all of the physics, and I’m a physics Ph.D. and it is still a daunting proposition for me. But the energy balance you can understand without knowing a damn thing about “upwelling”, “lapse rate”, convection, conduction, thermodynamics and so on. All you need to know is that ins have to equal outs in (dynamical) equilibrium, and the higher the average temperature of the whole thing, the greater the outs. Lower the effective temperature of part of the outs, you raise the surface temperature to compensate and keep ins (fixed) equal to outs.
Done. End of story. The proof is in the measured spectrum of the Earth and elementary knowledge, it isn’t complex or difficult to understand. The details are difficult, the feedback, convection, radiation balance inside and all that are difficult, but the proof that the process occurs isn’t theoretical, it is purely observational. We might have the mechanism(s) completely wrong. Invisible fairies could be responsible for channelling heat from the surface into the atmosphere to radiate out in the IR at cooler temperatures. It wouldn’t matter. The net effect would be surface warming.
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January 14, 2012 10:16 am

Joe Postma says:
January 13, 2012 at 1:13 pm
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Phil. says:
January 13, 2012 at 12:19 pm
Indeed it was speculation when I was discussing where we might find the collisional emission from the N2 and O2 in the atmosphere. It would be interesting to see it and acknowledge it rather than jump down its throat. But it doesn’t bear on my central theses in any case.
Around 50-200cm^-1 and very weak, and it doesn’t have any bearing on anything.
As Phil’s post was mostly antagonistic I will just fill in the blanks for others who are here willing to learn and have a scientific discussion with experts.
Interesting that you regard your errors being pointed out as ‘antagonistic’, also that you are unwilling to learn and have a scientific discussion with experts.
Phil made a fundamental error in his critique when he criticized my “talking about stellar atmospheres”. I wasn’t talking about stellar atmospheres.
You certainly weren’t talking about the Earth’s atmosphere.
The case of an interstellar gas cloud, and the physics we talk about with them, is entirely analogous to that of the terrestrial atmosphere in the functionality of the radiation. In both cases, you have reduced optical thickness “looking out”, and increasing optical thickness to complete opacity “looking in”. Of course, the idea that spectral absorption and line emission is different just because it’s found in a gas cloud, a star, or a planetary atmosphere, rule by different physics is absurd – it’s the exact same phenomenon, one set of physics describes it.
Indeed, but under different situations different approximations are used, in your case you appear to use the one where collisional deactivation of the excited states is negligible, this is not the case in the lower earth’s atmosphere!
The next step comes when the CO2 molecules radiate the heat energy they’ve internally picked up from the previous collision. This radiation is emitted isotropically; the outward component can eventually escape due to the reducing optical thickness of the cloud, but the inward component can not escape because the gas cloud is optically thick & opaque inside.
So this describes, pretty much precisely, the exact same phenomenon in our terrestrial atmosphere.

No it does not for the reasons given above.
Now, given the history of malfeasance by alarmist climate science, is it astrophysics or is it climate science which is more likely to be correct, on the question of cooling vs. heating…
It is perfectly logical from the astrophysical perspective: damped collisions reduce heat build-up, check, and radiating molecules move energy out of the system, check, rather than adding more energy and heat than was already there, major check.

I have no problem with astrophysics, my problem is with an astrophysics student who’s done some classes of interstellar gases and thinks that he can apply the same equations to the earth’s atmosphere and assumes that those scientists who specialize in the area of atmospheric physics and chemistry are too stupid to understand what’s going on. Perish the thought that he should read some of the science on the subject and realize why the equations he uses are an approximation which doesn’t understand that the relationship between the radiative life time and the mean time between collisions is important!

Joe Postma
January 14, 2012 11:02 am

Hi Phil,
Well, astrophysics is generally recognized as a super-set of all other physics because it has to incorporate molecular, atomic, quantum, gravitational, atmospheric, electromagnetic, relativistic, Newtonian, strong & weak, physics in the practice of its research to explain phenomena in which these universal principles do (or do not) apply, and in situations that, by definition and observation, bound the conditions found on Earth. I think it’s a very good perspective to approach things from…the best, in fact, I can’t imagine a better field of physics to come into this from, given the breadth astrophysics covers. The Earth is a small sliver somewhere in the middle of the bound of conditions which astrophysics characterizes.
If you look at the type of “science” that AGW alarmists have peddled, it is clear that the poorer scientists who don’t understand the basic moral method of it are ending up in a particular field. Not understanding the difference between correlation vs. causation, as a simple example in climate science, is telling.
Anyway, I will report on further findings from this angle at a later date, after discussing it with other astrophysical experts who study it.

