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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I wonder if the 1st order variable are pressure system oscillations. Pressure systems would be the driver for clouds, would they not? Are not clouds a symptom of an oscillating driver, defined by both short and long term oscillating variable patterns?
ferd berple says:
Don’t humor yourself. You are not asking hard questions; you are asking silly questions and you just keep repeating the same nonsense over and over again. That is why RC sometimes (often?) does not publish your posts. They moderate the comments to try to keep the signal-to-noise ratio from descending too low. They do let through intelligent questions, even ones that challenge their points-of-view, but they have a low tolerance for excessive repetition of debunked contrarian talking-points.
The Fraud in the down-welling IR energy can clearly be seen in the chart Wilis posted above.
Take a close look at the down-welling IR from the Sun, you will see that 169 w/m2 is absorbed, and 29 w/m2 is reflected.
Now, take a close look at the down-welling IR from GHG. You will that 321 w/m2 is absorbed and 0 w/m2 is reflected. That is right 0 w/m2 reflected.
That is the difference between IR from the sun and IR from GHG. The IR from the GHG is not being reflected, which explains why you cannot use it to do work, and why it is not equivalent to the IR from the sun, and why it is meaningless to compare IR from the sun to IR from GHG in terms of w/m2.
The IR from the sun comes from a source that is hotter than the earth and can be used to do work. The IR from GHG comes from a source that is colder than the earth and cannot be used to do work by any science we know today. If you can’t do work with the energy, then it is meaningless to talk about w/m2 because watts are a measure of work.
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). So to get work out of it, you’ll need to have a still lower temperature sink to which to reject the heat … what do you plan to use for that?
You are confusing heat with energy, I think. Heat only flows in one direction, from warm to cold.
No, it is your treatment that is confused. if you look at the w/m2 from the sun striking the earth, that is only 169+29 = 198 w/m2, which corresponds to a temperature significantly lower than 0 C. Therefore by your reasoning you should not be able to get work from sunlight, but we of course know you can.
This shows that the IR from GHG at 320 w/m2 if FUNDAMENTALLY DIFFERENT than the 198 w/m2 from the sun and they cannot be compared apples to apples by simple addition and subtraction.
This is the mistake climate science has made in calculating the energy budget for the earth and it is the mistake you have repeated in your analysis. You are attempting to violate the 2nd law of thermodynamics, by equating radiation from a cold source as being equivalent to radiation from a hot source, and trying to add and subtract them
We know from observation and experiment that you cannot concentrate radiation from a cold source the way you can with radiation from a hot source to actually do any heating. Therefore you cannot add and subtract energy simply based on w/m2, because there is no usable energy in the IR from GHG, while there is usable energy in the IR from the sun.
This in a nutshell is why the theory of GHG is wrong. As soon as you try and change the surface temperature of the earth you are doing work. The atmosphere does not change the surface temperature of the earth through down-welling IR because the source of the IR is colder than the earth itself.and thus cannot do work. Some other mechanism must be the reason that planets with atmospheres are warmer at the surface than planets without atmospheres.
Note to Willis. The figures of 169 + 29 = 198 w/m2 for sunlight are from your chart above.
Please explain why,
1) down-welling IR radiation at 320 w/m2 cannot do work while sunlight at 198 w/m2 can do work. By your analysis, the black body temperature of 198 w/m2 is significantly colder than 320 w/m2 so if they are apples to apples, sunlight should never be able to warm the earth.
2) Since IR from sunlight can do work but down-welling IR from GHG cannot do work, why it is appropriate or scientifically valid to add and subtract these two numbers as though you were dealing with apples to apples.
3) Since down-welling IR from GHG cannot do work, how can it have any effect on the surface temperature of the earth? To change the surface temperature in the slightest involves work by all known physical laws.
Mr Eschenbach,
“But when you change the alcohol content of your blood, you are changing it from the natural blood alcohol content of about 0.03 (present in all humans from childhood on), to say 0.08, the legal limit in California. This is a huge increase of 260% in the blood alcohol level, and you are just barely legally drunk … so your claim that it s a small change doesn’t hold water. You’ve jacked your blood alcohol level by 260%, and you claim that is a tiny forcing?”
