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 agree with you here. I agree that it does not look like a single temperature body, and this is why I have said here in a few places that it looks more like a T^4.6 function, which would produce the effect you describe. As to exactly where the holes come from… Some bands are so highly absorptive that you could see them in the spectrum from a couple of meters above the surface; whereas others are weaker and do not develop fully until a substantial thickness of atmosphere is passed. I don’t know enough IR spectroscopy to tell you myself which are which.
Joe Postma says:
January 13, 2012 at 5:41 pm
“Otherwise, without that spectral radiation, the gas would just continue to heat because the energy wouldn’t be able to escape via radiation.”
This is a rather fascinating observation, and on the one hand, it would be just desserts if it turned out that the added CO2 were actually cooling the planet. However, in 30 years when we are at the bottom of the incipient cooling part of the natural ~60 year cycle, I foresee that it will be seized upon to argue that we are driving the Earth into a new deep freeze, and the only thing to do is hand unaccountable power over to the political class to deal with it by drastically lowering the standard of living for those not of the nomenklatura.
eyesonu says:
January 13, 2012 at 8:36 am
//////////////////////
eyesonu
You are right to point out the energy involved in techtonic plate movement and a by product of which must be heat going into the oceans.
Following the Japanese Tsunami (last March/April – I can’t recall the exact dates), I posted a comment on one of the threads (discussing the Tsunami/nuclear issues) raising this very point.
I firmly consider that oceanic geomechanical and geothermal issues have not been adequately considered.
What about atmospheric tides? These are mostly thermal, rather than gravitational, but represent another form of energy transfer from the Sun to Earth besides temperature. They also influence the upward transfer of energy back towards space.
Here is a very preliminary integration test set. Apologies in advance if there are any mistakes within.
These numeric integration cases were created taking Dr. Brown’s suggestions in the top post above. I have highlighted a few average temperatures that most of you will recognize. The first is the figure you will find in the IPCC reports and seems what current climate science is built upon. The second you will find within Dr. Nikolov & Zeller’s poster summarizing their paper. They are all hypothetically smooth cases and have not been thoroughly tested, so if you question them, run your own integration to verify.
The cells are cosine weighted using normal Simpson rule interpolation to find the exact center point of the cells. Latitudinal, the cell spacing is every degree. Latitudinal, the spacing is every three degrees. These were chosen for efficiency, but, running a test at 0.1 degree spacing in both dimensions returned the same results up to the fifth digit of precision. So these use 10800 points on the globe and the finer resolution was using 3,240,000 points on the globe. Funny, very little difference but the latitude direction is much more sensitive to the cell spacing and that does make sense due the decreasing area of latitude bands. The solar temperature was set to 5774 K to give a TSI of 1362.3 W/m^2 which seems very close to today’s readings.
These can also be used to evaluate the moon, for none of the case have an atmosphere yet, so the 0.12 albedo cases are close for both the Earth and the moon at this point.
Dr. Brown’s words in quotes.
[A case]
“Start with a non-rotating superconducting sphere, zero albedo, unit emissivity, perfect blackbody radiation from each point on the sphere. What’s the mean temperature?”
This run leave all points on the entire globe at equal temperatures, both lit & unlit sides:
254.6 K, 0.30 albedo, 1 emissivity
272.8 K, 0.12 albedo, 0.955 emissivity
278.4 K, 0 albedo, 1 emissivity
[B case]
“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.”
Rotating or non-rotating, non-conducting.
This run leaves all points on the globe at different temperatures:
154.3 K, 0.12 albedo, 0.955 emissivity
157.5 K, 0 albedo, 1 emissivity
[C case]
Rotating or non-rotating, superconducting only vertically or only horizontally.
This run leaves all points latitude-wise at the same temperatures:
165.8 K, 0.12 albedo, 0.955 emissivity
168.2, 0 albedo, 1 emissivity
[D case]
Rotating or non-rotating, superconducting only vertically or only horizontally.