davidmhoffer
January 14, 2012 11:08 am

Joel Shore;
blah blah blah>>>
Shrug.
Robert Brown;
(Boldface my addition.) Sure, with the addition, since we now have multiple mechanisms in place. This doesn’t mean that differential radiation atmospheric effect (not really “greenhouse”) warming or cooling doesn’t also take place>>>
Agreed. My point is that until (and unless) we accurately quantify how much of a given temperature trend is due to a change in distribution rather than an increase in net energy, we have no possible way of calculating how much of the trend is due to any given mechanism. Calculating GHE without knowing what the baseline is, is impossible.
gbaikie;
It seems that most energy loss occurs in the tropics.>>>
Of course. The warmest regions radiate the most energy to space. BUT, the tropics still absorb more energy than they lose, so the tropics are a net absorber over all. Here is ERBE outbound LW showing that the tropics lose WAY more heat to space than any other regions:
http://eos.atmos.washington.edu/cgi-bin/erbe/disp.pl?olr.ann.
and here is ERBE net LW showing that the tropics still absorb more than they lose to space:
http://eos.atmos.washington.edu/cgi-bin/erbe/disp.pl?net.ann.
If you scroll back upthread to Joe’s first comment on the issue, you’ll see that he pretty much nailed exactly where the “break even” latitude is just from theoretical physics.
Joe;
Ever notice how Alaska and the Arctic are the showcase for global warming because their temperatures are increasing two or three times faster than the average global increase? For that to be true, and I do not doubt that the measured temperature rise is true, someplace else on the earth’s surface of equal area must be decreasing in temperature in order for the average world-wide temperature increase to be only 1 degree.>>>
I’ve been harping on that exact issue for months and months, though one could still have the effect you speak of but still with a warming trend across the board, one doesn’t actually need to have one section of the earth to be cooling to show that there is a balance that does not meet the eye if all one looks at is raw temperature data because 1 degree in the Arctic and 1 degree in the tropics are two differen things. By SB Law:
+30C + 1 degree = +6.3 watts
-40C + 2.15 degree = 6.3 watts
Every time I hear the “itz happening in the arctic already!” I think…uh huh. I’d expect warming from ANY given source to be more pronounced in the artic! More to your point however, it would be very possible for an increase in temperatures in the arctic to be balanced by cooling in the tropics, and this would be hard to spot because the temperature decrease in the tropics required to establish a balance versus warming in the arctic would be a much smaller change in temperature than would be exhibited in the arctic warming. In fact, I’ve demonstrated via some very simple models in other threads that it is in fact possible to have a set of conditions in which average temperature is increasing, but net energy is actually negative, so temps can actually say “warming” when earth is actually “cooling”.

Bart
January 14, 2012 11:19 am

wayne says:
January 13, 2012 at 8:00 pm
” Latitudinal, the spacing is every three degrees. “
To get equal area coverage of a sphere, you should not space uniformly by latitude, but by vertical height. That is why you had to do the workaround you describe at January 13, 2012 at 8:35 pm. Remember, the area element is cos(theta)*d_phi*d_theta, where theta is the latitude. Transform to a new set of coordinates with z = sin(theta) and the area element becomes dz*d_phi.
Tim Folkerts says:
January 13, 2012 at 8:00 pm
“There is no hint of any effect of N2 in calculations of spectra for the atmosphere.”
Why would there be any hint in calculations which do not assign it any particular weight? You appear to be using a model to confirm… the model.
Robert Brown says:
January 14, 2012 at 7:40 am
“Empirically one has to understand all of the dynamics, not just simplified idealized pictures of the dynamics, in order to “measure” it.”
So true. Nature is complex. Climate science is in a panic due to back-of-the-envelope calculations. Nature is not cooperating.

