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

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).

rgb

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JeffC
January 12, 2012 8:22 am

seems to me that the 33 degree greenhouse effect is wildly overstated …

tallbloke(@tallbloke)
January 12, 2012 8:22 am

Great article Dr Brown!
I guess it depends what you are setting out to prove as to whether all the effort is worthwhile. perhaps Hans Jelbring made a smart move with his model atmosphere and isometrically heated planet surface in his 2003 paper:
http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/
At least if he is right you won’t have to worry about including radiative effects of GHG’s

Randall Harris
January 12, 2012 8:25 am

It is a very tough problem. I hope you can get some sleep tonight.

G. Karst
January 12, 2012 8:29 am

Yes, it truly is a Gorgon’s knot. We are all waiting for an Alexander, to appear, with a very sharp sword. GK

January 12, 2012 8:29 am

If the IPCC had spent $1b trying to do this before they started telling everyone what the solution was, we may have not only got somewhere by now but also had some respect for them. As it is, I get the feeling those telling us how to solve the problem don’t even know what the question is — or even where to start looking for the question. Victor Barney January 12, 2012 8:29 am BERESHITH 8:22…as long as the earth remains, seedtime and harvest, and cold and heat, and winter and summer, and day and night shall not cease.” AND, it doesn’t matter if you believe it or not because it’s going to occur anyhow… because that’s exactly what’s written! Francois January 12, 2012 8:30 am Are you serious? You know there are a few books which might help you understand how the system works. January 12, 2012 8:30 am Would it be impossile to build a physical model? Mike M January 12, 2012 8:30 am But but.. the ‘settled science’ is so settled that we’re already spending over$2.5 billion per year to ‘combat climate change’. Ain’t no physics in the universe gonna slow down a gravy train with that much inertia.

January 12, 2012 8:30 am

When I see those magic words “lapse rate”, I hope that what you are talking about makes sense.

pd
January 12, 2012 8:31 am

And then you haven’t even mentioned that the rotation of the earth around the sun isn’t a perfect circle, which influences the amount of radiation from the sun on the earth.

michael hart
January 12, 2012 8:34 am

The problem is [well, one of the many problems], that I fully expect climate modellers to say “Yes, of course we know all this. We take it fully into account. Now, run along, while we tell politicians how to run the world.”
But where can us lesser mortals examine the algorithms and computer code, not to mention the assumptions about which bits can be safely ignored?

kwik
January 12, 2012 8:35 am

You need to write a CSharp program and combine it with a ball made in WPF. WPF (Windows presentation Foundation) is perfect for this. We use it in my business every day.
If we could get some money from some rich guy, and I could take a 2 years leave from my day job, I would love to join you.
We could patch up the globe with small triangles with texture. The globe can be made in any 3-D package and exported to xaml. You can then import it into a WPF project and then write a CSharp program that starts turning the globe….and start calculating stuff…..ahh…a fantastic project…. Click “play” and it comes alive….
But for crying out loud; Dont make a “Report for Policy-Makers” when we are finished!!!!!

Simpleton
January 12, 2012 8:39 am

I’d be tempted to try the Earth as a simple disc (ie, what the sun ‘sees’), flipping over once per day, to give a global average. Then let temperature rise by 1 degree for each doubling of CO2. Then use average albedo, clouds increasing with temperature (more water vapour), hence more albedo and less temperature. Fudge something in for leads and lags if you must.
I’m interested to see if more CO2 eventually ends up with a faster cooling Earth, and therefore a route to the next ice age.
My view is that if the actual situation is too complicated to model, then move to a simpler picture and play around with it.

higley7(@higley7)
January 12, 2012 8:39 am

Looking back at the historical record for clues regarding the character or behavior of these many factors might helpt he effort, at least to decide whether a given addition is going in the right direction.
I like to point out that maybe kids are right to not like vegetables. After all, everybody who ate green peas during the Civil War died

January 12, 2012 8:39 am

You are on the right track. Have you looked at what Ferenc Miskolczi has done? You should because he has some very important conclusions about the greenhouse effect.

Joules Verne
January 12, 2012 8:41 am

@rgb
I’m surprised at your surprise. Anyone who’s been paying attention to this blog knows that the 255K baseline is an ideal grey sphere which has no mass and superconducts. The only difference between gray and black body is albedo. The only difference between sphere and uniformly lit plane is angle of incidence adjustment.
We can at least use some good old experimental science to get us to what an airless world made out of the same rocks as the earth at the same distance from the sun does as far as average surface temperature. At mid-latitudes on the moon that measured number is 250K.
The moon’s slower spin and thermal conductivity of rocks combine to lower its temperature some more from a gray body and the earth’s faster spin would then serve to make it closer to the black body. So I guess what I’m saying is that arguing with 255K as a baseline is probably something only cranks, pikers, and pedants find unsatisfactory for most purposes.
is of course massless and superconducting. I prefer to at least say, for laymen, that the ideal grey sphere is spinning so fast the temperature is equal at every point. An ideal gray body is pretty darn basic physics. High school level stuff int the NYS regents science course I took in the 1970’s anyway. It’s been described here on Watt’s Up With That many times too.
The problem is the body is painted with all kinds of colors other than levels of grey (albedo). And even the grey changes in a very poorly characterized manner. Then there’s like an orchestra playing with different frequencies of light instead of sound and a fairly large assortment of different arrangements of matter that interacts with it to figure out just the radiative part. Then, as long as this remains a water planet, the three phases of water and other unique properties like high latent heat capacity and solid form lighter than liquid to deal with. Then there’s convection up the wazoo which doesn’t happen on grey bodies and has a large effect on temperature stratification. The grey body is an anchor and of course it must be understood what a grey body is and everything that can act to change things.

January 12, 2012 8:42 am

Thank you Dr. Brown. For us non physicists a lucid description. Like all good scientific investigations it raises way more questions then answers. It also illustrates better then I have ever been able to do how dependent any of these numeric models, even the ones we have confidence in, are to voracity of the underlying empirical measurements.

Stephen Wilde
January 12, 2012 8:42 am

Excellent article.
One question:
How do we know that the Earth is any warmer than it would be without greenhouse gases if the standard assumptions are so obviously inappropriate and/or incomplete ?
I don’t believe there is any model anywhere that is based on empirical data rather than flawed guesswork.

January 12, 2012 8:45 am

If we absorb radiation as a disk and radiate away as a sphere the cards are already stacked in favour of cooling. Without the oceans we would be icicles.

Larry Kirk
January 12, 2012 8:48 am

Deliciously put! With that many variables (ie. more than about two), nobody could ever HOPE to model the system, or the effect on it of changing a single, relatively minor factor. Anybody who thinks that they can has got to be kidding themselves. (Nobody but an economist, that is. But they do not have a particularly good track record, knighted or otherwise)

TerryS
January 12, 2012 8:48 am

Re: Francois

You know there are a few books which might help you understand how the system works.

List a few for me please. I would like to read them.

Joe Soap
January 12, 2012 8:52 am

Just out of curiosity what is the geothermal input?
Or heat from magnetic flux eddy-currents?
Or the energy input from lunar gravity moving the oceans?
Maybe these are very small but it would be good to see some estimation of them.

crosspatch
January 12, 2012 8:59 am

One question I have had is the impact of changes in solar UV on the troposphere by indirect means via changes in stratospheric heating. For example, if there is an increase in UV, the stratosphere experiences more heating. If the stratosphere is warmer than this means the top of the troposphere is warmer. If the tropopause is warmer, then if I due the adiabatic lapse to the surface, the surface will be warmer. If the temperature at the tropopause cools, then figuring the temperature down the column to the ground also cools. Unless — the affect from stratospheric changes is a change in altitude of the tropopause. If the stratosphere warms, the tropopause happens at a lower altitude — it finds the temperature inversion “sooner” as stuff is convecting upwards. In that case, since the troposphere is now “thinner” and the stratosphere is “thicker” the change is compensated for and the temperature at the surface is unchanged.
We are currently experiencing less UV than usual with a cooler Sun. That would be reflected in a cooler stratosphere. That might be reflected in a rise of the tropopause (or might not if the troposphere also cools, we are talking about temperature deltas here, not absolute temperatures). The whole thing is like squeezing a water balloon.
Nice article. I think the models currently assume an infinitely thick atmosphere with no convection, radiative heat transfer through it with no evaporation, condensation, clouds, etc.

January 12, 2012 9:00 am

seems to me that the 33 degree greenhouse effect is wildly overstated …
Well, or understated. I thought I had a relatively simple argument that would have suggested that the true baseline should be more than 33 degrees; temperature differentiation favors faster cooling, so both a static perfectly insulating sphere and a rotating sphere with heat capacity and with poles would respectively cool relative to the superconducting sphere and warm relative to the non-rotating sphere. But then I head that voice — dooo theee integrallll. Assume make an ass outa u and me. The problem really is — does the rotating sphere with heat capacity warm relative to the superconducting sphere? Intuitively, I’d say no, it still cools. But at this point I want to do the integrals. Which means first I have to derive them, which I can’t do right now because I’m about to be ass-deep in alligators teaching (really, I already am).
So it might take me weeks or even months to do so, although I don’t think it is that hard. I can probably use e.g. octave/matlab to do them numerically, although the rotating sphere with heat capacity technically requires the solution of a set of time dependent ODEs as a point at a given latitude rotates, through enough rotations to approach a steady state. Basically you have something like dQ/dt for a surface element equals dP_in/dt – dP_out/dt, = CdT/dt, where dP_in/dt is \vec{S}\cdot \hat{n} dA for incoming Poynting vector from sun, dP_out/dt is blackbody power out of dA, and C is the heat capacity of dA. \hat{n}(t) is an outward directed normal (as a function of time as the sphere rotates). The solar flux is modulated by a periodic square wave so it is zero as the point goes darkside.
One should be able to start this from any temperature distribution and spin forward to equilibrium as a function of theta, and only have to do this for the upper half sphere as it is symmetric. Then one has T(\theta, \phi, etc) and one can plot, integrate to find averages, and so forth, for different values of this and that. I think it would be very educational to do this and would take the guesswork out of the question “what does water do” or “what does an atmosphere do” to the sphere (relative to superconducting or insulating static sphere). With a bit more work, one could probably add in depth and do the vertical heat equation as well (only conduction for some conductance) — I think octave would still solve it in less than eternity, although it might well be hours per sphere. A small cluster and you could do a whole range of spheres in a day of compute time and generate pretty pictures without resorting to C coding.
So I don’t pretend to be able to guess the answer. Time to do the work instead.
rgb

Allanj
January 12, 2012 9:00 am

Dr Brown beautifully demonstrates the complexity of the problem. I don’t think we know how much of that complexity is embodied in the IPPC models but I suspect not enough. I also know from experience that you can reach a point of complexity in models that you cannot really understand what your own models are doing. Then you start running sensitivity analyses until they become so complex you don’t understand them.
It is a wonderful world of uncertainty. It is fun to play with. Just don’t bet the farm on the results.

A physicist
January 12, 2012 9:00 am

Professor Brown, please let me express my appreciation for this outstanding WUWT guest post!
Regarding the physics of radiation transport, please allow me to recommend the web page that the American Institute of Physics maintains on this topic, titled Basic Radiation Calculations.
One merit of the AIP’s page is that it covers the history in parallel with the physics: definitely it’s taken a long time and a huge effort to work through these details.

“Dear reader: You have made your way into one of the most difficult corners of this experimental site, and it would be very useful to know why. Would you take just three minutes to answer a few questions? Please click here”

Professor Brown, you have earned everyone’s appreciation, and please accept my sincere thanks, for working to bring a comparable level of understanding to the skeptical community here on WUWT. Your post shows rational skepticism at its finest and best!

Joules Verne
January 12, 2012 9:04 am

@rgb (con’t)
So I do agree the ideal grey body baseline is horrible. I prefer to start with the moon as the baseline. That gives us an actual sphere made out of the same rocks as the earth at the same distance from the sun. The earth spins faster than the moon which makes it several degrees warmer which is fairly straightfoward.
So here’s what I say. The next biggest difference between earth and moon is that earth basically presents as a ball of brine instead of a ball of rocks. There’s a lot of radiative heating/cooling implications in just that alone. Water is very much different from rocks in physical properties.

January 12, 2012 9:06 am

Bravo Dr. Brown.
The 33 K figure is based on treating the earth as a spherical cross section, which is obviously completely wrong. The AGW’ers are off by over 100 K to start with and they are trying to make predictions accurate to tenths of degrees : )

January 12, 2012 9:09 am

When I see those magic words “lapse rate”, I hope that what you are talking about makes sense.
It does. The lapse rate is just the rate that the temperature of the atmosphere drops off with height. As the Earth’s surface cools via radiation, the vertically stratified volume over a given piece of surface (including the surface) radiates at different temperatures if/when the frequencies associated with those temperatures become unblocked by “high albedo” GH gases that have a large absorption cross section there. CO_2, for example, tends to radiate from near the top of the troposphere where it is much colder. Colder means that it radiates less power (in this part of the spectrum) than the warm surface underneath would have due to BB radiation alone. Radiating away less heat creates a differential warming (less cooling). In Caballero’s nice online book, you can look at figure 5.15 and see- the measurements of the IR spectrum from the Sahara Desert that perfectly illustrate the point, and the book itself defines and derives e.g. the adiabatic dry air lapse rate.
It’s complicated, in other words — very complicated when you add clouds, varying albedo, convection, wet air, global circulation — but not senseless or unreasonable.
rgb

Joel Shore
January 12, 2012 9:14 am

Robert,
(1) Arthur Smith has already tackled the issue of the temperature variation on a planet with some rotation rate and some uniform heat capacity: http://arxiv.org/abs/0802.4324
(2) While the issue of average temperature is complicated, it is not quite as bad as you seem to think. First of all, we have Holder’s Inequality, which tells us that the 4th root of the average of T^4 is greater or equal to the average of T for any distribution of temperature T. (The equality occurs in the case of a uniform temperature distribution, and it turns out that the current Earth is close enough to having a uniform temperature that the difference between these two ways of computing average temperature is small.)
Second of all, what is probably the best way to characterize the radiative greenhouse effect is by considering the average emission (in W/m^2) of the planet’s surface (given its actual temperature distribution) vs the average intensity (in W/m^2) that is absorbed by the planet and its atmosphere. So, for example, for Earth we know that the average intensity absorbed is ~240 W/m^2 and the average emission is ~390 W/m^2 or so. We also know that the average surface temperature of the Earth is ~288 K. In the absence of a radiative greenhouse effect, an Earth (with everything otherwise the same, including the albedo) would have to an average temperature such that it is emitting 240 W/m^2. The highest average temperature that a blackbody can have and emit 240 W/m^2 is 255 K (by Holder’s Inequality). To the extent that the temperature distribution is non-uniform, the average temperature could be lower…even considerably lower for very non-uniform distributions. (To the extent that the Earth is not a perfect blackbody emitter in the infrared, the average temperature could be a little higher…but in fact the emissivity of the Earth is very close to 1 over the relevant wavelengths.)

January 12, 2012 9:15 am

Great article.
I like your ‘well, lets try to figure it out from first principles approach’.
Most others slide past the awkward bits leaving the reader feeling inadequate.
A sign of a good teacher!
I thought you might be interested in a new peer reviewed paper by Gerhard Kramm and Ralph Dlugi.
Its a review of the current understanding of the atmosphere effect.
Of particular interest
A detailed application of Keplers Laws to Earth/Sun situation.
Equation 2.17 which includes a ground flux contribution as well as the radiative contributions.
The energy reservoir diagram Fig 11
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233

January 12, 2012 9:15 am

So here’s what I say. The next biggest difference between earth and moon is that earth basically presents as a ball of brine instead of a ball of rocks. There’s a lot of radiative heating/cooling implications in just that alone. Water is very much different from rocks in physical properties.
I think you’re right, although it isn’t just water — water alone is just a matter of changing the heat capacity per unit area of the surface in the model series I suggest. It has to be water with circulation, I think. And as I said, until I formulate and do the integrals I won’t try to guess the answer. Too difficult, and there is Kirchoff lurking behind Arrhennius and Stefan-Boltzmann. Minimizing temperature differences warms, but only up to where there is none and you’re back to the superconducting limit, I think. But I want to do the integrals and see.
rgb

Mydogsgotnonose
January 12, 2012 9:15 am

Read up Misckolczi’s paper: he’s done a lot of the maths.

Larry Kirk
January 12, 2012 9:20 am

What one could in theory do, would be to simply change one of the variables of this immensely complex system and then sit back for an appropriate length of time and observe the effect that this change had had.
Not in the case of this planet however, as we are already dealing with a dynamic, ever-changing system, of which we do not know the detailed history, nor the full nature or history of the numerous factors that acted upon it to date.
So, looking forward: as we do not know how this constantly changing system would have changed anyway, without our intervention, then we can never deduce the effect that our interference with one single variable has had.
And that is the flaw in global warming modelling. We do not understand the pre-existing system, let alone the effects of our intervention. And we never could, because it is too complex.
Economics seems equally flawed, and equally subordinate to political expediency and the strange human desire to always have been ‘right’, regardless of the facts.

Joules Verne
January 12, 2012 9:21 am

@rgb
I don’t think there’s much argument that building a climate model from the bottom up is hard. Climate boffins do it from the top down. This drastically simplifies things as it’s all radiation at that point and these days you can measure it with satellites. Believe it not though we still can’t get satisfactory agreement between different methods of global average albedo better than a few percent accuracy. About the the only thing all the methods agree on is it’s not constant from year to year. The more sophisticated models take obvious seasonal variation into account but from year-to-year it holds constant. So it becomes a prime candidate for a fudge factor which can be tweaked to make your model more agreeable with history. A variation in global average albedo of just 1% is equivalent to the net of all anthropogenic forcing estimates. Experiments measuring albedo, those few that have been running for long, find albedo variation of that amount from year to year.

Joel Shore
January 12, 2012 9:23 am

Stephen Wilde says:

How do we know that the Earth is any warmer than it would be without greenhouse gases if the standard assumptions are so obviously inappropriate and/or incomplete ?

Because we know that the Earth + atmosphere are absorbing ~240 W/m^2 from the sun and that the Earth’s surface is emitting ~390 W/m^2 or so. The only way that this can happen without rapid cooling is if the Earth’s atmosphere absorbs some of the radiation emitted by the surface, which means there is a radiative greenhouse effect. (People like you have desperately tried to explain it other ways, but alas none of those ways use correct physics principles.)
This notion that the atmosphere is absorbing the surface radiation is in fact seen to be empirically-correct by looking at the emissions from the Earth as seen from satellites in space. They see an Earth emitting only ~240 W/m^2 and the spectrum shows that the reason it is emitting less than the 390 W/m^2 that the surface is emitting is because certain wavelengths are getting strongly absorbed. These wavelengths correspond precisely to those wavelengths at which the various greenhouse gases (and clouds) absorb radiation.

Viv Evans
January 12, 2012 9:23 am

Yep – a damn hard problem, and that’s without sticking stuff into the model which mess up things like volcanoes or plants (forget SUV-driving humans for the moment, they mess up everything anyway!!!) and all the small critters in the oceans doing their things as well …
I thoroughly enjoyed reading this post!

January 12, 2012 9:32 am

Start from the definitive facts, of my Venus/Earth temperatures comparison, and don’t lose sight of them, ever. At least half of what is written in this article as unquestioned assumption, I consider rank speculation. The Venus/Earth comparison demolishes all climate models with the simple facts. Someone earlier likened the problem to the Gordian (not “Gorgons”) Knot, and looks for an Alexander to cut it. Well, you cut it by not jumping on the radiative transfer theory as holy writ, and by not ignoring the Venus/Earth facts. I submitted the following comment to tallbloke’s web site just this morning:
In the context of public debate, the “greenhouse effect” is not about radiative equilibria with and without an atmosphere, or even with or without “greenhouse gases” in the atmosphere. It is about whether atmospheric temperature at the surface (or at any given pressure level) increases with an increase in atmospheric carbon dioxide. I am astonished that even skeptics cannot focus upon this obvious fact in the real world; everyone can’t seem to stop themselves from launching into radiative transfer theory arguments. And in that context, of the public and political debate — that irreducible, unarguable reality — the FACT (not theory) is, my utterly simple and transparent comparison of the temperatures in the atmospheres of Venus and Earth demonstrates there is no such greenhouse effect, whatsoever. All the supposedly learned theorizing by one and all is precisely worthless, because everyone uses it to ignore the simple, definitive fact that disproves the tyrannously-promulgated carbon dioxide greenhouse effect, and reveals the radiative transfer theory as unconnected [or better, disconnected] from the real thermodynamics of the atmosphere. (And that last should be obvious, since the radiative theory ASSUMES a fixed temperature distribution, with every incremental layer of the atmosphere at thermal equilibrium. So the radiation levels in the atmosphere are, by that assumption, the EFFECT, not the CAUSE, of the thermodynamics — the radiative EFFECT of the gravitationally-imposed tropospheric lapse rate.)
Where I stand at the moment (and don’t even bother trying to change my mind, I am still learning, and I will develop my understanding on my own, unless and until I see “experts” recognize what I have done, and do better than I have already done): You can’t consider the Earth’s surface a blackbody, or each differential layer of the atmosphere as contributing as a “gray body” (blackbody times emissivity) without the assumption of detailed thermal equilibrium (radiative transfer theorists, are you listening?). More specifically, you can’t do it in the presence of convection and conduction of heat energy between the layers, and expect to get the thermodynamics right. That’s why the blackbody is traditionally described in terms of an enclosed cavity, held at constant temperature, with just a small hole to allow transfer of radiation (no convection, no conduction) into and out of it (Christopher Monckton followers, are you listening?). And even with such detailed thermal equilibrium as the radiative transfer theory imagines, you can only recover the observed radiation levels, and pretend you know the thermodynamics from them; you can’t predict their thermodynamic effect, because the cause-and-effect works the other way — the thermodynamics (in the presence of incident solar infrared irradiation) gives the temperatures and those determine the measured radiation levels. And the presence of CO2 and other IR-active gases only funnels the radiation portion (but not the convection and conduction portions) of atmospheric heat transfer through them, it doesn’t necessarily heat the atmosphere (in particular, in passing from the surface upward, as my Venus/Earth analysis demonstrates). The Gordian Knot does not exist.

tallbloke(@tallbloke)
January 12, 2012 10:08 am

Harry Dale Huffman,
Dont worry, your comment was noted. Just been too busy at work to reply.
Call back soon.

January 12, 2012 9:32 am

I’m surprised at your surprise. Anyone who’s been paying attention to this blog knows that the 255K baseline is an ideal grey sphere which has no mass and superconducts. The only difference between gray and black body is albedo. The only difference between sphere and uniformly lit plane is angle of incidence adjustment.
Well there you have it. I haven’t been “Paying attention to this blog” or reviewing climate physics in detail until, well, yesterday. Having a topical textbook really helps. All the meandering above was my attempt to mentally organize some of what I’ve learned so far from it — I didn’t really intend for it to be a toplevel post but rather the last post I was going to make in a thread.
Now I may have to make this one the last. I”ve got a ton of work to do (of the teaching variety) before I can come back to WUWT, although it is addictive.
I’ll make one last comment. Do not assume (and this goes for everybody) that all of the physics in the standard models is ill conceived or overtly wrong. The real differences between well-educated skeptics (where I am not one, not yet, not in the right physics in the right context) and dilettantes is that the former tend to think that the GCMs are “mostly right” in their physics, but are getting some pretty subtle stuff wrong, notably climate sensitivity. None of them doubt the greenhouse effect, most of the good ones include the ocean and so on. Perhaps not at the right level of detail — not all of the work done is of high quality — but it is probably mistaken in small details with large effects, with certain notable possible exceptions.
So I’m pretty “skeptical” that current climate science gets the kind of stuff I’m considering above in the first few steps at all wrong — I just want to work through it on my own as “homework”, to learn it properly. Far better to derive things yourself than to trust or rely on a textbook, better still to do both, derive it yourself and learn to understand it and then check your work against texts and resolve the differences, learn from your errors (and look for possible errors in the accepted literature — they are not unknown:-).
Believing that you know the answer before you work it through is OK, right up to the point where it becomes self-fulfilling prophecy and you make choices that make your beliefs work out. Confirmation bias (and its close cousin, cherrypicking) are often just as seductive to skeptics as they are to non-skeptics — they are just polarized the opposite, contrary way. The best thing to do is just plain work through it. When I have time, now, I will.
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Mac the Knife
January 12, 2012 9:32 am

Excellent summary!
You ‘painted’ a very complex thought experiment with sufficient fidelity to reality and attention to detail that I could visualize contributions from each added element as you constructed the global warming picture. I have a much clearer mental picture of the problem and a better grasp of the daunting complexities associated with any ‘modeling’ attempts, as a result. I’m going to read this through several times more, to reinforce my understanding and appreciation of your ‘modern physics masterpiece’. As I’m malingering at home with a minor bout of ‘flu’ today, this will provide appropriate distraction, education, and entertainment.
Thank You!!!
MtK

January 12, 2012 9:34 am

At Earth orbital distance from the Sun the total incoming energy provided by the Sun is 1366 / 4 = 341.5 W m-2 .
(solar constant divided by 4 to take day/night and spherical shape into account).
Without an atmosphere, reflection and absorption of the solar irradiance would only take place at the Earth surface, composed by ice, rocks and sand. With an assumed albedo of 0.4 (reflecting power of a surface) the earth surface would absorb 341.5*(1-0.4) = 204.9 W m-2 and re-emit this energy to the outer space.
According to the Stefan- Boltzmann law, the mean temperature at the earth surface would establish itself at:
T= (E / ε σ)^¼ = (204.9/(1 x 5.6710-8))^ ¼ = 245.2 K (-28°C)
Obviously, large differences would be observed at different latitudes and wide changes would take place during every day-night cycle, including some ice melting and water freezing (but with water evaporating an atmosphere would exist… no water is left on the surface of planet Mars).
Also, the assumed albedo is quite hypothetical since we have no clue about what would be the Earth’s surface if no atmosphere were present.
Actually, the mean Earth surface temperature is approximately 15 °C, or 43 K higher than the assumed naked planet. If you assume 33 K it is also within the ballpark.
This is the warming contribution of the atmosphere, mostly by absorbing some of the INcoming sunlight (UV/visible) AND some of the OUTgoing long wave radiation from the Earth surface (by so-called greenhouse gases such as water and carbon dioxide).
Actually the mean surface temperature doesn’t make any physical sense in this hypothetical calculation. The surface temperature would swing between extremes over the night/day cycle (incoming radiation between 0 and 1366 W m-2), with the heat capacity of the material at the surface contributing to a dampening effect.
For a simple 2 layers atmospheric model look at: http://climate.mr-int.ch/TwoLayersClimateModel.html

