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 …
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One point to keep in mind is that the measure of power flow in watts per square meter or W/m² is a property of a surface in three-dimensional space. It may refer to the surface of a real object or a mathematically defined surface. A given value may be valid at only one point on that surface or it may be true for the whole surface. In the real world this value usually changes with position on the surface, just as temperature also changes with position.
If you were in a room having a constant, uniform temperature, you would see the same power level and thermal electromagnetic radiation level in W/m² coming from every surface you looked at. This fact was used in the Pierce Brosnan remake of the movie “The Thomas Crown Affair” to make people invisible to an IR monitor when a room was heated to human body temperature.
If you have two large walls facing each other, the power transfer per unit surface area from wall A to wall B will be the radiation level emitted by Wall A, W/m², minus the radiation level received from Wall B at the surface of Wall A, W/m². In other words, the power per unit area measured going out minus the power per unit area seen coming in at the surface of Wall A.
If you spend 300 dollars a day and earn 300 dollars a day, your bank account will remain stable. Usually, this is independent of the total cash outflow required by your boss to keep you employed.
Willis Eschenbach says:
Willis,
I can’t say I know exactly how RC’s moderation policy works in practice because in general one doesn’t get to see the comments that do not appear. However, my point is:
(1) People like ferd perple are only humoring themselves if they think that their comments don’t appear because they are such brilliant challenges to AGW. We now have many examples in this very thread of ferd’s comments. Do you think they fall into the category of brilliant challenges to AGW or the category of nonsense and noise?
(2) Many challenging comments do get through their moderation.
This thread has actually become a “poster child” of what can happen when a thread is only lightly moderated. You posted something and some of us have raised serious objections to aspects of what you said. However, instead of the focus being on those, the comments section has been taken over by several people who are posting nonsense (and just a few people like ferd and I who are attempting to explain why the nonsense is nonsense). You yourself seem to have abandoned your own thread.
jae says:
I honestly don’t know where to begin. If one of the students in my intro algebra-based physics class wrote that, I would say there is little hope that he could escape with higher than a D in the course. It is nonsense from start to finish. First of all, the temperature of an atmosphere that does not exist is not zero…It is undefined. Second of all, you can’t just assume values for all the other variables and determine T. If you assume values for all the other variables, then you have assumed the value of T. I could just as easily assume different values and get a different value of T.
pV = nRT does not uniquely constrain the temperature at the surface, just as the adiabatic lapse rate does not constrain the temperature at the surface. In the absence of IR-absorbing matter in the atmosphere, the temperature at the surface is constrained by energy conservation.
mkelly says:
Energy conservation is a bedrock principle of physics. K&T are “equating” these, because they are both energies…and their diagram illustrates how energy moves around in the climate system as measured by various empirical means and in harmony with the principle of conservation of energy.
ferd perple says:
Nonsense. If you treat sunlight as a blackbody, you find that the spectrum equates to a blackbody having a temperature of 5800 K. You can’t figure out the blackbody temperature of an object by looking at the amount of radiation impinging on a square meter somewhere far away from the object. The Stefan-Boltzmann Law only tells us what the rate of emission is from the surface itself.
On the other hand, given how much sunlight per square meter is absorbed by the earth system (including atmosphere), energy conservation tells us that the earth can only be emitting 240 W/m^2 back out into space (which corresponds to a blackbody at about -18 C). The fact that the earth’s surface emits ~390 W/m^2 (and is thus at a higher temperature of ~15 C) is something that is impossible to explain without invoking the fact that the atmosphere of the earth absorbs a lot of the terrestrial radiation. This is what we call “the atmospheric greenhouse effect”.
Joel Shore said:
Whoops…Major mistake…I meant “Tim Folkerts and I”, of course!
jae says:
You seem to have a view that is akin to the old Aristotelian view that it takes a net force to keep an object moving at a constant speed. No, it does not take any net energy to maintain the thermal energy of the atmosphere. If the thermal energy remains constant (with no transfers of energy to other types), then the First Law of Thermodynamics says that the net energy flows into and out of the system are zero.
In practice, there will tend to be flows out (e.g., radiation), so there have to be flows in…But that doesn’t get you around obeying conservation of energy. It is simply another way of stating conservation of energy, which you appear to want to violate at will.
jae says:
October 7, 2011 at 8:04 pm
Please look to see if this is wrong, folks:
It is Jae, the temperature of the planet would be unchanged because N2 has no ability to absorb IR radiation, since you have fixed n/V then P will be a function of T.
P=nRT/V
Anything is possible says:
October 4, 2011 at 2:49 pm
What you are assuming, in effect, is that an Earth with an atmosphere comprised exclusively of nitrogen, oxygen and argon would have an identical surface temperature as an Earth with no atmosphere at all, and that doesn’t pass my “smell test”.
Yes he’s assuming that a planet with a transparent atmosphere would have the same temperature as one without an atmosphere which is correct, there is something wrong with your sense of smell.
Willis Eschenbach says:
October 4, 2011 at 7:06 pm
The second is the temperature of the tropopause, which runs at about -40 to -50°C or so, or a corresponding blackbody temperature of somewhere around 150 W/m2.