davidmhoffer
January 14, 2012 11:57 am

Bill Illis;
I can probably put this up in a spreadsheet if someone wants.>>>>
You gave me an idea.
Seems to me what we need to get this discussion back from thrashing around theoretical physics to understanding the meaning of the observational data we have, is not lots of calculus, but a means of manipulating the grid data we have but with the relationship of T^4 understood as part of the manipulation. We don’t have data that would mimic dx/dt so why bother? Can we not get a better approximation of the data that we do have, granular though it may be, by just using the grid data properly?
To do that, we could start with the NASA/GISS temperature data. What they do is average all the grid data from the globe. Each grid cell is in turn averaged from the annual data which is in turn averaged from whatever increments (hourly?) the weather stations in that grid cell use. By the time one gets done with the average of the average of the average of the who knows what, we’ve got a cute graph showing a trend in T that is meaningless.
What we need (I think) is to go back to as granular a copy of the data as possible, daily at a minimum if not hourly, and convert each and every value for T in each and every grid cell to P via SB Law.
Once that is done, THEN average P over the course of a day and year and the globe and graph THAT trend. We could then look at the change in ACTUAL DIRECTLY MEASURED w/m2 and see what change has occurred over the course of the temperature record. I will bet that if there is a significant increase in w/m2 at all, the trend will be well under what we see by trending T calculated from a global average of an annual average of a daily average which tells us NOTHING about the change in energy balance of the planet over the course of time because the only way to calculate that is from the trend in average P, the trend in T is USELESS and misleading.
That’s quite beyond my spreadsheet skills however. Probably beyind the memory capacity of my aging notebook too.

January 14, 2012 12:48 pm

That’s quite beyond my spreadsheet skills however. Probably beyind the memory capacity of my aging notebook too.
Almost all of the things we are discussing aren’t spreadsheet computations. Nor are they particularly trivial numerical computations. Just covering a sphere with “cells” is nontrivial (think about the patches of leather that make up a soccer ball). The simplest coordinates are spherical polar, but they have a horrible “bias” in the Jacobian because of azimuthal compression at the poles. Integrating over a sphere is a pain in the ass, in other words (been there, done that).
rgb

Joel Shore
January 14, 2012 1:56 pm

davidmhoffer says:

Joel Shore;
blah blah blah>>>
Shrug.

What you are saying here is essentially, “Don’t bother me with details, such as the fact that the magnitude of the effect that I am making such a big deal about is demonstrably small. I will just continue to believe in the overwhelming importance of my result, because…Well, just because it is what I want to believe.”

Myrrh
January 14, 2012 2:04 pm

davidmhoffer says:
January 14, 2012 at 8:15 am
Myrrh;
I’m not interested in the blackbody arguments, far too much maths for me >>>
Shrug.
Chuckle. Par the the course, you’ve missed out “time” from my sentence and changed the meaning..
Robert Brown says:
January 14, 2012 at 10:09 am
Re Myrrh to davidmhoffer; “But… you’ve never come up with any proof! Most of the time what I get is the arrogant response from y’all to go read books on physics! Hello, is anybody in? I’m arguing about the physics in those books.. ”
The proof isn’t theoretical, although you do have to understand at least the idea that as far as the Earth as a whole is concerned, the fundamental issue is how hot the Earth has to be in order for radiation in to equal radiation out.
At that point, one goes up into space, measures the radiation coming out as a function of wavelength (or frequency, if you prefer) and goes “wow, the fact that the atmosphere is experimentally observed to take up some of the total heat delivered and radiate it at cooler temperatures than the surface means that etc.

Not what I asked you for, but interesting. Oh, did you miss my p.s. to you on your other thread re text books on this?
http://wattsupwiththat.com/2012/01/09/strange-new-attractors-strong-evidence-against-both-positive-feedback-and-catastrophe/#comment-862221
I asked you for proof of the claim you keep making that the ‘greenhouse gas warming effect is real’ and it’s therefore only the detail of that which should be argued about. As you’ve just written again here in this discussion:
Robert Brown says:
January 14, 2012 at 7:40 am

Re Joe says:
January 14, 2012 at 12:49 am
“When writing my first post last night, I realized an answer to question of whether the greenhouse effect is a real phenomenon. This answer is a resounding YES!”
Absolutely, which is why I try not to let it pass when people assert otherwise. The radiation data are absolute proof of it. The question isn’t “is there a GHG effect that contributes to the warming”, it is “what are the feedbacks, and what are the other mechanisms that also contribute to warming among which total observed warming (or cooling) must be split up”.