DeWitt Payne
January 12, 2012 9:38 am

Robert,
Hölder’s Inequality requires that the average temperature on a non-isothermal sphere at radiative equilibrium, assuming the same emissivity and incident power level, must be less than the average temperature of an isothermal sphere. That’s something that G&T do correctly ( http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v4.pdf Section 3.7.4 ).

steven mosher(@stevemosher)
January 12, 2012 9:39 am

ask scaffeta, he models all that with one function.
ha.
sounds like you are on your way to building a GCM

Thermodynamic professor, power plant manager
January 12, 2012 9:41 am

I’m sure that thermodynamic atmosphere effect explains everything much better, it’s the only method that is based on physical facts. If you try to model earths temperature with this very clear Anthonys description you can argue everything until you are dead or used 1 bn$;) Backradiation is bullshit from cooler gas to warmer surface, physically impossible! Gases can’t heat up with infrared radiation without incredible W/m2, only surfaces. David L. January 12, 2012 9:44 am All this reminds me once again why we talk about “average temperature”? The number, as has been mentioned on this site many times, is meaningless. Let’s talk about my house. I have a wood stove in the living room and it pretty much heats my entire house. I have a grate in the ceiling above the wood stove and being a stone farmhouse there is convection throughout the main part of the house. The kitchen is on the opposite side end of the house from the woodstove. Our TV room is perpendicular to this arrangement and the bedroom is above the TV room on the second floor. Now I like it cool and my wife likes it warm so we are constantly changing the draft on the stove or kicking on the oil burner for extra heat, especially in the bedroom which has it’s own heating zone since it gets very little convection from the woodstove. Now my wife and I never talk about the average temperature of our house. Typically when it’s 20F outside, the equilibrium temperature distribution in my house is: The stove is 400F, the living room is 80F, the kitchen is 64F, the TV room is 70F, the bedroom is 62F, and the second floor is 67F. Oh, by the way, inside the fridge is 30F and the freezer is 10F. The basement is 56F. The attic is 32F. Some of the house is insulated by stone, some by modern R33 fiberglass…some by 1940’s R8 insulation. So when I’m cold in the bedroom I kick on the furnace. When I’m too warm in the living room I close the woodstove damper. When the milk goes bad in the fridge I turn down the thermostat in the fridge. My point is that no one would ever think of this system as an average temperature. It has no meaning. There are different temperatures and gradients all over that house for real physical reasons…a good physicist may actually even attempt to model it and get it close…maybe with a degree or two? Why does the average not matter? Why should it? If I did somehow calculate an everage home temperature what would it mean? I can’t act on that information. If the average temperature of the house increased because the fridge broke and warmed up, then that’s not helping my wife who says she’s freezing in the living room. I can’t say “hey, the average home temperature is actually going up so you can’t be freezing in there”. What’s important is knowing the actual temperatures at the various locations and how they change or their distribution changes over time. One last point: I couldn’t ascertain an average temperature of my home to better than a few degrees. I certainly couldn’t tell if that average changed by a few degrees or even if it mattered. And they think they can 1) get a handle on the average temperature of the entire planet to +/- 0.1 and 2) that it provides any useful information? AC January 12, 2012 9:44 am This may be simplistic, but would it be fair to say that the 33K of temp attributed to CO2 is really 33K of temp attributed to the non simple BlackBody? What I mean is if we assume the black body gets us to 255K, then all the complexity (including, but not limited to rotation, circulation, CO2 ppmv, atmosphere and water ingeneral, etc) makes up that 33K? Or did I miss something. I’m wondering if each comonnent mentioned in the article can be thought about AFTER a baseline is used. I know that PV=nRT is for ‘ideal gasses’ and non of them exist, but it is a decent enough guide to teach in intro Chem classes. is the T_b=255K derived in a similar fashion? jim hogg January 12, 2012 9:44 am A roadmap to a possible approximate answer from someone who knows where to start: our messy and incredibly complex reality. A pleasure to read a first rate and honest mind at work. Great Greyhounds January 12, 2012 9:46 am Ahhh! Those fine words… “Do the Integral!” Thank You for the explanation of how a model should be developed, but the big question for me is: How do we hope to test the output of the Model? I worked for a number of years doing E-M simulations for Antennas and Radomes, and at least we had the ability to build real models to test our simulations against! January 12, 2012 9:52 am RE: R. Brown, 9:00am But then I head that voice — dooo theee integrallll. Assume make an ass outa u and me. The problem really is — does the rotating sphere with heat capacity warm relative to the superconducting sphere? Intuitively, I’d say no, it still cools. But at this point I want to do the integrals. Another big complication is the heat capacity effects of water turning into ice. First, there is the simple heat of fusion where heat is released while maintaining a temperature of 0 degC while water changes from liquid to solid. But then you form a crust of ice whose surface can be much colder than the water under the ice. I cannot imagine the differential equations describing these effects filled with discontinuities, much less attempt to integrate them. I very much appreciate you contributions here over the past week. I envy your students at Duke. Carrick January 12, 2012 9:58 am Kevin Kilty January 12, 2012 9:59 am Dr. Brown, Some time ago I read a paper by Gerlich and Tscheuschner, who pointed out a number of inconsistencies in the usual presentation of the Greenhouse effect. Some of these are trivial (such as the atmospheric heating is not the way a greenhouse works) but others are quite substantive. The article inspired me to think about putting together a more realistic model of a rotating earth that could store heat in the crust and ocean, but it is a problem that presents huge difficulty and may not be worth the effort anyway–Gerlich and Tscheuschner suggest it is intractable. Let’s start with a point we can probably all agree with, which is, the model of a uniformly radiating earth (i.e. uniform temperature) illuminated on one side and reflecting some fraction of the radiation is an unphysical model for the problem at hand. Without atmosphere it is 255K and with it is 288K–who cares? What is of real importance is the actual temperature distribution of the earth, because that is the radiator we have to work with. At one time Victor Starr pointed out that the polar regions are the radiator for Earth and they are efficient in this task because they are so large–i.e. a large, cool radiator can work as well as a small hot one. But surely it is important that some radiation in the tropics and subtropics switches back and forth from surface to cloud tops, a huge change in radiator temperature, or that high plateaus, with little water vapor above radiate very efficiently, and so forth. We waste a lot of breath huffing and puffing over the mean temperature of the planet and whether or not it is increasing or decreasing. I suggest that this arithmetical mean temperature is beside the point because it is not connected with the radiator itself. Because of the disconnection between the physical radiator and the arithmetic mean, there are many mean temperatures that are consistent with an Earth in equilibrium, each one a function of the internal dynamics of the oceans, atmosphere, and crust. Even when the forcing is not changing we may see mean temperature vary. So, why should we even care about your build-a-bear effort, when it will likely turn out to contain options that make the problem tractable rather than features that are essential? What are the essential features, bare minimum, of a realistic model of how the Earth gains and rejects radiative heat? Maybe we could call it the build-a-bare model. JPeden January 12, 2012 10:05 am Francois says: January 12, 2012 at 8:30 am Are you serious? You know there are a few books which might help you understand how the system works. Right, in fact it’s so simple that the CO2 = CAGW Climate Scientists haven’t got even one relevant empirical prediction right yet, and are hard pressed to even be able to “explain” any more than about the first 20 of the last 32 years of the most recent past, another one of their records which is continuing to get even worse as we speak. Right Kevin Kilty January 12, 2012 10:06 am steven mosher says: January 12, 2012 at 9:39 am sounds like you are on your way to building a GCM Except the GCM will parameterize the interesting smaller-scale physics in the problem, and we won’t know if this has a small or large impact on the solution. Gary Pearse January 12, 2012 10:19 am “Basically you have something like dQ/dt for a surface element equals dP_in/dt – dP_out/dt, = CdT/dt, where dP_in/dt is \vec{S}\cdot \hat{n} dA for incoming Poynting vector from sun, dP_out/dt is blackbody power out of dA, and C is the heat capacity of dA. \hat{n}(t) is an outward directed normal (as a function of time as the sphere rotates). The solar flux is modulated by a periodic square wave so it is zero as the point goes darkside.” Francois says: January 12, 2012 at 8:30 am Are you serious? You know there are a few books which might help you understand how the system works. Dr. Brown is serious, Francois, it is this hard. So pitch in and give him a hand. jorgekafkazar January 12, 2012 10:26 am Ocean albedo is in itself a huge problem. Not only does the reflectance vary [zero to 1.00] with zenith angle, it also is a function of wind velocity and direction, tides, sea foam, temperature, humidity, viscosity, density, and, so help me, plankton content. Assuming “average” values for any or all of these variables will NOT produce a dependable model, similar to the situation with clouds. Theo Goodwin January 12, 2012 10:35 am Wonderful article, Dr. Brown. Your presentation is lucid and clear. I wish that this kind of work had been available twenty years ago. I thank you for doing it now. Dan Kirk-Davidoff January 12, 2012 10:37 am Michael Hart: Many climate modeling groups make their code public. NCAR’s is here: http://www.cesm.ucar.edu/models/cesm1.0/ GFDL’s is here: http://data1.gfdl.noaa.gov/~arl/pubrel/m/am2/doc/ NCAR’s is not too hard to download, set up and run, if you have the time and inclination, and a good sized computer. Neo January 12, 2012 10:37 am The Earth radiates it’s own heat generated at the core. The function of how it is emitted at the crust is quite complicated because it depends both the local surface material and geological faults. It might be interesting for map AGW hot spots with known high geothermal emissions. January 12, 2012 10:40 am Dr. Brown, It is kinda complicated. I have a question that sounds off topic but is on topic to a degree. When I started thinking about how to build a better model, I was struck by the stability of the tropopause minimum temperature. Yes, stability is a bit relative in this case, but it tends to bounce back nicely. The coldest temperature on Earth and in its lower atmosphere is around 184K degrees -89C, with the tropopause making excursions to -95 C from time to time, but bouncing back rather quickly to below -90C. Oddly, Venus, the granddaddy of greenhouse effect, has a black body temperature of about 184K which is around 65Wm-2. This seems to be a non-thermal limit to the atmospheric effect (the better term since a lot of crap is going on). Since Venus and Earth don’t have a heck of a lot in common other than mass, this is circumstantial evidence that the gravitational constant may be the prime suspect. Crazy talk right? So once you iron out all the issues you are looking into now, be aware that there are possibly a few more shoes to fall. If the approximate 65Wm-2 is a gravitationally set limit, not numerical happenstance, it adds some neat thermomagnetic and thermoelectric atmospheric chemistry to the problem which may involve ozone and CO2 and/or CH4. Which is totally bassackwards to the Venus atmosphere building mass with runaway greenhouse effect. I believe someone theorized that Earth and Mars started out like Venus, but picked a different path. He may have been smarter than most of his buddies thought. Tim Folkerts(@tjfolkerts) January 12, 2012 10:49 am It is great to have another voice of a physicist here. The problem is indeed complicated, but not insurmountable. As Dr. Brown noted (“I just want to work through it on my own as “homework”, to learn it properly”), the sort of things he is doing are the “homework” to even start to discussing the topics. Anyone who wants to intelligently discuss the climate and the greenhouse effect really needs to understand the science at the level he is addressing. One thing that often bothers me is the assumption by many people that scientists in the field have not thought of these things before. Nothing that Dr. Brown said is “new” or “unknown”. These would be the sorts of problems that grad students in the field would work through in their coursework. (The source that Dr Brown references is, after all, a textbook with sample problems.) So this is “basic” science for those specializing in climate modeling. Finally, even though the topic is difficult and certainly not “settled” as a whole, many individual parts of he problem are “settled”. 1] the starting scenario (“Start with a nonrotating superconducting sphere, zero albedo, unit emissivity, perfect blackbody radiation from each point on the sphere. What’s the mean temperature?”) would give a planet with a uniform temperature of ~ 278.5 in earth’s orbit around our sun. 2] raising the albedo would lower the temperature of the planet (to ~ 255 K for the earth’s current ~ 0.3 albedo) 3] lowering the emissivity would raise the temperature of the planet (but experimentally the emissivity is very close to 1, so this is not a major concern). 4] a nonuniform temperature would lower the average temperature of the planet. (so any conduction or convection or fast rotation would help make the temperature more uniform and hence warmer on average). 5] GHGs high up in the atmosphere where it is colder would raise the surface temperature. These are all “settled” in terms of the general affect on global temperatures. Of course, the details and exact extent are not “settled” (or we could perfectly predict weather and climate). One big challenge is that some things have two or more effects. For example, more H2O in the atmosphere adds GHG and would warm the atmopshere [5], but it would also lead to more clouds which raises the albedo and cools the planet [2]. January 12, 2012 10:50 am Harry Dale Huffman said @ January 12, 2012 at 9:32 am And in that context, of the public and political debate — that irreducible, unarguable reality — the FACT (not theory) is, my utterly simple and transparent comparison of the temperatures in the atmospheres of Venus and Earth demonstrates there is no such greenhouse effect, whatsoever. [Emphasis mine]. It is a fact that p = it is true that p, or it is the case that p. A theory is a set of propositions providing an explanation of a subject matter. Even a single proposition can be a theory. Such as it is true that p, or it is the case that p. Thus you contradict yourself rendering whatever else you are saying incoherent. January 12, 2012 10:52 am “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. ” – A. Einstein ‘Chaos Theory’ teaches that even the simplest of non-linear systems can be ultimately unpredictable, and the earth is a definitively non-linear system. January 12, 2012 10:53 am Robert. What a wonderful world ! What you have shown is that the Earth, or any other planet for that matter, can never reach thermal equilibrium since energy is constantly flowing through the system. A single black body temperature is therefore an idealized myth. For the same reason it is also a fairly gross simplification to measure or to predict just one single globally averaged temperature (GAT). There are plenty of non anthropogenic phenomena which continuously change this average temperature. For example plate tectonics including the raising of the Tibetan plateau by 5 km which not only reduced the surface temperatures but also increased albedo. Then we know that albedo is anyway constantly changing due to clouds, let alone volcanic ash and deforestation. The greenhouse effect itself is also changing on an hourly basis as water vapor enters the atmosphere and then rains out again. Into this mixture we then introduce over the last 260 years about a 30% increase in one greenhouse gas – CO2. We go back and measure GAT over the last 160 years of weather station measurements and assume that the observed rise of about 0.6C is just due to CO2. Well maybe they are right and it is all due to CO2. However, this can never be proved until measurements or experiments are designed which can eliminate all other effects except CO2. There are only a few places on Earth where such an experiment may even be possible. Firstly it would have to be somewhere with zero or stable water vapor at least for a fixed period each year far away from civilization. Ideally we would need a reliable weather station with a long historic time span. Does such a place exist ? I wonder if there is perhaps just one long term weather station somewhere in the Sahara for example ? January 12, 2012 10:54 am Dr Brown, You’ll go insane trying to develop a deterministic model because the boundary conditions are effectively indeterminate. Stochastic. As you have observed; non-linearities are rife in the climate system; beyond T^4 effects. Especially convective heat transfer and the phases change of water, in all their phases make a big difference. Then there are topographical effects; mountain-sides, canyons, hills … which change the angle of incidence of light dramatically throughout the day; and hence when and how much heat is stored and then released. IIRC, even water has different reflectivity at low angles of incidence.. When smooth. Wave action makes things a great deal more complicated. It’s not valid to assume that the average will be the same.. Vegetation is also highly variable in terms of albedo and the energy which it stores and how/when it releases that energy. Seasonal variations are substantial. And if you’ve ever looked out of the window of an aircraft flying at altitude, you may have noticed that the green forests appear to be almost black from directly above yet green from the sides at a distance. Plants orientate themselves (leaves turn) in order to optimise the balance between photosynthetic takeup and loss of water. Vegetation changes seasonally with species becoming dominant during growing their peak; and for those who stimulate the climate neurons; their seasonal stasic, decline and death are also important because that has a strong effect on albedo. There are very many factors which are known to have an effect on weather and hence climate. Many of those known factors can be described in isolation, under controlled conditions (i.e. with reality adjusted to impose assumptions). But because the climate system is non-linear, the principles of super-position cannot be applied to combine two or more non-linear factors. And that’s without even considering the coupling effects between the variables; which also tend to be non-linear in magnitude. Keep in mind that climate is entirely synthetic; an arbitrary statistical artifact, based on poor statistics. Only weather is real. Although one can build simplified models of the climate system, those work on bulk averages (and fantastic assumptions). But those bulk averages imply that the condition of the climate system withing each cell is uniform. Which might be a reasonable approximation if it’s say 1000 cubic metres, but in the case of the models, it’s more like 1000 cubic kilometres for the smallest cell size. (Order of magnitude) And it’s extremely unlikely that conditions will be uniform throughout. It is the internal differences in conditions that act as a perturbation (“disturbance”) to provide interesting weather. The non-linear response to the perturbation is impossible to determine a priori without knowing the boundary conditions; the state of the system. January 12, 2012 10:55 am To simplify the energy flow problem pick the South Pole during the six months of night where it has very little atmospheric water vapor to cause a “greenhouse effect” and see if the rise in CO2 in the last thirty years has had any significant effect on the rate of energy radiated to space. Energy is being delivered via wind and lost via radiation to space. There is no direct input from the sun to complicate the balance. Also, nights and days are six months long. The air is thinner at that altitude and the TOA will be closer to the surface. Bill Illis January 12, 2012 10:58 am How about if one makes it a non-rotating planet first with some set heat capacity (and I’m not sure there is really a limit to how much heat a surface or gas can absorb). How hot does it get at the equator at the spot that is directly facing the Sun. hswiseman January 12, 2012 10:59 am Lubos “crickets,” Lubos “crickets,” Bueller… January 12, 2012 11:00 am Robert Brown said @ January 12, 2012 at 9:32 am So I’m pretty “skeptical” that current climate science gets the kind of stuff I’m considering above in the first few steps at all wrong — I just want to work through it on my own as “homework”, to learn it properly. Far better to derive things yourself than to trust or rely on a textbook, better still to do both, derive it yourself and learn to understand it and then check your work against texts and resolve the differences, learn from your errors (and look for possible errors in the accepted literature — they are not unknown:-). And as Joseph Joubert once said: to teach is to learn twice (except he said it in French). Peter Miller January 12, 2012 11:02 am Mr Watts It is all very simple, trust us, we know!. Let us explain: rising carbon dioxide levels cause lots and lots of heat and that changes climate and that means our children are all going to die horribly unless we do something about it now. Most important we need more grants. Then we need to create lots of nice new taxes and send the money to the nice people who lead the countries in the Third World. You are making this simple situation much too complex and confusing, we would never dream of considering the things you discuss in your article. KISS has always been our motto, we don’t want to confuse those nice politicians, after all they are very simple people who don’t want to try and understand complex issues. So, just remember this simple motto: carbon dioxide very bad, climate scientists very good – climate scientists understand, you don’t, and they can always be trusted to tell the truth. Yours affectionately The Team /sarc Wenson January 12, 2012 11:06 am As I mentioned in the another thread, Earth is not a true black body. Using “average T” would “increases” the earth temperature. And I don’t believe CO2 has any meaningful effect on earth temperature. I’m a layman. Here is more question about CO2. In anyway can I think a photo is much smaller than a Co2 molecule? If so How many photos will miss the target of CO2 molecules? Since CO2 only 0.3% , 0.4% in the air plus there a lots of empty space ( to the photo and air molecules) in the air. What is the percentage of the photo will miss the target CO2? (at each “layer “of the air) (In layman’s thinking, Only very very small portion of the photos will hit the CO2 molecules.) the following is a layman’s another thinking. (based on NASA uses photo to drive a spaceship) What happens After a photo hit CO2 molecule. (Assume a moving photo has momentum,layman’s photo just a glass ball now) will the CO2 molecule change speed? If the CO2 molecule really had speed change, then its energy changed. Assume CO2 molecule randomly moving. Case 1. CO2 molecule moving faster, Case 2. CO2 molecule moving slower. Case 3. CO2 molecule changes moving direction only. In which case the CO2 molecule will “reflect” a photo out? What is the “reflected” photo’s energy compare to the incident photo? (Layman’s thinking: maybe not all the “hits” generate a “reflection “. If “reflection” occurs, the energy of the photo would be less than the incident photo’s energy. Because part of the energy transferred to molecule’s kinetic energy. How much less?) And a molecule with increased speed will dissipate energy more quickly. ( how to relate the speed change to the temperature change? ) Layman’s conclusion: CO2 cannot have big “green house” effect. I like to learn what is wrong in my thoughts. Wenson wayne January 12, 2012 11:07 am Robert Brown: Hi Robert. Just read you post and later comment (and kwik’s). http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-861864 Guess you know I was the one that jumped into the Unified Theory of Climate thread and coded up that simple integration in c. Kwik’s thoughts are very close to mine. I have already ported that to CSharp and have had thoughts along the same lines: how far could you carry the next steps to an integrated surfaces so all of the pertinent parameters which could be altered to give us all of the variant questions you so well laid out in words. It would be quite easy to program such a model, staying strictly in CSharp for portability. The integrations to me would pose no problem. I already have in CSharp a set of very fast adaptive Simpson 3/8 interpolators, Runge-Kutta of various orders and my favorite Yashida 6th order sympletic integrator for minimal energy error terms, fast and very precise. After all, all integrators will have round-off error, it’s just where you want them minimize, in the spatial terms or the energy terms. But the jump to multiple vertical layers is more challenging memory wise and performance. Performance is why some flavor of c would be preferred to MatLab or other script language. Yes, I have been pondering on these very same questions, could you simulate this whole question that Dr. Nikolov brought up and carry it further towards reality. Good post Robert. stumpy January 12, 2012 11:08 am Its a key issue, as the greenhouse gasses are assigned their importance on the 33k warming they may or may not actually make – no one never actually took the time to do it right though! Phil. January 12, 2012 11:11 am Stephen Wilde says: January 12, 2012 at 8:42 am Excellent article. One question: How do we know that the Earth is any warmer than it would be without greenhouse gases if the standard assumptions are so obviously inappropriate and/or incomplete ? It’s quite straightforward. The emission spectrum of the Earth from space is grey body with numerous missing bands which can be unambiguously assigned to the GHGs (CO2, H2O, O3, CH4 & N2O), the spectrum of the Earth absent those GHGs would be grey body but would have to have the same area under the curve which requires a lower temperature. Therefore there is a GHE due to the presence of those gases. George E. Smith; January 12, 2012 11:11 am “””””Thermodynamic professor, power plant manager says: January 12, 2012 at 9:41 am I’m sure that thermodynamic atmosphere effect explains everything much better, it’s the only method that is based on physical facts. If you try to model earths temperature with this very clear Anthonys description you can argue everything until you are dead or used 1 bn$;) Backradiation is bullshit from cooler gas to warmer surface, physically impossible! Gases can’t heat up with infrared radiation without incredible W/m2, only surfaces. “””””
So Thermodynamic Professor, whether or not one believes that the ordinary atmospheric mono or homo-diatomic gases: Argon, Nitrogen, Oxygen (maybe Hydrogen) etc, do, or do not absorb and emit Electromagnetic Radiation under ordinary atmospheric conditions (circa STP), it is an experimental fact that the earth atmosphere DOES emit EM radiation, and there is no theoretical physical basis for believing that such atmospheric emission is not locally isotropic. That is, there is no preferred direction of emission; all directions are equally likely. And some declare on their mother’s grave, that it is solely the triatomic (or more) or hetero-diatomic molecules generally grouped as GHGs that emit this isotropic atmospheric EM radiation.
So whether you or I like it or not, it is an experimental fact that at all levels in the atmosphere, EM radiation IS emitted downwards; and those emitting GHGs can have no a priori knowledge or information as to the Temperature of the earth surface, or whether that Temperature is lower or higher than the local Temperature of the emitting atmospheric gas, at the time such radiation leaves its originating gas molecule.
So now what is it; in your view; as a Thermodynamic Professor, that instructs that radiation that it may not land on the surface, because that surface happens to be at a higher Temperature than was the emitting gas molecule; about which the near surface arriving EM radiation, carries absolutely no information, by which to inform the surface that it originated from a colder gas molecule.
Or is it perhaps that such matters are managed, as in your role as a power plant manager, rather than the laws of Physics, which would be relevent to a Thermodynamics Professor.
How it it that EM radiation emitted from the earth at averaged 288 K Temperature, is safe to land on the moon at average Temperature 240 K but the same solid angle beam may NOT land on the sun, at its surface Temperature of about 6,000 K ??
Some of us non thermo-dynamic professors, and non power plant managers, are anxious to learn the answer to that from you ?

Septic Matthew
January 12, 2012 11:23 am

Francois: Are you serious? You know there are a few books which might help you understand how the system works.
First off, how the system works is not known completely, though a great deal is known.
Second, the main questions are the rates of energy transport through the many parts of the system, and most of those rates are not known exactly. Without knowing those rates, even the notional equilibrium for a constant input can’t be computed accurately. The author has shown that there are substantial reasons for believing that the widely accepted figure is significantly inaccurate.
Robert G. Brown, that’s a good summary. I think it’s something everyone sort of “knows”, but has decided to ignore. It is worth repeating from time to time, until everyone asks “Where has it been shown that the errors in the simplified approximations are negligible.”

wayne
January 12, 2012 11:24 am

Robert, what I was trying to say is if you should ever need any help, let me know. I have written six different solar system simulations able to hold accuracy up to about one thousand years, not a NASA Horizon system clone, but close, and I already know many of the problems such a program would entail when you carry it into the non-linearities.

Lars P.
January 12, 2012 11:27 am

Thank you for the article! Great, we need more of these!
I wonder does the 33°K difference play any role in the assumptions of greenhouse warming for the models?
Hm, what would be the temperature on a rotating sphere covered with water – as stated in the article, before considering the atmosphere and the land, simply 4 km deep ocean everywhere.

Joseph Dunn
January 12, 2012 11:28 am

Robert Brown says:
January 12, 2012 at 9:00 am
…I can probably use e.g. octave/matlab to do them numerically, although the rotating sphere with heat capacity technically requires the solution of a set of time dependent ODEs as a point at a given latitude rotates, through enough rotations to approach a steady state….

