Guest Post by Willis Eschenbach
When I’m analyzing a system, I divide the variables into three categories—first-, second-, and third-order variables.
First-order variables are those variables that can change the system by more than 10%. Obviously, these must be included in any analysis of the system.
Second-order are those that can change the system by 1% to 10%. These are smaller, but still too large to overlook.
Finally, third-order variables are those than can change the system by less than 1%. These are small enough that they can be ignored in all but the most detailed analyses. To give you an idea of why we can neglect the third order variables, here’s how those three forcings would look on a graph, for an imaginary signal of say 500 W/m2.
Figure 1. Showing the relative sizes of first-, second-, and third-order variables.
Note that the series containing the third-order variable is almost invisibly different from the series where the third-order variable is left out, which is why third-order variables can be safely ignored except when you need extreme precision. So … what does this have to do with climate science?
Let’s do the same kind of analysis on the forcings of the climate system. At the TOA, the “top of atmosphere”, there is downwelling radiation from two sources: the sun, and the longwave “greenhouse” radiation from clouds and “greenhouse” gases (GHGs). The globally-averaged amount of downwelling solar radiation at the earth’s TOA (which is total incoming solar radiation less a small amount absorbed in the stratosphere) is on the order of 330 watts per square metre (W/m2). The amount of downwelling longwave radiation at the TOA, on the other hand, is about 150 W/m2.
Finally, if CO2 doubles it is supposed to change the downwelling radiation at the TOA by 3.7 W/m2 … here’s how that works out:
Figure 2. Sources of downwelling radiation at the top of the atmosphere (TOA), defined as the tropopause by the IPCC.
By that measure, CO2 doubling is clearly a third order forcing, one that we could safely ignore while we figure out what actually makes the climate run.
Or we could look at it another way. How much of the earth’s temperature is due to the sun, and how much is due to the earth’s atmosphere?
If there were no atmosphere and the earth had its current albedo (about 30%), the surface temperature would be about 33°C cooler than it currently is (see here for the calculations). Obviously, downwelling longwave radiation from the greenhouse gases is responsible for some of that warming, with DLR from clouds responsible for the rest. Cloud DLR globally averages about 30 W/m2 (see here for a discussion). So the 150 W/m2 forcing from the GHGs is responsible for on the order of 80% of the 33° temperature rise, or about 25°C.
But if 150 W/m2 of GHG forcing only warms the surface by 25°C, then the so-called “climate sensitivity” is only about 25°C warming for 150 W/m2 of TOA forcing, or a maximum about six tenths of a degree per doubling of CO2, or about 0.2% of the earth’s temperature … again, it is a third order forcing.
Now, if someone wants to claim that a change in the forcings of less than 1% is going to cause catastrophes, I have to ask … why hasn’t it done so in the past? Surely no-one thinks that the forcings have been stable to within 1% in the past hundred years … so where are the catastrophes?
Finally, most of the measurements that we can make of the climate system are imprecise, with uncertainties of up to 10% being common. Given that … how successful are we likely to be at this point in history in looking for a third-order signal that is less than 1% of the total?
w.
PS – In any natural heat engine of this type, which is running as fast as the circumstances permit, losses rise faster than the temperature. So in fact, the analyses above underestimate how small the CO2 effect really is. This is because at equilibrium, losses eat up much of any increase in forcing. So the effect of the CO2 at general climate equilibrium is less than the effect it would have at colder planetary temperatures. In other words, climate sensitivity is an inverse function of temperature.
PPS – Please don’t point out that my numbers are approximations. I know that, and they may be off a bit … but they’re not off enough to turn CO2 into a second-order forcing, much less a first-order forcing.
PPPS – What is a first-order climate variable? Clouds, clouds, clouds …
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Glenn Tamblyn: So too the supposedly ‘small’ impact from CO2 is more than enough to have a significant impact.
Nicely written. You expanded my point well.
I do not believe AGW, but this post by Willis Eschenbach has cavities.
Joel:
“It is all in balance — there is no “storage”. (Well, if there is a slight imbalance, then there could some storage and a subsequent increase in global temperature.)”
