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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According to the Stefan-Boltzmann law, radiant energy is proportional to the fourth power of the temperature. Thermal heat balance equations are based on average radiated energy. The characteristic temperature associated with a given average radiant energy flow is *NOT* supposed to be an average temperature in any usual sense. It is just a handy reference number. In this case, an average temperature is actually less useful and more complex because it depends on factors unrelated to energy balance equations. This should be an obvious apples and oranges situation, but it appears this is one of those fine distinctions that has gotten lost in the communication noise.
I note that there is one exception sometimes used in climate science and that is to assume that such a narrow range of temperatures are involved that the Stefan-Boltzmann equation can be ‘linearized’ by treating the average third power of the temperature as a ‘constant.’ This is being done whenever you see a number involving degrees per W/m².
“It seems to incredibly obvious. I think the nay sayers are so caught up caught up in how every little detail fits together thah they’ve lost sight of the big picture.”
I agree, it seems incredibly obvious but only once the bulb lights up in the mind. There are so many out there that will fight tooth and nail against any such ideas that it is going to be an uphill struggle.
George E. Smith; says:
January 13, 2012 at 11:12 am
“”””” NASA had to junk Stefan-Boltzmann to get real moon temps “””
Total BS, absolute nonsense and moreover, quite false.
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.
Shrug. The thing I found confusing at first in all these arguments was that pro AGW’s are perfectly content to argue with whatever out of context or made up physics came to hand, actually as I later concluded because they don’t have real physics to argue from as their base premise is junk. I don’t know all the ways that SB and Planck is used, argued from, in these calculations, there were countless arguments and i found myself drawn rather to the other silly physics that wasn’t discussed and the history, so if you have a problem with that message I suggest you take it up with the source I got it from, John O’Sullivan. The link I had to the article is now defunct, he had some problems with suite101 as I recall, and I’d been trying to find it, but got distracted by a more recent piece on the debunking of the claim that a colder object can heat up a warmer which grabbed my interest because it was debunking something I had read a while back and which at the time finally convinced me that using crap physics was par for the course in pro AGW arguments, regardless for how apparently well educated in science and mathematically literate they appeared.. .
Ah, here it is:
I’ve lost count of the number of times I’ve been told to ‘educate myself in the real physics of SB and Planck’, and the number of times a given story suddenly changes and a different argument presented and even denial that anything to the contrary had been said…, so I’m not interested in arguing about it. Not that I’m suggesting you’d do such a thing, but this commonly has the effect of confusing these arguments even more and the subject isn’t one that grabs me enough to put in the effort. I gave it in for background.
“(2) Come up with an explanation of how you can take GHGs away and still have the current average radiative emission that the Earth’s surface has.”
You mean just taking away non condensing GHGs presumably.
Whether David has the equations exactly right or not doesn’t really matter. The fact is that even without non condensing GHGs the surface temperature would be set by solar input to the oceans which would keep them liquid and produce the necessary water vapour for a water cycle.
The water cycle might be a little less vigorous with no non condensing GHGs but that would just mean a slight adjustment in the positions of the permanent climate zones.
No need for any change in the equilibrium temperature of the system (primarily the oceans) at all.
All climate change is just a redistribution of surface energy as the rate of energy flow from surface to space varies over time. The equilibrium temperature for the system as a whole (as opposed to just the atmosphere) is set by solar shortwave into the oceans, atmospheric pressure and the phase changes of water.
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Phil. says:
January 13, 2012 at 12:19 pm
No, it’s been investigated and found to be negligible under the conditions of the Earth’s atmosphere, that’s why we don’t see it. The final speculation is nonsense, just look at the spectrum given above from above Antarctica.
That’s the problem with astrophysicists like Postma when they look at the Earth’s atmosphere they think of it as a stellar atmosphere and therefore make elementary errors as Postma has here. Below ~3 scale heights in the Earth’s atmosphere CO2 predominantly loses its excess energy to the surrounding atmosphere by collisions not radiation and thereby warms that part of the atmosphere hence Greenhouse warming. Above that altitude CO2 radiational loss to space starts to win hence the ‘cooling’ of the stratosphere due to GHGs.