This run leaves all points longitudinal-wise at the same temperatures:
179.5 K, 0.12 albedo, 0.955 emissivity
183.2 K, 0 albedo, 1 emissivity
[E case]
Rotating or non-rotating, superconducting on lit side only
This run leaves the temperatures of all points the same on 1) the lit side and 2) the dark side:
192.9 K, 0.12 albedo, 0.955 emissivity
196.8 K, 0 albedo, 1 emissivity
After looking at these results, to me is seems the case D with an actual albedo and emissivity would be the one showing the moon’s true average temperature. Just a hunch.
You will notice the emissivity and albedo have just a few degrees of variance while the differences between each case is much larger.
Now to add the capability for rotation and thermal inertia at the surface interface. First in the soil and oceans, later an atmosphere.
– Wayne Jackson
Kevin Kilty,
I should have been a little more specific. I meant “The ‘entire profile’ from the ground is known to be very close to a blackbody curve AT GROUND LEVEL WHERE IT IS EMITTED.” By the time you are a few km up, then the “bites” due to GHGs begin to show up. If N2 had any major effect, then you should see the absorption or emission from N2 affecting the spectrum more and more as you go up. But even above the entire atmosphere, there is no hint of any effect of N2 shown in the satellite images I have seen. There is no hint of any effect of N2 in calculations of spectra for the atmosphere. (people can play around with the calculations here: http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.html)
Joe Postma says: January 13, 2012 at 5:41 pm …
Joe, I would prefer sticking to my planet-in-a-nebula case. Stars have many complicating factors (they DO have gravitational heating, they have nuclear energy, the plasma is good at absorbing/emitting radiation so they don;t need polyatomic molecules to radiate, … )
You never addressed my conclusion –> the planet-in-a-nebula will cool slower than the naked planet. Can you argue in this simple case that I am wrong? (BTW, I am pretty sure I can argue that even your protostar situation leads to a warmer star if there is a surrounding cocoon of GHG, so even that doesn’t support your conclusions.)
Wayne,
I like your work on calculating the various radiative balances. I haven’t confirmed them independently, but they seem reasonable.
One note: when Dr Brown said ‘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. ” I am 99% sure he meant that it conducts heat in a truly vertical direction (ie into/out of the ground). Your C & D instead allow heat conduction north-south or east/west, both of which are “horizontal”. They are still interesting cases, but not the next step Dr. Brown was envisioning.
richard verney @ur momisugly January 13, 6:42 pm
Richard, concerning geothermal stuff, I’m sorry, I can’t remember the commenter’s name, (you maybe?), but there was mention on another thread that the oceanic crust is generally very much thinner than the continental, with uhm erh implications.
Furthermore, that at some of the depths spoken of for the oceans, it would be rather hot at the same depth on land. AND, sea water is a far better conductor of heat than rock, and being so cold at the water’s bottom, it would seem to be a HUGE heat sink via conduction and convection/advection. (T1 – T2). I don’t know what assumptions were involved in others suggesting that average geothermal heat loss is only ~0.08 W/m^2 (I recall ?), but seeing how hot it can be in deep mines, intuitively, given an apparently better conduction path, it don’t look right to me for over 70% of the surface.
Incidentally, I’m no geologist, but I suspect that the greater sedimentary layering on the continents, resulting in more conduction interfaces, and some rocks such as sandstones and limestones notionally being perhaps the worst conductors, there seems to be a big curly: ?.
Bob Carter, where are you? Help!
Some may wonder why I was using Simpson’s rule to calculate the cosine weights.
Let’s say your cell spacing is 30 degrees, using huge cells to divide up a sphere. At first glance some might just chose 15 degrees for middle of the cell and take the cosine of that, but you will find your results are skewed to high, for cos(15) gives 0.966 which is really to large. You need to take (cos(0)+4*cos(15)+cos(30))/6 to give 0.955 or the cosine at 17.2626 degrees which is much, much closer to the actual average of the cosines of all points in one dimension within that cell, when squared it gives you the best “center”. (wonder if IPCC knows that trick?)