I don’t get it. If I increase the temperature of 1 gram of dry air by 1 degree C, I have STORED 1 joule of energy in that gram of air. I see no way that the atmosphere is not storing a tremendous amount of energy at all times, and this has consequences via the gas laws. This Of course, there is still a balance, as you say.
Tim Folkerts says:
October 6, 2011 at 2:26 pm
“Both solar photons and DWLR photons provide energy to the surface.”
Yeah but DWLR photons are immediately rejected by the ocean without raising either the water or air temperature. LWIR is absorbed in the first micron of surface water and only serves to raise the evaporation rate. The energy is then contained within the water molecule as latent heat of vaporization which of course rises upwards as soon as it is liberated from the ocean.
People need to understand that radiative cooling plays a very small role in ocean heat budget which is dominated by evaporative cooling.
Tim Folkerts says on October 6, 2011 at 2:26 pm:
“Changing either the absorbed solar photons or the absorbed DWLR photons by 10 W/m^2 will have the same effect on temperature.”
Just out of curiosity Tim; have you ever been present, outside in the open air at the place and time when a “Total Solar Eclipse” takes place? – If you have, then you will know that during the, fortunately, short time of total solar absence there is a considerable temperature drop. – Unfortunately, for validation of your statement, DWLR cannot be blocked in quite the same manner.
However if you have got proof, other than theoretical, to back up your statement, then I shall be more than willing to read about it.
jae says:
“I don’t get it. If I increase the temperature of 1 gram of dry air by 1 degree C, I have STORED 1 joule of energy in that gram of air. “
Actually, I was the one who made the comment you were responding to.
Of course, as the air warms during the day, it will be absorbing energy, and during the night it will be emitting energy. During the spring it will be gaining energy and during the fall it will be losing energy.
But the average for the year is (very close to) zero. There is no “rest of the energy” that is continuously being added to the atmosphere. Or perhaps I misunderstood what you meant when you said “The SURFACE may be emitting 390 wm-2, but the EARTH is not emitting 390 wm-2; it is emitting only what it receives–240. The rest is stored in the atmosphere.” What “rest” were you referring to?
jae says:
Okay, so where in the atmosphere is this infinite heat sink that can store energy accumulating at a rate of 150 W/m^2 ?!?!
Do you realize how ridiculous it sounds?
O H Dahlsveen asks:
Just out of curiosity Tim; have you ever been present, outside in the open air at the place and time when a “Total Solar Eclipse” takes place?
Unfortunately I have only seen a partial eclipse. Even that was enough to provide noticeable cooling. An eclipse is certainly one way to block the direct sunlight, which could be close to 1000 W/m^2 at noon with the sun overhead. And this will certainly cool the earth dramatically.
Unfortunately, for validation of your statement, DWLR cannot be blocked in quite the same manner. However if you have got proof, other than theoretical, to back up your statement, then I shall be more than willing to read about it.
There are some applications that use I similar principle to provide cooling by blocking IR. For instance, google “cold mirrors” that are designed to only reflect visible light and not IR. As the name implies, this limits the heating by the beam by removing the IR. (in this case, it is mostly an effect of near IR, not thermal IR, but the principle applies.)
You could also look at the plans for this solar cooker/IR cooler http://solarcooking.org/plans/funnel.htm . By blocking IR, it allows water to freeze even with air temperatures well above freezing. This is closer to your “eclipse” example. The foil “blocks” the IR from the ground and other warm surroundings, substituting the cool IR from the sky, (much like the eclipse substitutes light from the dark side of the moon for the much warmer sunlight).
Of course, for my original statement to be wrong, then conservation of energy would have to be wrong. I suppose you could call that simply “theoretical”, but conservation of energy is one of the very best established principles, so overturning it would take some extraordinary evidence.
Joel:
“Okay, so where in the atmosphere is this infinite heat sink that can store energy accumulating at a rate of 150 W/m^2 ?!?!
Do you realize how ridiculous it sounds?”
??????? Is this a strawman? Did I mention an infinite heat sink? Did I say the atmosphere is ACCUMULATING energy? What the hell are you saying, fella?
What I AM saying is that the atmosphere CONTAINS a certain amount of heat energy–on average enough to maintain an “average global temperature” of 15 C. I can’t see any flaw in that statement.