You might want to check out the following paper, which works through a model similar to the one you describe.
Vasavada, A. R., D. A. Paige, and S. E. Wood, Near-surface temperatures on Mercury and the Moon and the stability of polar ice deposits, Icarus, 141, 179-193, 1999
Available online at:

January 12, 2012 11:31 am

Bernd Felsche said @ January 12, 2012 at 10:54 am

Keep in mind that climate is entirely synthetic; an arbitrary statistical artifact, based on poor statistics. Only weather is real.

So the trees I planted 30 years ago that reduce windspeed and evaporation from the soil, thus warming it, haven’t affected the climate on my property? It seems odd to me that I grow more grass as a result of something “entirely synthetic; an arbitrary statistical artifact, based on poor statistics”. Perhaps you meant global climate. I always have trouble imagining something to be both local and global.

jorgekafkazar
January 12, 2012 11:33 am

Joe Soap says: “Just out of curiosity what is the geothermal input?…”
I’ve done the estimate and it’s negligible. I’ve also steam heated a cylinder of dirt 12′ deep by 3’Φ and still found the spot quite hot two weeks later. Earth is a great insulator.
Francois says: “…there are a few books which might help you understand how the system works.”
Then you must have read these books, Francois, and understood them. Please tell us in your own words what they say. Maybe Anthony will want to post what you have to say.
crosspatch says: “One question I have had is the impact of changes in solar UV…
You may be onto something. I suspect the impact is significant, despite Leif having said the density of the ionosphere (rather than the stratosphere, as you suggest) is too low to have an effect. But you can’t shoot a photon through the ionosphere without hitting something…
Joel Shore says: “…Holder’s Inequality, which tells us that the 4th root of the average of T^4 is greater or equal to the average of T for any distribution of temperature T. (…it turns out that the current Earth is close enough to having a uniform temperature that the difference between these two ways of computing average temperature is small.)”
True, but when doing the energy balance calculations, any error in Tavg must later be taken to the 4th power, which makes it large once more. Remember, we’re looking at a very few W/m² of putative imbalance in all this global warming nonsense.
David L. says: “…“average temperature”? The number, as has been mentioned on this site many times, is meaningless.”
Yes, as in Joel Shore’s hand waving, above. It’s the energy flows that have meaning. It’s all too easy to brush the hair-splitting nature of the GHG problem under the rug by talking temperature or, better yet, anomaly.

January 12, 2012 11:34 am

tl;dr version:
A black body model won’t, can’t, tell you *anything* about the temperature at the Earth’s surface.
Mike.

TomB(@dragineez)
January 12, 2012 11:36 am

Geckko says:
January 12, 2012 at 8:30 am
Would it be impossile to build a physical model?

There was a book that described this. I believe it was “The Hitchhiker’s Guide To The Galaxy”. If I recall correctly the scale was 100cm to the meter.

George E. Smith;
January 12, 2012 11:36 am

“”””” Bill Illis says:
January 12, 2012 at 10:58 am
How about if one makes it a non-rotating planet first with some set heat capacity (and I’m not sure there is really a limit to how much heat a surface or gas can absorb).
How hot does it get at the equator at the spot that is directly facing the Sun “””””
Bill, the highest officially recorded in shadow atmospheric Temperature, was about 136 deg F (57.8 deg C) somewhere in North Africa. US troops in Iraq apparently often went on patrols in air Temperatures of 130 deg F. I take +60 deg C (140 deg F) to be a common dry desert surface Temperature max. and it has often been reported of black top surfaces reaching +90 deg C
At 333 K BB Temperature rather than 288 K to BB total radiant emittance is 1.787 times higher than Trenberth’s 390 W/m^2.
More importantly, the emission spectrum peak wavelength shifts to a shorter wavelength, further removed from the CO2 15 micron band, reducing the CO2 effect and the peak spectral emittance at that shorter wavelength is 2.067 times what it is at 28 K since that goes as T^5, not T^4.
George
PS when that highest record Temperature occurred, it was of course Winter midnight in Antarctica and at Vostok Station; and the lowest Temperature that has been recorded there was below -128 deg F -88.9 deg C. Anecdotal reports of lower Temperature further up the hill are of course not official numbers. I take -90 deg C (-130 deg F) to be the low limit, and note that whole range could occur simultaneously, and therefore there would be an infinity of places on the earth that can have ANY Temperature within those extreme limits, and all at the same time. So much for hundredths of a degree changes being relevent.

January 12, 2012 11:37 am

All of the above ignore one more highly relevant factor. Climate scientists, alarmists and skeptics alike, usually assume that all the temperature at the surface is due to incoming solar irradiance (except for very trivial lunar and stellar, etc. inputs).
The majority of the heat at the Earth’s surface is due to its radioactive core, especially U-238. Since the half-life of uranium is about 4.5 billion years, that is a factor in changes since the Hadean, or even Cambrian ages, but is effectively a constant for the duration of human existence on the planet.
It is a constant that should be included in estimates and calculations.

Septic Matthew
January 12, 2012 11:41 am

Tim Folkerts: These are all “settled” in terms of the general affect on global temperatures. Of course, the details and exact extent are not “settled” (or we could perfectly predict weather and climate).
Dr. Brown’s point is that the details and “exact extent” are not known accurately. Thus you affirm his main point, and affirm my point above that everyone already knows it. It bears repeating: even something relatively simple like the mean temperature of the earth without atmospheric GHGs can not be computed accurately from the known science.

wayne
January 12, 2012 11:43 am

Why not a game. Gore’s got a game, let’s make a game. As Robert was saying, a tinker-toy put together GCM astronomic body climate simulator for any planet/moon system. Why not. Let’s out do him. A physics law tutorial of kids and parents alike. It seems to have some merit.
If you could simulates all known bodies as Ned laid out in his paper, with the same parameters and functions, that actually performs very close to what is seen and measured on all bodies, I would trust that hugely over the current GCMs being used to solely point at CO2. I think most citizens of this world would too.

Ian W
January 12, 2012 11:45 am

It would have been nice to see a mention of enthalpy. Atmospheric temperature is meaningless as a way of quantifying heat content without knowing the enthalpy of the atmosphere at that point and that is largely dependent on the water content of the atmosphere and the state the water is in ice, liquid or vapor. It then goes without saying that ‘average’ atmospheric temperatures are completely meaningless as an input into energy content.
The main problem is that with a chaotic system of chaotic sub-systems any ‘simplification’ or assumptions of linear behavior lead to results that are rapidly divergent from the ‘real world’. Even mesoscale modeling of the atmosphere 10 km around a point with best feasible start parameters from normal observations plus LIDAR and RADAR etc., is only feasible out to around 30 minutes with any accuracy. Yet the standard mathematician’s approach is to simplify, as demonstrated by many suggestions on this thread. The assumption that those mathematical simplifications have little effect or only a known effect that can be calculated out afterward, is almost certainly false and impossible to validate.

Willis Eschenbach(@weschenbach)
Editor
January 12, 2012 11:46 am

Dr. Brown, as someone else said, I envy your students.
All that you have said is true. However, let me suggest that there are some things we can conclude despite the difficulties.
First, we have a pretty good handle on how much energy hits the earth system after albedo. It’s on the order of 240 W/m2. I often model the simplified, theoretically perfect situation as an airless spherical blackbody in space heated from the inside by unspecified nuclear reactions, with 240W/m2 emitted everywhere on the surface of the sphere. This has an equivalent blackbody temperature on the order of -18°C. Using this model avoids some of the conceptual difficulties with a rotating planet heated from the outside. I will call the Stefan-Boltzmann temperature of such a sphere the “theoretical S-B temperature” of the planet given the 240 W/m2 radiation.
Now you have done an excellent job of discussing all of the ways that an actual rotating planet with axial tilt will diverge from the theoretical number of -18°C. The important point, as you pointed out, is that in all cases, assuming total emitted radiation stays constant, any divergence from a perfectly even surface distribution of emitted radiation will lower the average temperature from the theoretical S-B temperature.

Knowing this inequality, that all temperature swings and variations only cause average cooling and never warming, will let us draw important conclusions.
Second, we have a pretty good handle on how much the earth surface is emitting. It’s on the order of 400 W/m2. It is estimated from temperatures taken on the surface as well as from satellite observations.
This plus the first fact allows us to put a minimum value on the heating which comes from the “greenhouse effect”. The earth is warmer than its theoretical S-B temperature by at least thirty degrees Celsius. As you point out, it is assuredly more than that. How much more? “Dooo theee integral”, as the wise man said … but for some purposes, it doesn’t matter how much more. That gives us the minimum amount of the greenhouse effect.
This becomes important given the recent prominence of such hypotheses as Jelbring’s and Nikolov’s. As I understand the claims of their proponents, these are said to explain that thirty degrees of warming above the theoretical S-B temperature. However, they say the thirty degrees C of warming is from some atmospheric gravitational effect which doesn’t depend on GHGs.
Now, I hold the following, based on your statements above. My claim is much more general than the specific hypotheses of Jelbring and Nikolov:
If the atmosphere is transparent (contains no GHGs), there is no way for any atmospheric gravitational effect to raise the average surface temperature of a planet above the theoretical S-B temperature.
The proof is by contradiction. Assume as above a planet heated from the inside by radiation. Give it a perfectly transparent, GHG-free atmosphere.
If any such atmospheric or gravitational or any other effect existed, and the surface temperature were raised above the theoretical S-B temperature by such an effect, the inequality noted above means that the outgoing radiation would have to increase.
But since the atmosphere is perfectly transparent, that means that the surface would be radiating more than it is absorbing. This is a perpetual motion machine, and as such a violation of conservation of energy. Q. E. D.
Professor Brown, many thanks for your contributions. I’d be interested in your comments on my proof that no possible atmospheric-based mechanism can push a planet warmer than its theoretical S-B temperature, and I know you are late for class. If you have time.
All the best,
w.

Septic Matthew
January 12, 2012 11:50 am

Harry Dale Huffman: In the context of public debate, the “greenhouse effect” is not about radiative equilibria with and without an atmosphere, or even with or without “greenhouse gases” in the atmosphere. It is about whether atmospheric temperature at the surface (or at any given pressure level) increases with an increase in atmospheric carbon dioxide. I am astonished that even skeptics cannot focus upon this obvious fact in the real world; everyone can’t seem to stop themselves from launching into radiative transfer theory arguments.
I agree, but addressing the main issue entails addressing a lot of other issues. The effect of additional CO2 can’t be known if the rest of the system is not known well enough.

Scarface
January 12, 2012 11:53 am

@Wenson: It’s worse than you thought. CO2 is only 0,04% of the air!

John West
January 12, 2012 11:55 am

What is the rational behind the statement: “where it is emitted at a cooler temperature”? I’m not convinced that the Stefan-Boltzmann Law applies to GHG’s any more than it does fluorescent or neon lights. It seems to me that a CO2 (or H2O) molecule can emit IR at a rate not proportion to it’s temperature as long as the temperature is above the “freezing” point of it’s vibration modes (degrees of freedom), such that temperature is merely a threshold variable to IR emissions from GHG’s.
Consider the following:
1) The temperature of a gas is a measure of the kinetic energy of translation not vibration. “Fundamentals of Modern Physics”
2) The specific heat of a gas increases proportionally to degrees of freedom availability. More energy is required to increase the temperature of a gas as degrees of freedom other than translation are “unfrozen” suggesting energy stored in non-translational modes do not effect temperature directly.
http://theory.phy.umist.ac.uk/~judith/stat_therm/node81.html
3) Even though equipartition of energy occurs within a mass of gas, the likelihood for a collision capable of imparting a translational motion from a vibration motion is the same as the likelihood for a collision capable of imparting a vibration motion from a translational motion for a given set of circumstances. Whether the atmosphere would be heated or cooled is dependant on the probability of a collision capable of transferring motion to/from translation to/from vibration encountering the opposite condition; or to put another way, the proportion of GHG to IR input. Consider the atmosphere if the Earth did not radiate IR; any collisions resulting in vibration motion could be emitted as IR, reducing the overall translational motion of the atmosphere, thus cooling it. Considering the other extreme where the Earth radiated so much IR that all available vibration modes were always immediately exited by IR input; then equipartion of energy would be “averaging” energy from vibration induced by IR input into translational movement through collisions thus heating the atmosphere. Obviously, the actual atmosphere is somewhere in between these two extremes. Whether GHG’s heat or cool the atmosphere depends on the amount of GHG’s (increases may result in less direct heating), the amount of IR input, and the availability of vibration modes. Only the availability of vibration modes is dependant upon temperature and then only as a threshold.
4) Absorption and emission of specific bands of IR by GHG’s corresponding and limited to vibration modes also suggests that IR absorption and emission by GHG’s are not black body emissions but instead exhibit this characteristic of “cold radiators”.
5) Earth’s atmosphere temperature profile does not correlate with GHG concentration appreciably warming the atmosphere.
http://regentsearth.com/Illustrated%20ESRT/Page%2014%20(Properties%20of%20Atm.)/ESRT10-Properties%20of%20Atmosphere.jpg
6) Anecdotal evidence: IR heaters and lamps do not heat the air in a room directly but heat the IR absorbing surfaces exposed to its output.
I conclude from the above that IR emissions from the atmosphere are not directly proportional to its temperature and therefore cannot be black/grey body emissions or Stefan-Boltzmann Law would be violated. Therefore, a temperature increase is not required for an increase in atmospheric IR emissions (atmospheric radiance is not proportional to temperature). How can an increase in GHG mass in the atmosphere cause an increase in GHE (back radiation) prior to any significant atmospheric temperature increase if a temperature decrease (emitting from higher, colder position) reduces the radiance of the atmosphere? Until I see some evidence to the contrary, I maintain that no temperature increase is required in order to emit an additional amount radiation from GHG’s both down and up.

GregO
January 12, 2012 12:07 pm

Dr Brown,
Thanks for your thought provoking post. I am a big fan of (attempting) to put into words and logical arguments tough modelling problems. An excellent, though non-related text on the topic of CFD is “Computational Fluid Dynamics” by John D. Anderson, Jr and I only mention this text because Anderson illuminates the wall-to-wall Navier-Stokes equations of CFD with actual physical and logical descriptions. For me, this really brought the topic to life. You have done the same here in this post for modelling GHG and I appreciate your work.
Carrick – thanks for the link; I’ve printed out the paper and will study it. As usual, you rock.
Francois says:
January 12, 2012 at 8:30 am
“Are you serious? You know there are a few books which might help you understand how the system works.”
Francois, I’m a mechanical engineer only interested in climate change since Climategate 1.o but since then have read over 800 pages (on last count) of scientific papers and one text book on climate change, and (14) more books on the topic – not necessarily highly technical books. I come away finding that mankind has far more impact on humanity than we on this dead orb circling a massive star while embedded in a complex solar-system. If you can suggest “a few books” that would not be beyond the understanding of a graduate-level mechanical engineer I am sincerely interested in knowing the titles. BTW, of those books I read, the textbook was the most unsatisfying.

Scarface
January 12, 2012 12:11 pm

Dear Mr. Eschenbach,
Please allow me to combine the things you said with a comment of Neo, to ask you a question:
You said:
First, we have a pretty good handle on how much energy hits the earth system after albedo. It’s on the order of 240 W/m2. This has an equivalent blackbody temperature on the order of -18°C.
Second, we have a pretty good handle on how much the earth surface is emitting. It’s on the order of 400 W/m2. This plus the first fact allows us to put a minimum value on the heating which comes from the “greenhouse effect”.
The earth is warmer than its theoretical S-B temperature by at least thirty degrees Celsius.
Neo says:
January 12, 2012 at 10:37 am
The Earth radiates it’s own heat generated at the core.
My question is:
How much of that 30 degrees could earth have produced by itself?
Kind regards,
Scarface

Tim Folkerts(@tjfolkerts)
January 12, 2012 12:17 pm

Lady Life Grows says: “The majority of the heat at the Earth’s surface is due to its radioactive core …”
All estimates I have seen suggest that the geothermal heat flow is less than 1 W/m^2 (compared to 100’s of W/m^2 for the sun). People are welcome to find their own estimates, but I am 99.999% sure they will find that geothermal contributions are very far from being “the majority”.

Kelvin Vaughan
January 12, 2012 12:20 pm

Dont forget the earths magnetic field!

Stephen Wilde
January 12, 2012 12:24 pm

“I maintain that no temperature increase is required in order to emit an additional amount radiation from GHG’s both down and up.”
Would it follow that acceleration of energy flow by radiation upward to space would offset deceleration of energy flow by radiation downward to the surface for a zero net effect ?

Lars P.
January 12, 2012 12:32 pm

Michel de Rougemont says:
January 12, 2012 at 9:34 am
At Earth orbital distance from the Sun the total incoming energy provided by the Sun is 1366 / 4 = 341.5 W m-2 .
(solar constant divided by 4 to take day/night and spherical shape into account).
Without an atmosphere, reflection and absorption of the solar irradiance would only take place at the Earth surface, composed by ice, rocks and sand. With an assumed albedo of 0.4 (reflecting power of a surface) the earth surface would absorb 341.5*(1-0.4) = 204.9 W m-2 and re-emit this energy to the outer space.
According to the Stefan- Boltzmann law, the mean temperature at the earth surface would establish itself at:
T= (E / ε σ)^¼ = (204.9/(1 x 5.6710-8))^ ¼ = 245.2 K (-28°C)
Michel, how does it look like with a water planet with 12 hours of 1366/2 = 683 W m-2 and 12 hours night?
Water emisivity and albedo are known. Ignore any atmosphere, clouds, evaporation but waters heat capacity, keeping also in mind that light is warming into depth.

Stephen Wilde
January 12, 2012 12:37 pm

“But since the atmosphere is perfectly transparent, that means that the surface would be radiating more than it is absorbing. This is a perpetual motion machine, and as such a violation of conservation of energy. Q. E. D.”
No atmosphere is transparent to conduction.
Conduction being a slower process than radiation an increase in the amount of conduction relative to radiation is what causes the equilibrium temperature to rise.
A planet with no atmosphere receives radiation in and sends it back out again virtually instantly.
The more mass in the atmosphere the more conduction takes place, the slower is the rate of energy loss to space and the higher the equilibrium temperature must rise.
Gravitationally induced pressure at the surface increases density of the gas at the surface by reducing volume so as to make conduction occur sooner/faster than if the gas were less dense which increases the greenhouse effect of the atmosphere.
That is the true greenhouse effect and it is nothing to do with radiative characteristics of individual gas molecules.
It is a matter of mass and gravitationally induced pressure reducing outward radiation in favour of an increase in conducted energy accumulating in the atmosphere.

David L.
January 12, 2012 12:42 pm

Temperature swings are cyclical at least daily and yearly (if not decadal, etc.). Daylight temps are higher and night temps are cooler. This daily cycle is superimposed on a yearly cycle where the temperature is coldest in the winter and warmest in the summer. Yet all this cyclic temperature behavior is boiled down to an average. All the information is in the cycle, not in the average.
It’s analogous to an AC voltage: a sine wave or “alternating current” that swings from -170V to 170V. You can measure Peak, (170V), peak to peak (340V) or RMS (120V) voltage. What don’t they measure? The average voltage. What is the average? Zero volts. Which climate scientist would stick their finger in a wall socket when told the average voltage was zero?

Russ in Houston
January 12, 2012 12:44 pm

Why are we worried about the temperature of the sphere. We live in the atmosphere near the surface of the sphere. Also, average global temperatures have no value other than for curiosities sake.

January 12, 2012 12:49 pm

Too complicated. Start like this: Earth is on average warmer than Moon. Earth day (+20°C) is much cooler than Moon day (+130°C), so the Earth night (+10°C) is much, much warmer than Moon night (-230°C). Why?
Some say it is a thick arrow of IR radiation, blazing on the Earth surface from black cold sky. At least Kiehl-Trenberth diagram says so. That every-present beam of downward IR radiation is so powerful, that our night has 10°C instead of -230°C. Must be so, since our day is, cough cough, mightily cooled by abundant “greenhouse gas” in form of clouds, ice/snow and evaporation. So that invisible stream of energy, falling at our heads in a speed of light is at every moment warming the night surface by incredible 240°C!!! Dare you to switch it off for a moment, like hiding under a roof; you would freeze instantly! And what is even more awesome, the whole stream of energy, similar to heat wave produced by nuclear explosion or what, is just a less half of recycled outgoing radiation, since the night surface of 10°C, well, also radiates something upwards. It means, however, that the “something” leaving the night surface from under our feet is more than twice powerful as the night sky downward radiation! Are you roasting already? Feel the heat?
Sorry gents, this radiation nonsense is just nonsense. At night, I am warmed by a bulk atmosphere, nitrogen and oxygen, which is keeping the daily heat.
PS. Is there any consensus what the elephant in the room (nitrogen and oxygen warmed by conduction and convection from the surface warmed by Sun) actually do? If they radiate IR (as all matter with temperature >0K should do), good luck in recognizing the IR coming from one molecule of CO2, compared to 25,000 other molecules (this is the ratio of CO2 above the “safe” 350 ppm level). If they do not radiate IR, they simply keep the daily accumulated heat, working as a thick blanket.
PPS. How is that 17W in Kiehl-Trenberth diagram, assigned to thermals, calculated? Is it a physically reasonable number, compared to 333W of outgoing radiation from the surface?

B.Klein
January 12, 2012 12:49 pm

Dr. Brown has done a good job of restating a very simple statement : The Earth is not a “theoretical Black body ” of course this was also stated by Gerlich and Tscheuschner in the abstraction of their paper (see below) in 2009.
Now lets see if Dr. Brown can come up with a similar analysis to show that the Hypotheses of the “greenhouse gas effect” is a fairy-tale – a hoax. below is a list of references for him to ponder.
List of references:
The paper “Falsification of the Atmospheric CO2 greenhouse effect within the frame of physics” by Gerhard Gerlich and Ralf D. Tscheuschner is an in-depth  examination of the subject.  Version 4 2009
Electronic version of an article published as International Journal of Modern Physics
B, Vol. 23, No. 3 (2009) 275{364 , DOI No: 10.1142/S021797920904984X, c World
Scientific Publishing Company, http://www.worldscinet.com/ijmpb.
Report of Alan Carlin of US-EPA  March, 2009 that shows that CO2 does not cause global warming.

Greenhouse Gas Hypothesis Violates Fundamentals of Physics” by Dipl-Ing Heinz Thieme This work has about 10 or 12 link
that support the truth that the greenhouse gas effect is a hoax.
R.W.Wood
from the  London, Edinborough and Dublin Philosophical Magazine , 1909, vol 17, p319-320. Cambridge UL shelf mark p340.1.c.95, i
The Hidden Flaw in Greenhouse Theory
By  Alan Siddons
from:http://www.americanthinker.com/2010/02/the_hidden_flaw_in_greenhouse.html at March 01, 2010 – 09:10:34 AM CST
The below information was a foot note in the IPCC 4 edition. It is obvious that there was no evidence to prove that the ghg effect exists.

“In the 1860s, physicist John Tyndall recognized the Earth’s natural greenhouse effect and suggested that slight changes in the atmospheric composition could bring about climatic variations. In 1896, a seminal paper by Swedish scientist Svante Arrhenius first speculated that changes in the levels of carbon dioxide in the atmosphere could substantially alter the surface temperature through the greenhouse effect.”

After 1909 when R.W.Wood proved that the understanding of the greenhouse effect was in error and the ghg effect does not exist. After Niels Bohr published his work and receive a Nobel Prize in Physics in 1922. The fantasy of the greenhouse gas effect should have died in 1909 and 1922. Since then it has been shown by several physicists that the concept is a Violation of the Second Law of Thermodynamics.

Obviously the politicians don’t give a dam that they are lying. It fits in with what they do every hour of every day .Especially the current pretend president.
Paraphrasing Albert Einstein after the Publishing of “The Theory of Relativity” –one fact out does 1 million “scientist, 10 billion politicians and 20 billion environmental whachos-that don’t know what” The Second Law of thermodynamics” is.
ILEUniversity of Pennsylvania Law School
INSTITUTE FOR LAW AND ECONOMICS
A Joint Research Center of the Law School, the Wharton School,
and the Department of Economics in the School of Arts and Sciences
at the University of Pennsylvania
RESEARCH PAPER NO. 10-08
Global Warming Advocacy Science: a Cross Examination
Jason Scott Johnston
UNIVERSITY OF PENNSYLVANIA
May 2010
Social Science Research Network Electronic Paper Collection:
http://ssrn.
Israeli Astrophysicist Nir Shaviv: ‘There is no direct evidence showing that CO2 caused 20th century warming, or as a matter of fact, any warming’ link to this paper on climate depot.
[1] [2] Slaying the Sky Dragon – Death of the Greenhouse Gas Theory [Kindle Edition]
Tim Ball (Author), Claes Johnson (Author), Martin Hertzberg (Author), Joseph A. Olson (Author), Alan Siddons (Author), Charles Anderson (Author), Hans Schreuder (Author), John O’Sullivan (Author)

Israeli Astrophysicist Nir Shaviv: ‘There is no direct evidence showing that CO2 caused 20th century warming, or as a matter of fact, any warming’ link to this paper on climate depot
Web- site references:
http://www.americanthinker.com                                            Ponder the Maunder
wwwclimatedepot.com
icecap.us
http://www.stratus-sphere.com
SPPI
The Great Climate Clash -archives December, 2010 , G3 The greenhouse gas effect does not exist.(  peer reviewed and revised  but not yet released).
Wood is correct: There is no Greenhouse Effect
Posted on July 19, 2011 by Dr. Ed
Repeatability of Professor Robert W. Wood’s 1909 experiment on the Theory of the Greenhouse (Summary by Ed Berry. Full report here or here. & PolyMontana.)
by Nasif S. Nahle, June 12, 2011
University Professor, Scientific Research Director at Biology Cabinet® San Nicolas de los Garza, N. L., Mexico.
many others are available.
The bottom line is that the facts show that the greenhouse gas effect is a fairy-tale and that Man-made global warming is the World larges Scam!!!The IPCC and Al Gore should be charged under the US Anti-racketeering act and when convicted – they should spend the rest of their lives in jail for the Crimes they have committed against Humanity.
The only thing more dangerous than ignorance is arrogance.”
—Albert Einstein
“Democracy is two wolves and a lamb deciding what to have for dinner. Liberty is a well-armed lamb.”   Benjamin Franklin
[1]HTML:
[2]HTML:

January 12, 2012 12:51 pm

Worst of all, the Earth has no lid!