Postma, understand the way planetary atmospheres work before modelling them as a stellar atmosphere, the lecture notes recommended above would be an excellent start.
http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf
Yes but we aren’t concerned with a stellar atmosphere here and the ‘perspective from astrophysics’ is wrong! Perhaps you should stick to stars?”
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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.
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.
Phil made a fundamental error in his critique when he criticized my “talking about stellar atmospheres”. I wasn’t talking about stellar atmospheres.
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.
The point remains: in astrophysics, a gas cloud cools due to the presence of radiating molecules like CO2. They absorb heat energy collisionally and then radiate that heat away due to their ability to do so. The other molecules in the gas cloud, like N2, O2, etc, don’t radiate the heat away, just like we talk about in the terrestrial case. The heat that these molecules pick up due to collapse needs to be shed out of the system or else the gas cloud would heat up too fast and blow itself apart before it collapsed. The heat from gravitational collapse, that N2, H2, O2, etc, pick up, is transferred collisionally to radiating molecules like CO2, and others. Because the more complex molecules like CO2 have internal vibration which can be excited by collision, these thermal collisions are damped, and this is the first step in reducing the rate of heat build-up.
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.
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.
“However, you are proposing that this effect still occurs (i.e., the atmosphere reduces the net radiative emission) even if the atmosphere is transparent to IR radiation, i.e., it neither emits nor absorbs it”
I am considering an atmosphere with water vapour and some naturally occurring non condensing GHGs. The real world in fact.
Conduction warms ALL the gases whether GHGs or not. The Nitrogen and Oxygen warm up via conduction from the surface and from collisions with GHGs.
Warmer air at the surface inhibits upward energy transfer of all types in that situation.
wayne says:
“Radiation therefore allows an atmosphere to equalize faster that without it.”
Agree.
Robert Clemenzi says:
“That ignores the energy added by conduction.”
True, I should’ve included that in my “list”.
Ian W says:
“This energy output is NOT shown by Stefan Boltzmann maths nor is it linked to ‘temperature’.”
Cool, thanks for the additional info.
So, do we all (at least us 4) agree that an increase in temperature will result in an increase in outgoing longwave radiation (IR); such that the premise espoused by certain pro-CAGW advocates (SKS, RC) that an increase GHG’s necessarily increases the representative emission height (TOA) that is cooler thereby reducing the outgoing longwave radiation is complete hogwash?
Tim Folkerts says:
January 13, 2012 at 12:17 pm
“The “entire profile” from the ground is known to be very close to a blackbody curve…”
How? In what way, specifically? Here are my thoughts.
A blackbody with purely radiative outward energy flux will settle to a Planck energy distribution, and the integral of that distribution across frequency gives you the Stefan-Boltzmann relationship. But, when you have energy being dissipated by convection and conduction from that surface, will the dissipation be uniform across frequency of the blackbody emitters, and simply scale the energy distribution so that it still looks like a Planck distribution? Or, will it distort the distribution, picking off specific frequency bands, so that the distribution is now non-Planckian? If the latter, then the S-B relationship no longer holds.
How do we know? Proponents of the GHG hypothesis point to measures of the emissivity in laboratory and in-situ experiments conducted in calm conditions, e.g., the emissivity of ocean water near the coast in clear weather with particular wind speeds. But, can such behavior actually be extrapolated to the entire oceanic surface of the Earth? I do not think that is a given.
Moreover, the emissivity numbers are given as single bulk numbers. Do the sensors used measure the entire frequency spread, or do they sample a narrow band, and extrapolate emissivity based on assuming an underlying Planck distribution?
Why does the emission spectrum at TOA (a href=”http://www.john-daly.com/smoking.htm”>Figure 3) look like two separate distributions reflecting radiating bodies at two distinct temperatures, with a gap in between due mostly to water vapor? Is it possible the water vapor gap reflects energy removed by conduction and convection at the surface, rather than absorption within the higher atmosphere? Since convection occurs with moist air, is it not possible that these energy bands are precisely the ones which would be preferentially dissipated from the surface?
It is also noted that emissivity of ocean water very much depends on the observation angle, and this is hypothesized to be due to surface roughness or waves. Should not the emissions, then, be de-weighted by the ratio of the integral of the angle sensitivity to the integral of normal diffuse emission?
Don’t forget the moon and tidal dragging… that really had some interesting effects earlier in the planet’s history….