I asked you for proof of this. You haven’t actually come back with any proof. You don’t appear to have noticed that you haven’t come back with any proof or any detail of the experiments you say there’s an abundance of. Can’t you find any?
But meanwhile as I’ve given above, in the real world of convection and gravity in the fluid volume of gaseous ocean pressing down a ton on your shoulders,
YOU’VE MISSED OUT THE MAIN GREENHOUSE GAS WATER VAPOUR,
WHICH:
COOLS THE ATMOSPHERE BY 52°C.
COOLS IT DOWN TO 15°C.
Carbon dioxide is fully part of the Water Cycle, therefore, greenhouse gases COOL the Earth.
therefore, greenhouse gases COOL the Earth
The proof isn’t theoretical – just walk out into a desert.
Now imagine the whole Earth without the unique (to our present knowledge) WATER CYCLE.
Now, just how significant is any warming that the trace gas carbon dioxide can manage against the daily 52°C cooling of the Earth by the greenhouse gas water vapour? Of which it’s any way integrated into the cooling of that cycle as carbonic acid?
“Hello, is anybody in? I’m arguing about the physics in those books.. ”
Neither shall I let this pass – “The radiation data are absolute proof of it.”
It’s irrelevant against the great greenhouse gas cooling by water vapour in the Water Cycle.
Greenhouse gas warming is fiction not real world physics.
Now, back to your “The proof isn’t theoretical, although you do have to understand at least the idea that as far as the Earth as a whole is concerned, the fundamental issue is how hot the Earth has to be in order for radiation in to equal radiation out.
At that point, one goes up into space, measures the radiation coming out as a function of wavelength (or frequency, if you prefer) and goes “wow, the fact that the atmosphere is experimentally observed to take up some of the total heat delivered and radiate it at cooler temperatures than the surface means that the surface temperature is somewhat higher than it would be if it were an ideal black body.”
Now you have where it comes from – an Earth heated to 67°C directly by the straight lines of thermal energy, heat, from the Sun which is the invisible thermal infrared, of which the greenhouse gas water vapour removes 52°C from the surface by evaporation and release of heat in condensing out in the colder heights.
The “greenhouse effect” is not a real phenomenon – it is fiction not fact.
Greenhouse gases in the “greenhouse effect” do not warm the Earth from -18°C to 15°C
Greenhouse gases in the real world and real physics cool the Earth by 52°C to 15°C

davidmhoffer
January 14, 2012 2:05 pm

Robert Brown;
Almost all of the things we are discussing aren’t spreadsheet computations. Nor are they particularly trivial numerical computations. Just covering a sphere with “cells” is nontrivial >>>
Agreed again, but I think you missed the point.
What NASA/GISS and Hadcrut use, is gridded temperature data. They average that gridded temperature data spatially and over time and then trend it. They attribute the rising trend that results not just to warming in general, but to increased GHE from CO2 in particular. They even take their average of an average of an average to calculate what the surface radiance is, and they also take an average of an average of an average for insolation to calculate the “non GHE” temperature of the earth, and then subtract the latter number from the first to arrive at a conclusion as regards what the total GHE of the atmosphere is. This calculation is invalid.
The “average” of 240 w/m2 (P) cannot be used to arrive at an “average” T anymore than the average of T can be used to arrive at an average P. The relationship between T and P doesn’t exist. Only the relationship between P and T^4 exists. 240 w/m2 can arrive at a surface temperature of 255K if, AND ONLY IF, P is uniform in both time and space. It is not. The planet is exposed to insolation which varies from 0 to 1000 watts every day and does based on both latitude and time. The “real” effective temperature of earth calculated via blackbody would not only be less than 255K, it would be a LOT less. Similarly, one cannot average T across the temperature record in both time and space to calculate average T to determine how many degrees above 255K should be attributed to GHE. That results in an average of 288K and 390 w/m2 that is valid if, AND ONLY IF, T is uniform in both time and space. It is not. 288K is the lower bound of T for a surface emitting 390 w/m2 in a uniform temperature distribution, the actual T is higher.
So would my spread sheet idea provide the correct answers? No. But what it would provide is proper mathematical evaluation of the temperature record as maintained by HadCrut and GISS which would show conclusively the fallacy of two things. The first is the fallacy that the total GHE is 33 degrees. My back of the envelope estimate is about 150 degrees, commensurate with N&Z. The other thing it would show is that the supposed warming trend is due in part to the temperature of the earth becoming more uniform over the course of the temperature record (it has, tropics up 0.2 degrees arctic zones up 1 degrees) and that much of what is being attributed to CO2 is actually just a consequence of math, not a change in energy balance.
Is there NO change in energy balance? Probably not! The point is to take the data we have and see if we can come up with a way to extract the warming trend in T introduced by increasing uniformity in the earth’s temperature profile and then see how much is left over to attribute to other factors such as changing GHE.
Would the results be accurate? H*ll no! The data isn’t granular enough, it doesn’t even provide sufficient coverage of large tracts of the global surface. BUT, itz the only data we have, and we should deal with the only data we have via proper mathematical analysis rather than the total hocum that NASA/GISS and HadCrut are using to make conclusions about GHE and earth’s energy balance that they cannot possible make on the basis of the math they have used