I maintain that the atmosphere is also radiating to space about the same amount as the Sun is radiating to the Earth. Is there something wrong with that statement?
The atmosphere and oceans are also STORING VAST AMOUNTS OF ENERGY (HEAT) in the form of kinetic and potential energy (you guys seem to agree that the oceans can store heat, and even “hide” it somehow, but you don’t seem to acknowdge that the atmosphere stores heat, also???). I guess because it can’t “hide there?”
I still think that the stupid radiation cartoons ignore real physics. But maybe I am just a nut.
Speaking of orders of magnitude, I note that the change in outgoing IR energy flow seem looking down from 99 km up, I₀, as reported by MODTRAN (unreliable as it may be) hosted by the University of Chicago, appears to show a change only on the order of a half of a percent in clear tropical air when only the CO2 concentration is changed from the supposed pre-industrial level of 280 PPM to a near modern level of 396 PPM, (a 41.4% change) or from 289.163 W/m² to 287.561 W/m² energy leaving the Earth with the same default ground temperature. I believe MODTRAN only calculates on the basis of the raw properties of the gases with no climate feedback assumed.
jae,
Perhaps you would like to clarify your statement:
“The SURFACE may be emitting 390 wm-2, but the EARTH is not emitting 390 wm-2; it is emitting only what it receives–240. The rest is stored in the atmosphere”
What specifically do you mean by “the rest” and how is is being “stored”? How is it related to the 390 wm-2 and 240 wm-2 you were referencing?
Tim:
“But the average for the year is (very close to) zero. There is no “rest of the energy” that is continuously being added to the atmosphere. Or perhaps I misunderstood what you meant when you said “The SURFACE may be emitting 390 wm-2, but the EARTH is not emitting 390 wm-2; it is emitting only what it receives–240. The rest is stored in the atmosphere.” What “rest” were you referring to?”
I guess I’m not being clear about the “rest.” All I am saying is that the air gains and disposes of a certain amount of energy day-to-day, season-to-season. Which is exactly what you are saying, I think. The DIFFERENCE is that there is no magic “atmospheric greenhouse effect,” only a gain and loss of energy, day-to-day.
It takes a certain amount of energy to keep the air temperature at it’s current levels. THAT IS THE “REST.” It is “heat storage.” Same with the ocean, which also stores heat (but which nobody seems to question).
Tim: Thanks. You say:
“Perhaps you would like to clarify your statement:
“The SURFACE may be emitting 390 wm-2, but the EARTH is not emitting 390 wm-2; it is emitting only what it receives–240. The rest is stored in the atmosphere”
What specifically do you mean by “the rest” and how is is being “stored”? How is it related to the 390 wm-2 and 240 wm-2 you were referencing?”
Tim: don’t you think it takes a certain amount of energy to maintain the atmosphere at an average of 15 C? All those molecules of air have to have some kinetic energy to make that “average thermometer” register 15 C, right? Don’t you think that means that the quadrillion, quadrillion, quadrillions of molecules in the atmosphere have to receive energy every day to maintain that temperature/molecular motion/ energy? Doesn’t that mean that those molecules are, at any given time, STORING ENERGY? Are they just passive radiation machines????
Do you think that the “radiation” makes the thermometer read 15 C? If so, you need a review of physics 101 (it’s molecular motion that makes that makes the thermometer rock).
SO, the “REST” is the amount of energy that it takes to keep the atmosphere at that magic average temperature of 15 C. .
Please let me know where that does not make sense.
According to wikipedia, a human male has about 2 square meter of skin. That is approximately 1 sq meter per side. So, if you lie outside naked at night in the dead of winter, you will be receiving (according to Willis’ chart above) 350 watts from the earth and 325 watts from the GHG, for a total of 675 watts. That is almost 1 HP of energy from the earth and sky radiating on the human body.
For sure that amount of energy will without any problem keep you warm and toasty. Contrast this will the meager 200 watts your body receives on average from the sun, or the 150 watts the human body produces. We should replace solar panels with IR reflectors to channel the energy from the gound and the sky to power our cities, as it is apparently so much greater than solar energy.
mkelly says:
October 6, 2011 at 9:38 am
This shows that K&T equate IR with sunshine. The two are not the equal in their ability to do work or heat my sun tea. I believe this is what Ferd in talking about.