January 12, 2012 12:51 pm

So, for example, for Earth we know that the average intensity absorbed is ~240 W/m^2 and the average emission is ~390 W/m^2 or so….
If this is true.
? How many Earths are needed to increase the sun’s surface temperature in 100K???

wayne
January 12, 2012 12:56 pm

John West says:
January 12, 2012 at 11:55 am
How can an increase in GHG mass in the atmosphere cause an increase in GHE (back radiation) prior to any significant atmospheric temperature increase if a temperature decrease (emitting from higher, colder position) reduces the radiance of the atmosphere? Until I see some evidence to the contrary, I maintain that no temperature increase is required in order to emit an additional amount radiation from GHG’s both down and up.
– – – –
John, think you hit it on the nose. One additional viewpoint I might add, the way I see it, is that in all aspects but one radiation in an atmosphere is but a fast conductor. The exception is radiation can leave the atmosphere into space of course. But within the thick of the gases, radiation performs everything conduction performs but on a larger, faster scale and depending on the concentration of other molecules (usually the same but not always) with the exact frequencies to absorb the radiation.
Radiation therefore allows an atmosphere to equalize faster that without it. I see like you seem to see that there is no magic concerning radiation at the surface-atmosphere interface. Radiation just bounces from molecule to molecule over many meters instead of directly from molecule to molecule as seen in conduction.
Mix that in with the thermalization, re-excitation and the equipartition points you made and you might see it the way I do. Phil seems to see radiation in a different manner, totally separate that the other means of transfer… like it had a magical aspect compared to conduction, I see none (but being able to leave that is).
I have a hard time to get others to view it that way, but that view is much simpler to visualize while remains proper in physics.

gbaikie
January 12, 2012 1:02 pm

Earth’s baseline black-body model – “a damn hard problem”
And Willis quote from pg 3:
“But in practice, the fact that you can buy a handheld remote thermometer, which uses the strength of IR radiation plus the S-B equation to measure the temperature of common objects around us means that S-B almost holds almost everywhere. Most things radiate at a level which is quite close to their theoretical S-B radiation of epsilon sigma T^4.”
And post I didn’t post. Which could summed up as the temperature you take isn’t the energy radiated. It involved warm concrete and evaporation rate. But anyhow, that’s on my mind.
So there no doubt about S-B equation measuring temperature. No doubt about energy must balance- incoming energy “absorbed” must roughly equal out going radiation. If they don’t balance it means the planet is warming or cooling.
What we do know without doubt is the earth balance does not change in a day or week- the whole planet does not get warmer or cooler is short period time- it’s at most like .001 K for very fast warming or cooling globally if occurs in a less than week’s time
But as obviously know the each day it warms and cools- it’s always warming or cooling- it’s the sum total which isn’t changing- it’s warming in one part of planet and cooling at same time in another.
In post I didn’t post I was attempting to argue that a warmed piece sidewalk which was 20 C warmer than same sidewalk in the shade, was radiating significant amount energy and the shaded wasn’t radiating any or small amount. the proof was that if shaded the warm sidewalk and put few grams of water on it, it evaporate the water much quicker than sidewalk always in shade.
In other words I could measure how heat the warmed sidewalk emitted. Or something at temperature of 400 watts per meter [shaded] will evaporate less than warmed sidewalk which was emitting 500 watts. Or in other words I going to propose a test if the 400 watt surface could do work as compared something something emitting 100 watts more. 2 square meters at 400 watts “should” do more work than 1 sq meter at 500 watts? But it’s flawed because doesn’t make anything clearer. Hence the non post.
Or surface is covered little pyramids thereby at least doubling the surface area, come anywhere close to radiating twice the energy? it will radiate more, that pretty I am certain, but a lot more?
Just to be clear, if surface is in sunlight, and it’s reached about hot as it going to get, it will radiate the same amount energy it is receiving from the sun. So sidewalk in sunlight will radiate the solar energy- it will radiate 1000 watts minus maybe 10 watts it is absorbing [heat conducted thru concrete and very amount to ground below it]. So incoming sunlight 1000 watts, and sidewalk in sun radiating around 1000 watts. When you shade the sun and sidewalk is reflecting less sunlight, but continues to radiate around 900 watts of energy.- and this recently shaded sidewalk can lots of work. It has power, it has watts of energy- maybe roughly 100,000 watts seconds of work it can do.
The always shaded sidewalk won’t do work. Put both in space in which they can radiate to 2 K, and both can do work.
Or pour liquid nitrogen on either and they both can do work. But my point is the shaded sidewalk with same temperature as the air, doesn’t do work. So it can be said to be at 400 watts. But 400 watts per second of energy it is not emiting- it is possible to emit it, but it’s not doing it.
So of course this point, we get: “Of course, this is the greenhouse effect, you idiot!!!
Measure the sky it’s 400 watts and is warming the sidewalk or preventing it from radiating it’s energy!!!”
But this isn’t really true. “It” might doing a little bit.
You have similar thing if in space. Yes it cools, how much power does it cool at? It’s a question of the conduction rate of the material.
If the magical perfect bodybody, it’s not question- it radiates 400 watts of energy per second. But this concrete we talking about it, not magical material. The magical material isn’t just colored black, it conducts heat perfectly- which isn’t vaguely a descriptive of concrete. Copper or diamond get somewhat close to a blackbody- as far as conductivity.
Now, I can do better than a black body as far as losing heat/doing work. Liquid Nitrogen, will cool that sucker fairly fast, not immediately, but explosively. Simple water will also cool it fairly fast- and water in vacuum of space is probably better than liquid nitrogen.
One way of saying this is the sun in terms of radiating heat is pretty good, but what it heat up isn’t as good at radiating heat. And the closer you are the the sun the better it is at radiating- it heats things faster.
So Greenhouse gases and/or conduction of air might be slowing an shaded concrete to from cooling, but even in space it doesn’t radiate at 400 watts- it’s that temperature, but temperature can’t measure the work it does, different things at same temperature can do more work per square meter- and the fictional black body does the most work.

More Soylent Green!
January 12, 2012 1:03 pm

kwik says:
January 12, 2012 at 8:35 am
You need to write a CSharp program and combine it with a ball made in WPF. WPF (Windows presentation Foundation) is perfect for this. We use it in my business every day.
If we could get some money from some rich guy, and I could take a 2 years leave from my day job, I would love to join you.
We could patch up the globe with small triangles with texture. The globe can be made in any 3-D package and exported to xaml. You can then import it into a WPF project and then write a CSharp program that starts turning the globe….and start calculating stuff…..ahh…a fantastic project…. Click “play” and it comes alive….
But for crying out loud; Dont make a “Report for Policy-Makers” when we are finished!!!!!

Let’s make a report to the policy-makers before we finish!

Brian H
January 12, 2012 1:09 pm

clivehbest says:
January 12, 2012 at 10:53 am

Does such a place exist ? I wonder if there is perhaps just one long term weather station somewhere in the Sahara for example ?

There was, but Lawrence’s Bedou reassembled it into a couple of muskets. And one ceremonial daggar.

Brian H
January 12, 2012 1:10 pm

[Yes, I know, wrong desert. But somebody did it!!]
😉

mkelly
January 12, 2012 1:18 pm

George E. Smith; says:
January 12, 2012 at 11:11 am
“…that instructs that radiation that it may not land on the surface, because that surface happens to be at a higher Temperature than was the emitting gas molecule; …”
Mr. Smith, it is agreed that the EM can land on a warmer surface the question is does it get absorbed, as some say, there by increasing the W/m^2.
Sir, if I have 2 torches at 1000 C and point one at a spot what is the max temperature that spot can get? If I then point the other torch at the same spot at the same time what is the max temperature the spot can get? When I remove one of the torches what is the max temperature the spot can get?
I was taught, years ago admittedly, that a higher energy state object does not absorb lower energy. Maybe poorly said but I think you understand.

Thermodynamic professor, power plant manager
January 12, 2012 1:19 pm

George E. Smith; says:
January 12, 2012 at 11:11 am
So Thermodynamic Professor, whether or not one believes that the ordinary atmospheric mono or homo-diatomic gases: Argon, Nitrogen, Oxygen (maybe …..
Sorry but we have never managed to warm up anything with colder objects or gases, the nonsense you are talking about. This is based purely for Thermodynamic laws. It would of course be very nice if such unphysical [snip] happens, our power plant production costs would be much lower;)

January 12, 2012 1:25 pm

The Earth’s core is molten and heat rises to the surface unevenly. We have fewer data points on this heat transfer than on the solar flux. Mid ocean ridges are literally boiling with heat (trapped because the pressure can raise the temperature of the water WELL above 100°C (boiling at sea level).
No one has disproved that El Nina/El Nino are not actually due to fluctuations in heat from the dense number of ridges in that area of the Pacific. Speaking of Coriolis effects, why aren’t rotation directions of the PDO and ANO etc driven by super hot water coming from the depths instead of solar heating at the surface????

Stephen Wilde
January 12, 2012 1:26 pm

“The emission spectrum of the Earth from space is grey body with numerous missing bands which can be unambiguously assigned to the GHGs (CO2, H2O, O3, CH4 & N2O), the spectrum of the Earth absent those GHGs would be grey body but would have to have the same area under the curve which requires a lower temperature. Therefore there is a GHE due to the presence of those gases.”
That could also happen if the initial warming was from surface to atmosphere via conduction could it not ?
Thus there is a GHE effect but not necessarily caused by those gases.The energy that would have been in the missing wavelengths could just be offset by an increase in other outgoing wavelengths.No one is denying that GHGs radiate 50% upwards are they ?
Suppose that the radiative effect of GHGs were net zero because they send as much energy out of the system as they retain within the system. (non GHGs retain 100% within the system).
What does it matter if GHGs utilise different spectral bands to those used by the surface ?
They could be acquiring all of their energy from the other non GHG molecules which can be heated by conduction from the surface and would pass it on to the GHGs via conduction. Once the GHGs reach the ambient temperature for other molecules at the same height (via conduction) they cannot get any warmer from longwave coming up from the surface so they would have no more ‘blocking’ ability than the non GHGs already have (100%). Meanwhile they are busily radiating upward.
They may pass 50% of their energy back down again but by radiation rather than by conduction and unlike non GHGs that 50% passed down would be matched by 50% sent out of the system altogether which is something that non GHGs cannot achieve.
I think it is conduction intervening between radiation coming into the system and radiation going out of the system that creates the greeenhouse effect and not radiative physics.

Jean Parisot(@jeanparisot)
January 12, 2012 1:35 pm

How does the ovoid shape of the surface effect the energy model, the seasonal tilt angles do not have the same surface areas presented to the sun.

Robert Clemenzi
January 12, 2012 1:36 pm

John West says:
January 12, 2012 at 11:55 am

Whether GHG’s heat or cool the atmosphere depends on the amount of GHG’s (increases may result in less direct heating), the amount of IR input, and the availability of vibration modes.

That ignores the energy added by conduction. Because the amount of energy emitted is always greater than the amount absorbed, increasing greenhouse gases will always reduce the temperature of the atmosphere. (Does not apply above the troposphere.)

Robert Clemenzi
January 12, 2012 1:39 pm

Tim Folkerts says:
January 12, 2012 at 10:49 am

5] GHGs high up in the atmosphere where it is colder would raise the surface temperature.
These are all “settled” in terms of the general affect on global temperatures.

I fully agree with points 1 thru 4, but 5 is a problem. First, what do you mean by “high”?
Below the tropopause? Above it? Also which GHG are you suggesting?
In general, it is my understanding that GHGs cool the atmosphere, with the obvious exception of the stratosphere. It is also my understanding that GHGs below about 2 km warm the surface, and that those higher up have no effect on the surface temperature.

January 12, 2012 1:39 pm

Robert Brown (and others)
Thank you. It’s great to see fundamentals coming up for rethink with clarity. Two points
(1) Two others have referred to Miskolczi here, suggesting you might be interested to check him out. I second that. I still don’t understand his theory, but I do recognize that it has an extraordinarily close fit with actual measurements both from Earth and from Mars. This makes me think he is really onto something significant, if only he could be explained to duffers.
(2) What is the significance of the “W” shape temperature profile of our atmosphere? Is this prime evidence of the GHG effect of ozone formed at these heights? and by extension, proof of the GHG effect of CO2 which tends to lie low?

timg56
January 12, 2012 1:53 pm

Robert Brown shows why he is one of the commentors I most admire here.
(So much so I’m willing to ignore he’s a Dukie.)

January 12, 2012 2:01 pm

Hölder’s Inequality requires that the average temperature on a non-isothermal sphere at radiative equilibrium, assuming the same emissivity and incident power level, must be less than the average temperature of an isothermal sphere. That’s something that G&T do correctly ( http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v4.pdf Section 3.7.4 ).
As always, an awesome post (although I know of the inequality and derived a special form of it last week, I am infected with G&T’s skepticism about ALL of the physics now and want to see it all for myself). I’m about halfway through G&T, getting a bit bogged down in the rhetoric but looking forward to chapter 5 and the promised (hopefully correct) physics. I’ve already concluded that while top-of-atmosphere measurements do mean something with respect to the absorption properties of CO_2 (and probably with the warming) that a) it ain’t like “a greenhouse” except in the most metaphorical of senses; and b) the physics is way more difficult than even Caballero suggests. How it all works out — I’m open minded.
rgb

January 12, 2012 2:03 pm

Thank you. It’s great to see fundamentals coming up for rethink with clarity. Two points
Neither of which I’m prepared to answer. My reading list is (still) full to the brim, and I have no good idea of why there is a stratosphere and a troposphere and an exosphere and all that. I’ve read a few things that purport to explain parts of it, but none of them have completely convinced me, in part because I suspect one needs a “wholistic” explanation, not an explanation by parts.
rgb

January 12, 2012 2:06 pm

It is also my understanding that GHGs below about 2 km warm the surface, and that those higher up have no effect on the surface temperature.
Although there may be some surprising (?) evidence that water vapor content in the stratosphere may play some role. But separating cause and effect is difficult here. Relatively warm water vapor, very high up — what’s not to like?
rgb

Robert Clemenzi
January 12, 2012 2:10 pm

Lucy Skywalker says:
January 12, 2012 at 1:39 pm

(2) What is the significance of the “W” shape temperature profile of our atmosphere?

That is caused by greenhouse gases. The tropopause is cold because the water vapor emission bands are transparent above that point. The primary greenhouse gas in the stratosphere is CO2 (380 ppm). Water vapor is 5 ppm and ozone is less than 1 ppm. CO2 in the stratosphere emits radiation toward the surface. At the tropopause, that radiation is absorbed by other CO2 molecules, those heat the local atmosphere, which then heats the water molecules, which finally emit the heat to space.
None of the stratosphere heat makes it below the tropopause because the air pressure makes the spectra bands more opaque as the pressure increases.
I have written a full description of this here.

January 12, 2012 2:11 pm

How does the ovoid shape of the surface effect the energy model, the seasonal tilt angles do not have the same surface areas presented to the sun.
An excellent question. The answer is that as far as energy influx is concerned for the simple models, one has to consider the flux of the poynting vector (an integral over the surfaces) associated with the vector-directed intensity distributions. This really can’t be done by pretending that everything is one-dimensional as is commonly done (as G&T, linked above, point out). This makes the math considerably more difficult, but not intractable numerically if you know the shape and rotation and tilt and all that. Just a major pain of direction cosines, I guess.
Things get even nastier, as one might imagine, once you add a relatively thick atmosphere and a nice thick asymmetrically distributed ocean and mountains and plains and forests and rocks and swamps and ice and clouds and circulation. I’m waiting to see if G&T have any suggestions for a decent decomposition of the problem, but I’m prepared for the answer to be “no”.
rgb

January 12, 2012 2:29 pm

Joel Shore says:
January 12, 2012 at 9:14 am
…So, for example, for Earth we know that the average intensity absorbed is ~240 W/m^2 and the average emission is ~390 W/m^2 or so… [as] in fact the emissivity of the Earth is very close to 1 over the relevant wavelengths.
In fact, we do not know this, because we have not tested under conditions reflecting the true environment.
B.Klein says:
January 12, 2012 at 12:49 pm
“After 1909 when R.W.Wood proved that the understanding of the greenhouse effect was in error and the ghg effect does not exist.”
He found that it did not exist in a laboratory setting. But, in a dynamic atmosphere which results in Doppler broadening of the spectral absorption bands, any GHG effect is likely more pronounced.
Both of these evidences, both pro- and con-, rely on laboratory experiments which do not represent the actual physical environment.

Myrrh
January 12, 2012 2:33 pm

Robert Brown says:
January 12, 2012 at 9:00 am
I think it would be very educational to do this and would take the guesswork out of the question “what does water do” or “what does an atmosphere do” to the sphere (relative to superconducting or insulating static sphere).
Why not start from where water has been included?
Earth temperature 15°C
Earth without any atmosphere: -18°C
Earth with atmosphere but without water, therefore no water cycle: 67°C
Therefore, the plus 33°C ‘warming’ from -18°C to 15°C comes via a 52°C cooling through the Water Cycle.
And there’s also that forty years ago NASA had to junk Stefan-Boltzmann to get real moon temps estimated for the landings, somewhere on-line, as they needed three dimensions not the flat earth of SB and they had to include that thermal energy absorbed from the Sun penetrated and was released later.

Anders L.
January 12, 2012 2:33 pm

“I can’t figure this out. Considering how smart I am, it must mean that noone else can, either.”

Septic Matthew
January 12, 2012 2:38 pm

Willis Eschenbach: First, we have a pretty good handle on how much energy hits the earth system after albedo. It’s on the order of 240 W/m2.
Second, we have a pretty good handle on how much the earth surface is emitting. It’s on the order of 400 W/m2.

I have a feeling that you have left out something important, or I have forgotten something important — I note you wrote “earth system” in the first sentence and “earth surface” in the second. If this were true as written, we would have a pretty good handle on the earth losing 160 W/m^2. What do you mean by “on the order of”? that the error can’t be more than 1%? 10%? 100%? Since electronic communication can sound snarky when not intended so, let me apologize in advance if this sounds snarky.

J. Bob
January 12, 2012 2:39 pm

Francois says:
January 12, 2012 at 8:30 am
“Are you serious? You know there are a few books which might help you understand how the system works”.
I guess, I would have to say are you serious? Have you ever had to model a multidimensional fluid model ( i.e. including Naiver-Stokes )? Not to mention the multiple layers of radiation and convective heat transfer in the atmosphere and ocean.
Even simple models, can take hours on a Cray. We had to run these on the night shift, to keep costs down.

January 12, 2012 2:40 pm

The majority of the heat at the Earth’s surface is due to its radioactive core, especially U-238. Since the half-life of uranium is about 4.5 billion years, that is a factor in changes since the Hadean, or even Cambrian ages, but is effectively a constant for the duration of human existence on the planet.
The majority of the heat flux out is due to U-238? Doing what? As you say, the half-life is 4.5 billion years, meaning that it is really not terribly radioactive. It’s decay channels are also not terribly energetic — this isn’t fission, it is alpha decay, IIRC.
Also, does this make sense? Why is it cold at the poles and hot at the equator, if this is true? Why does it get hot in the day and cold at night? I’m open to there being more geothermal heat (not terribly uniformly distributed) than is currently estimated because there is a lot of unexplored territory out there in the world even today (on the ocean floor, for example). But places where there is an unmistakable surplus of geothermal energy — Iceland, Yellowstone, near active volcanoes — don’t even warm the ground in general enough to prevent winter locally anywhere but right on top of a hot spot.
I think this fails the common sense test, as well as contradicting a whole lot of measurements by hapless geologists who have no dog in the AGW fight, sorry. Although I’d be happy to be convinced otherwise if you can provide me with a quantitative basis for your estimate. Sure, the Earth’s core is very hot, because it is wrapped in a big blanket of insulation — the crust and mantle. What heat is generated in there, stays in there a long, long time, but we live on the outside of the blanket and are heated and chilled with the vagaries of, well, the weather!
rgb

Truthseeker
January 12, 2012 2:47 pm

thepompousgit says:
January 12, 2012 at 10:50 am
Since you cannot seem to even comment in complete sentences, I do not think that you calling Harry Huffman’s comment incoherent has any validity whatsoever.

January 12, 2012 2:49 pm

Any wealthy folks listening? Here’s my proposal. Fund someone like Prof Lindzen to design a research programme including physics and statistics and computing to review fundamental issues relevant to the current controversies around climate variation and its causes. Work such as that outlined by Prof Brown is exactly the kind of thing I have in mind. The aim? To bring more 1st class science and analysis into a field taken over by superficial analyses, tawdry manipulations (just look at the dross in CG1 and CG2 for example), and pandering to destructive political activists.

January 12, 2012 3:02 pm

Ian W says: several things I don’t repeat…
but reply to as “Damn skippy, you are so very right….”
However, Enthalpy, the Earth’s climate viewed as a self-organizing heat engine, and chaotic fluid dynamics of open systems are for later. First I need to take baby steps… even if they follow in the footsteps of others or if future things will confound them.
rgb

Mike McMillan
January 12, 2012 3:03 pm

And after all that figgerin., you just have weather, not climate.

Joe Postma
January 12, 2012 3:03 pm

Robert Brown:
You might be interested in reading my critiques of standard theory here:
http://principia-scientific.org/publications/Copernicus_Meets_the_Greenhouse_Effect.pdf
here:
http://principia-scientific.org/publications/The_Model_Atmosphere.pdf
and here:
As to your post and the questions/analysis you present, I have developed the code and theory for modeling the Earth in real time just as you have described – modelling, that is, the differential equation of heat input and output as a function of time, latitude, eccentricity, local albedo, local extinction, etc. This is the question and task I left posed at the end of my 2nd paper, linked above. My background is astrophysics so I already had on hand the theory of how to do much of this…as it is described in the Astronomical Almanac, but for a different context of course.
It can be simplified for demonstrative purposes to an analytically solvable equation; otherwise, a numerical approach would not be difficult to perform, as all the equations are intrinsically smooth, aside from any perturbations one might eventually want to introduce, for example, a cloud passing over-head.
Such a model gives MUCH greater insight into the real physics of the Earth-Sun interaction. Treating the Earth as flat, being shone with a cold Sun at -18C, just can not be a philosophically valid model or paradigm. For example, if Sunshine is -18C, then why does water exist? Due to the GHE? Of course not. Direct, real-time, non-averaged into night-time sunlight, is more than energetic enough to melt ice into water, and thus dive a climate system. The instantaneous solar input to the Earth actually has a heating potential of anywhere between +30C to +121C. And this DOES lead to an average output from the Earth corresponding to -18C, or 240 W/m2, in accordance with the expected conservation of total energy.
Anyway, if you would like to work on this together, let me know and I will look up your email on your university’s website and contact you. Or you may find and contact me, at the University of Calgary.
Regards
Joe Postma
MSc Astrophysics

January 12, 2012 3:15 pm

As the ‘standard model’, used by warmistas, gives a -18 deg C temperature due to solar irradiation, how on earth did earth ever manage to unfreeze? so-called GHGs would be at very low levels in the atmosphere – being either ice or trapped/dissolved in the ice. Also they mistake conservation of energy – which is real – as conservation of power which is meaningless.

Joe Postma
January 12, 2012 3:19 pm

“Myrrh says:
January 12, 2012 at 2:33 pm
And there’s also that forty years ago NASA had to junk Stefan-Boltzmann to get real moon temps estimated for the landings, somewhere on-line, as they needed three dimensions not the flat earth of SB and they had to include that thermal energy absorbed from the Sun penetrated and was released later.”
That’s quite interesting. In the model I have been developing, it seems apparent that such a term needs to be introduced in order to capture all of the physics…you can’t ignore the massive thermal mass and extremely long time-constant of “dirt”. You also therefore question the idea that the ground surface has zero contribution from geothermal energy – if this were true, the ground would go down to zero kelvin at some point. But in fact it never actually gets all that cold beneath the ground surface, in fact it is MUCH higher than 0 Kelvin! You have to include that…and it WILL raise the temperature. The same effect from the atmosphere is known to be much less significant, having a much, MUCH shorter time-constant, and much less thermal energy stored within in.
Hopefully this is something that Robert and I could work on together…

Dave Wendt
January 12, 2012 3:39 pm

“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”
The problem I have always had with all these efforts to reduce the Earth to a simplistic radiative energy model is that there are very significant energetics continually ongoing on the planet that are not captured in the calculation. Every time a molecule moves from coordinate abc to coordinate xyz there is energy involved. Most of everything in the atmosphere, the oceans, lakes rivers, even the solid earth is in constant motion. Admittedly some, maybe most, of that motion is driven by gravity and the rotation of the planet, but some of it is driven by the conversion of the radiative input of insolation from the Sun into kinetic energy. Is anyone willing to suggest we know enough about what that number is to conclude that it is insignificant, particularly given the almost infinitesimal marginal changes we are trying to estimate in the climate?
Then there is the real difference that differentiates the Earth, from simple S/B models or from any other planetary body or satellite we are aware of. The Earth is covered not only by a large atmosphere and massive oceans, it is covered by LIFE. Almost everything that lives, grows, reproduces, and moves by swimming, slithering, crawling, hopping, walking, flying or any other mode of motivation, ultimately draws the energy to do so from the energy falling on the planet from the Sun and most of it is accomplished without any accompanying radiative signature. Again I would ask is anyone willing to suggest that we can create even a ballpark estimate of the energy use of life on this planet? Given all we don’t know about that life, I would suggest that even our best efforts couldn’t come within 1000 Superdomes of an accurate estimate.