But the atmosphere at the tropopause is not a blackbody and will therefore emit much less than 150 W/m2.
joel shore:
“I honestly don’t know where to begin. If one of the students in my intro algebra-based physics class wrote that, I would say there is little hope that he could escape with higher than a D in the course. It is nonsense from start to finish. First of all, the temperature of an atmosphere that does not exist is not zero…It is undefined. Second of all, you can’t just assume values for all the other variables and determine T. If you assume values for all the other variables, then you have assumed the value of T. I could just as easily assume different values and get a different value of T.”
If you don’t know where to begin, then maybe you don’t know what you are talking about. Again, (almost) pure rhetoric, with no supporting logic. Just a nasty slur.
Perhaps you have a closed mind? I doubt that you understand nearly as much as you think you do, and I think you are coming across as very arrogant, joel. A D in your “class” would not mean a thing to me.
It is a simple FACT that you cannot have an atmosphere (a gas pressurized by gravity) without the temperature automatically increasing over what it would be with no atmosphere, SIMPLY because there must be added ENERGY to keep all those molecules “afloat.” Not only kinetic energy, but also potential energy. That HAS to have a temperature component, since the temperature is simply a measure of the kinetic energy of the molecules. Try, for once, to compare the moon to Earth, without thinking about just the radiation component. Also please note that all planets with atmospheres have surface temperatures much higher than calculated from radiation.
I keep trying to find a better explanation for my ideas, and maybe someday I will. Your lame insults don’t help and just make you look arrogant and shallow, I think. I sure hope you are not that kind of tyrant in your classroom!!
Jar, the nitrogen atmosphere you described would indeed have temperature, it would be the same as the surface was in the absence of the atmosphere with the appropriate lapse rate. Since you specified the density the pressure would depend on the temperature, not vv as I showed above.
Sorry Jae, I guess my fingers are too big for typing on the phone!
I may be all wrong, but I ask to be heard, and I appreciate the chance to be heard. But I really, really object to some amazingly arrogant know-it-all (evidently a junior educator of some kind) telling me, essentially, that if I don’t agree completely with him he would give me a D in his class! Tell me WHERE AND WHY I’M WRONG, NOT WHAT “GRADE” YOU WOULD GIVE ME IN YOUR “CLASS.”
Gawwwwd, he has to be one of the bossy liberals that are wrecking the world!
Phil:
“Jar, the nitrogen atmosphere you described would indeed have temperature, it would be the same as the surface was in the absence of the atmosphere with the appropriate lapse rate.”
And you MAY be correct (I readily admit to the possibility that I am wrong, but I insist on the right to be so), but I don’t think it’s so. I really think an atmosphere indicates the STORAGE of much more heat than a situation with no atmosphere, and therefore, a higher temperature, than a planet with no atmosphere. That there are morons that think only in terms of radiation, while ignoring simple heat storate, blows my mind. Don’t they think the oceans (a more dense atmosphere) are storing heat? Of course they do. But then they engage in cognitive dissonance and declare that “radiation rules!” in the atmosphere. Man, this is truly the 1984 LIB. GENERATION, where WAR is nothing but “Kinetic Military Action,” and Terrorism is “Man-Caused Disaster,” and the way to a better economy is to tax the hell out of everyone!
But I do appreciate your willingness to try to tell me what you think. Your response is much better than that from a previous poster who seems to assume that I am an idiot and will somehow be swayed/humiliated/ whatever by his supremely arrogant (“scientistific ?”) suggestion that I would get a “D” if I were a student in his obscure “algebra physics class,” where he evidently poses as some kind of “world-renowned physicist” and demands his “students” view him as a possessor of all the truth (or something, I don’t know too many details of this sagev, do you?). Actually, he sounds only like the typical liberal “educator, ” of which we have millions too many.
Whatever, you cannot “create” an atmosphere without adding a LOT of energy. AND that will be reflected in a temperature that is higher than would be without no atmosphere.
Just look at the data for other planets and moons with atmospheres.
Jae check out Mars which has a close to transparent atmosphere. How does your transparent atmosphere get hotter than the surface?
JAE says “Whatever, you cannot “create” an atmosphere without adding a LOT of energy. AND that will be reflected in a temperature that is higher than would be without no atmosphere.”
You seem to be thinking along the lines that if you pump gas into a container, the temperature of the gas will increase. This is certainly true. Similarly, as an atmosphere forms, gravity will warm it up. When the earth’s atmosphere was formed, the compression from gravity would have indeed warmed up the gas. This happened on the sun, raising the core temperature high enough to initiate nuclear reactions. This is still happening on Jupiter, which is slowly collapsing and generating continued heating.
But once you stop compressing, the temperature stops increasing. In fact, the temperature will eventually settle back to the temperature determined by the surroundings. The # of moles of gas in the atmosphere is pretty stable and the ground below does not allow the atmosphere to continue compressing, so gravity is causing no ADDITIONAL compressional heating. And like the compressed tank in the first paragraph, the atmosphere will settle to a temperature determined by the surroundings. Any heating from gravitational compression would have been radiated away billions of years ago.
jae: In your tirades, you seem to have missed the fact that I have explained where you are wrong. Now, you seem to be going on some sort of riff about how much energy it takes it create an atmosphere, which is completely irrelevant for an atmosphere which, last I checked, has been around for a while.