Agile Aspect
January 14, 2012 2:34 pm

Responding to the title, the goal is estimate an upper bound on the surface temperature of the Earth – which is an exercise in thermodynamics.
If the only thermodynamic tool you have at your disposal is the Stefan-Boltzmann Law, then you’re screwed.

George E. Smith;
January 14, 2012 3:02 pm

“”””” Kevin Kilty says:
January 13, 2012 at 3:56 pm
George E. Smith; says:
January 13, 2012 at 11:12 am
…Anybody who chooses to “junk Stefan -Boltzmann”, is invited to step up, and get tarred and feathered in the public square; Well of course unless you can present a serious peer reviewed paper setting out your new theory to replace the junked science you chose to discard.
The Stefan-Boltzmann “law”, is nothing more nor less, than a total integral of the Planck formula for the Spectral Radiant Emittance of a BLACK BODY, at a uniform Temperature…….
It is becoming very difficult to decide who says what in these exchanges; so, if these aren’t your words, George, then I apologize in advance. All you say is so, however, when the aperture to a cavity acts as a band-limiting filter, then S-B, if you wish to define it as a fourth power T function, does not describe the emitted power. If, on the other hand, you look at SB as an integral over all wavelengths including the band weights, then I suppose you can claim the universality of SB. I suppose the long and short of this is that once active gasses enter a radiation problem, it becomes quite difficult to describe in terms of the simple S-B , T to the fourth power, function “””””
Kevin, essentially everything you excerpted above is what I wrote; but the quoted part:
“junk Stefan -Boltzmann”, was a verbatim extract from some total nonsense that Myrrh posted, so those originally were his words, that prompted me to post what I did. I have no idea why I bothered.
And I thought I explained the issue quite thoroughly; I don’t see how there can be any misunderstanding. Now anybody who chooses to challenge the truth or accuracy of what I wrote is of ourse free to do so; my attitude simply is: believe it or not, it’s ok by me.
So the essence of my message was this. Earlier researchers, notably Wien, Lord Raleigh, and James Jeans investigated the “expected” electromagnetic radiation spectrum from a COMPLETELY FICTIONAL IDEAL, NON EXISTING OBJECT called a BLACK BODY. No such object exists anywhere in the universe, so it is inherently impossible; no matter what, to experimentally observe the spectrum of the radiation of a BLACK BODY, since there is no such thing.
BUT, those researchers still considered it instructive to use the discipline of Statistical Mechanics; a well known branch of CLASSICAL PHYSICS, to investigat the expected radiant emission properties from such an object it such existed.
The BLACK BODY fictitious object they investigated, is defined by one simple property; well two actually. The first requirment, is that the fictitious body was comprised of a very large number of individual particles, which could be atoms or molecules or any other extremely large collection of particles, comprised of REAL MATERIALS HAVING A FINITE MASS. The other requirement was that the fictitious object should completely absorb any and all electromagnetic radiation that falls on it; period; without restriction or conditions.
Other than that, the theory placed no restrictions, and assigned no special properties to any of the particles in the collection; they are of undefined composition, unrelated to any known element, or chemical or any other known material; so no atomic or molecular structure or “energy ;evels”, or any other trappings of atomic or molecular physics is germane to their investigation.
Kirchoff’s law for the state of a closed system where the material is in equlibrium with the electromagnet radiation in the system, requires that the emission of EM radiation from such material must be at every wavelength or frequency identical to the amount of such radiation absorbed by the material. The required state of thermal equilibrium of course requires the whole system is at a uniform Temperature.