Ian W
January 12, 2012 3:52 pm

John West says:
January 12, 2012 at 11:55 am
What is the rational behind the statement: “where it is emitted at a cooler temperature”? I’m not convinced that the Stefan-Boltzmann Law applies to GHG’s any more than it does fluorescent or neon lights. It seems to me that a CO2 (or H2O) molecule can emit IR at a rate not proportion to it’s temperature as long as the temperature is above the “freezing” point of it’s vibration modes (degrees of freedom), such that temperature is merely a threshold variable to IR emissions from GHG’s.
Consider the following:
1) The temperature of a gas is a measure of the kinetic energy of translation not vibration. “Fundamentals of Modern Physics”
2) The specific heat of a gas increases proportionally to degrees of freedom availability. More energy is required to increase the temperature of a gas as degrees of freedom other than translation are “unfrozen” suggesting energy stored in non-translational modes do not effect temperature directly.
http://theory.phy.umist.ac.uk/~judith/stat_therm/node81.html
3) Even though equipartition of energy occurs within a mass of gas, the likelihood for a collision capable of imparting a translational motion from a vibration motion is the same as the likelihood for a collision capable of imparting a vibration motion from a translational motion for a given set of circumstances. Whether the atmosphere would be heated or cooled is dependant on the probability of a collision capable of transferring motion to/from translation to/from vibration encountering the opposite condition; or to put another way, the proportion of GHG to IR input. Consider the atmosphere if the Earth did not radiate IR; any collisions resulting in vibration motion could be emitted as IR, reducing the overall translational motion of the atmosphere, thus cooling it. Considering the other extreme where the Earth radiated so much IR that all available vibration modes were always immediately exited by IR input; then equipartion of energy would be “averaging” energy from vibration induced by IR input into translational movement through collisions thus heating the atmosphere. Obviously, the actual atmosphere is somewhere in between these two extremes. Whether GHG’s heat or cool the atmosphere depends on the amount of GHG’s (increases may result in less direct heating), the amount of IR input, and the availability of vibration modes. Only the availability of vibration modes is dependant upon temperature and then only as a threshold.
4) Absorption and emission of specific bands of IR by GHG’s corresponding and limited to vibration modes also suggests that IR absorption and emission by GHG’s are not black body emissions but instead exhibit this characteristic of “cold radiators”.
5) Earth’s atmosphere temperature profile does not correlate with GHG concentration appreciably warming the atmosphere.
http://regentsearth.com/Illustrated%20ESRT/Page%2014%20(Properties%20of%20Atm.)/ESRT10-Properties%20of%20Atmosphere.jpg
6) Anecdotal evidence: IR heaters and lamps do not heat the air in a room directly but heat the IR absorbing surfaces exposed to its output.
I conclude from the above that IR emissions from the atmosphere are not directly proportional to its temperature and therefore cannot be black/grey body emissions or Stefan-Boltzmann Law would be violated. Therefore, a temperature increase is not required for an increase in atmospheric IR emissions (atmospheric radiance is not proportional to temperature). How can an increase in GHG mass in the atmosphere cause an increase in GHE (back radiation) prior to any significant atmospheric temperature increase if a temperature decrease (emitting from higher, colder position) reduces the radiance of the atmosphere? Until I see some evidence to the contrary, I maintain that no temperature increase is required in order to emit an additional amount radiation from GHG’s both down and up.

Reference your points. We actually have geostationary satellites watching the IR output from the Earth and available to anyone to look at.
See:
GOES East Water vapor imagery – this shows where there are front’s and other upwelling moist convection
http://www.ssd.noaa.gov/goes/east/natl/flash-wv.html
GOES East Rainbow IR imagery – this shows where there is IR being emitted to space and seen by the satellite.
http://www.ssd.noaa.gov/goes/east/natl/flash-rb.html
Note how the dry areas in the water vapor map do not show emission of IR in the IR imagery.
Note how the upwelling moist air is emitting IR at high ‘cool’ levels – this is presumably heat being emitted as water changes state condensing then freezing. This energy output is NOT shown by Stefan Boltzmann maths nor is it linked to ‘temperature’.
NASA/NOAA state that this convective transport to the tropopause is far greater than radiation from the surface. Looking at the surface and trying to use SB would appear to be incorrect it is looking inside the hohlraum.

u.k.(us)
January 12, 2012 3:52 pm

@ Robert G. Brown, Duke University
==============
Good stuff, keep it coming.
You’ve got a great writing style, and I look forward to any future contributions.
I can almost understand some of it 🙂

Willis Eschenbach(@weschenbach)
Editor
January 12, 2012 4:32 pm

Septic Matthew says:
January 12, 2012 at 2:38 pm
Willis Eschenbach:

First, we have a pretty good handle on how much energy hits the earth system after albedo. It’s on the order of 240 W/m2.
Second, we have a pretty good handle on how much the earth surface is emitting. It’s on the order of 400 W/m2.

I have a feeling that you have left out something important, or I have forgotten something important — I note you wrote “earth system” in the first sentence and “earth surface” in the second. If this were true as written, we would have a pretty good handle on the earth losing 160 W/m^2.

Thanks, Matthew. Not sure what the point is here. The earth doesn’t lose 160 w/m2 because of absorption in the atmosphere.

What do you mean by “on the order of”? that the error can’t be more than 1%? 10%? 100%? Since electronic communication can sound snarky when not intended so, let me apologize in advance if this sounds snarky.

What that means is that I’m tired of giving the best estimate and having someone bust me saying something like “it’s not 240 W/m2, you idiot, it’s 239, how could you make such an egregious error, or are you just lying on principle?” or the like..
Errors in both of those figures are likely within 10% of the true value, but as far as I know, we have no hard data on the error figures. I am merely trying to give a rough idea of the size of the hill that alternative theories have to climb. The exact numbers are not important for my discussion.
w.

George E. Smith;
January 12, 2012 4:50 pm

“”””” Thermodynamic professor, power plant manager says:
January 12, 2012 at 1:19 pm
George E. Smith; says:
January 12, 2012 at 11:11 am
So Thermodynamic Professor, whether or not one believes that the ordinary atmospheric mono or homo-diatomic gases: Argon, Nitrogen, Oxygen (maybe …..
Sorry but we have never managed to warm up anything with colder objects or gases, the nonsense you are talking about. This is based purely for Thermodynamic laws. It would of course be very nice if such unphysical [snip] happens, our power plant production costs would be much lower;) “””””
Well Prof Thermo, absolutely nowhere in my post did I state either specifically, or by inference, that “we managed to warm up anything with colder objects or gases.” If that is nonsense, you are the one who said it, not me.
I simply enquired how a surface can possibly tell the Temperature of an object or gas that is emitting Electromagnetic Radiation, since such radiation carries NO Temperature information whatsoever. Nor can the source determine the Temperature of some remote surface, to decide whether it is legal for it (the object or gas) to emit EM radiation or not. Since the emission of EM thermal radiation from a body or gas is of necessity isotropic, that would imply that such a body or gas can either emit EM radiation towards ANY other surface or object in any direction, at any surface Temperature at all, or else it must omit nothing, if by your assertion, a warmer surface in some direction prohibits the emission of such radiation. Or alternatively, if such a warmer surface does not prohibit isotropic emission from some remote colder source ( could be light years distant), what is the mechanism by which it prevents such radiation from landing; and if it doesn’t land; where does it go.
Is it possible to examine the spectrum of EM radiation emitting or reflecting from some surface; say the earth, and sort out which is emission and which is “reflected” rogue radiation that tried to land from some rejected colder source (which also might be light years away. ??
So why don’t you let us all in on what academic institution you Profess Thermodynamics instruction at; so we can all enroll in your classes.

beng
January 12, 2012 5:31 pm

The 33K “difference” obviously isn’t right. If you take away the GHG water vapor, they’ll be no more clouds (or snow/ice). Also no more latent heat available to cool the ocean surface & increase convection. Water (as liquid/solid or vapor) serves a dual purpose — both warming & cooling.
I’m not sure what it is, but it isn’t just the simple difference between the surface temp & the temp at the average radiating “surface” in the troposphere/tropopause — 288K-255K.

Bill H
January 12, 2012 5:37 pm

Mike M says:
January 12, 2012 at 8:30 am
But but.. the ‘settled science’ is so settled that we’re already spending over 2.5 billion per year to ‘combat climate change’. Ain’t no physics in the universe gonna slow down a gravy train with that much inertia. —————————————————————————————— One Super volcano would do the trick….. 🙂 richard verney January 12, 2012 5:41 pm Joel Shore says: January 12, 2012 at 9:23 am “….Because we know that the Earth + atmosphere are absorbing ~240 W/m^2 from the sun and that the Earth’s surface is emitting ~390 W/m^2 or so….” Joel Please will you provide details of the latitude and longitude of where on planet Earth, the Earth is absorbing 240W per sq.m and the date and time when that occurs. Please will you provide details of the latitude and longitude of where on planet Earth, the Earth/s surface is emitting 390W per sq.m and the date and time when that occurs. January 12, 2012 5:45 pm Earth is 259 trillion cubic miles of mostly MOLTEN rock with a temperature above 2500F. Uranium-235 is approximately 4 PPM, or 700,000 cubic miles; Thorium app 1.2 million cubic miles. These fissionable materials are NOT limited to standard half-life decay and are in fact variable in time and location. Estimates of this force had a magnitude increase from ~6 terawatts to 66 TW with the KamLAND experiment, see “First Measurements of Earth’s Core Radioactivity”, New Scientist, July 27, 2005. Fission decay can involve up to a dozen unstable daughter atoms which also release heat, see “Potassium-40 Heats Earth’s Core”, Physics World, May 07, 2003. Massive amounts of geothermal energy are released, but hidden in plain sight. Some geothermal energy is disgused at ocean floor vents, per “Earth’s Missing Geothermal Flux”. Additional fission energy is converted to hydrocarbon molecular energy as described in “Fossil Fuel is Nuclear Waste” and “Earth’s Elemental Petrol Production”. We live on a far more complicated and interesting planet that we are FORCED to believe. Please find and share Truth. Joseph A Olson, PE Brian H January 12, 2012 5:50 pm Stephen Wilde says: January 12, 2012 at 1:26 pm They could be acquiring all of their energy from the other non GHG molecules which can be heated by conduction from the surface and would pass it on to the GHGs via conduction. Once the GHGs reach the ambient temperature for other molecules at the same height (via conduction) they cannot get any warmer from longwave coming up from the surface Individual molecules can’t be said to have any temperature; they move at a huge range of speeds, depending on the net ‘vector’ after their latest collision, from nearly dead stop to kps. It’s the gas-mass that has a characteristic number and violence of collisions which can be said to have a temperature. So there’s no problem in any CO2 molecule, at any speed, absorbing radiation from the surface (or other CO2 molecules, or anywhere) and gaining vibrational energy. But the lag before it gets hit by another molecule (O2, N2 probably) and exchanging thermal energy with it is far shorter than the probable time to re-emit. So, as Cao Jinan points out, most of the radiation from CO2 results from energy acquisition from a recent collision, not from absorbed radiation, which has long since been thermally passed on: the odds are many orders of magnitude greater, actually. Net-net, CO2 thermalizes incoming radiation, and occasionally radiates acquired thermal radiation. Since O2 and N2 don’t do the latter, CO2 constitutes a “hole in the bucket” at higher altitudes, radiating (leaking) thermal energy to space that would otherwise hang around longer (raising local/average temperatures). The question of where the O2-N2 mix gets most of its thermal energy is thus key. Since H2O is so much more common in the atmosphere, and picks up far wider up-welling and downwelling frequency bands, it’s the obvious suspect, aside from its potent role in using its huge latent heat phase changes to cool the surface and heat (at cloud level) the atmosphere. As a heating tool, CO2 is very small — micro-small — potatoes. Brian H January 12, 2012 5:54 pm Edit: “radiating (leaking) thermal energy to space that would otherwise hang around longer.” markx January 12, 2012 5:58 pm @Lucy Skywalker says: January 12, 2012 at 1:39 pm “….CO2 in the stratosphere emits radiation toward the surface. ….” Quick question – perhaps a dumb one (I have checked you link but am none the wiser) – does the CO2 in the troposphere really only emit radiation towards the surface, heating the CO2 below and thence H20 in the tropospause, so the H20 then can emit it to space? I’d expect the majority of it was being emitted (to space) via CO2 in the stratosphere? Or does this just refer to a trapping mechanism for that portion of the radiation going downwards? Myrrh January 12, 2012 5:59 pm Joe Postma says: January 12, 2012 at 3:19 pm “Myrrh says: January 12, 2012 at 2:33 pm And there’s also that forty years ago NASA had to junk Stefan-Boltzmann to get real moon temps estimated for the landings, somewhere on-line, as they needed three dimensions not the flat earth of SB and they had to include that thermal energy absorbed from the Sun penetrated and was released later.” That’s quite interesting. In the model I have been developing, it seems apparent that such a term needs to be introduced in order to capture all of the physics…you can’t ignore the massive thermal mass and extremely long time-constant of “dirt”. You also therefore question the idea that the ground surface has zero contribution from geothermal energy – if this were true, the ground would go down to zero kelvin at some point. But in fact it never actually gets all that cold beneath the ground surface, in fact it is MUCH higher than 0 Kelvin! You have to include that…and it WILL raise the temperature. The same effect from the atmosphere is known to be much less significant, having a much, MUCH shorter time-constant, and much less thermal energy stored within in. Hopefully this is something that Robert and I could work on together… ===================== I really would like to see a proper basic model, desperately needed to have something to pin all the variables on.., I hope this collaboration or one like it takes off. Also to bear in mind that water wasn’t a problem for NASA’s rejigging to get Moon temps, and the Earth’s great ocean with its high heat capacity has the ability to store the heat energy it gets direct from the Sun without ostensibly showing any great difference in temperature and regardless the atmospheric temp changes going on surrounding it – it takes longer to heat up and so correspondingly longer to cool down, higher heat capacity than dirt. And, I’m very much in agreement with http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-862218 Especially re his LIFE, which other planets don’t have and didn’t have to be considered in the moon landings. Adding to Dave Wendt – there are two distinct categories of energies reaching Earth, Heat and Light. Heat, the direct thermal energy of the Sun on the move, transfer, via radiation is that which directly heats land and oceans, and us as water is the great absorber of thermal energy and we’re mostly water, so to some extent all Life absorbs direct thermal energy from the Sun, but, we also manufacture our own via the energy we get from food in burning it for work and this food chain has plant life at its base which manufactures food direct from Light, sugar from visible, and in burning this for work releases heat into the atmosphere via transpiration. Photosynthesis isn’t limited to the land, some 90% of the oxygen in the atmosphere is said to be produced by photosynthesis in the ocean. As if all that isn’t complicated enough addition, it’s the variables created by all the heat exchanges through convection in the heavy fluid gaseous atmosphere around us, which gives us our weather and great wind systems around the globe, which makes me get out the popcorn.. Good luck.. 🙂 KevinK January 12, 2012 6:02 pm Dr. Brown; VERY WELL PUT, thank you. In the engineering fields we consider these “intractable” analytic problems, meaning that we cannot ever hope to solve them analytically. So, to make forward progress we turn to alternative approaches. As a simple example; You have a complex Earth orbiting satellite with mechanical, optical, electrical and other components that are held together with an assortment of nuts/bolts/glue, etc. (sorry, no rubber bands allowed). You wish to launch it into space on top of a big roaring rocket that is going to shake Holy H—l out of it before it reaches the vibration free nearly zero-G altitude where it will operate. How do you ascertain that it will survive the launch ? Well here is how; You write down everything you and others have learned from launching other things into space. You do not repeat their mistakes, and copy what worked for them (if applicable) Then, (get this all you true believers in the value of computer models); you make a test copy (aka a Qualification Model) and you SHAKE IT EVEN HARDER THAN the rocket ever could. Yes indeed, that’s how’s it’s done, imagine a big honking table that you bolt your satellite to and the table shakes Holy H—l out of it and then some. If it survives (about 95% of the time) and if you make a Flight Model using exactly the same extremely well documented assembly processes it is “very likely” that your satellite will make it into space and operate as advertised. But some still fail (lately about 5%, historically less than 1%). Nobody attempts to analytically model the strength of all those mechanical interfaces when subjected to vibration, it would take forever and nobody would believe the “heritage” of your computer models (i.e. has it worked in the past ?) anyway. Ok, as another example, how can you determine how long your satellite will operate once in orbit ? Satellites operate in a very rough environment where radiation (those nasty cosmic rays) strike semiconductor junctions and render them useless, atomic oxygen rips material away from optical coatings and the occasional micrometeorite slices through a critical power supply wire. Well, you could just make lots of satellites with different designs and wait a few years to see how long they last while on orbit. But given the cost of satellites (50 million and up to lots and lots of millions of dollars) this would be wasteful. Also, since modern satellites often last 5-10 plus years (Chandra was launched in 1999 and is still functioning) this would take decades to get useful information. So we use (drumroll please) COMPUTER MODELS, these models are fairly simple and use empirically derived data (we put a satellite up with the Space Shuttle to do nothing but expose different materials to the space environment for years, then retrieved it to find out which lasted the longest) to predict how long a satellite designed with certain materials will last. We also predict how often a micrometeorite can be reasonably expected to take out an important electrical cable. So we come up with an analytical prediction (i.e. a computer model) to predict the lifetime of the satellite. These predictions have been aligning pretty well with the performance of actual space vehicles, but we still get a mission failure every once in a while. Sorry this has become quite a bit of a post, but the point is, you need to carefully assess when a computer model helps and when it just fools you. The climate models which have been programmed to explicitly behave in correspondence with a hypothesis (“The Greenhouse Effect”) are just a silly and expensive attempt to beat an intractable analytical problem into submission with more computer power. I believe they are useless. Cheers, Kevin. LazyTeenager January 12, 2012 6:03 pm So Robert reckons he can work out the whole of atmospheric physics in one night and then discovers it is complicated. People smarter than Robert have been working on this for a century or so, so I figure they will be able to tell him it is even more complicated than what he has discovered so far. But I get the uncomfortable feeling this argument is going to devolve into a bit of logic that looks like this: 1. We do not understand everything about how blackbody radiation determines the baseline temperature. 2. Therefore we know nothing about how blackbody radiation determines the baseline temperature. 3. Therefore we know with absolute certainty that the blackbody radiation determines the baseline temperature to be 25C. 4. Therefore the greenhouse effect does not exist. Please oh please prove me wrong. Bill Illis January 12, 2012 6:03 pm Robert’s post mentions it takes “time” to raise the temperature of the components of the Earth system. I thought I would point out some of those lags. – daytime temperatures peak 3.5 hours after the peak of the solar radiation. – water evaporates from the surface (taking some heat with it) and it eventually falls back to Earth as rain or snow (after dumping off its heat in the atmosphere) anywhere from 2 hours to an average 9 days later (side question, what is the temperature of layer where rain or snow forms versus the temperature of where it evaporates from). – land temperatures lag behind the solar cycle by an average 34 days (the warmest day of the year is July 25th and solar radiation peaks about June 21) (the accumulation rate is about 0.5 W/m2 per day from the coldest day of the year, January 25th, to the warmest day of the year, July 25th). – lakes and rivers peak about 45 days behind the seasonal cycle. – ocean temperatures lag behind solar radiation by about 45 to 70 days. – it takes 1500 years to warm up the entire ocean versus the Earth Surface temperature. – it takes about 10,000 years to completely melt out a continental ice age. – Venus is so much hotter than it really should be. In other words, the components of the Earth system slowly accumulate and slowly release energy received from the Sun. The Stefan-Boltzmann equation includes a mathematical expression called “Emissivity” but this is mostly ignored and mostly not understood that it contains a “time” element in it that must be taken into account. It is entirely possible that emissivity varies over time and over energy levels and it is entirely possible that an object can go on forever having an imbalance between the energy it is absorbing and the energy it is releasing (it can certainly last up to 10,000 years). Emissivity needs to be further defined. It has a non-Zero effect on temperatures but it is treated as if it is Zero. For example, the lag in temperatures of the Earth system’s components means that they slowly accumulate very small amounts of energy per second. This could go on forever or it may reach an equilbrium level at some point. The Greenhouse Effect may simply be a function of Emissivity. Bill H January 12, 2012 6:08 pm Brian H says: January 12, 2012 at 5:50 pm “Net-net, CO2 thermalizes incoming radiation, and occasionally radiates acquired thermal radiation. Since O2 and N2 don’t do the latter, CO2 constitutes a “hole in the bucket” at higher altitudes, radiating (leaking) thermal energy to space that would otherwise hang around longer (raising local/average temperatures). ” ——————————————————————————— This is the key as to why CO2 is actually a cooling device rather than a heat storing one.. as the levels increase it has the black body effect increase… much more than the intake it keeps under solar input.. its that darkside net loss that is killing the AGW theory dead.. but they refuse to look at it… Surfer Dave January 12, 2012 6:10 pm @Tim_Focketts I looked up the geothermal heat flux at the surface and found that there is a paucity of real measurements globally. The USA has been studied reasonably well and while the average on continental USA is estimated at about 250mWm-2 there are hot spots up to 15Wm-2. That was from the Southern Methodist University website, very instructive. No-one really knows what the global average is, especially given that 70% of the planet is underwater. It is assumed that the flux on continental USA is representative of the flux on the entire planet. Some measurements in Australia, South Africa and Russia seems to confirm this but even so there are hot spots with fluxen well above 1Wm-2. Given that seems like quite a low rate, how come the temperature below about 10m is 22C (295K) and increasing with depth? Is that 22C from heat that has gone down from the surface, or is it the balance between the steady outward flux from the geothermal sources (which include radioactive decay, heat from the earth’s EM currents, gravitational friction internally and the residual heat from planetary formation) and the inward flowing heat from the insolation? Would that internal temperature at 10m deep change in the absence of an atmosphere? Also, on the original topic, one point to remember is that most of the physics of heat conductance in materials assumes that the heat flux is perpendicular to the surface of a flat plane. This is probably an acceptable simplification because in a uniform infinite plane the generally spherical flow of heat (either convective or radiative) from a point is balanced out by all the surrounding points so that the nett flow can be assumed to be perpendicular. My point is this, on a sphere each point has it own perpendicular that all converge on the centre of the sphere. The assumption of flux parallel to a flat surface is not valid for a sphere. I suspect that in some sense a sphere acts like a lense for the heat flow, the density of the flux and thus the temperature of the material of the sphere increases towards the centre. I know the earth seems “big” so that the flat plane analogy sort of makes sense, but that’s probably not correct. Brian H January 12, 2012 6:10 pm Edit: “occasionally acquired thermal radiation energy.” Brian H January 12, 2012 6:12 pm ARRrr, he said like a pirate but a week early: Edit edit “and occasionally radiates acquired thermal radiation energy.” LazyTeenager January 12, 2012 6:16 pm Michael Hart says But where can us lesser mortals examine the algorithms and computer code, not to mention the assumptions about which bits can be safely ignored? ———– There is some GCM source code dowloadable but these codes, even the old obsolete ones are rather large, and beyond mere mortal understanding. In fact they are probably so large they are beyond the in-depth understanding of people who use them and challenging to understand for people who wrote them. The assumptions, math and experimental work behind each individual component of a GCM program the will be found in the scientific literature and is also likely beyond your understanding. Each such thing represents 5 years work for 1-5 technical specialists. So, in short, you can download the code but the exercise will not be useful to you. Just learning how to get the data and create the input files is going to take several weeks of study and work. eyesonu January 12, 2012 6:26 pm @ Robert Brown I sense that you have a class of ‘students’ here at WUWT greater than you can imagine! Some are commenters and many more are ‘lurkers’. I am of the ‘lurker’ class and will not miss a lesson and strive to learn every bit of knowledge that you offer. I will not get an ‘A’ as no written exam is required. The ‘test’ will come when I refute the bullshit of the many uninformed. I sincerely thank you. You still get no apple! Tim Folkerts(@tjfolkerts) January 12, 2012 6:26 pm Bill, I like what you say, but I don;t see how emissivity is going to save the day. >Emissivity needs to be further defined. emissivity = (Actual thermal radiation) / (ideal thermal radiation) The definition is pretty straightforward. This definition can be applied at each wavelength or (more commonly) as a weighted average over all wavelengths. I don;t see what more definition is needed. >but it is treated as if it is Zero … If anything, it is treats as if it is exactly 1.00. Measurements show that it is indeed pretty close to 1 for many parts of the earth (water, many soils, many leaves … ). I understand the the emissivity is included in many calculations, but this will only be a correction of a few percent — far too little to account for major effects. >the lag in temperatures of the Earth system’s components means >that they slowly accumulate very small amounts of energy per second. This is most certainly true. That is why people worry about small changes in atmospheric IR radiation having long-term effects on climate. But it is also most certainly true that a few percent error in emissivity cannot account for the difference between outgoing IR seen from space (~ 240 W/m^2 on average, with clear effects of CO2 and H2O) and outgoing IR as seen from just above earths surface (~ 390 W/m^2 on average, with a nearly blackbody spectrum). LazyTeenager January 12, 2012 6:32 pm Thermodynamic professor, power plant manager on January 12, 2012 at 9:41 am said: Backradiation is bullshit from cooler gas to warmer surface, physically impossible! ——– You don’t need billions of dollars to prove this statement to be false. Just go down to your local electronics shop and use100 to buy an IR thermometer.
Point it at the sky. Measure the temperature. You have just measured the long wave down welling infrared radiation.
Case closed.
But if that is not enough consider unglazed thermal collectors used for swimming pool heaters. The LWIR from the sky figures in the efficiency calculations for those.
Score: checkout chick 1, professor 0.
So professor needs to go back to school and learn the laws of thermodynamics properly this time

eyesonu
January 12, 2012 6:35 pm

I should also add that I am also a student of the several ‘associate’ teachers here @ WUWT University.

Tim Folkerts(@tjfolkerts)
January 12, 2012 6:38 pm

Surfer Dave says:
>Given that seems like quite a low rate, how come the temperature
>below about 10m is 22C (295K) and increasing with depth?
>Is that 22C from heat that has gone down from the surface,
Certainly not.
>or is it the balance between the steady outward flux from the geothermal sources
Yes, the early earth was much hotter and has been cooling for a long time. But there are literally miles of insulation, so the heat flow will be rather small.
>Would that internal temperature at 10m deep change in the absence of an atmosphere?
Certainly it would be a bit cooler. I strongly suspect the temperature gradient would stay about the same, so you could pretty much subtract ~ 33 K (give or take a bit depending on exactly how you want to model the earth with no atmosphere) from the temperature at any depth.
(Of course, over the course of billions of years, this could have a significant effect all by itself. An earth that NEVER had an atmosphere would presumably be cooler than an earth that lost its atmosphere recently. )

KevinK
January 12, 2012 6:43 pm

Dr. Brown;
My last post got a bit verbose, so I split it into two parts for the comfort of any that wish to read further.
While you have captured many of the concerns with respect to our ability to predict the temperature of the Earth with/without “GHGs” I believe you may have missed a few important ”wrinkles” in the problem. I will suggest just two for everybody’s consideration.
First, the Albedo of a surface is HIGHLY dependent on the angle of the arriving optical radiation. This is well known and has been adequately characterized by the Bi-Directional Reflectivity Function, aka the BDRF. This is well known among those folks that design Earth Imaging Satellites. This surely seems to call into question the simplifying assumption that the spherical Earth can be replaced by a flat disk, IF only it was this simple.
Secondly, I see no discussion amongst the climate science community of the speed at which heat travels through the materials comprising the atmosphere of the Earth. It is well understood among engineers that heat propagates through different materials at different speeds. For example, most computers use aluminum as a “heatsink” to remove heat from the microprocessor. Like most engineering decisions this is a tradeoff between cost and performance. Aluminum is less costly and provides a reasonable level of performance for most applications. However, when higher performance is desired without concern for cost Copper is used instead of Aluminum. Why is that some may ask? well… it’s because the thermal diffusivity of copper is higher than that of aluminum. Thermal diffusivity is (from a system perspective) an effective measure of the “speed of heat” through a material. Heat flows through copper at a higher speed, thus allowing higher performance. In some applications synthetic diamond is applied to give even higher “speeds of heat” when the cost is justified.
My hypothesis is that increases in “GHGs” are displaced by decreases in “non-GHGS” (after all there are only 1,000,000 ppmv of gases in the atmosphere,by definition). Heat travels through “non-GHGs” at the “speed of heat”. Heat (or its equivalent IR radiation) travels through “GHGs” at close to the “speed of light” (albeit there are some slight delays introduced from a few (10-20max) short side trips backs towards the surface as “backradiation”). Hence the addition of “GHGs” to the atmosphere only make the gases in the atmosphere warm up faster, or cool down faster after any change in the energy input to the system (i.e. sunrise/sunset/accumulation of clouds/dissipation of clouds). This clearly indicates that no “higher equilibrum” temperature can be caused by “GHGs”.
Cheers, Kevin.