Further, (cos(0)+3*cos(10)+3*cos(20)+cos(30))/8 is Simpson’s 3/8th rule and is even closer to the actual mean of the cosines across each dimension in the cell, the cosine of 17.2652 degrees.
Most here know it well, but just in case someone here had never happened across that neat “trick”, just had to put it out, it can save you from being WAY off in many cases.
A commenter has pointed out an error in my descriptions of the integration cases. Thank you.
These should have read: (somehow my changes got reverted)
[C case]
Rotating or non-rotating, superconducting only vertically. (very unrealistic)
[D case]
Rotating or non-rotating, superconducting only horizontally. (very realistic)
davidmhoffer: If the Earth absorbes 240 w/m2, then it emmits 240 w/m2.
Unless it’s warming or cooling. Whether it’s warming or cooling, and whatever CO2 may be doing to (transiently) change the balance of incoming and outgoing, are the unknowns. You seem to assume what everyone else wants to test.
davidmhoffer quoting Joe: “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.”
The variation within the bounds of that incredible 4-billion year stability is not negligible for human and other life, and is indeed the topic of the AGW debate. The arguments based on thermodynamic equilibria are inadequate to determine whether a doubling of CO2 will produce a transient change in the surface temperature distribution or rainfall distribution sufficiently to reduce crop production disastrously. The argument is that by reducing the rate of radiation of heat the CO2 will cause an increase in temperature until at some time, when the earth surface has heated, the eflux matches the influx.
All you have shown is that the CO2 does not change the equilibrium rate of eflux. How does this matter in a system that has never been in equilibrium?
davidmhoffer: The laws of thermodynamics require this statement to be true. The amount of net loss of energy in high latitudes must balance, to the last photon, the net absorption in low latitudes.
Again you are assuming what has to be decided: whether there is or is not net accumulation of energy on the earth, either now, over the last 10 years, over the last 150 years, over the last 10,000 years, or whenever; and whether CO2 accumulation affects that net accumulation, if it occurs
You have shown that if the total heat content of the climate system can not change, then CO2 changes can not change it.
Septic Matthew;
Unless it’s warming or cooling. >>>
Don’t be silly, I said “at equilibrium” half a dozen times in first comment. The debate revolves around what the actual equilibrium temperature because we can’t calculate any of the other numbers (like GHE) unless we know that first. I’m not assuming anything and actually stipulated otherwise.
Tim Folkerts;
The OTHER effect of CO2 is to move the location of the radiating surface from the ground level up higher in the atmosphere. Some of the radiation comes from the very cold upper atmosphere and some comes from the ground, with the net result being 240 W/m^2 on average. This has been discussed multiple times and until people understand the implications of this, they will continue to misunderstand the GHE.>>>
Agreed. My point was that CO2 only moves the location from which radiance is emitted to space, not the amount that is emitted to space. This applies to both geographical location (decreased emission in the tropics, increased at high latitudes) but the exact same thought process applies to altitude as well, thanks for bringing that up, I’d missed it.
Myrrh;
Shrug. >>>
Gee, you stole my response to you. Thread after thread you ask for proof of this thing or that thing and when it is offered to you, your response is, yeah but I want proof. 2+2=4 and Myrrh hollers, yeah, but I want proof. Well, here’s two pospsicle sticks Myrrh and here’s two more popsicsle sticks and if we put them together and count….one, two, three, four…to which the inevitable rebuttal from Myrrh arrives…. yeah, but I want proof. To which I reply with my new stock answer to your serial idiocy. Shrug.