Say, it has been an idea floating around in my head that the major difference between the K and the T, beyond that boloid, is the break of a pangea into sub-continental masses that also break up the single ocean. Plus once a continent got into the southern polar position we seem to get these little glacial periods… like it was acting as a hit sink for the planet.
Going from nice, warm, placid oceans covering continents and having polar regions closer to today’s WA State to getting a broken up oceanic system with a continent at the pole seems to be doing something to the entire climate deal.
If you ever get a model running, I’d like to check this out.
“Should not the emissions, then, be de-weighted by the ratio of the integral of the angle sensitivity to the integral of normal diffuse emission?”
Rather, that would be the ratio of the integral of normal diffuse emission weighted by the angle sensitivity to the integral of normal diffuse emission. Thus, the result would always be less than unity.
Stephen Wilde says:
Well, when did this change occur? I thought your argument was that one could have the current Earth surface temperature even in the absence of a radiative greenhouse effect. Now, you seem to be saying that it is necessary to have the radiative greenhouse effect to explain the Earth’s surface temperature. That has been what Willis, I and the rest of the scientific community have been trying to tell you for the last couple of weeks!
Davidmhoffer says:
“That being the case, the ONLY affect that CO2 can have in terms of GHE is to become part of the mechanism that redistributes energy from the tropics to the poles. “
That is one part (although a very small one, since all gases can transport energy via large scale movements like Hadley cells).
The OTHER effect of CO2 is to move the location of the radiating surface from the ground level up higher in the atmosphere. Some of the radiation comes from the very cold upper atmosphere and some comes from the ground, with the net result being 240 W/m^2 on average. This has been discussed multiple times and until people understand the implications of this, they will continue to misunderstand the GHE.
Bob Fernley-Jones says:
January 12, 2012 at 10:53 pm
Oh, piss off with your ugly sexual innuendo, it does not make me want to continue the conversation. I have a life. I have a day job. Sometimes I ignore people because they can’t see the obvious. If you want an answer, ask an intelligent question. Hang on, let me see which comment that was …
Ahhh … right, I remember you now. That was your opening salvo, your first contribution to the discussion. In it you accused me of a variety of unpleasant things, said I was of “ranting” and claimed I was somehow plagiarizing Richard Courtney. I went on past that, I ignored your rudeness and answered your question.
Then you went (from my perspective) drifting off into statements that had little to do with what I’d done in the head post. For example you said:
I know that, THAT WAS ONE POINT OF THE ARTICLE. So of course, I didn’t do that. I converted each individual temperature into radiation and then averaged the radiation. So you were accusing me of something I did not do.
Now, I could have tried to correct your lack of reading skills. But I’m constantly doing triage on the new posts—short answer, long answer, or no answer. And you had come in full of spite and unpleasantness. So at that point, since you hadn’t even read the head post, you went into the “not worth it” pile. I’m here to talk to people who are following the bouncing ball.
And now you are making nasty sexual innuendoes about how I didn’t answer you? Were you born that dumb, or do you have to work at it?
I can see I was foolish to answer such an offensive, venom-filled introductory message as yours. You walk in the door and you start slanging me like that, my friend, you are on a very short leash. I may drop the discussion with you at a moments notice.
When will you learn to QUOTE MY WORDS, you unpleasant man? Where am I wrong about the atmosphere? Yes, it can reduce the cooling from the temperature fluctuations, but that’s all it can do.
w.
Joe Postma says January 13, 2012 at 1:13 pm
>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…
We know science is not decided by consensus; it is also not decided by the politics or personalities of the scientists involved. So let the science speak for itself.
>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.
But you are missing one major component — the warm object in the center (the earth). Lets start with the warm earth – suppose it is 300K. It will be radiating energy into space and will start to cool at some rate. Now consider a second earth (also at 300 K) with a nebula of your N2/CO2 mix around it. Earth2 will radiate as much energy as Earth1. But now the gas around it will also be radiating. Yes, some of that energy will head outward, but some will head inward. Earth2 will absorb some of that energy. No matter what the temperature of the surrounding nebula (as long as it is above 2.7 K), the net loss from Earth2 will be less, and Earth2 will cool slower that Earth1.