Tim Folkerts(@tjfolkerts)
January 12, 2012 6:43 pm

One more thing, Surfer Dave,
Geothermal energy fluxes might well be a few W/m^2 rather than a few 0.1 W/m^2 — I am certainly not an expert on the topic. This would be interesting and it would have some bearing on energy balances. But even the highest estimates you gave sill less than 10% of the power flows attributed to GHG’s so geothermal energy [transmission] is still a perturbation, not a replacement for GHG’s and atmospheric effects.

Bill Illis
January 12, 2012 6:53 pm

Tim Folkerts says:
January 12, 2012 at 6:26 pm
But it is also most certainly true that a few percent error in emissivity cannot account for the difference between outgoing IR seen from space (~ 240 W/m^2 on average, with clear effects of CO2 and H2O) and outgoing IR as seen from just above earths surface (~ 390 W/m^2 on average, with a nearly blackbody spectrum).
———
Crunch the numbers on a per second basis since the energy coming in during the daytime is actually an average 956 joules/second/m2. How much does the surface energy level change? At night, basically zero is coming in. How much does the surface energy level change (per second).

Surfer Dave
January 12, 2012 7:11 pm

@Tim_Folkerts
Thanks Tim, useful
Given that Hansen’s recent “Imbalances” came up with an imbalance of 500mWm-2 then I would think that a geothermal heat flux of almost the same magnitude as the “imbalance” should be brought into the complete story?

Tim Folkerts(@tjfolkerts)
January 12, 2012 7:14 pm

Dr Brown is doing his homework. I’ve been doing some homework as well to understand this all a bit better. For all those claiming that CO2 would only have a small warming effect — or even a cooling effect — here is your homework. Explain the shape of the IR spectrum as observed from space looking down and from the surface looking up. (there are good examples here: http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/)
* Explain the shape of the dotted lines labeled with different temperatures
* Explain the cause of the various “bites” in the spectrum.
* Estimate the order of magnitudes of the GHG effects at a given place and time (ie when a specific satellite image was taken). .
This is what you need to be able to do to start discussing the GHE intelligently. Otherwise, you are free to keep idly speculating, but don’t expect much support except from other idle speculators.

eyesonu
January 12, 2012 7:21 pm

While I’m on the topic of ‘teachers, let me suggest this as follows. Every teacher/professor of physics, thermodynamics, ‘climate science’, real science, meteoroligical, or other related disipline should direct his/her students to study the past several days of WUWT as related to this discussion/topic.
The topic is very important and the forum is a model for exchange of knowledge.

AusieDan
January 12, 2012 7:39 pm

Hi Willis
I think that you may be missing the possibility that the extra heat at the surface, is just borrowed by the work due to gravity, from the higher up regions of the atmosphere.
If you work through the data for the various planets and moons, you will see how it works very simply, regardless of the percentage of GHGs in the atmosphere of the planet or moon under study.

johndo9
January 12, 2012 8:33 pm

For Dr Brown or anyone wanting to run the integral surface temperature.
Just back on the atmosphere less world (moon average temperature) problem.
The very small amount of heat coming from radioactive decay, (I thought about 0.5 watt/sq metre while someone above suggested 1 watt/sq metre) limits the minimum temperature of the never sun exposed parts.
The lowest temperature then would be around 50 to 60 K. It may add 20 to 30 K to the average for the moon.
On earth where the lowest surface temperature may be around 180 K the contribution from the interior of 0.5 to 1 watt/sq metre is quite insignificant.

January 12, 2012 8:48 pm

I second the request of Joules Verne 1/12 09:21 for greater information on the uncertainty in the albedo. Everytime I see a value, it is 30%. Ok, is that 3E-01 or is that 3.00000E-01? How many significant digits is that “30%” good to?
But there is another more basic question I have about the albedo. For this I have to return to “square 3.” Why do we account for albedo only on the direct-from-sun energy, but everyone seems to ignore it on surface-to-sky path?
Please humor me for a moment…. I haven’t seen this concept explained.
Let’s set up a thought experiment where we normalize energy from the Sun as 1.
That energy hits some atmospheric phenomena and 30% of it (call it A) is reflected as albedo into space. That leaves (1 – A)=B passing through the phenomena to strike the ground.
All of that B that hits the ground must reradiate (over some time) or else the ground would continuously heat up. So we also have an upward amount of energy B [so far so good..]… that strikes the underside of those albedo phenomena…. And then what happens? Almost everything I read has B just passing through into space as if the phenomena didn’t exist. Really? That’s quite a trick.
Let us suppose, in a general formulation, that upward B radiation encounters the phenomena and a fraction “a” is reflected back downward (and 1-a continues into space). ( a does not necessarily equal A ). Now we have some extra energy (b*a) traveling back down on a second leg…. By superposition, downward b*a is hits the surface and must be returned upwards, only to meet with the partial reflector and we have a third downward leg b*a^2, to be repeated in an infinite series.
By this “reverberation” within a partially trapped wave guide, we have energy striking the surface in the series: b + b*a + b*a^2 + …b*a^n. Rewrite as: b*(1 + a + a^2 + … a^n) which infinite series (if a<1) can be replaced with b*(1/(1-a)), or b/(1-a).
Finally, lets remember that b = 1-A. So that means the energy hitting the ground can be calculated as (1-A)/(1-a). What if the albedo phenomena reflects upward and downwards equally well? A=a. Then the ground energy is not (1-A) but it is 1.0000. The actual value of the albedo doesn’t matter if A=a.
I did this in the general case because it is quite possible that because of changes in spectra of the direct energy and the ground reflected energy, “a” may very will not be equal to “A”. In the steady-state, “divide insolation by 4”, without day-night, world, I can be talked into a A.
But I am having an increasingly hard time accepting a=0, which seems to be the value for “a” used by default in many examples. Where have I gone off the rails?
Finally, I cannot quit without returning to the real world where insolation is really divided by 2, we have day and night, and albedo is a function of time and season. You can warm the morning in a cloudless Pacific, then bring on the afternoon clouds as Nature’s thermostat (Willis: WUWT 6/7/11) and bask in the warmth of ( a = A approximately.)

January 12, 2012 8:51 pm

formatting correction to above: “I can be talked into “a” not equal to “A” .

January 12, 2012 9:01 pm

Embellishment on the trapped waveguide….
Have I short changed the earth’s total albedo? Nope.
The escaped energy off the first leg is B*(1-a). What leaks through the second bounce is B*a*(1-a). What leaks on the third leg is B*a^2*(1-a). Which again becomes an infinite series of B*(1-a)*(1+a+a^2+..) which rewrites to B*(1-a)*(1/(1-a)) which reduces to B, the same result you get if you treat the albedo as transparent when going up.

Jim D
January 12, 2012 9:32 pm

It is very simple. Net incoming solar radiation for a spherical earth with albedo 0.3 is 240 W/m2.
Black-body temperature required to radiate 240 W/m2 is 255 K. QED. Any questions?

Joe Postma
January 12, 2012 9:34 pm

I think there must be something wrong with the way standard theory treats the geothermal contribution to energy, whether it be from past absorption from sunlight energy or true geo-energy.
1 Watt/m2 is 65 Kelvin. The ground beneath the surface is NOT 65 Kelvin. If I take a shovel and dig a hole 1 meter deep, the newly exposed ground WILL be radiating at its temperature, say 5C or 338 W/m2. So, that means the ground went from contributing 1 W/m2, suddenly to 338 W/m2, just because I dug a hole. Something is amiss here, and it isn’t with the fact that exposed ground will radiate fully according to its temperature.
Look at it this way: the geothermal temperature contribution coming from deep below will, at some depth nearer to the surface, blend with the average temperature of the soil being induced by sunlight. In other words, going down beneath the surface, we expect the soil temperature to drop until it stabilizes, and then start rising again, due to the temperature from geo-energy. This merge-point temperature is not anywhere near 60K. In fact, I think for most of the planet, the merge-point temperature is actually quite shallow in depth, relatively very near the surface, and also well above 273K.
This merge-point temperature, being supported by below from the geo-energy, or from past absorbed solar energy, or both, presents a baseline temperature upon which the temperature induced by solar radiation at the surface will vary. In the real-time differential heat-flow equation I’ve been developing, which models all the other parameters of the system, this baseline temperature can to be taken into account. (BTW, this model reproduces the daily temperature lag to solar insolation, as well as the seasonal lag.)
In effect, there is SUPPORT to the surface temperature coming from beneath – that means that the night-time will not cool as fast, and warming in the day-time from solar insolation will also start from a base plateau…not 0K. The effect of this is to raise the average temperature at the surface, given that the real-time solar insolation reaches noon-time heights of up to +121C (factoring in extinction reduces that, but the value is still anywhere between 50C and 90C).
So however they’re calculating the negligible 1 W/m2 from geo-energy, it doesn’t make sense at all if you just think of the actual temperature the ground is beneath the surface, and why it has this temperature to begin with. In a physical heat-flow equation which models the actually accumulated and existing energy, or the actual direct temperature, you simply can not say that the sub-surface has near-zero temperature and/or near-zero internal energy – because the simple fact is that it doesn’t. Their is a GREAT DEAL of energy contained in the soil and sub-surface, and it is generally much closer to 0C than to 0K.
What’s really interesting is that if I DO incorporate a term for the sub-surface temperature and energy, the response of the real-time differential heat-flow equation acts just like what you expect current theory to say about the greenhouse effect: it raises the surface temperature.
What the atmosphere comes out as, in any solution to this heat-flow equation with or without the geo-temperature included, is that it is a very simple responding parameter – the temperature of the near-surface air is simply something that responds to the direct-surface temperature, and when night falls, the whole system simply cools according to its thermal time-constant. When the Sun comes back up, the surface starts warming and THEN the near-surface atmosphere starts warming; when the Sun passes the point in the afternoon when its incident-angle insolation temperature matches that of the reached-surface temperature, the system plateau’s and starts cooling again. This is the origin of the daily temperature lag. The origin of the seasonal lag comes in from the soil having such a large thermal capacity, and therefore, much slower response to the seasonal variation in solar insolation, as the Sun slowly swings up and down over the celestial equator.

DR
January 12, 2012 9:36 pm

@Bill Illis
I always find your posts interesting and informative. These two sentences caught my eye:

– it takes 1500 years to warm up the entire ocean versus the Earth Surface temperature.
– it takes about 10,000 years to completely melt out a continental ice age.

I am interested in understanding more how this relates to CWP. It would seem to me that sea level rise is a direct function of this “lag” of 10,000 in that we should not be surprised that glaciers wax and wane, and sea levels continue to rise, but rather be very worried when glaciers advance and sea levels drop.
So where are we in the geological time frame with regard to the “10,000 years to completely melt out a continental ice age”? What happens after that? I wonder if Nir Shaviv’s hypothesis on the spiral arm/GCR explanation for interglacial periods is valid. IIRC he postulates we are near the end of the current warm period and may begin transitioning to the next ice age.
Looking at the various cooling/warming periods, each warm period looks to be a step below the previous…..RWP > MWP > CWP. Is the inertia from the Holocene losing its mojo? Sorry Mike, the hockey stick is dead.

Stephen Wilde
January 12, 2012 9:39 pm

Any atmosphere, whether composed of GHGs or not reduces the ability of the surface to radiate to space by diverting some of the surface energy to conduction into the atmosphere which warms up to match the surface temperature.
Applying the Ideal Gas Law then redistributes the energy in the atmosphere to create a temperature gradient from surface to space.
Due to the atmosphere having the highest temperature just above the surface the effect of the Ideal Gas Law feeds back to the surface by reducing the rate at which the surface can conduct and radiate energy upward with the result that the surface can then itself achieve a higher temperature in reponse to the same level of solar energy input.
Thus the equilibrium temperature at the surface rises as a result of atmospheric density and pressure.
That is the Greenhouse Effect.
The radiative abilities of the atmospheric gases are relevant to the patterns of energy movement between surface and space but do not affect the surface temperature unless they also significantlly increase atmospheric mass.

u.k.(us)
January 12, 2012 10:01 pm

Wow, the colossal waste of ingenuity, perpetrated by activists.

January 12, 2012 10:28 pm

Jim D says:
January 12, 2012 at 9:32 pm
It is very simple. Net incoming solar radiation for a spherical earth with albedo 0.3 is 240 W/m2.
Black-body temperature required to radiate 240 W/m2 is 255 K. QED. Any questions?>>>
Yes. Do you understand that this number is invalid except for the case where the temperature of the earth is 100% uniform around the entire globe?
Earth is 255K across the entire planet. P= 5.67*10^-8*255^4 = 240 w/m2.
Now let’s suppose an Earth that is 310K over exactly half the planet and 200K over the other half.
(310 + 200)/2 = 255K “average”.
BUT
For T = 310K P= 5.67*10^-8*310^4 = 524 w/m2
For T = 200K P= 6.57*10^-8*200^4 = 91 w/m2
“average” P = (524 + 91)/2 = 307.5 w/m2
Uh oh. We’ve got two scenarios, each with an “average” T of 255K, but one radiates at an “average” of 240 w/m2 and the other radiates at an “average” of 307.5 w/m2.
The larger the temperature distribution, the more pronounced this becomes. For example, if we used a T of 350K and 160K, we’d still get an “average” of 255K, but the average P would rise to 444 w/m2!
In other words, the larger the temperature distribution, the MORE w/m2 it takes to maintain the “average” temperature of 255K. Put more simply, given that the temperature distribution of the earth ranges from -80C at the south pole to +40C at the equator on any given day, that the day/night cycle imposes a 20 degree temperature swing nearly every day, and that temperate zones swing by 60 degrees or more annually, there is no way the 240 w/m2 is anywhere NEAR enough of an “average” radiance to support an “average” temperature of 255K!
If the average temperature of the earth, with the kind of variance I just pointed out, actually was 255K, it could not possibly be supported in radiative balance by a mere 240w/m2. conversely, if the absorbed radiance actually is 240 w/m2, then the “average” temperature cannot possibly be anywhere near as high as 255K!
Since we at least have some arguments to suggest that 240 w/m2 is a not bad guestimate, then we can only conclude that 255K is WAY TOO HIGH as an estimate of temperature via SB Law. If that is the case, then the oft quoted 33 degrees from GHE arrived at by subtracting 255K from 288K cannot possibly be right.

January 12, 2012 10:47 pm

Robert Brown wrote:

However, Enthalpy, the Earth’s climate viewed as a self-organizing heat engine, and chaotic fluid dynamics of open systems are for later. First I need to take baby steps… even if they follow in the footsteps of others or if future things will confound them.

Here’s a comment I wrote earlier.
The only reason that I can see why one would spend time taking those baby steps; if all you have down the road is broken glass, mirrors and wolves; is to gauge the expanse of folly. 😉
Of course, I don’t get paid to do climate research.
Enthalpy is only about the amount of heat stored. It says nothing about how the weather (thus climate) works as a heat engine. If you “measure” the enthalpy, you can tell if the heat content is rising. I you only measure temperature of one or two components at their extremes, it tells you nothing about the state of the real world. Those temperatures are only useful as Lotto numbers and for political purposes.

Bob Fernley-Jones
January 12, 2012 10:53 pm

Robert G. Brown
Robert, whilst I totally agree with the wide sentiments here that your article is very interesting, after some pause in posting this, I’d like to say that all that you have achieved so far is to give yourself and others a headache. Yes, it is indeed all very complicated, but how about tackling a small part of it at a time? For instance this silly business of some experts asserting that there is an effective radiative T for an airless Earth, when albedo distribution and thermal characteristics of regolith and rocks/geology and stuff galore such as volcanism over what age, is purely speculative for an airless Earth.
Oh OK, let’s look at the moon instead where Willis asserts its albedo is 0.11, ho hum.
What IS clear is that there is a huge variation in surface T, and that under the “Noon solar hotspot”, the rate of heat loss must be comparatively huge, (per T^4), compared with the rest of the spherical surface area of the moon, which is simplistically argued to share and shed the insolation uniformly per unit area!!!
Furthermore, might I suggest, (because I’m past my prime in the maths), perhaps you or your students might take-on the task of doing an integration of insolation and emission over the entire lunar surface, based on Willis’s albedo, and a range of plausible thermal characteristics for the lunar regolith? It would be most interesting to see!
I’ve had some interesting intercourse with Willis starting in the link below, but after several exchanges he seems to have taken a premature withdrawal:
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/#comment-860094
Oh, and I think he also does not understand the warming effect of even a transparent atmosphere, but one thing at a time!

ferd berple(@ferdberple)
January 12, 2012 11:22 pm

davidmhoffer says:
January 12, 2012 at 10:28 pm
Since we at least have some arguments to suggest that 240 w/m2 is a not bad guestimate, then we can only conclude that 255K is WAY TOO HIGH as an estimate of temperature via SB Law. If that is the case, then the oft quoted 33 degrees from GHE arrived at by subtracting 255K from 288K cannot possibly be right.
Which pretty much explains why the IPCC climate models went off the rails 12+ years ago.

ferd berple(@ferdberple)
January 12, 2012 11:37 pm

Bob Fernley-Jones says:
January 12, 2012 at 10:53 pm
Furthermore, might I suggest, (because I’m past my prime in the maths), perhaps you or your students might take-on the task of doing an integration of insolation and emission over the entire lunar surface
Such a task is much better suited to a computer. It could get the wrong answer much quicker than a class of students.

Joe
January 12, 2012 11:57 pm

Dr. Brown,
I have been waiting a long time for someone to start this discussion. Yours was a fantastic explanation that highlights the incredible complexity required of any model for the earth’s surface and atmospheric system. An integrated circuit designer may spend a day or more in processor time to simluate a few microseconds of a slice of circuit that covers a volume a square millimeter by a few microns deep. Simulating an IC with well constrained operating conditions is far simpler than a first principles simulation of the thermodynamics of atmospheric gasses or ocean water on the same fraction-of-a-square-millimeter volume. Forget simulating the entire earth! But, simple models can constrain the allowed degrees of freedom.
One operating principle of the system can be derived from the numerous comments above this one. All of the thermal models explained above used 240W/m2 or 341W/m2 but the real number is 1366W/m2. That is the insolation upon the square meter of earth’s atmosphere at high noon at the equator, ignoring the earth’s tilted axis. At that point on the earth at that time, the incoming energy to deal with is the full 1366. At the pole it is the microwave background radiation equivalent to 3K with zero coming from the sun. Same for the night side.
In a simplified model, the breakeven point where the 1366 drops by a factor of 4 due to lattitude to match the average insolation across the globe occurs at 75.5 degrees north and south. (arccos 0.25) Thus, with no atmosphere, the points on the earth that match the average insolation for the globe occur at 75 degrees north and south. South of that lattitude, the incoming radiation is higher than the assumed average and north of that lattitude it is lower, decreasing to zero at the pole. With the atmosphere absorbing or reflecting half of the incoming energy, as noted by NASA on their web site, the breakeven lattitude drops to 60 degrees north and south. (arccos 0.5)
The conclusions to be drawn from this extension of the standard 1366/4 model are:
1) The local average temperature at lattitudes less than 60 degrees is lower than that necessary to balance incoming solar radiation.
2) The local average temperature at lattitudes greater than 60 degress is higher than that necessary to balance incoming insolation.
NOTE: NASA publishes a map of satellite measurements that actually show this differential.
3) The primary mechanism responsible for maintaining the incredible 4-billion-year stability of our system must be the physical transfer of heat from the equator to the poles where it is radiated away. This means weather and ocean currents physically moving heat are the primary means of thermal regulation of the earth’s surface. The carbon dioxide content of the atmosphere probably affects the efficiency of that transfer but it is the physical transfer that counts, not radiative balance at each point on the earth’s surface.
4) The poles, even at -90C, are still 177K above the 3K microwave background so they are not cold, they are frying pan hot and radiate heat into space at a prodigious rate across the largest temprature differential on the globe.
5) The Arcitc is unique because it has liquid water underlying all of its ice. The thermal differential of that water to outer space is even larger at 270C. Ice is an effective insulator so it prevents the radiation of surface thermal energy into space, a stopper in the drain so to speak. The incredible conclusion from this line of thought is that if the Arctic ice melts completely, it will not result in the world warming up but just the opposite. Without the insulation blanket at one of the two primary net-positive thermal radiation points on the earth’s surface, the earth will cool rapidly when the Arctic goes ice free as I am sure it has many times in the past. This effect provides the sign inversion in the system equation necessary to induce the oscillations we see.
6) I did not even try to throw in an analysis of the impact of the rotation rate of the earth but it can be quickly appreciated that it is an essential contributor to the dynamics of our system and helps limit the temperature variation. The temperature due to the sun can never exceed the boiling point of water anywhere on the earth’s surface at any time ever or we would be doomed when all water evaporated into the atmosphere. If the atmosphere did not block 50% of the incoming radiation and the earth did not rotate, that square meter at the equator would equilibrate at a temperature above 100C.
NOTE: The boiling point of water is the difference between Venus and Earth. Venus gets twice as much energy and its water boiled. Water vapor rose to the top of the atmosphere where UV broke it apart. The hydrogen drifted into space while the free oxygen combined into something more stable like carbon dioxide. All of Venus’ carbon is still in its atmosphere. On Earth, water stayed liquid and close to the surface away from the UV. Life formed, captured the carbon, and buried in the ground. All of Earth’s carbon is in its limestone, not its atmosphere. 700GT of carbon is in our atmosphere. 100,000,000GT of carbon is sequestered in the earth. Good job Life!
Conclusion: models using thermal radiation balance are static models that simply cannot represent the earth’s system. More importantly, averages don’t count. As you pointed out, Dr. Brown, energy input varies with lattitude and the length of the day. The fact that a large portion of the earth’s surface averages a temperature below the geometric mean for its incoming energy indicates that static thermal balance is not the primary determinant of surface temperature. The excess incoming energy must be removed physically by the weather and ocean currents to the colder reaches of the earth.

ferd berple(@ferdberple)
January 12, 2012 11:58 pm

Jim D says:
January 12, 2012 at 9:32 pm
Black-body temperature required to radiate 240 W/m2 is 255 K. QED. Any questions?
Why are the hottest places on earth those land areas that are below sea level? Why are deep mine shafts hotter still. It can’t be GHG radiation at the bottom of a mine shaft.

Robert Clemenzi
January 13, 2012 12:31 am

markx says:
January 12, 2012 at 5:58 pm

Robert Clemenzi says: January 12, 2012 at 2:10 pm
“….CO2 in the stratosphere emits radiation toward the surface. ….”
Quick question – perhaps a dumb one (I have checked you link but am none the wiser) – does the CO2 in the troposphere really only emit radiation towards the surface, heating the CO2 below and thence H20 in the tropospause, so the H20 then can emit it to space? I’d expect the majority of it was being emitted (to space) via CO2 in the stratosphere?
Or does this just refer to a trapping mechanism for that portion of the radiation going downwards?

No. In the atmosphere everything radiates in all directions. However, since those gases mainly radiate in the frequencies where the atmosphere is already opaque, that radiation is better than 90% reabsorbed in 100 meters or so. Near the band edges, the distance to absorb 90% increases.
At the tropopause, the water molecule mixing ratio is about 80 ppm. In the stratosphere, it drops to about 5 ppm. About 1km below the tropopause (in the troposphere), it is about 160 ppm. (These are very approximate numbers.) As a result, water vapor radiation toward the Earth is easily absorbed and energy toward space is not absorbed. This is the reason that the tropopause is colder than the air both above and below it.
CO2 is different because the mixing ratio is the same (about 380 ppm) from the surface to the mesopause. As a result, any emitted photons only travel a few 100 meters before being reabsorbed. In the stratosphere, the top is quite warm (just below freezing) and the bottom (the tropopause) is very cold. As a result, and because net heat flow is always from hot to cold, the “net” CO2 emission is toward the surface. The fact that the “typical” tropopause has an isothermal thickness of 10 km or so also supports the conclusion that heat flows from the stratosphere toward the tropopause.
CO2 will also emit the energy at the band edges to space since the spectra line widths are pressure sensitive. This partially explains the central spike seen in spectra taken from space.

Stephen Wilde
January 13, 2012 12:59 am

Further to my post of 9.39 pm.
It follows that IR sensors pointed at the sky are not measuring downwelling IR from GHG molecules higher up.
All they are measuring is the warmth of the air molecules directly in front of the sensor and those warmer molecules (whether GHGs or not) have been warmed by operation of the Ideal Gas Law (which automatically causes warmer molecules to be found lower down in the atmosphere) and NOT by so called downwelling IR.
There is no need to propose any downwelling IR at all. The warmth is already present in the lower molecules by virtue of the Ideal Gas Law working via pressure and density.

wayne
January 13, 2012 1:15 am

Bob Fernley-Jones says:
January 12, 2012 at 10:53 pm
… , perhaps you or your students might take-on the task of doing an integration of insolation and emission over the entire lunar surface, based on Willis’s albedo, and a range of plausible thermal characteristics for the lunar regolith? It would be most interesting to see!
——
Bob, I’d rather he spend the time writing more here at WUWT. Dr. Brown has covered all of the various aspects you will find over some 200,000 comments of last few years plus many never mentioned and has clearly and graciously laid it all out in one single post. I’m elated!
Sounds like you need to address Joe Postma who sounds like he has that already programmed, or, if he can’t easily convert his to the moon, I am writing what you are asking for, as I type this. Seems best to conserve our efforts and not get spread too thin with multiple duplications of the same thing. Mine is across any body, you just set the many parameters defining the orbit, body and the type of analysis of temperatures you wish to run. Keeping it simple for now (kind of), any grid size limited by memory, and am not going to create multilayered surfaces and atmospheres yet (if ever)… ( 🙁 have no supercomputer ). Since this morning I already have the dialogs written, cell/data structures created, integration comes next, just hang on. Comment to Joe, you might not have to wait the week.
See: http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-862486

Robert Clemenzi
January 13, 2012 1:47 am

Tim Folkerts says:
January 12, 2012 at 7:14 pm

For all those claiming that CO2 would only have a small warming effect — or even a cooling effect — here is your homework. Explain the shape of the IR spectrum as observed from space looking down and from the surface looking up.
* Explain the shape of the dotted lines labeled with different temperatures
* Explain the cause of the various “bites” in the spectrum.
* Estimate the order of magnitudes of the GHG effects at a given place and time (ie when a specific satellite image was taken).