Stephen Wilde;
I agree, it seems incredibly obvious but only once the bulb lights up in the mind. There are so many out there that will fight tooth and nail against any such ideas that it is going to be an uphill struggle.>>>
So…you’re saying the lights aren’t on over at Joel’s place…. 😉
Joel Shore;
Congratulations, David. You used to make fun of posters who claimed that the greenhouse effect violates the laws of thermodynamics (and the Second Law specificially). Now you have become one of them…and, like them, you make that claim on the basis of no evidence whatsoever.>>>
I’m sorry that you can’t follow the logic nor the physics and so understand neither my explanation of the matter currently being discussed, nor how it differs from isolated and specific instances of radiation balance. The GHE is of course a real change in energy transfer that can be measured and verified. The notion that the GHE breaks the laws of thermodynamics isn’t correct. What is ALSO not correct is that one can determine if the earth is gaining or losing energy by averaging T instead of T^4. what is further not correct is that a change in CO2 levels results in an energy imbalance rather than an energy redistribution that results in a higher average T without changing average T^4 and average P. If you cannot understand these dead simple issues, then I have little choice but to relegate you to the Myrrh bin. Shrug.
Joel Shore;
(2) Come up with an explanation of how you can take GHGs away and still have the current average radiative emission that the Earth’s surface has.>>>
But that is exactly what my previous comments explain. Shrug.
Joel Shore;
(1) Show that if one averages T^4 instead of T, the warming seen disappears. Good luck doing that, as Essex & McKitrick (& one other co-author) have already tried…>>>
The point was to understand what the actual theoretical average black body temperature of the earth is when properly calculated so that we can COMPARE to the observed temperatures and determine how much should be allocated to insolation and how much to GHE. REALLY JOEL? YOU DIDN’T GET THAT?
Shrug.
wayne says:
January 13, 2012 at 8:00 pm
Interesting analysis, wayne. Props for running the numbers yourself.
All the best,
w.
Septic Matthew;
The arguments based on thermodynamic equilibria are inadequate to determine whether a doubling of CO2 will produce a transient change in the surface temperature distribution or rainfall distribution sufficiently to reduce crop production disastrously. The argument is that by reducing the rate of radiation of heat the CO2 will cause an increase in temperature until at some time, when the earth surface has heated, the eflux matches the influx.>>>
Given that an increase in CO2 must result in an increase in P (w/m2) that in turn results in an increase in T (degrees K) at earth surface, let us put aside for a moment the question of what the equilibrium temperature of earth actually is or isn’t and simply demonstrate what an idiotic statement this is when the fact that P varies with T^4 is taken into account. Let us consider the tropics, temperate zones and arctic zones to be at “average” temperatures of +30C, +10C and -20C respectively. Let us further use 3.7 w/m2 as the accepted increase in P at earth surface for a supposed doubling of CO2 (direct effects only for this example).
For an additional 3.7 w/m2, the increase in “average” temperature would be:
Tropics +0.58 degrees
Temperates +.72 degrees
Arctics +1.0
Now let’s take the next step and see how that “average” temperature change is distributed. too many combinations and permutations to bother doing them all, particularly when we only need to do one to demonstrate the issue at hand. Let’s use the temperate zones with Winter, spring, summer and fall “average” temps of -20C, +10C, +30C and +10C which “average” to plus 10. The increase in each of those due to 3.7 w/m2 would be:
Winter +1.0
Spring +0.72
Summer +0.58
Fall +0.72
See the pattern emerging? The tropics heat up the least, the arctic zones the most. Agricultural ouptut doesn’t get adversely affected a whole lot by +.58 and the warming in the temperates actually moves the “average” temperature into a temperature range that his MORE beneficial to agricultural output in the temperates and arctics, not LESS. But wait! There’s more!
Those numbers are WRONG!!!!!!
I added 3.7 w/m2 to the “average” temperature in the temperate zones and calculated via SB Law that the “average” temperature went up by 0.72 degrees. But then I took four values for the different seasons that average to the exact same number, but this time, I calculated the temperature increase for each season due to 3.7 w/m2 on a season by season basis. The average of those numbers isn’t 0.72, it is 0.75! Uh oh, which one is right?