So the researchers sought to explain the OBSERVED emission spectra of carefully constructed systems, that approximated the conditions required of the mythical black body. Cavities with small apertures, were systems with such properties, and they showed observed spectra with constantly occurring similarities.
So they sought to describe the expected EMISSION SPECTRUM from their ideal BLACK BODY, AT A FIXED TEMPERATURE.
Wien discovered a mathematical form for the spectrum, that was not a bad fit to the observations from experimental approximations to a black body, particularly at short wavelengths; but it deviated at long wavelengths.
Jeans, and Raleigh on the other hand, using an analysis based on the equipartition principle, obtained a fomula, that gave good agreement at long wavelengths, but predicted an ever increasing amount of radiation at ever shorter wavelengths and consequently an infinite total energy emission; the so-called ultraviolet catastrophe.
now recall, this is a purely mathematical derivation, without reference to the known properties of any material; statistical mechanics,based on the equipartition principle, in this case assigning equal amounts of energy to each and every possible frequency or wavelength. So it was equipartition of radiant energy, rather than kinetic energy such as was used successfully in studies of the thermal capacities and specific heats of gases and solids.
So the failed spectral formulae for the black body spectrum, were purely mathematical exercises in statistical mechanics, and CLASSICAL PHYSICS. In particular, they did not even contemplate what the basic physics that caused the emission of ANY em radiation was, and it takes no part in the derivation.
Max Planck introduced a completely arbitrary restriction sans any precedent for such a rule. Namely that although there was to be equipartition of energy among all the possible radiating frequencies (which were infinite in number). He simply decreed thatthe energy aqssigned to any frequency must be a quantized function of that frequency; that is the energy had to be n.h.f where f was the frequency of the radiation, (h) was a new constant (Planck’s constant) and (n) is just some integer.
With that restriction, a higher frequency component, could only have a smaller set of values for (n) which prevented the total energy from taking off to infinity.
The result of that restriction was to lead to the Planck formula for the expected radiation from a fictitious BLACK BODY, that didn’t actually exist. The calculated spectrum was found to match with ever increasing accuracy, the observed of real approaches to making a body that absorbed all radiation that fell on them.
So the Planck radiation formula describes a fictitious object; not ANY real object. The formula is difficult to integrate in closed form over all frequencies, but when it is so integrated, the result it the Stefan-Boltzmann equation for the TOTAL RADIANT EMITTANCE OF A BLACK BODY
It isn’t the emittance for ANY other object.
So the Planck formula, and the S-B result are useful starting points to investigate emission from real objects. No real object obeys either the Planck radiation law, or the S-B law. In particular, the earth’s moon, is not even approximately close to being able to absorb ALL EM radiation that falls on it so the moon doesn’t obey either Planck or S-B, but despite Myrhr’s declaration; it doesn’t “junk” S-B, nor does NASA
The Planck Radiation spectrum, and the Stefan-Boltmann law, are results of classical physics; statistical mechanics; it isn’t quantum mechanics.

davidmhoffer
January 14, 2012 3:28 pm

Joel Shore;
What you are saying here is essentially, “Don’t bother me with details, such as the fact that the magnitude of the effect that I am making such a big deal about is demonstrably small>>>
I will ask you sir, to not put words in my mouth.
I am giving up because you raised the exact same issue using a nearly identical example in another thread and then completely ignored my response showing you where your error was and wht the magnitude must be considered from BOTH sides of the equation which you have not done either because you don’t want to or you don’t understand in the first place. There’s no point repeatedly going over known ground, hence:
Shrug.