Tim, this is an excellent explanation of the greenhouse effect. That by moving the effective radiator partially up into cooler regions, the surface must warm, and in turn lead to a somewhat warmer atmosphere to achieve the same energy balance. This explanation avoids the non-pertinent argument that CO2 cannot be effective because one cannot transfer heat from a cooler place to a warmer one. Sol maintains input to the absorber end; and, CO2 affects the radiator end of the thermal circuit.
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.
Tim Folkerts says:
January 13, 2012 at 2:30 pm
“The OTHER effect of CO2 is to move the location of the radiating surface from the ground level up higher in the atmosphere. Some of the radiation comes from the very cold upper atmosphere and some comes from the ground, with the net result being 240 W/m^2 on average. This has been discussed multiple times and until people understand the implications of this, they will continue to misunderstand the GHE.”
I doubt that you mean what you wrote. If some of the radiation comes from the ground then it can contribute to UHI but nothing else. What percentage of CO2 molecules do you see as near the ground?
“Kevin Kilty says:
January 13, 2012 at 3:33 pm
Tim, this is an excellent explanation of the greenhouse effect. That by moving the effective radiator partially up into cooler regions, the surface must warm, and in turn lead to a somewhat warmer atmosphere to achieve the same energy balance. This explanation avoids the non-pertinent argument that CO2 cannot be effective because one cannot transfer heat from a cooler place to a warmer one. Sol maintains input to the absorber end; and, CO2 affects the radiator end of the thermal circuit”.
All you have said would be correct, except for the thermal dynamic entropy of pressure.
This is hard to decipher, Tim, and maybe I ought to return to Joe P’s comment to figure it out, but the spectrum of the ground from space only looks like a BB at some fixed T if you are willing to interpolate over the reject bands. The spectrum is full of holes.
What’s that?
Kevin Kilty says:
January 13, 2012 at 4:09 pm
“The spectrum is full of holes.”
And, where do the holes come from? Atmospheric filtering, or is it that way very close to the ground already? That is what I have been trying to nail down..
Moreover, it looks not like a single blackbody, but a piecewise paste together of two blackbodies, with a reference 275K blackbody at low wave number, and 300K blackbody at high (before getting to the apparent methane band, where it drops off precipitously (Figure 3).
Figure 3. I seem to keep having trouble getting that link right.
Mr. Shore, it appears you have labelled the suggestion that the true average radiation temperature would be done better by using the n-th root of the sum or integral of T to the n-th power, where n is not one as nonsense. Now maybe it is true that the difference with the arithmetical average is not material, but taken literally you are, in effect, saying that T to an exponent of one describes emitted power.
Willis Eschenbach @ur momisugly January 13 3:08 pm
Willis, it was partly in payback for your arrogance and rudeness to me some months ago, when amongst other things you described me as a member of the faunal order; Rodentia.
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Tim Folkerts says:
January 13, 2012 at 3:08 pm
But you are missing one major component — the warm object in the center (the earth). Lets start with the warm earth – suppose it is 300K. It will be radiating energy into space and will start to cool at some rate. Now consider a second earth (also at 300 K) with a nebula of your N2/CO2 mix around it. Earth2 will radiate as much energy as Earth1. But now the gas around it will also be radiating. Yes, some of that energy will head outward, but some will head inward. Earth2 will absorb some of that energy. No matter what the temperature of the surrounding nebula (as long as it is above 2.7 K), the net loss from Earth2 will be less, and Earth2 will cool slower that Earth1.
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However, the situation is still exactly the same, but you might have overlooked it not being familiar with stellar formation. At the center of the gas cloud we DO have a warm object – the primordial stellar core. So it is correct to say that the surrounding gas mixture will be heated by both conductive and radiative effects from the warmer thing in the center; however, in our gas-nebula case, this outward propagation of thermal energy, assisted by the radiating molecules, effects exactly just that: an outward propagation of energy. The heat/energy isn’t returned in such a way as to heat the core even more, the CO2 (etc) molecules KEEP the surrounding gas from getting too hot, thus allowing the cloud to continue collapse. Agreed that the surrounding gas will also be radiating bc of the CO2 (etc) molecules, and that represents a vector for energy loss out of the system. Otherwise, without that spectral radiation, the gas would just continue to heat because the energy wouldn’t be able to escape via radiation.