Your suggested image at http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/ is garbage (extremely low resolution). I suggest using http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf Figure 5.17 from Petty (2004).
“the dotted lines labeled with different temperatures” represent expected blackbody emissions at those temperatures.
In both images, 600 to 780 cm-1 is the CO2 emission from the stratosphere. These are almost the same temperature in both the desert and ice cap images, proving that the surface temperature has no effect. In both images, there is a sharp spike in the middle of the CO2 feature. This is from the warmer parts of the stratosphere or the lower mesosphere. I have seen additional satellite data where clouds were present, and this feature was still present, proving that it is an emission feature from above the clouds.
1050 cm-1 is due to ozone. It is much warmer than the 600 to 780 cm-1 CO2 emission indicating that it is from higher in the stratosphere. It is also still present on cloudy days.
In figure B, Ice Sheet, emissions on the 180K contour are from the ice. It is obvious that he CO2 and ozone features are produced by gases much warmer than the surface.
In figure A, Sahara desert, 40 to 550 cm-1 is from water vapor in the troposphere. (I know that image starts at 400 cm-1.) This crosses many temperature contours because the band width gets narrower with increased altitude. The warmer points are lower in the atmosphere. The source of the 150 cm-1 value (not shown) should be near the tropopause. 800 to 950 cm-1 is the atmospheric window where IR radiation is not absorbed in the atmosphere. As a result, it indicates the temperature of the surface. 1300 to 1800 cm-1 is more water vapor – colder in the center of the band, warmer at the edge.
Even these spectra have a fairly low resolution since the instruments have only a moderate line resolution. In particular, the height (temperature) of the CO2 and Ozone peaks is probably much higher than shown. In addition, the bottoms of those 2 bands appear to follow blackbody contours and I don’t understand how that is possible.
“Estimate the order of magnitudes of the GHG effects” – sorry, I don’t understand the question.

January 13, 2012 1:59 am

Dr. Brown
I love the physics of this and it is why I became a skeptic, the models for the behavior of IR absorbing and emitting gasses were simply wrong. You mentioned in passing the QM aspects, which most people ignore but are the dominant factor related to absorption and emission of energy in IR absorbing gasses.
There is a great textbook that has the pertinent equations for CO2 and other IR absorbing gasses.
“The Quantum Theory of Light” by Loudon, page 81-90.
That gives you want you need for the QM treatment of IR absorption/Emission.

richard verney
January 13, 2012 2:33 am

davidmhoffer says:
January 12, 2012 at 10:28 pm
////////////////////////////////////
David
Good to see some sanity in all of this. Averages only distort what is going on. The claimate science community uses averages because this simplifies matters but they overlook that this inevitably leads to the wrong result. It is imperative to get away from averages in all aspects of this science. There is no such thing as global warming (some areas may be warming, others are staying bvroadly static and some areas are cooling). One cannot begin to understand the climate and how it may behave in the future, what problems or benefits changes may bring until one looks at it locally.
I think that your extremes of temperatures, if anything underestimate matters. But even in equitorial areas, it can be cool, eg., the Himalayas. Further, the Earth is only ‘spherical’ over the oceans, over land it is far from smooth and has nothing like a spherical surface area (albeit it will both absorb and radiate heat over this larger non spherical area).
One needs to know where the energy is being received, in what quantity , its local albedo and its latent heat capacity. The oceans respond differently to land and they retain and give up their heat in very different manners, not forgetting the phase changes in the water cycle and the latent heat involved.
The entire Earth BB model is fundamentally flawed and until this is corrected, it is impossible to get a proper and accurate handle on the radiative budget (which in any case is not the whole story).

richard verney
January 13, 2012 3:15 am

Surfer Dave says:
January 12, 2012 at 6:10 pm
@Tim_Focketts
///////////////////
As regards the oceans, don’t forget that the oceanic crust is far thinner than the continental crust ( circa 7 to 10 km thick verses circa 36 – 40km) such that one would expect more geothermal heat to make its way through the oceanic crust AND due to the depth of the ocean (average circa 3,800 meters but extending to nearly 11,000 metres), the seabed is nearer the hot core than continenetal land again suggesting that more geothermal heat would make its way through the oceanic crust in order to heat the deep oceans. To some extent, these differences may be countered by different density of crust material (generally the oceanic crust is more dense).
I have for years been suggesting that consideration needs to be given as to whether the oceans are effectively sitting on a warm hotplate and this is contibuting to keeping the deep ocean warm.
I do not know how large the effect is but I do consider it to be an area which is overlooked especially since this pertains to over 70% of the surface area of the Earth. .

richard verney
January 13, 2012 3:26 am

Don’t forget that as regards land, we are not measuring the temperature at the surface but rather at about 1.5 metres above the surface.
Are there any studies dealing with temperature profiles between the surface and the height at which global land temperatures are taken? In other words, if we were to measure temperature (using the same equipment but scaled down stevenson scrrens) at 1 cm, 5 cm, 10cm, 15 cm etc through to 1.5 metres what results would be achieved? Likewise if we were to use an IR thermometer pointing at the ground compared to the adjacent weather station? Perhaps Mr Gates will know since he is always a good source of information and I would welcome any comments that he may have on this specific issue.
I would like to know whether there is any substantial difference and if so to consider the implications of this.

GabrielHBay
January 13, 2012 3:29 am

Phil. says:
January 12, 2012 at 11:11 am
Stephen Wilde says:
January 12, 2012 at 8:42 am
Excellent article.
One question:
How do we know that the Earth is any warmer than it would be without greenhouse gases if the standard assumptions are so obviously inappropriate and/or incomplete ?
It’s quite straightforward. The emission spectrum of the Earth from space is grey body with numerous missing bands which can be unambiguously assigned to the GHGs (CO2, H2O, O3, CH4 & N2O), the spectrum of the Earth absent those GHGs would be grey body but would have to have the same area under the curve which requires a lower temperature. Therefore there is a GHE due to the presence of those gases.
—————————————————————————————
Well, sorry, but I do not buy this “straightforward” explanation. Just as an example, how does one know that the energy of the missing bands did not “change colour”, so to speak, and exit under the cloak of one or more of the other bands? Like 10 women with full spectrum of hair colours enter a salon and after a while only blondes emerge… can one conclude that there is a serial killer favouring brunettes lurking in the salon? Not unless you do a headcount. Just noting the colour is meaningless… And even with a reduced headcount, when it comes to cause, it may actually be blondes disappearing but everyone else being turned to blonde to the confusion of the observer. I agree with other posters here that NOTHING is straightforward and I suspect that Phil is deluding himself. Just because his reply sounds scientific does not mean it is correct.

michael hart
January 13, 2012 3:47 am

Lazyteenager, Dan Kirk-Davidoff has kindly posted a couple of GCM links for me. You’re quite correct about the code likely being little practical use to me. I’ve had similar experiences with far simpler free programs from academic sources [and I only own a laptop, not a Cray].
I am more interested to look at accompanying documentation to gain insights into how they go about performing the calculations they do, and how open the authors are about assumptions made [as these are frequently not obvious, and are easy to forget].

Joel Shore
January 13, 2012 6:35 am

Stephen Wilde says:

Any atmosphere, whether composed of GHGs or not reduces the ability of the surface to radiate to space by diverting some of the surface energy to conduction into the atmosphere which warms up to match the surface temperature.

Stephen has freed himself of the limitation of actually having to come up with explanations that use correct principles of physics. Apparently, he finds correct physics to be too constrictive.
What correct physics principles would tell you is that a surface radiates according to its temperature (and its emissivity, which is a property of the surface). There is no “diversion” of surface energy to conduction. Any conduction that occurs is in addition to whatever radiative transfer occurs due to the surface’s temperature.

HankHenry
January 13, 2012 6:49 am

When speaking of “surface temperature” of the earth what is usually meant is surface air temperature. The textbooks quote it as 14° C (or 288° K). It seems there are several surface temperatures, for instance: the top of atmosphere surface, the surface air temperature, or the surface temperature integrating in the temperature of land and ocean. If the third choice is the correct one then 14° C is too high because the volume of the ocean is huge (the weight of the atmosphere amounts only 33 feet of water) and the typical temperature in the depths is something like 4° C. In some ways the top of atmosphere temperature seems the proper choice but the problem is that you are then comparing a gas temperature to the black body temperature. I believe there is a presumption in the notion of black body temperature that your speaking of a *solid* black body. I am not sure if there are good measurements of temperature at the top of the atmosphere where radiation escapes. It also seems that if you are using top of atmosphere temperature you need to take atmospheric lapse into consideration.

HankHenry
January 13, 2012 6:56 am

There is a nice infrared picture of the moon taken during an eclipse that shows that the surface temperature of the moon is not at all uniform.
http://apod.nasa.gov/apod/ap050423.html

Joe Postma
January 13, 2012 7:08 am

“HankHenry says:
January 13, 2012 at 6:49 am
When speaking of “surface temperature” of the earth what is usually meant is surface air temperature. The textbooks quote it as 14° C (or 288° K). It seems there are several surface temperatures…….. It also seems that if you are using top of atmosphere temperature you need to take atmospheric lapse into consideration.”
—————————-
One other useful temperature to look at is the integrated average emission temperature of the entire planet. This is reported to be -18C, just as the law of conservation of energy and the S-B Law predicts. As you point out, applying the lapse rates via the Ideal Gas Law in the troposphere explains the rest of the temperature distribution, including that of the near-ground “surface” temperature, of 14C. And it does this without need for back-heat temperature self-amplification.
The paradigmatic problem with standard, now defunct, theory is that it doesn’t properly define, or properly understand, the exact question you posed.
For reference I will post the links again:
This first paper describes how to incorporate lapse-rates with the average emission temperature:
This one takes apart the logical errors of standard “self-heating theory”, and presents a new cognitive-physical model which we should start using to characterize the system:
http://principia-scientific.org/publications/The_Model_Atmosphere.pdf
This one summarizes in a short, and very readable and fun, the entire paradigmatic issue:
http://principia-scientific.org/publications/Copernicus_Meets_the_Greenhouse_Effect.pdf
I have continued developing the model introduced in the second paper and now have a differential heat-flow equation which can describe the heat and energy flow for any given square meter of surface in real time (daily, seasonal, yearly, etc, variations in local conditions, inputs and outputs). I will try to publish a new paper describing the theory soon.

January 13, 2012 8:07 am

Joe Postma says
“I have continued developing the model introduced in the second paper and now have a differential heat-flow equation which can describe the heat and energy flow for any given square meter of surface in real time (daily, seasonal, yearly, etc, variations in local conditions, inputs and outputs). I will try to publish a new paper describing the theory soon.”
How to determine the surface temperature with radiative and ground flux contributions is the missing link in atmospheric theory.
Kramm and Dlugi are working on a similar approach.
See equation 2.17
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233

January 13, 2012 7:13 am

Joe Postma says:
January 12, 2012 at 3:03 pm
Robert Brown:
You might be interested in reading my critiques of standard theory here:

I am, and the second one, at least (which I started with) is very well written indeed, very clear. I’m still just at the “Fictions at the Boundary Conditions” section, but there are two things that I’m already itching to do, both of them “trivial” but potentially revealing. Note well that they both only address the (somewhat silly) basic model that assumes that = ^4 for a fluctuating T(t), but let’s go with that for the moment.
* The albedo \alpha is not constant, nor is it “equal to 0.3”, any more than “\pi = 3”. dT_s/d\alpha is easy to (algebraically) compute and/or plot. If one writes \alpha properly as \alpha \pm \Delta \alpha where \Delta \alpha is your choice of the uncertainty in \alpha or the observed secular variance of \alpha (assuming that as an astrophysicist you can read latex as easily as I write it:-) then one adds (at the very least) some extremely useful error bars (or fluctuation limits) to T_s. (Sadly, I don’t think this interface supports any easy way for me to insert the rendered algebra inline other than using html for the characters, which I’m allergic to doing, so I hope the rest of you can follow as well).
When I do this (from your equation 14 as good as any of them) on the back of what would be an envelope except that I keep my whitepaper clipboard with me at all time, I get (and bear in mind that I suck at arithmetic):
\Delta T_s = – 91 \Delta \alpha (degrees K)
(this is at \alpha = 0.3, T_s = 255K — the formula is actually \Delta T_s = -1/4 T_s/(1-\alpha)). Variations on the order of 0.01 in \alpha thus produce variations on the order of a degree K in T_s, even in this rather abusive treatment. Note well that this is on the order of the supposed effect of CO_2 doubling over the last 100 years, meaning that even in this simple stupid treatment first order variation in the albedo is a confounding effect.
* The thing that really struck me about the simplified GHG model that you presented is that there’s “not a thing wrong with it” as a very crude descriptive energy flow. Sure, it’s missing details (like the way that the atmosphere doesn’t absorb as opposed to reflect any of the incident solar flux ) but bear with me. The assumption is that the sunlight reaches the surface and warms it to one temperature (that radiates), that some of the energy is transferred to the atmosphere and radiated at a different temperature, and that the whole system has to self-consistently achieve detailed balance.
For the sake of argument, let’s go with this. Why not? f is then the parameter that describes the total energy transfer from the surface to the atmosphere. Forget the fact that it in the algebra it is presumed that this transfer is to all be blackbody radiative transfer and absorption (which is on the face of it absurd and even in standard models is modulated by e.g. the real spectra and absoption/emission bands and so on). The point is that heat is transferred to the atmosphere as a monotonic function of T_s (so as T_s increases the transferred heat increases) and that it is radiated from the atmosphere at a different temperature than T_s because the mean temperature of the atmosphere, T_a, is always lower.
All this means is that any monotonic coupling whatsoever between the surface and an atmosphere that warms the atmosphere ultimately warms the surface. This makes sense! It doesn’t make a damn bit of difference whether the atmosphere has GHGs in it or not — the transfer from the surface to the atmosphere need not be radiative although there is nothing at all wrong with some of it being radiative. The only thing that matters is that the atmosphere take up some of the heat delivered to the surface by any means whatsoever and then symmetrically radiate it up or down at a lower temperature.
This is very close to what I was getting from Caballero, but hadn’t quite been able to grasp because I was distracted by the fallacy that non-GHG-containing atmospheres don’t radiate. Of course they do. All that matters is that the radiating atmosphere, containing some sustained fraction of the energy of the sun, be thermally equilibrated (approximately).
Wow, epiphany. I do believe that without reading further I could just write down a modified (and equally “dumb”) model that takes incoming radiation, transfers a parametric fraction of the received heat to the atmosphere my non-surface-radiation means (adding back in the missing absorption, since it still comes out of the energy budget for the surface as if it were “transfer”) and the rest by radiation absorption, and get a perfectly lovely equation for T_s that lets one smoothly trade off “the Greenhouse Effect” (radiative absorption f\sigma T^4) against energy flux transferred by conduction/convection. Since in the end one simply fits T_s to the data, that part cannot fail, can it?
I look forward to reading the rest, and the third paper as well. As for working together, that would be lovely but let’s see how much time I end up having after I get to work proper next week and start to have student contact. I’m uncertain as to how much surplus energy I’ll have and don’t want to promise something and then end up disappointing you. But if you send me email at rgb at phy dot duke dot edu, I’ll save your address and if I have time to cook something up I’ll certainly communicate it to you.
I was in brief communication with Steve McIntyre yesterday (who like my “build-a-bear” climate model idea:-) and the idea surfaced that perhaps it would be a good idea to build an open climate model. Here’s what I would propose. We (collectively, not just you and/or I) write a modular open source software package to facilitate the general understanding of climate, with everything open and subject to modification and criticism. Anybody can download it. Anybody can make local modifications. If it is Gnu Public Licensed (viral) software (perhaps with a small codicil requiring that any modifications made that lead to a publication derived from it be published, made available according to the usual GPL rules) it both levels the playing field and establishes a common basis for climate modelling.
I’m far more inclined to do something like this (where I don’t have to do all of the work:-) than to try to build the whole thing from scratch myself. Since I am (I humbly postulate) a WGE on beowulfery and parallel computing, we could even make the (relevant parts of the simulation/statistical parts) of it parallel out of the box, ready to run on a compute cluster in a reasonably scalable way.
The fact that you are an astrophysicist makes me smile. I’ve thought for some time that physical climate modelling is something that should be done by astrophysicists working with condensed matter theorists working with computational fluid dynamicists working with statistical mechanics, perhaps with a few quantum mechanics and complex systems humans thrown in for good measure. Any single physicist knows something about all of this, but can’t possibly be an expert in it all. The traditional “I work over here all by myself with a one or two collaborators and a grant” model just doesn’t look big enough to be able to crack this particular nut.
Crowd-sourced physical climatology. I like it.
rgb

mkelly
January 13, 2012 7:13 am

LazyTeenager says:
January 12, 2012 at 6:32 pm
Sir, since path and gradient are the basic requirements for any heat transfer, with gradient sloping down from higher T to lower T. Can you explain how these are satisfied by your understanding of LWIR from above.

Pierre R Latour
January 13, 2012 7:18 am

GHG Theory 33C Effect Whatchamacallit
Robert Brown is catching on.
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.
Here is the science for what is happening. Thermal T is a point property of matter, a scalar measure of its kinetic energy of atomic and molecular motion. It is measured by thermometers. It decreases with altitude. The rate of thermal energy transfer by conduction or convection between hot Th and cold Tc is proportional to (Th – Tc).
Radiation t is a point property of massless radiation, EMR, a directional vector measure of its energy transmission rate per area or intensity, w/m2, according to the Stefan-Boltzmann law. It is measured by pyrometers and spectrometers. Solar radiation t increases with altitude. Black bodies are defined to be those that absorb and radiate with the same intensity and corresponding t. Real, colorful bodies reflect, scatter, absorb, convert and emit radiant energy according to the nature of the incident radiation direction, spectrum and body matter reflectivity, absorptivity, emissivity and view factors. The rate of EMR energy transfer from a hot body, th, is Q, w = 5.67A*e*(th + 273)**4. But it may not be absorbed by all bodies that intercept it, as GHG theory assumes.
Above Earth’s stratosphere, thin air T is rather cold, about -80C. Yet solar radiation t is rather hot, about 120C. So spacesuits have thermal insulation and radiant reflection. The difference 200C is meaningless. On a cold, clear winter day on snowcapped mountains, dry air T = -10C and radiation t = 50C.
Much of GHG theory fails to make clear distinctions between these two different kinds of temperature, T and t. One temperature, t, is analogous to velocity, 34 km/hour north; the other, T, is analogous to density, 1 kg/liter. So 34 km/hour – 1 kg/liter is indeed 33 whatchamacallits by arithmetic, but nobody will ever know what a whatchamacallit is because velocity and density are not connected by nature.
To clarify this enormous intellectual flaw, take boiling point of water is 100C (true) and freezing point is 32F (true), subtract 100 – 32 = 68 (correct arithmetic) and declare atmospheric pressure is 68 psia. The declaration is false because a) the difference between C and F has no meaning, b) there is no physics to connect 68 to pressure, psia, and c) atmospheric pressure is actually 14.7 psia. That 33C greenhouse gas effect that has everybody so upset and is researched ad nausea to death is not an effect, merely an easily explained pair of facts.
Therefore, it is quite true the 33C greenhouse gas effect defined by James Hanson in 1981 as thermal T = 15C at surface minus radiant t = -18C to space is whatchamacallit nonsense. Everybody knows you can’t compare apples to eggs; except perhaps Greenhouse Gas theorists. Since this is irrefutable logic, no experiment is called for. Logic trumps nonsense; that is why humans invented it around 400bc. No one needs to prove or disprove the existence of whatchamacallits. They are not even imaginary. There is no greenhouse in the sky.
Planetary atmospheres reflect, scatter, transmit, absorb, emit and diminish stellar radiation intensity at the surface according to Beer-Lambert Law, 121C incident to Earth’s stratosphere to 15C at surface. Thermal T of atmospheres increase as gravity compresses gas and converts potential energy to kinetic energy closer to the surface, -80C in stratosphere to 14.5C at surface. Therefore atmospheres cause the surface to be colder than it would be if atmosphere were thinner or non-existent. The more O2 is exchanged for higher heat capacity CO2, the colder the surface radiation intensity temperature. Atmospheres are refrigerators, not blankets.
GHG theory postulates back-radiation from cold atmospheric CO2 is absorbed by the surface, heating it more. This violates Second Law of thermodynamics (energy can only be transferred from hot to cold bodies), leading to creation of energy, a violation of the First Law of thermodynamics (energy conservation), and the impossible perpetual motion machine AGW promoters need to cause eternal global warming.
CO2 does not trap radiation; like all molecules, it absorbs some incident radiation according to its absorption spectrum and promptly emits it according to its emission spectrum. CO2 is not a pollutant; it is inert green plant food. CO2 should not be curtailed, starving Earth’s flora. Minor solar driven global warming from 1974 to 1998 has stabilized through 2011. CO2 has nothing to do with global warming; it actually cools Earth. Arctic ice does not melt because of global warming, increasing T; it melts when average T > 0, at rate proportional to T, no matter whether T is increasing or decreasing.
This essay has seven scientific facts (33C whatchamacallit, no blanket, no back-radiation, CO2 no trap, CO2 inert food, no AGW, ice melts), each of which refute GHG and AGW. It has not been peer reviewed because it is well known to professional physicists and engineers; it does not merit a research paper, or research, or experiments. Logic just needs clear definitions and common sense, not government spending and regulation.

January 13, 2012 7:20 am

Ah. Your figure 3 from your third paper here is exactly what I want to compute, but correctly and parametrically, with what is still a nearly analytical and dimensionally reduced model. I’m not quite ready to try to solve a system of time dependent PDEs over the entire volume, but eventually that is where one has to go. For starters, actually making your figure 3 quantitative in a two color map polar view for a series of model parameters would be simply peachy, don’t you think? And quite doable. Pretty easy, even.
rgb

January 13, 2012 7:45 am

There is a great textbook that has the pertinent equations for CO2 and other IR absorbing gasses.
“The Quantum Theory of Light” by Loudon, page 81-90.
That gives you want you need for the QM treatment of IR absorption/Emission.

Funny that you should mention it, but around twenty years ago I worked in Quantum Optics (before being distracted into magnetism and critical phenomena, in part because the Optical Bloch equations and the equations of magnetism are seductively similar in certain contexts and I was postulating a possible dynamical second order phase transition for a very nonlinear quantum system). Loudon was one of my “bibles” of the time. My colleague and lifetime collaborator, Mike Ciftan, was one of the early co-discoverers of the laser — he observed the nonlinear gain in ruby before the laser work was published, but didn’t quite know what he had.
I’ll dig out my old copy and take a look (if I can still find it in my office, which is a mess, and if I didn’t loan it to a student over the years in between, sigh). It was right behind Allen and Eberly, and in front of Knight and a few others. One of my favorite Loudonisms from that book is his observation that spontaneous decay is understandable in a coupled oscillator model — in a closed system it isn’t really irreversible, but the lifetime for return diverges with system scale quite rapidly. These things all lead to a Generalized Master Equation (GME) approach to quantum optics as outlined IIRC by Agarwal, which brings it all back in context.
The GME is the “correct” formal description for the dynamics of an open subsystem of a larger Universe. This is true even if you make classical or semiclassical approximations (a la Jaynes) to bring the problem within the range of computability. As you make these approximations, depending on the level of detail you retain you end up with e.g. a Langevin equation, which I would argue is formally the right way to deal with the Earth in climate models — a set of coupled ODEs (or better, PDEs) describing the gross time evolution with a stochastic noise term, best studied with a dynamical Monte Carlo (of exactly the same sort I used in quantum optics, but the approach is quite general — set up a Markov process running in parallel with DE solution and with a correspondence between real time and “Monte Carlo Time”.
To make it concrete, start with a purely model rotating earth in sunlight, with heat capacity, and then add a noise term that causes (nucleates) albedo fluctuations. What does this do to the resulting temperature distribution? Break the surface up into equal area cells at some granularity and admit some sort of heat transport laterally (forbidden in the original model). What does this do? Give the heat transport some “inertia” (or hell, go ahead and make it crudely hydrodynamic with coriolis forces, a bullet that sooner or later you have to bite). What does this do? Adding the noise terms helps you identify instabilities, the additional dynamics, and maybe even the self-sustaining oscillations.
This is the kind of thing that would be a signature of being on the right track. A general model that spontaneously broke symmetry and created long-lived oscillations like the ENSO, PDO, AO, NAO etc would suggest that it is starting to have a lot of the right physics in it.
rgb

wayne
January 13, 2012 7:49 am

Robert Brown:
“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. ”
Shouldn’t the word in italics be horizontal in that case? You might want to fix it in the top-post. Caught while coding those, but that is a curious combination, might just program it anyway, no cold poles.

January 13, 2012 7:50 am

There is a nice infrared picture of the moon taken during an eclipse that shows that the surface temperature of the moon is not at all uniform.
Interestingly, there is surprisingly little right-left asymmetry, suggesting that over this sort of timeframe either little cooling has occurred or else it was overall so fast that it has already come into cool side equilibrium. I’d guess the former. R. Gates? Weren’t you suggesting that overall the temperature drop was fast enough to cause a substantial asymmetry (as points on one or the other side of this picture should have been “in the dark” for hours longer than points on the other)?
rgb

January 13, 2012 7:52 am

Must… stop… reading… Work… to… do… Arrrrgggh.
rgb
(Maybe I’ll come back later to catch up, sorry, gotta have a life and all that for a bit.)