Neither. We haven’t accounted for daily fluctuations. Let’s just consider winter and summer with a daily temperature fluctuation of 16 degrees. That would mean that the “average” day in winter would range from -28C to -12C and the average day in summer would average from 22C to 38C. (OK, I may have picked an unrealistic range but I typed too much to go back and start over so just live with it, focus on the principle being illustrated). That would give us for an additional 3.7 w/m2:
Winter night time low +3.3
Winter day time high +2.7
Summer night time low +0.63
Summer day time high +.54
See the pattern more clearly now? Winter night time lows go up 3.3 but summer day time highs go up only 0.54. Do we grow crops in winter at -20C? No? Then plus 3.3 is immaterial to crop production, and an increase of day time highs of 0.54 is neglible.
Of course if you average those numbers you won’t get the same amount as adding the 3.7w/m2 to the seasonal average either. Which one is right?
Neither. The numbers are STILL wrong. Why? So glad you asked!
The “average” increase in P from a doubling of CO2 MIGHT be 3.7 w/m2, but the increase at any given point on earth surface will almost (almost) NEVER be 3.7 w/m2. The GHE is based on upward bound LW being absorbed by CO2 and then re-radiated back to earth surface. OK,let’s walk through a couple more easy SB Law calcs.
In the tropics at +30C, the upward bound LW is 478 w/m2
In the arctic at -20C, the upward bound LW is 232 w/m2
OK geniuses, can someone exlain to me how doubling of CO2 can, when exposed to upward bound LW of 478 w/m2 return 3.7 w/m2 and how the exact same concentration of CO2 when exposed to 232 w/m2 returns 3.7 w/m2 also? Of course it doesn’t.
So if you’ve followed all of this the take aways are:
1. The most warming for a given increase in w/m2 occurs at night time lows, in winter, in the arctic zones.
2. The least warming for a given increase in w/m2 occurs at day time highs, in summer, in the tropics.
3. In other words, the warming occurs the least where it could do potential harm and the most where it can only improve conditions.
4. Averaging T to understand a change in energy balance is hopelessly useless.
5. Averaging P from a doubling of Co2 is equally nonsensical.
There can be no usefull discussion about how much the earth is warming, if the earth is warming, how much GHE raises the surface temperature, what the actual equilibrium blackbody temperature is, or if we are in a positive or negative energy balance if we do not first understand the implications of P varying with T to the 4th power.
Hey. I forgot to include the variance introduced by altitude and terrain. T at the top of as mountain versus T in the valley below. Then I also left out the fact that the earth orbit is elliptical and so P varies a few percent over the course of the year from that. I also left out the Gore effect which has to be added in by tracking the location of Al Gore at any given time “on average” and since we have no clue how the Gore Effect works and what factors govern the magnitude at any given time or place of the Gore Effect,the task of coming up with any meaningful numbers to base any discussion on is that much more impossibler.
Septic Matthew;
Again you are assuming what has to be decided: whether there is or is not net accumulation of energy on the earth, either now, over the last 10 years>>>
Please Matthew, try and keep up.
The whole point of the explanation is that we CANNOT draw any conclusions about the energy balance from trending of temperature data. The whole point of my explanation was to show that there can be a change in uniformity of the planetary temperature that would be interpreted from the trending and averaging of T to be an increase in accumulated energy when, in fact, no increase had occurred.
In order to determine how much of any given temperature trend is due to ACTUAL energy imbalance and how much is due to NO change in energy balance but a change in distribution of temperature, all we’ve got is a bunch of numbers and a bunch of trends that mean nothing. It is possible, as I have demonstrated through simple examples in other threads, to produce a scenario in which the “average” temperature is increasing while the earth is actually LOSING energy, not gaining it.
I haven’t assumed a single thing. I have shown why the assumptions regarding the trending of temperature data are false and misleading.
wayne says:
January 13, 2012 at 8:35 pm
That’s slick, and I like the use of Simpson’s rule, but it’s roundabout and at the end of the day still an estimate.
When I area weight, I do it by the actual area. As a percentage of the total sphere, the area between two latitudes Lat1 and Lat2 is given by ( sin(Lat1) – sin(Lat2) ) / 2. For your example, 0-30° N latitude is a quarter of the globe,
Additionally, if you are doing the whole globe, this method lets you use a simple sum of the weighted values to give the weighted average.