You’ve hit the nail on the head.
“Willis Eschenbach says:
October 4, 2011 at 11:51 pm
Downwelling DLR, however, is at about 320 W/m2, which equates to a blackbody temperature of about freezing (0°C).”
In your diagram above it shows solar energy at the surface of earth is about 200 watts/m2 on average. In other word, K&T equate the effects of the sun at the surface with a blackbody temperature of about MINUS 30 C !! I’m pretty sure that the sun does not work that way, that it is not equivalent to a blackbody at -30C, or we caould not use it to heat water or power solar panels. As such the K&T analysis that AGW rests on is bogus.
RE: R. Gates: (October 5, 2011 at 2:19 pm)
“Especially important is the LW absorption of CO2 at around 15 microns. The fact that CO2 has this high absorption right at the peak where the bulk of the LW is coming from the ground and that CO2 is a non-condensing gas is key to our greenhouse world:”
Actually, while the 15 micron or 667 kayzer (cycles per centimeter or CM-1) CO2 hole is near the peak point of emission, it only blocks or reduces a fraction of the total flow. At 99 km up,(according to MODTRAN) the half-depth width of the CO2 hole is about 100 kayzers wide in a stream that has an overall half-peak-flow width of about 950 kayzers, including the CO2 band.
I believe that the non-condensing nature of CO2 is the reason that it is *less* important than H2O, where attempted condensation due to electric attraction during collisions between these sticky water molecules in the atmosphere can increase the probability that unusual, absorption-unlikely, LW photons will be generated.
Fred says:
“In other word, K&T equate the effects of the sun at the surface with a blackbody temperature of about MINUS 30 C !! I’m pretty sure that the sun does not work that way, that it is not equivalent to a blackbody at -30C, or we could not use it to heat water or power solar panels. ”
Several people seem to have this strange notion that black body temperature is determined by the power arriving at an arbitrary location. The black body temperature is determined by the power LEAVING the SOURCE (*). As stated above, the sun has a BB temperature of ~ 5800 K and delivers ~ 6,000,000 W/m^2. K&T are, I am sure, fully aware that the BB temperature of the sun is indeed ~ 5800 K and are not equating the sun’s photons with any temperatures of – 30 C.
By the time the photons have reached earth, they have spread out to ~ 1370 W/m^2. This does not mean they have cooled off to ~ 395 K! They still are “5700 K photons”. By cleverly focusing the these photons, we could in principle warm an object as high as ~ 5800 K .
By the time some of the photons have been reflected by clouds and the remaining photons have been averaged over the entire surface of the earth, power is down to ~ 170 W/m^2. This does not mean the photons have cooled off to ~ 235 K! By cleverly focusing the these photons, we could still in principle warm an object as high as ~ 5800 K.
However, once the photons have been absorbed, these solar photons cease to exist. The earth will radiate its own photons. The EARTH would have the BB temperature of ~ 235 K. And you are right, THIS energy from “235 K photons” cannot be focused (because they are already coming from every direction, unlike the sunlight) to warm anything above 235 K. (If you add in the ~ 70 W/m^2 that are absorbed by the atmosphere, this gives the more typical BB temperature of ~ 255 K.)
* The one exception I know of is due to the expansion of the universe. “Hot photons” that were emitted ~ 13 billion years ago when the universe was ~ 3000 K have “cooled” to form the current 3 K microwave background radiation.
Thank you Tim Folkerts for your response on October 6, 2011 at 6:41 pm which I found to be, in keeping with all/most of what you write, very good, interesting and informative and I now have got some more studying to do as most of it was new to me. – Well, that is to say I have no quibbles with the “conservation of energy” bit. – I shall not trouble myself trying to disprove that one.
jae says:
October 6, 2011 at 6:44 pm
I still think that the stupid radiation cartoons ignore real physics.
It does ignore physics, because it equates sunlight with IR radiation from the sky to form an “energy budget”. Here is the reason why this is wrong:
K&T treat the earth and sky as black bodies that radiate 350 and 325 w/m2, which corresponds to the average temperatures of the surface and sky of 15C and 0C. Under K&T, 200 w/m on average from the sun is added to these figures to form an “energy budget”.
