By Robert G. Brown, Duke University (elevated from a WUWT comment)
I spent what little of last night that I semi-slept in a learning-dream state chewing over Caballero’s book and radiative transfer, and came to two insights. First, the baseline black-body model (that leads to T_b = 255K) is physically terrible, as a baseline. It treats the planet in question as a nonrotating superconductor of heat with no heat capacity. The reason it is terrible is that it is absolutely incorrect to ascribe 33K as even an estimate for the “greenhouse warming” relative to this baseline, as it is a completely nonphysical baseline; the 33K relative to it is both meaningless and mixes both heating and cooling effects that have absolutely nothing to do with the greenhouse effect. More on that later.
I also understand the greenhouse effect itself much better. I may write this up in my own words, since I don’t like some of Caballero’s notation and think that the presentation can be simplified and made more illustrative. I’m also thinking of using it to make a “build-a-model” kit, sort of like the “build-a-bear” stores in the malls.
Start with a nonrotating superconducting sphere, zero albedo, unit emissivity, perfect blackbody radiation from each point on the sphere. What’s the mean temperature?
Now make the non-rotating sphere perfectly non-conducting, so that every part of the surface has to be in radiative balance. What’s the average temperature now? This is a better model for the moon than the former, surely, although still not good enough. Let’s improve it.
Now make the surface have some thermalized heat capacity — make it heat superconducting, but only in the vertical direction and presume a mass shell of some thickness that has some reasonable specific heat. This changes nothing from the previous result, until we make the sphere rotate. Oooo, yet another average (surface) temperature, this time the spherical average of a distribution that depends on latitude, with the highest temperatures dayside near the equator sometime after “noon” (lagged because now it takes time to raise the temperature of each block as the insolation exceeds blackbody loss, and time for it to cool as the blackbody loss exceeds radiation, and the surface is never at a constant temperature anywhere but at the poles (no axial tilt, of course). This is probably a very decent model for the moon, once one adds back in an albedo (effectively scaling down the fraction of the incoming power that has to be thermally balanced).
One can for each of these changes actually compute the exact parametric temperature distribution as a function of spherical angle and radius, and (by integrating) compute the change in e.g. the average temperature from the superconducting perfect black body assumption. Going from superconducting planet to local detailed balance but otherwise perfectly insulating planet (nonrotating) simply drops the nightside temperature for exactly 1/2 the sphere to your choice of 3K or (easier to idealize) 0K after a very long time. This is bounded from below, independent of solar irradiance or albedo (or for that matter, emissivity). The dayside temperature, on the other hand, has a polar distribution with a pole facing the sun, and varies nonlinearly with irradiance, albedo, and (if you choose to vary it) emissivity.
That pesky T^4 makes everything complicated! I hesitate to even try to assign the sign of the change in average temperature going from the first model to the second! Every time I think that I have a good heuristic argument for saying that it should be lower, a little voice tells me — T^4 — better do the damn integral because the temperature at the separator has to go smoothly to zero from the dayside and there’s a lot of low-irradiance (and hence low temperature) area out there where the sun is at five o’clock, even for zero albedo and unit emissivity! The only easy part is to obtain the spherical average we can just take the dayside average and divide by two…
I’m not even happy with the sign for the rotating sphere, as this depends on the interplay between the time required to heat the thermal ballast given the difference between insolation and outgoing radiation and the rate of rotation. Rotate at infinite speed and you are back at the superconducting sphere. Rotate at zero speed and you’re at the static nonconducting sphere. Rotate in between and — damn — now by varying only the magnitude of the thermal ballast (which determines the thermalization time) you can arrange for even a rapidly rotating sphere to behave like the static nonconducting sphere and a slowly rotating sphere to behave like a superconducting sphere (zero heat capacity and very large heat capacity, respectively). Worse, you’ve changed the geometry of the axial poles (presumed to lie untilted w.r.t. the ecliptic still). Where before the entire day-night terminator was smoothly approaching T = 0 from the day side, now this is true only at the poles! The integral of the polar area (for a given polar angle d\theta) is much smaller than the integral of the equatorial angle, and on top of that one now has a smeared out set of steady state temperatures that are all functions of azimuthal angle \phi and polar angle \theta, one that changes nonlinearly as you crank any of: Insolation, albedo, emissivity, \omega (angular velocity of rotation) and heat capacity of the surface.
And we haven’t even got an atmosphere yet. Or water. But at least up to this point, one can solve for the temperature distribution T(\theta,\phi,\alpha,S,\epsilon,c) exactly, I think.