All the best,
w.
@ur momisugly Wayne
Yes Thanks for trying the integrals.
I can’t help but think the non-conducting case is nearest to reality. Perhaps look at the post a few days ago from Willis with actual on Moon temperature observations and his first pass at estimating heating and cooling rates. These may suggest approximately the low rate of conduction and some sort of heat capacity for the near surface few metres.
However the rate of rotation will also make a significant difference.
Nikolov and Zeller also had 154 K, perhaps its time for some interaction with them? Or to suggest some revision or qualification to their poster?
I wonder if Anthony has given consideration to a specific page for
“Crowdsourcing” modelling and “sauce”.
Perhaps in “References” or “Resources”?
It may need to include sections such as
Blackbody or SB calculations
Albedo Models
Atmosphere models
GHGs and how they effect the atmosphere models
In relation to Albedo, P.R. Goode, E. Palle´ / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1556–1568 suggest up to 10% change in albedo from clouds over two decades (up to 1998).
Also from remote observation, Tyler D. Robinson, et al. Astrobiology. June 2011, 11(5): 393-408. doi:10.1089/ast.2011.0642. say 4 different cloud types are needed to get a vaguely reasonable model of the albedo of Earth as measured from space.
The atmosphere and albedo model sensitivities will be complicated before getting to GHGs.
The “Team” have spent millions of manhours on the GHG part, perhaps when the basics have been defined, some of them may be prepared to contribute.
David M Hoffer,
Thank you for finding the link to the NASA satellite data showing net in-flow and out-flow of energy spatially across Earth’s globe. I had seen it so long ago I did not know where to find it again. NASA’s own data proves beyond a shadow of a doubt that local radiative balance does not occur across most of the earth’s surface. In the lower latitudes the average temperature is below that which it should be in local radiative balance. The opposite is true at the higher latitudes. The excess incoming energy in the lower latitudes must go somewhere if the temperatures there are to stay stable at values below that required for local radiative balance. That somewhere can only be in one direction: orthogonal to the incoming radiation, i.e. parallel with the earth’s surface. The very fact that the poles are hundreds of degrees above the temperature at which they should be if driven only by incoming solar radiation means that some other place on the face of the earth must be below the temperature at which it should be for the local incoming solar radiation flux. That is the true meaning of the parameter “average global temperature”. If heat is really flowing from the equator to the poles, mathematics states beyond a shadow of a doubt that these deviations from local radiative balance must occur. NASA’s data say it does.
That last sentence leads me to an interesting yet disturbing aside. Ever notice how Alaska and the Arctic are the showcase for global warming because their temperatures are increasing two or three times faster than the average global increase? For that to be true, and I do not doubt that the measured temperature rise is true, someplace else on the earth’s surface of equal area must be decreasing in temperature in order for the average world-wide temperature increase to be only 1 degree. Where is that place? Another way to reach the average of a 1 degree global increase is for the temperature to decrease slightly over the rest of the planet to average out the large increase in the north. Is that global warming? You could also achieve the small average global increase with a large increase in the north even if no other place in the world is increasing its temperature. Would that constitute global warming? The only variable that changes to create these different scenarios is the relative surface area of the warming and non-warming or cooling regions. And yet I do not hear questions in the community about the non-warming or cooling regions. Where are they? What is the temperature doing in those regions? Do these regions move around constantly or do they remain in the same geographical region all the time? I ask this question because the above-average warming is sticking to one spot, the Arctic. When global maps of temperature change over the previous 30 years are released by researchers, does the average change across the entire map equal the average change in the temperature record? This is middle school mathematics and any valid model must withstand this type of evaluation.