Addition is only valid if the sun, earth and sky are equivalent. Thus, the K&T treatment means we must be able to equate the sun to a black body as large as the sky and the laws of physics will still hold.
Now, 200 w/m2 is equivalent to a black-body as big as the sky with a temperature lower than 0 C, something like – 30 C according to one on-line calculator. So, if the K&T treatment is correct, then we should be able to replace the sun with a black-body the size of the sky at -30 C and the physics of the earth, the climate would be unchanged.
However, that is nonsense. If you replaced the sun with a black-body that filled the sky at – 30 C the earth would freeze. Therefore you cannot treat the energy from the sun equivalent to the black-body IR from earth and sky. Therefore the K&T energy budget for the earth is WRONG and as such much of the basis for AGW is wrong.
Tim Folkerts says:
October 6, 2011 at 2:26 pm
Sunlight has the energy concentrated in a small number of photons, while the thermal IR has the energy spread out over a larger number of photons.
Have we a count of these numbers? If so what is it? Is there a ratio? Please explain this.
Mr. Folkerts a couple of questions: If I have two tourches, whose flames are a says 6000 F, and I point one torch a a plate of steel what is the max temperature the steel can attain? IF I now point the other torch at the same spot and have two 6000 F torch pointing to the same spot on the steel what is the max temperature the steel can attain? I have doubled the W/m^2 of the point on the steel. I have doubled the items providing temperature to the steel. If I now take away one torch and the W/m^2 of that torch what will happen to the max temperature that can be attained by the plate of steel?
Say for instance that the K&T treatment is correct, then if we replaced the sun with another black-body equivalent to the earth and sky, then at TOA the average radiation from the sun would be something like 1368/4 = 342 W/m2 averaged over the entire globe.
So, it K&T are correct, then we could replace the sun with a sphere of energy circling the earth at the TOA and the temperature of the earth would remain unchanged. However, 342 w/m2 correlates to a black body temperature of much less than the current surface temperature, because according to K&T, the surface radiates 392 w/m2
Thus, according to the 2nd law of thermodynamics, the sun could not warm the earth using K&T’s own figures at TOA, because as a black-body that fills the sky, the sun is already colder than the surface of the earth.
Clearly this is contrary to observation, because the sun does warm the earth. This means you CANNOT treat a hot point source of energy equivalent to a large source of energy at a lower temperature, even though they both appear to be radiating the same amount of w/m2.
Also, we know from Carnot’s theorem that efficiency depends on the temperature ratio between the cold and hot side of the engine. There is a large temperature ratio between the earth and sun, but only a small temperature ratio between the earth and sky.
This alone suggests that it is not appropriate to simply add and subtract w/m2 between energy sources at different temperatures the way K&T have, because they will have different efficiencies.
mkelly says:
October 7, 2011 at 7:31 am
If I have two tourches, whose flames are a says 6000 F, and I point one torch a a plate of steel what is the max temperature the steel can attain? IF I now point the other torch at the same spot and have two 6000 F torch pointing to the same spot on the steel what is the max temperature the steel can attain?
A very good example that shows that temperature is not determined by w/m2.
Wow. There are some fascinating questions. Fortunately, physics can still provide the fascinating answers.
mkelly asks: If I have two tourches, whose flames are a says 6000 F, and I point one torch a a plate of steel what is the max temperature the steel can attain? IF I now point the other torch at the same spot and have two 6000 F torch pointing to the same spot on the steel what is the max temperature the steel can attain?”
Since we were discussing radiation and black bodies, let me re-frame this as a 6000 F tungsten filament in an “electric torch” (ie an incandescent light bulb).
In principle a single 6000 F filament would be able to heat an object to 6000 F. Just place the 6000 F flame/filament at one focus of a perfectly reflecting ellipsoid and place the object to be heated at the other focus. The object will “see” the filament no matter which way you look, so the object “thinks” is it surrounded by a sheet of 6000 F tungsten (ie all 4 pi steradians will be sending “6000 F photons” at the object).
COROLLARY 1) no amount of refocusing will raise the temperature of the object any higher than 6000 F.