Furthermore, one can actually model something like water pretty well in this way. In fact, if we imagine covering the planet not with air but with a layer of water with a blackbody on the bottom and a thin layer of perfectly transparent saran wrap on top to prevent pesky old evaporation, the water becomes a contribution to the thermal ballast. It takes a lot longer to raise or lower the temperature of a layer of water a meter deep (given an imbalance between incoming radiation) than it does to raise or lower the temperature of maybe the top centimeter or two of rock or dirt or sand. A lot longer.
Once one has a good feel for this, one could decorate the model with oceans and land bodies (but still prohibit lateral energy transfer and assume immediate vertical equilibration). One could let the water have the right albedo and freeze when it hits the right temperature. Then things get tough.
You have to add an atmosphere. Damn. You also have to let the ocean itself convect, and have density, and variable depth. And all of this on a rotating sphere where things (air masses) moving up deflect antispinward (relative to the surface), things moving down deflect spinward, things moving north deflect spinward (they’re going to fast) in the northern hemisphere, things moving south deflect antispinward, as a function of angle and speed and rotational velocity. Friggin’ coriolis force, deflects naval artillery and so on. And now we’re going to differentially heat the damn thing so that turbulence occurs everywhere on all available length scales, where we don’t even have some simple symmetry to the differential heating any more because we might as well have let a five year old throw paint at the sphere to mark out where the land masses are versus the oceans, and or better yet given him some Tonka trucks and let him play in the spherical sandbox until he had a nice irregular surface and then filled the surface with water until it was 70% submerged or something.
Ow, my aching head. And note well — we still haven’t turned on a Greenhouse Effect! And I now have nothing like a heuristic for radiant emission cooling even in the ideal case, because it is quite literally distilled, fractionated by temperature and height even without CO_2 per se present at all. Clouds. Air with a nontrivial short wavelength scattering cross-section. Energy transfer galore.
And then, before we mess with CO_2, we have to take quantum mechanics and the incident spectrum into account, and start to look at the hitherto ignored details of the ground, air, and water. The air needs a lapse rate, which will vary with humidity and albedo and ground temperature and… The molecules in the air recoil when the scatter incoming photons, and if a collision with another air molecule occurs in the right time interval they will mutually absorb some or all of the energy instead of elastically scattering it, heating the air. It can also absorb one wavelength and emit a cascade of photons at a different wavelength (depending on its spectrum).
Finally, one has to add in the GHGs, notably CO_2 (water is already there). They have the effect increasing the outgoing radiance from the (higher temperature) surface in some bands, and transferring some of it to CO_2 where it is trapped until it diffuses to the top of the CO_2 column, where it is emitted at a cooler temperature. The total power going out is thus split up, with that pesky blackbody spectrum modulated so that different frequencies have different effective temperatures, in a way that is locally modulated by — nearly everything. The lapse rate. Moisture content. Clouds. Bulk transport of heat up or down via convection. Bulk transport of heat up or down via caged radiation in parts of the spectrum. And don’t forget sideways! Everything is now circulating, wind and surface evaporation are coupled, the equilibration time for the ocean has stretched from “commensurate with the rotational period” for shallow seas to a thousand years or more so that the ocean is never at equilibrium, it is always tugging surface temperatures one way or the other with substantial thermal ballast, heat deposited not today but over the last week, month, year, decade, century, millennium.
Yessir, a damn hard problem. Anybody who calls this settled science is out of their ever-loving mind. Note well that I still haven’t included solar magnetism or any serious modulation of solar irradiance, or even the axial tilt of the earth, which once again completely changes everything, because now the timescales at the poles become annual, and the north pole and south pole are not at all alike! Consider the enormous difference in their thermal ballast and oceanic heat transport and atmospheric heat transport!
A hard problem. But perhaps I’ll try to tackle it, if I have time, at least through the first few steps outlined above. At the very least I’d like to have a better idea of the direction of some of the first few build-a-bear steps on the average temperature (while the term “average temperature” has some meaning, that is before making the system chaotic).
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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.
Some things to think about…
@Bill Illis
I always find your posts interesting and informative. These two sentences caught my eye:
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.
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.
Wow, the colossal waste of ingenuity, perpetrated by activists.
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?
Please allow me to illustrate.
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.
Robert Brown wrote:
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.
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!
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.
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.
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.
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.
markx says:
January 12, 2012 at 5:58 pm
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.
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.
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
Tim Folkerts says:
January 12, 2012 at 7:14 pm
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.
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.
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).
Surfer Dave says:
January 12, 2012 at 6:10 pm
@Tim_Focketts
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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. .
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.
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.
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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.
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].
Stephen Wilde says:
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.
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.
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
“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.”
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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:
http://www.tech-know.eu/uploads/Understanding_the_Atmosphere_Effect.pdf
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.
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.”
Look forward to your paper.
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