The spatial distribution of the heating gives an indication of what is happening to the earth’s stored heat. If the heat flow to the poles slows down, they will cool while the lower latitudes will heat up. If the poles heat up while the lower latitudes remain the same, more energy must be entering into the surface system. If the lower latitudes retain more heat due to carbon dioxide in the atmosphere, the poles will heat up as more energy is transferred in that direction at a higher rate. If the poles heat up and the lower latitudes cool slightly, the earth is losing energy. If the poles heat up enough to melt the ice caps, the earth will lose energy fast and the lower latitudes will cool more quickly.
When writing my first post last night, I realized an answer to question of whether the greenhouse effect is a real phenomenon. This answer is a resounding YES! It can be proved using the same trigonometry I used last night. In my previous post, I approximated values for NASA’s energy budget numbers, which can be found at
http://earthobservatory.nasa.gov/Features/EnergyBalance/page4.php
I simplified that budget to 50% absorbed at the surface, 25% reflected by the atmosphere and surface, and 25% absorbed by the atmosphere. Keep in mind that this absorbed energy is from the energy in-flux from the sun and is not from the earth’s surface as heat. Therefore, that special 1 square meter column of atmosphere at the equator at high noon sees 25% x 1366 or 341W/m2. 341W/m2 is the average value across the entire globe so we can assume that if that square meter column of atmosphere at the equator at high noon was in radiative balance only with the incoming energy, it would be at 288k or there abouts. As that square meter rotated away from high noon, its temperature would fall. At any latitude north or south from the equator, the incoming energy absorbed by the local atmosphere will be less so, everywhere else on the face of the earth besides the equator at high noon, the atmosphere should be colder than the average global temperature of the earth as a black body, a grey body, or a greenhouse body! We know that this is not true, especially those folks in New York City that see 32C (90F) in the summer at their latitude. If we ignore magnetic field coupling, the solar wind, cosmic rays, or other yet-to-be-explored incoming energy sources, the only other source of energy to enable the atmosphere to remain at its elevated temperature is the warmer ground. Energy transfer from the ground to the atmosphere will take place by conduction, convection, and radiative transfer. I am not an expert in the area of fluid thermodynamics so I cannot begin to construct the equations to describe how the atmosphere is warmed but it is beyond doubt that it is warmer than it should be in radiative balance with the incoming flux. Hence, the greenhouse effect.
How much does carbon dioxide contribute to that warmth is an excellent question. It most likely does since the physics are relatively easy to prove. Does it balance the local radiative transfer in and out of the system? No because the local temperatures in the lower latitudes remain lower than they should be in balance with the sun during daylight. How will it affect the transfer of energy to the poles? It helps because it increases the heat content of the air which is then moved by weather and the Coriolis effect to the poles to be released. It probably also reduces heat loss at night when the energy flow for the surface goes only one way -> out. This is good because if the temperature dropped so far every night that ice formed everywhere every night, things would not be good for us. It is startling that the rate of Earth’s rate of rotation is exactly right so water does not freeze everywhere every night! That could happen if our day was twice or three times as long.
“I’m having just a bit of difficulty with this, in the context of the extended discussion on radiative balance. Although (as I’ve said) I’m withholding judgement until I’ve done the integrals, it appears to be strictly true that radiative loss is always favored by higher radiation temperature inhomogeneity. In other words, moving heat from the tropics to the poles cools the tropics and heats the poles so it provides a more uniform temperature, but a more uniform temperature is always a warmer temperature on average because in fact you lose heat far faster from the hot tropics than you do from the poles.
In fact, “most” of the net heat (the gain) absorbed during the day in the tropics is lost during the night, at least in any sort of naive static BB model.”
It seems that most energy loss occurs in the tropics. And tropic ocean doesn’t change in much in terms of temperature. But the tropics have a lot of heat to lose.
The tropics should be absorbing more joules of energy as compared to anywhere else, and dumping more joules of energy into space- in terms of joules of energy per sq meter. The tropics also is 40% of the surface area of the planet, to poles have.. well antarctic is “The total surface area is about 14.2 million sq km” earth is 510 million. So say 30 million for both pole 5 % of surface. And the poles are cold so can’t radiate much energy.
I would say it this way, the pole allow the tropics to absorb more energy.