COROLLARY 2) adding a second filament in this case will not make the object any hotter.
In practice you won’t have a 100% reflective surface. You also will not have an ellipsoidal mirror completely surrounding the filament and object. You could make some difference in the heat transfer by putting a mirror behind the filament (like a flashlight uses to concentrate light toward one spot) or putting a mirror behind the object (like a solar collector).
The temperature of the object being heated depend on the W/m^2 of the heater, but the final result has to also include the solid angle of the heater.
Fred suggests: “So, if K&T are correct, then we could replace the sun with a sphere of energy circling the earth at the TOA and the temperature of the earth would remain unchanged. “
That’s a great thought experiment! Assuming that all other factors in the diagram remained the same, the nthe results would indeed be the same.
However, there are some significant “first order” differences (getting back to the language of the original post!) that would affect the diagram drastically. The surface and clouds are great absorbers of IR, so the albedo in this case would be very close to 0, rather than 0.3) — this would tend to make the surface even WARMER than now. However, the radiation going both directions would essentially be the same set of wavelengths, so the idea of “transparent to visible light” disappears. Since this is a key factor in the GHE, this would destroy most of the GHE — which would tend to make the surface COOLER.
Given two first order changes in opposite directions (and given that I can’t make a reliable “back-of-the-envelop” calculation to know which is bigger), it would be hard pressed to know if the planet would be warmer or cooler in this circumstance. The idea of a lapse rate suggests that the plant could and wold still be warmer at the surface than the ~ 255 K BB temperature of the posited uniform 255 K radiator.
Fred also suggests “According to wikipedia, a human male has about 2 square meter of skin. That is approximately 1 sq meter per side. So, if you lie outside naked at night in the dead of winter, you will be receiving (according to Willis’ chart above) 350 watts from the earth and 325 watts from the GHG, for a total of 675 watts. That is almost 1 HP of energy from the earth and sky radiating on the human body. “
But a 2 m^2 37 C person will be radiating ~ 525 W/m^2, or nearly 400 W more than they are receiving = ~ 100 cal/s = ~ 0.1 Cal/s. Rather than being “toasty warm” from the incoming radiation, you will be radiating away a net ~ 8000 Cal per day. Rather than this radiation keeping you warm and toasty without any problem, the actual net radiation would require massive food intake to keep from freezing!
Tim Folkerts says:
October 7, 2011 at 1:07 pm
Fred suggests: “So, if K&T are correct, then we could replace the sun with a sphere of energy circling the earth at the TOA and the temperature of the earth would remain unchanged. “
That’s a great thought experiment! Assuming that all other factors in the diagram remained the same, the nthe results would indeed be the same.
Not they would not, because the sun radiates on average 342 w/m2, which equates to a black-body temperature of 279K, or 6 C. The 2nd law tells us that the temperature of the earth could not exceed 6 C if you can treat sunlight as a black body.
However, the earth is 15 C, and since there is no other heat source that could warm the earth beyond 6C, this “proof by contradiction” shows you cannot treat sunlight as equivalent to black-body.
Thus, the T&K energy budget cartoon above, which does treat sunlight as equivalent to black-body radiation is false, because it leads to a logical contradiction that violates the 2nd law of thermodynamics as demonstrated.
Please look to see if this is wrong, folks:
Say we have a planet way out in space with no atmosphere, no water, but a Sun. Kinda like the moon. Now, remember that we don’t have any GHE or atmosphere at all on this planet.
Now, say we ADD an atmosphere of pure NITROGEN to that planet which is equivalent in molecular composition (number of molecules) to one atmosphere on Earth. That means we would have about 14.7 psi “air” pressure at the surface. 100 pascals. 29 mm Hg.
The Ideal Gas Law says that the temperature of that planet would have to increase by 12 K:
PV = nRT;
T = PV/nR
R = 0.082 atm. L/mol.K
Hold V = 1 litre, constant amount of N2 (mol volume) and let P increase to one atmosphere.
We would thereby increase the Temp. by 1/0.082 = 12 K
So, the “GHE” has already been reduced from 33 C to 33-12 C = 21 C.
And this difference is easily explainable by considering the amount of heat storage by the oceans and the air.
No GHE required.