RACookPE1978(@racookpe1978)
Editor
January 13, 2012 8:02 am

It appears essential that the atmosphereless, rotating, spherical, partially-gray “blackbody” problem be solved first. The “blackbody” idealized simulation that begins most CAGW scenarios is not worthless, but it does NOT even begin to describe ANY so-called “average” real world, much less the actual earth. Further, any CAGW model scenario that begins with an “average” radiation over an “average” flat-earth earth albedo over an “average” (non-rotating) day is worse than worthless.
This rotating “graybody” has, to a rough degree, been started by several writers that apply the moon’s approximate (average) albedo and (average) rotation to its theoretical blackbody characteristics, then try to factor the dwell delay of soil mass to “slow” the moon’s cooling each night. But, these early approximations need “calibrating” against actual lunar temperature sensor depth, actual lunar dust heat transfer coefficients, better heat capacity assumptions for the dust/rock combination at each lunar probe site, and accurate “calibration” of actual lunar temperatures against each site’s latitude. Also, the albedo changes on each face from the flat/darker lunar “Mares” to the crater-pocked rougher and lighter highlands need to become a part of this realworld “graybody” lunar calculator. (The varying “albedo-by-location-and-geography” factors for the moon will translate directly to the final earth’s albedo and physical-factors-by-location for the earth’s oceans and land masses.)
A program that can accurately back-calculate the moon’s temperature at all latitudes as it slowly rotates through the sun (simply and directly receiving radiation energy, moving it through conduction, and then re-radiating that energy WITHOUT the interferes of any convection, season changes, greenhouse gasses, surface gasses, winds and surface liquid phase changes!) is then a real-world start as we try to move from an idealized Einsteinian “thought experiment” of infinitely accelerating weightless elevators carrying twin brothers moving ever-closer to the speed of light to an design solution for temperatures within atmospheres. Adding surface soil heat capacities and depths, lunar soil emissivities, and actual rotation to the lunar calculator is the programming beginning to doing that for the earth’s calculator. Adding the complexities of varying solar radiation with day-of-year and latitude of the grid, and changing grid size with latitude for a lunar graybody program writes the same equations that need to be used for the earth’s more complex problem. After all,should not one be able to solve a “simple” problem without atmosphere and with no water before one begins “solving” a radiation problem with changing greenhouse gasses?
Then, after one’s computer program can correctly plot the moon’s actual temperatures in space across all latitudes across each lunar “day” exposure to the sun and the cold blackness of space, then one can begin to approximate the earth’s more complex geography of:
– vastly different albedoes (that vary somewhat with temperature and vary greatly with time-of-year!) on land from ground cover and geography (ice to tundra to prairie/steppe grasses to mixed forest/crops, to forests, to rocks, to deserts, to jungles, swamps and wetlands;
– vastly differing chemical reactions to heat (oceans and bare land and ice-covered land);
– vastly different absorption, reflection, re-radiation and movement of the surface heat energy and sub-surface heat flux
Now, one gets grossly simplified half-disk “averages” for radiation received, radiation emitted, and even worse whole-earth assumptions for average albedo. Polar circumstances are ignored – but the models are used to prove future arctic temperatures will rise catastrophically.

Tim Folkerts(@tjfolkerts)
January 13, 2012 8:09 am

HankHenry says: “There is a nice infrared picture of the moon …”
That is a cool image — thanks. I would warn that the conclusion that “the surface temperature of the moon is not at all uniform” is not6 necessarily true. False-color images like this often have the contrast enhanced to hightlight particular information. The difference in contrast in such a picture could correspond to ar range of only 1 C, or it could correspond to a range of 100 C. Without knowing the scale, it is difficult to conclude how uniform or non-uniform the temperature is.

Joe Postma
January 13, 2012 8:12 am

Hi Robert,
My strength is in analyzing logic and developing conceptual models that conform to reality. Such is why I was able to disassemble the standard “flat-earth” model of the GHE, and expose that it TRULY IS “flat earth” science! It’s not just in the toy models…it’s in the entire paradigm. The Earth ain’t flat. The Sun ain’t cold. Anyway…
Agreed on your point about albedo. An entirely miniscule change in albedo more than overshadows the supposed effect CO2 is pretended to have. When you consider that the average actual-surface albedo of the Earth is around 0.12, and that it is clouds which raise the average albedo to 0.3, then that means that very small changes in cloud cover dominate the average albedo, and therefore the average temperature of the Earth. This is one reason why the cosmic-ray connection in so important, and why solar activity is so important. It isn’t merely as simple as the variation in solar insolation, which is known to be finite but small…it is also the variation in solar magnetic activity which has a sort of “back-door” approach to affecting the climate. And of course this is aside from the fact that standard alarmist climate science can’t differentiate between the importance and meaning of correlation vs. causation.
What I will do then is try to finish the paper I am working on which describes the theory and math of this new model. I have taken the conceptual model from my paper – the model with the pretty colors – and written out the equations that would describe the insolation and the output for any given latitude and in real-time, for a spherical and rotating Earth. These equations then simply go into a differential heat-flow equation which I will also describe. I should be able to get enough of the idea down that others could then take it up and develop it further – I see the big picture but I get bogged down in details, but if the theory is good, then others could take it up from there.
If you just model the heat input and output, i.e. the energy, in a general heat-flow equation (identical to an RC-circuit equation with a time-dependent voltage), you don’t need to worry about all the intricate details of spectral absorption & etc etc etc. Just like you don’t need to model the intricate details of the workings of the capacitor in order to get a good model of the voltage in an RC-circuit. You just model the general conditions of the heat flow itself, given the known and measured parameters which affect & effect such. For WEATHER modelling, yes you might need more than that. But my intent is to present a new, general, fairly simple model which captures the boundary conditions of the real system. Which is something that the existing paradigm does not, because of the flat-Earth, cold-Sun problem it has.
I mean think about that – with Sunlight at only -18C, that means that the ENTIRE mass of the oceans is turned from ice into liquid by the greenhouse effect in the atmosphere. The tiny thin little atmosphere with an average temperature of -18C has a greenhouse effect which melts the entire mass of the ocean water to a higher temperature. As said: fundamental logical problems in the paradigm.
Great idea about an open-source project for a climate model. That would automatically be better science than the secret sauces of existing models.
(in software lingo, “sauce” = “source code” 😉 )

Joe Postma
January 13, 2012 8:27 am

“Bryan says:
January 13, 2012 at 8:07 am
How to determine the surface temperature with radiative and ground flux contributions is the missing link in atmospheric theory.
Kramm and Dlugi are working on a similar approach.
See equation 2.17
http://www.scirp.org/journal/PaperInformation.aspx?paperID=9233
——————————–
Gave a skim of that paper and it looks as though they are doing essentially what I’ve been thinking about, but in much greater and advanced detail. I’ll still write my own paper because it will still capture the essential features and logic of the new real-world paradigm, and in language and much simpler math that more people will be able to follow. Thanks for the link.

eyesonu
January 13, 2012 8:36 am

richard verney says:
January 13, 2012 at 3:15 am
A partial quote from your comment above of which should be read in its entirity:
“I have for years been suggesting that consideration needs to be given as to whether the oceans are effectively sitting on a warm hotplate and this is contibuting to keeping the deep ocean warm”.
==========
I have given thought to the same concept often. Adding to this potential ‘hot plate’ could also include an enormous amount of heat generated by the friction of the movement of the tetonic plates.
I don’t recall the temperature at the bottom of the Macondo (Deepwater Horizon) well, but it was considerable. I think it may have been on the order of 450 F at about 35,000 ft below mean sea level. An undersea ‘hot plate’ is an important factor in the sea’s energy budget it would seem. Heat from the friction of the plates movement could be tremendous.
If you can’t tax it, best not to discuss it?

mkelly
January 13, 2012 8:52 am

Pierre R Latour says:
January 13, 2012 at 7:18 am
“But it may not be absorbed by all bodies that intercept it, as GHG theory assumes.”
Concur. I have mentioned this several times here at WUWT.
Another item that really baffles me is the “bait and switch tactic” of going from radiative heat transfer equations to get 240 W/m^2 to energy balance. Why not do the entire problem using what they started with radiative heat transfer equations?

Tim Folkerts(@tjfolkerts)
January 13, 2012 8:56 am

Dr Brown says:
>I was distracted by the fallacy that non-GHG-containing atmospheres don’t radiate.
>Of course they do.
This is only a “partial fallacy” (if such a thing is not too much of an oxymoron). To me this is akin to saying “I was distracted by the fallacy that relativity doesn’t apply to bullets. Of course it does”. The principles apply, but the next question is about orders of magnitude. No one uses relativity to calculate the trajectory of a bullet, because any relativistic corrections are orders of magnitude smaller than the newtonian predictions.
From everything I have seen, N2 radiates orders of magnitude less IR energy that CO2 or H2O. Even given that there is much more N2 in the atmosphere, the numbers still suggest that GHGs radiate much more. And simple satellite data shows that when you look down, you see very nearly 1) a blackbody radiation curve at the temperature of the ground and 2) “bites” taken out of this curve by cooler GHGs high in the atmosphere. There is no “signature” of the cool N2, so there is no noticeable radiation from the N2.
Beyond this, there is “simple quantum mechanics” (again a bit of an oxymoron) that predicts symmetric diatomic molecules will not have any vibration modes or rotation modes at the energy levels involved that could absorb or emit IR radiation. I believe that Rodrigo Caballero’s Lecture Notes on Physical Meteorology ( http://maths.ucd.ie/met/msc/PhysMet/PhysMetLectNotes.pdf ) discusses all this, but I can’t seem to open it right now. (Maybe all the traffic from WUWT has overloaded the server).
So, yes it is absolutely correct that N2 radiates. But my understanding of theory and experiment suggests that N2 is orders of magnitude less effective at this than CO2. So if you had a container with a mixture of hot N2 & CO2, the N2 could lose some energy via radiation, but it would lose more by transferring energy to CO2 via collisions, and then having the CO2 radiate the energy to space.

Stephen Wilde
January 13, 2012 9:04 am

Joel Shore said:
“What correct physics principles would tell you is that a surface radiates according to its temperature (and its emissivity, which is a property of the surface). There is no “diversion” of surface energy to conduction. Any conduction that occurs is in addition to whatever radiative transfer occurs due to the surface’s temperature.”
That begs the question as to how the surface temperature gets set in the first place.
Start with an atmosphere free planet. Solar energy comes in and goes out pretty much instantly.
Add an atmosphere and the only way for the atmosphere to acquire the same temperature as the surface is to take energy from the surface via conduction. Energy must therefore be ‘diverted’ to conduction from upward radiation that would otherwise have occurred.
In due course the atmosphere equalises with the surface (if all other things were to be equal).
However the Ideal Gas Law then kicks in and due to gravity and pressure all the warmest molecules in the atmosphere are to be found directly above the surface with a declining upward temperature gradient.
Now those molecules at the surface are the warmest atmospheric molecules of all. Their wamth exceeds that of the average for the whole atmospheric column.
As a result they inhibit the upward radiation and conduction from the surface more than would have been achieved if the air molecules above the surface had simply been at the cooler average temperature for the whole atmospheric column. Obviously the warmer the molecules just above the surface become the warmer the surface needs to get in order to push enough energy past those warmer molecules so as to achieve the necessary radiative output to space to match incoming solar energy.
In disproportionately inhibiting upward radiation and conduction those warmest atmospheric molecules raise the equilibrium temperature of the surface beyond that which would have been expected from the S-B equations.

eyesonu
January 13, 2012 9:06 am

@ eyesonu
January 13, 2012 at 8:36 am
The Macondo well depth should read approx 24,000 ft below mean sea level rather than 35,000 ft. I still haven’t found the bottom hole oil temp.

mkelly
January 13, 2012 9:19 am

Joe Postma says:
January 13, 2012 at 8:12 am
“I mean think about that – with Sunlight at only -18C, that means that the ENTIRE mass of the oceans is turned from ice into liquid by the greenhouse effect in the atmosphere. The tiny thin little atmosphere with an average temperature of -18C has a greenhouse effect which melts the entire mass of the ocean water to a higher temperature. As said: fundamental logical problems in the paradigm.”
Mr. Postma add this to your thoughts. The corona of the sun is 1-3 million K, but nobody would suggest that the corona heats the sun. If that were true we should be using that temperature (1-3E6K) to figure our surface temperature not the surface of the sun’s 5700K.

HankHenry
January 13, 2012 9:30 am

Joe Postma,
Thank you for the links. It will take time for me to digest them. What I always want to account for in these discussions is radiation energy that penetrates oceans. I understand that it reradiates from the surface but what’s the real temperature that the ocean radiates at if the total ocean is only 5 or 6 or 7 degrees C.
I also believe that it is understood that heat radiated away at the poles causes chilled water at the surface to convect downward. Hence I want to say that the surface temperature at the poles does not indicate how much is truly radiating away because there is gradual “deep sixing” of water at a lower temperature. The ocean is not a black body.
Once I digest what you have to say about lapse rate this may get clarified for me.

RACookPE1978(@racookpe1978)
Editor
January 13, 2012 9:30 am

wayne says:
January 13, 2012 at 7:49 am
Robert Brown:
“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. ”
Shouldn’t the word in italics be horizontal in that case? You might want to fix it in the top-post. Caught while coding those, but that is a curious combination, might just program it anyway, no cold poles.

1. “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. ”
That term must be “conducting”, not superconducting”.
2. Should the heat “flow” be horizontal? Well, no. To see why, please change your “design” from a laboratory-size 1x1x1 meter cube into something reasonable for a whole radiating body of real-world size.
To explain: Take a 10 km x 10 km square, at any latitude, and compare two scenarios for a 10 km x 10 km square: the moon and the earth.
On earth, the temperature about 30 feet (10 meters) below any land surface stays a constant 60-65 degrees F, regardless of season of year (long term surface temperature changes) or time of day (short term radiation heat flow changes). Only as you go very deep (more than 600-1000 feet) do you begin seeing temperature increases from our volcanic interior. Therefore, the heat capacity dwell times (change in stored heat energy with time due to changes in radiation received, radiation emitted, wind, humidity, air temperature, albedo, ice-melting, etc) only happens in the top 10 meters of soil.
Obviously, a difference in temperature is required for heat transfer of energy, and, as long as your 10×10 km square does not cross from ocean to land, the difference between any two adjacent squares of land is very, very low compared to all other differences: especially those difference between the 10km x 10 km surface “up” to the air above that surface. But notice that you can limit the depth of your analysis “cube” to the depth from a greatly changing surface (the top 6 inches to 1 ft) down to a “constant” temperature lower end. All this means that your 10 km x 10 km square need only be 10 meters deep, and you can “program”‘ that lower surface to be a constant temperature in your differential equation parameter setups. Also, since your “heat exchange” through each side is a function of area, each side of your “analysis cube” is 10,000 meters x 10 meters. The “upper surface” and “lower surface” of your cube is much larger (10,000 x 10,000 meters). transmit many thousand times more energy than do the sides of the “cube”.
Water-covered and ice-covered 10×10 km squares are different: they can move heat up from the “bottom” surface by conduction, convection from that water underneath; and then move that energy even further by currents under the “cube” moving the heated (or cooled) water. Further, ice-covered 10×10 km squares put another insulating boundary between the top of the water and the air, which will then prevent evaporation of the water. The water (or ice) will reflect and absorb very different amounts of energy depending on the angle of the received radiation. At very low angles of direct solar radiation, such as the arctic ocean’s ice-covered areas up north as the ice melts, both ice and water reflect equally well. At lower altitudes, ice reflects much more energy than smooth water. Both ice and water emit nearly identical radiation thermally. Indirect radiation, coming in at higher angles than direct radiation in the arctic, will be more strongly absorbed than direct radiation by water-covered 10x10m km surfaces. makes things difficult, doesn’t it? 8<)
On the moon, things are much simpler: There would only be three kinds of surface conditions to program:
– solid, flat, smooth, dark rock with few cracks (the plains),
– largely solid gray rocky surfaces with some cracks (the highlands and mountains) and highly irregular surfaces like canyons, hills and mountains.
-highly cracked and dusty very small solids.
Each may be made of similar material, but the heat transfer and heat capacity and albedo of each of the three surfaces is very different. A dust-filled surface made up of small grains will be almost like an insulator, but a solid "lunar "sea" is going to transmit heat very well. The rocky mountains and highlands are going to be somewhat in the middle.
The moon is not expected to have a molten core, so we would not expect to see any heat increase with depth as you look at your 10 km x 10 km x 10 m "cube". The bottom of the craters at the lunar poles where the sun never shines should come out very, very cold – They can radiate "out" every second, but the only heat that can come into such a spot can come from what (very) little bit gets transmitted from the rocks up at the top lip of each crater where the sun does shine. The rest of the moon's "steady state" temperature will need to be calculated based on radiation losses from the upper surface and thermal dwell times – I don't think it is known right now

January 13, 2012 9:33 am

@eyesonu:

First, from east to west, the geothermal gradient changes from values between 0.025 and 0.03 K/m (0.014 and 0.016F/ft) off the AlabamaMississippi shore to lower values of 0.0150.025 K/m (0.0080.014F/ft) off eastern Louisiana and to higher values of 0.030.06 K/m (0.0160.033F/ft) off western Louisiana through Texas. Second, thermal gradients tend to be lower toward the outer continental shelf (less than 0.02 K/m [0.0112F/ft]). Abstract: Nagihara et al 2008

Forget Macando, it wasn’t a hot well. There was a very interesting paper at an AAPG convention in 2010 about the “Will K” well, as a deep-high temperature test. (cannot find my notes at the moment.) It was unsuccessful and caused the company to revise their thermal cutoff from 350 deg F to 325 deg F. Above that temperature, permiability was nil.

Tim Folkerts(@tjfolkerts)
January 13, 2012 9:39 am

Joe Postma makes me smile (but shake my head) when he says:
>My strength is in analyzing logic and developing conceptual models
>that conform to reality.
but then also says:
>1 Watt/m2 is 65 Kelvin. The ground beneath the surface is NOT 65 Kelvin.
>If I take a shovel and dig a hole 1 meter deep, the newly exposed ground
>WILL be radiating at its temperature, say 5C or 338 W/m2. So, that means
>the ground went from contributing 1 W/m2, suddenly to 338 W/m2, just
>because I dug a hole.
It is clearly time to go back and rework that model and that logic. I would suggest figuring out this simple situation before tackling the greenhouse effect.

Joe Postma
January 13, 2012 9:40 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.
However, there is another important point to consider, which Alan Siddon’s has discussed elsewhere: if the spectraly-neutral gases like O2 and N2 don’t radiate, that means that they collect heat-energy from the solar-heated surface by conduction, and then hang on to that heat: they can’t shed it, they can’t radiate it away spectraly, they just hold on to it. A “GHG”, on the other hand, once having absorbed heat energy from outside into its internal vibration, can then shed that energy by radiating it away. Not being able to lose and radiate the energy away, vs. being able to, should be the difference between a heat-trapping gas and a heat-shedding gas.
In fact, given my perspective from astrophysics, this is exactly the theory that we use to explain how interstellar gas-clouds are able to overcome the thermal response from gravitational collapse (potential energy converts to kinetic = temperature), and continue to collapse to form stars. The spectraly-emitting molecules in the gas (like CO2, but typically CO and others) provide a “vector” through which the thermal energy build-up of the collapsing cloud can escape the cloud. They absorb thermal energy via collision into internal degrees of freedom, then radiate that energy away, out of the cloud. This effectively “damps” the thermal response and then causes cooling. This allows the cloud to collapse into a star.
The thing is, the molecules in these gas cloud don’t just radiate outwards, they also radiate inwards, i.e., back-radiate. If I was thinking as a greenhouse effect alarmist, I would then have to think that the back-radiation from the molecules causes FURTHER temperature increase internally to the gas cloud, because half of the radiation will be directed inward. This would have the opposite effect of helping the cloud to cool to assist its collapse!
So we have two scenarios in which the exact same physical processes are going on, but in one it is theorized to cause warming (alarmist GHE) and in the other it is theorized to cause cooling (modern astrophysical theory). It’s one thing to question colleagues on conformism in climate science; it would be another thing entirely if I asked them to completely re-write the standard theory of star formation: sorry, but your molecules now cause heating, not cooling, you need to find another way to explain how stars form out of gravitationally-collapsing gas clouds.
[Some of the generation 1 stars which formed right after the big bang would have been extremely massive, and these can collapse in any case; thus having seeded the interstellar/galactic medium with heavier elements and molecules, the stage was set for later low-mass star formation like our Sun via the assistance from radiating molecules like CO2 (etc).]

RACookPE1978(@racookpe1978)
Editor
January 13, 2012 9:52 am

Joe Postma says:
January 13, 2012 at 8:12 am
Agreed on your point about albedo. An entirely miniscule change in albedo more than overshadows the supposed effect CO2 is pretended to have. When you consider that the average actual-surface albedo of the Earth is around 0.12, and that it is clouds which raise the average albedo to 0.3, then that means that very small changes in cloud cover dominate the average albedo, and therefore the average temperature of the Earth. This is one reason why the cosmic-ray connection in so important, and why solar activity is so important. It isn’t merely as simple as the variation in solar insolation, which is known to be finite but small…it is also the variation in solar magnetic activity which has a sort of “back-door” approach to affecting the climate. “

In trying to capture (or analyze) the effects of a changing cosmic radiation levels, and solar TSI and UV levels, and global cloud cover averages (global albedoes); look also at the earth’s magnetic pole positions and earth’s magnetic field strengths.
The recent changes in global temperature between 1600 to 2010 correspond to the position and movement of the south magnetic pole’s latitude as it moves away from the Antarctic coast out into the south Atlantic waters. Notably, the only area of the Antarctic heating up is the small strip of land sticking out into those waters. Up north, that overly simplified relationship doesn’t seem to be the case since today’s north magnetic pole is very close to where it was in the 1600’s.

HankHenry
January 13, 2012 10:01 am

On the subject of variability of albedo:
http://www.sciencedaily.com/releases/2004/05/040527233052.htm
It seems scientifically established that earth’s albedo varies.

January 13, 2012 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.
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.
That’s why Joe’s treatment kicked off the thought that all that is important is energy transfer, not how it happens.
rgb

Septic Matthew
January 13, 2012 10:16 am

Willis Eschenbach says:
January 12, 2012 at 4:32 pm
Thanks. I was almost sure that I was forgetting something. It’s weird that in thinking through complexities, I sometimes forget something obvious that I already know.
RGB, I thank you and others for the comments on this thread.
The spatio-temporal averages simply can’t be depended on to produce accurate approximations to needed quantities. (a) every place on earth has a different temperature from the global mean temperature almost all the time; (b) every place on earth has a different solar irradiance (measured at earth surface and at a higher level subtended by the small earth “place”) almost all of the time; (c) every place on earth has a different radiation, evaporation, advection and convection of energy from the means of these things, almost all the time, and this is true at every altitude. Illustrative calculations show that mean temperature, mean insolation, and mean radiation into space don’t relate meaningfully to each other. Given this, predicting the effect of adding CO2 is impossible at this time; CO2 will have different effects at different times of day, over different parts of earth, at different seasons, and at different altitudes, and a mean effect can’t be computed from some sort of mean (or total) change. As someone else wrote, it is necessary to know all of the rates of energy flow, not their thermodynamic equilibria, in order to estimate/predict the effect of adding CO2 to the present atmosphere. At least that’s what it looks like to me, and I think RGB and others have made the case well.

eyesonu
January 13, 2012 10:31 am

Stephen Rasey says:
January 13, 2012 at 9:33 am
@eyesonu:
First, from east to west, the geothermal gradient changes from values between 0.025 and 0.03 K/m (0.014 and 0.016F/ft) off the AlabamaMississippi shore to lower values of 0.0150.025 K/m (0.0080.014F/ft) off eastern Louisiana and to higher values of 0.030.06 K/m (0.0160.033F/ft) off western Louisiana through Texas. Second, thermal gradients tend to be lower toward the outer continental shelf (less than 0.02 K/m [0.0112F/ft]). Abstract: Nagihara et al 2008 …………….
===============
Thank you for your response. If the temp gradient were to become less as the outer continental shelf ia approached, would that imply that possibly the heat from the subsurface of the sea floor is being removed by the ocean waters? If so, then the deeper into the ocean that you go (closer to the earth core heat source) could show a lesser gradient that would prove the above suggestion that heat enters the ocean from a ‘hot plate’ effect as considered by richard verney (January 13, 2012 at 3:15 am).
I do not consider this to be completely off topic to the original article/post as the arguments concerning the atmospheric energy budget are all inclusive yet some seem to only focus on incoming solar radiation for a base line and in fact there may be another greater influence here on earth.
This is a most interesting discussion that has now spanned several threads. Keep it coming!

Bill Illis
January 13, 2012 10:50 am

Just noting there are large differences in the looking up (back-radiation) and looking down (emission) spectra when clouds are present.
Low level clouds create a perfect blackbody spectrum for the back-radiation and higher clouds have a little more atmospheric window in them but far, far less than the clear-sky back-radiation spectrum.
When viewing the spectrum looking down from space and there is low cloud, the outgoing radiation is emitting from 10km high at 220K in the CO2 spectrum and otherwise it is emitting from 3 kms high at the cloudtops at 265K.
When clouds are not present, the spectrum is the same 10 kms high at 220K for the CO2 spectrum and now we have atmopsheric windows emitting at 288K or the surface along with water vapour and methane bands emitting at around 250K or 5 kms high.
The spectra are governed by the temperature of the layer where emission starts to become possible directly to space in that particular spectrum.
Clouds make a big difference on the looking up or looking down spectrum and clouds are present up to 65% of the time. Furthermore, nobody seems to know that Modtran has cloud cover options in it (clear-sky is selected as the default) since these options are NEVER charted on the internet.

January 13, 2012 10:51 am

Tim Folkerts says:
January 13, 2012 at 8:56 am
“And simple satellite data shows that when you look down, you see very nearly 1) a blackbody radiation curve at the temperature of the ground and 2) “bites” taken out of this curve by cooler GHGs high in the atmosphere. There is no “signature” of the cool N2, so there is no noticeable radiation from the N2.”
This is apparent. The question I have is, where does the “bite” get taken out?
What data do we have showing emission curves versus altitude? Is it even possible to determine this?
Is the emission curve from space uniform over the Earth? Or, is it an average over the entire Earth? If it is non-uniform, over what regions is the bite most pronounced?
What accounts for the fact that the two regions before and after the “bite” do not conform to the same blackbody curve (one side is representative of a ~300K isocline, and one ~275K).
And, on a side note, what is the “signature” of radiation from non-GHGs due to collisions? Is it necessarily the same as for spontaneous emission?