We seem to have somewhat different definitions of “arrogance”. In my world, one is arrogant when one does not even seem to possess the basic ability to understand fundamental concepts like conservation of energy but still seems to feel qualified to pontificate on how scientists who do understand these concepts and have been studying atmospheric science for their whole careers are all wrong.
And, it’s not like you are new to all this either. You have been haunting various blogs for years now and you have demonstrated a singular ability not to learn anything that might challenge your ideological beliefs, which makes it quite amusing when you make claims that show a complete lack of self-awareness like “I keep trying to find a better explanation for my ideas, and maybe someday I will.” No…What you do is desperately cling on to any nonsense you can that will let you believe exactly what you want to believe!
I am under no delusion that after several years of having lots of different people (from all sides of the larger “Is AGW a significant problem?” debate) try to get you to understand what you don’t want to understand that I will magically succeed any more than anybody else has. (What is that statement about insanity being trying the same thing over and over again and expecting a different result?) Really, I just want to make it apparent to others here that you really have not a clue what you are talking about.
JOEL:
“And, it’s not like you are new to all this either. You have been haunting various blogs for years now and you have demonstrated a singular ability not to learn anything that might challenge your ideological beliefs, which makes it quite amusing when you make claims that show a complete lack of self-awareness like “I keep trying to find a better explanation for my ideas, and maybe someday I will.” No…What you do is desperately cling on to any nonsense you can that will let you believe exactly what you want to believe!”
LOL. You are, indeed, a cargo-cult liberal AND, WORST OF ALL, ARE PROUD OF IT! Which means ALL TALK, NO SUBSTANCE, TRUE “PROGRESSIVE.”
INSTEAD OF SIMPLE INSULTS, PLEASE PROVIDE SOME CONCRETE FACTS TO SUPPORT YOUR RANTINGS. OTHERWISE I AND MOST OTHER READERS WITH SOME COMMON SENSE WILL WRITE YOU OFF! All I want is for someone to give evidence that “my haunting various blogs for years” has resulted in something that is WRONG! As Sargeant Friday said when I was just a kid, “Just the facts, man, just the facts.”
Can you distinguish between facts and what you teach in your “simple algebra physics class” (or whatever)? I really doubt it.
PS: the “lack of awarness” comment is surely a mark of your Orwellian association with the absolutely biased morons at NYT and WaPO. You evidently cannot speak straight science, so you resort to WaPO_NYT_WTF_HUFFPO….
Did I miss anything?
I shudder at hearing that YOU are teaching students something, because you, sir, are apparently a real idealogue.
We will deal with your nonsense in 2012.
LOL!
Addendum: For those that are not aware of the Orwellian bent of the current liberal moron establishment, here is a primer:
“Man-caused disaster” means a terrorist attack.
“Overseas Contingent Operation” means War on Terror
“Kinetic Military Activity” means War.
And Joel’s comical ” haunting various blogs for years now and you have demonstrated a singular ability not to learn anything that might challenge your ideological beliefs,”
aligns itself with the paradigm perfectly, dontcha think?
WHERE’S THE MEAT, JOEL?
Apparently, George Bush and the Pentagon are part of “the current liberal moron establishment”. News from 2002 included comments about “kinetic” warfare.
Tim: You must be quite young (compared to me, anyway). I would guess 35 years, max. Please tell me if I guess correctly…
I thought so. I doubt very much that you have read Orwell’s 1984, and I strongly suggest you do that. You will then appreciate the substitution of “Kinetic Military Activity” for WAR! Maybe you can help your students with some real reality??
You are not having much luck as a psychic, JAE. I am noticeably over 35 and I have read 1984.
My point was that:
1) inventing new language and new phrases is not the exclusive activity of any one party or ideology. Conservatives do it and liberals do it. Hawks do it and doves do it. Re-labeling and re-framing are ubiquitous.
2) you were quite happy to assign blame to “liberals” when the facts clearly show at least one of your Orwellian phrases are not theirs. In this sense, you are living out 1984, by trying to rewrite history to blame whoever the “current enemy” is.
3) none of this really has anything to do with the science. You can plaster labels on Joel (and some of them might actually be accurate) but none of that advances the science. Whether or not he reads the Huffington Post doesn’t matter one bit as to whether you or he are right about the nature of temperature and heat in the atmosphere.
Frankly, his understanding seems much better than yours. And that has nothing to do with the age or political views of any of us.
For example in this exchange
JOEL >>In the absence of an IR-absorbing atmosphere, the earth’s surface cannot for long be emitting ~390 W/m^2 when the earth system (including atmosphere) is only absorbing ~240 W/m^2 from the sun. This huge imbalance between emission and absorption would lead to rapid cooling.”
JAE >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
I like Joel’s statement better than yours. I still have not heard you explain what you mean by “rest” or how it is being “stored”. Do you mean 390-240 = 150 W/m^2 = “the rest” are going into the atmosphere but are not coming out?