So if no poles to give heat to, then tropic region absorbs less energy.
So Poles extracting a low tax rate, which doesn’t affect the tropics heat wealth.
If government were so wise as poles, we would have a better world.
Hmm, so what does that do with theory that antarctic is major cause of the last tens of million of years of cooler global climatic?
Let’s see, how energy could be transported to Antarctic from tropics per second?
Well first when tropics are near the poles, summer or winter [either pole] the distance is less and and if wind going same speed- no that will not make any difference.
How about this the atmosphere is equal to 10 meters height of water- only some portion of this can the transporting medium- and it high atmosphere so air density is much less. I am sure it’s less, but most it could equal the equivalent of 1 meter or water. Whereas you an ocean of water will probably transporting tens of sea water [per square meter surface area]- per mass water carries more energy than water. Though if tropics is transporting to pole as water vapor this can a lot of energy per mass, one very water vapor in high altitudes.
The other factor in term of the Antarctic the rotation air mass [entire atmosphere] which circles the Antarctic land mass. It seems the entire atmosphere and oceans have to be transporting more energy and the roaring nineties are going affecting the temperate regions, and ocean current going to tropics.
So what’s all this mean?
Well the tropics aren’t really involved much with this last tens of million of years of cooling- tropics are unchanging- very stubborn area.
I would say, it’s the roaring nineties are bigger effect. Hmm, no I give up. Wait- it seems if earth isn’t closest when southern hemispere is in summer- would get bigger sea ice around the Antarctic. You have deep water with ice floating on top of it exposing huge surface area to ocean water. Maybe this is lowering tropical sea surface temperature.
That’s seems unlikely.
It seems difficult to see how south arctic is affecting northern hemisphere where one getting all the glaciation.
So, got to go with arctic ocean sea ice melting – and that through various means cools northern hemisphere.
More ice around antarctic, more rain in Africa, and snow all over northern hemisphere.
Northern hemisphere cover ice and cold, is much large area than arctic. Arctic cold front, become North America and European cold fronts.
In current situation American and Europe are buffer states, when ice covered and cold, there are disrupting the tropics. And tropics are dumping moisture at them.
Let see, what is significant about Antarctic is it is cold and it has [with all it’s ice] a very high average elevation.
Oh here something:
“The winter sea-ice cover at the LGM [Last Glacial Maximum] was, therefore, twice the modern surface. Similarly, the LGM summer sea-ice edge was projected northward of its modern position, overlying the modern winter sea-ice margin (Fig. 2). The summer sea-ice cover was, therefore, 6-7 times greater than modern extent.”
http://pages-142.unibe.ch/products/newsletters/2007_2/Special%20section/Crosta_2007-2%2813-14%29.pdf
According graph in ref, the Antarctic sea ice it gets close to reaching the 45 parallel- or if compared to north hemisphere that reaches down to US. [49th parallel is most US/Canadian- west of Ontario. Or all of UK and the tip northern part of Japan].
Maybe with large area having sea ice and large amount cold water dropping into ocean something like Gulf Stream is drive huge amount warm surface ocean towards the south pole- having cooler surface in tropics would have global affects.
Joe ponders”
The short answer is that that place is the “top of the atmosphere”.
Adding more CO2 raises the average altitude for emission of IR. Higher altitudes are colder, so the CO2 will emit less IR.
I have a bunch of the basic climate numbers separated into each 10 degree latitude band.
Surface area, Albedo, Solar Forcing, Average Temp, Resulting Greenhouse Effect (which would include the temperature re-distribution from the equator to the poles through atmospheric circulation).
http://img24.imageshack.us/img24/9751/climatefiguresbylatitud.png
I can probably put this up in a spreadsheet if someone wants.
Bill Illis or anyone.
Does anyone have a link to a satellite obtained IR spectrum looking down at night?
I would like to compare it with one obtained during daytime .
I should have said that the numbers are off a little as a total but one would need more accurate numbers for solar forcing etc. (four decimal points really) than I have been able to find.