Gary wilson
January 14, 2012 3:29 pm

Robert,
Good luck. I have been working on it in excel in my spare time with some success but there is only so far you can go.
One comment I would like to make is the idea that you can calculate average temperature of a body from the average radiant flux. This is the basis of the 255K and many other wrong conclusions. Consider 2 1m2 surfaces varying in radiative flux such that the average flux is constant . For emissivities of 1 and an average flux of 340 w/m2 this is what you get:
Q1 w/m2 Q2 w/m2 Q avge T avge C T1 C T2 C Actual T avge
680 0 340 5.275 57.926 -273.000 -107.54
612 68 340 5.275 49.324 -86.906 -18.79
544 136 340 5.275 39.971 -51.696 -5.86
476 204 340 5.275 29.696 -28.087 0.80
408 272 340 5.275 18.252 -9.824 4.21
340 340 340 5.275 5.275 5.275 5.27
As pointed out by Willis the larger the difference in temperatures or range the larger the difference between true average temperature and calculated radiant temperature.
These cases can represent two opposite sides of a revolving sphere or even two areas on the same side such as equator and poles.
Another important point is that the atmosphere and the oceans does more than the greenhouse effect in that it squashes the temperature range by mixing. By the above analogy this action alone raises the average temperature without greenhouse. Each case above can be viewed as heat being transferred from surface 1 to surface 2.
This begs the question whether the warming of the Arctic is due to more efficient mixing hence raising average temperature. If it is purely CO2 then why not the Antarctic as well. As ocean circulations change and mixing reduces will the Artic start cooling again and we will see global temperatures falling. Are most natural variations in GAT just variations in mixing and heat transfer from one area to another.
Robert, I also suggest you enrol yourself in Chem Eng 102 Radiant Heat Transfer (too complex for 101) and get yourself a copy of what was the bible some 40 years ago “Radiative Transfer” by HC Hottel and A F Sarofim

davidmhoffer
January 14, 2012 3:36 pm

Robert Brown;
Re; Myrrh
Myrrh doesn’t believe that visible light is capable of transferring energy to earth surface. He doesn’t believe that the physics equations in modern text books are the same as, and/or applied in the same manner, as the equations in physics text books from last centurey. Myrrh is of the belief that there is a giant conspiracy to hide the “real” physics and seems to think that there is some sort of “fake” physics that has been substituded in the text books for “real” physics just to support the GHG theory. How it is that these “fake” physics are used every day to design everything from bridges to hair dryers to night vision goggles to internal combustion engines to nuclear reactors with success he hasn’t been able to explain to me.
But he wants proof. Obviously itz your choice to waste time on him, or not. But I’ve found that reason, logic and facts are about as effective as:
Shrug.

Myrrh
January 14, 2012 3:47 pm

There’s lot’s of interest in this piece, but the something of interest I found about Arrehnius was specificially this:

http://greenhouse.geologist-1011.net/
The Shattered Greenhouse: How Simple Physics Demolishes the “Greenhouse Effect”.
“While Arrhenius credits Tyndall with the thermal buffer idea expressed in Plimer (2001) and Wishart (2009), he then goes on to express the more complicated idea described in Press & Siever (1982) and Whitaker (2007). The “atmospheric re-emission” that “helps heat the surface of the earth” of Whitaker (2007, pp. 17-18) is the key to Arrhenius’ original proposition, which revolves around the backradiation notion first proposed by Pouillet (1838, p. 42; translated by Taylor, 1846, p. 61). However, Pouillet used this idea to explain rather than add to the thermal gradient measured in transparent envelopes while, as we shall see, Arrhenius treated backradiation as an addition to the conductive (i.e. net) heat flow indicated by the thermal gradient.
…….
Moreover, when Arrhenius (1896, p. 255) added the radiative transfer between the earth’s surface and the atmosphere to the conductive transfer between the earth’s surface and the atmosphere, he effectively duplicated the radiative transfer quantity because it was already included in the conductive transfer quantity (“M”). This quantity is representative of net heat flow in accordance with Fourier’s Law which, further, does not distinguish between kinetic and radiative modes of heat transfer across a thermal contact

My bold.
Compositional variation can change the distribution of heat within a body in accordance with Fourier’s Law, but it cannot change the overall temperature of the body. Arrhenius’ Backradiation mechanism did, in fact, duplicate the radiative heat transfer component by adding this component to the conductive heat flow between the earth’s surface and the atmosphere, when thermal conduction includes both contact and radiative modes of heat transfer between bodies in thermal contact. Moreover, the temperature of the earth’s surface and the temperature in a greenhouse are adequately explained by elementary physics. Consequently, the dubious explanation presented by the “Greenhouse Effect” hypothesis is an unnecessary complication. Furthermore, this hypothesis has neither direct experimental confirmation nor direct empirical evidence of a material nature. Thus the notion of “Anthropogenic Global Warming”, which rests on the “Greenhouse Effect”, also has no real foundation.

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