By that argument, a doubling of CO2 concentrations would represent a 100% change (a “first order” effect!). You are just illustrating my point that this sort of rhetorical game is purely subjective and does not shed any light on the physics. The relevant questions are: (1) What is the actual magnitude change in average temperature due to a 1% variation in radiative forcing, and (2) what is the impact of that change in heat content on the climate. The IPCC would answer: (1) probably a 3 degree change in global temp anomaly and (2) pretty bad. Guys like Spencer and Lindzen answer as (1) probably a 1 degree change and (2) not so bad. I don’t care which of these results you chose to believe. In either case, at least these people are attempting to answer physically meaningful questions. This article is just word-play.
“In addition, you have not given the slightest evidence that your claim (1% changes make big differences) is true about climate”
I did provide evidence. The ice ages in the last few 100k years were triggered by Milankovich cycles where solar insolation varies by just a few percent. Yet, these “second-order” changes in insolation trigger a climate response that represents the difference between our current inter-glacial period and a world covered in ice. So, yes, small changes can have big impacts. It is not enough to off-handedly dismiss a few percent change as “small” or even “large” without answering the question “small or large compared to what?”.
Here are two references on Milankovitch cycles.
http://www.falw.vu/~peef/teaching/orbital_forcing/assets/Ruddiman_2006_QSR.pdf
http://www.mantleplumes.org/WebDocuments/Hays1976.pdf
I like this article but may i suggest another variation. Instead of starting from the hypothetical position of the earth without any greenhouse gases, where there is the risk that there might be a tipping point (as it moves from the stability of say snowball earth to water earth analogous to a change of phase) as GHG’s are added eg No GHG’s at all and 33 deg C colder may mean snowball earth so high albedo and <0 deg C average temperature.
Instead what happens to DLR associated with CO2 if you work backwards from current position ie slowly remove all CO2 from the current atmosphere currently 390ppm = ~???? W/M^2 ie as it must stop being logrithmic somewhere but the current total CO2 contribution must be known? You then have a water earth still with some clouds and some but I assume less water vapour providing some level of DLR but I would be surprised if the earth became a snowball from this. Obviously for albedo issues, within this same phase state, assume the same level of greenness but it provides an equilibrium atmosphere on which your analytical method above should also work but with no potential phase change. It will also put in real perspective the diminishing affect of CO2.
Put another way, what would be the equilibrium temperature if there was no CO2 in the atmosphere but albedo was fixed and watervapour and clouds were allowed to vary appropriately?
Wouldn’t an ice age be a third-order change to the absolute temperature? Perhaps my difficulty here is that I cannot make any sense out of the statement “Small effects can make a big difference. Small changes in effects, not so much.” Can I propose “small changes in small effects, not so much”? But darn it, that looks like a tautology.
>>
Cementafriend says:
October 5, 2011 at 1:28 am
Willis, Trenberth has the IR “window” wrong (40 instead of the actual 66 w/m2) and knows it see slide 26 of the following . . . .
<<
Your paper says satellites measured the 66 W/m² value. Do you have a reference for that?
In KT 97, they make the following statement:
“The estimate of the amount leaving via the atmospheric window is somewhat ad hoc. In the clear sky case, the radiation in the window amounts to 99 W/m², while in the cloudy case the amount decreases to 80 W/m², showing that there is considerable absorption and re-emission at wavelengths in the so-called window by clouds. The value assigned in Fig. 7 of 40 W/m² is simply 38% of the clear sky case, corresponding to the observed cloudiness of about 62%.”
I’ve mentioned this several times. The term “cloudy” is ambiguous in KT 97. When they say “cloudy”, do they mean 100% cloudy, 62% cloudy, or something else?
In the above statement from KT 97, if cloudy means 62%, then the window should be 80 W/m². If cloudy means 100%, then they should interpolate between 80 W/m² and 99 W/m², which gives us about 87 W/m². What they actually are doing is interpolating between 99 W/m² and 0 W/m². That means KT 97 is claiming that 0 W/m² is the correct value for the IR window when it is 100% cloudy.
Jim
ferd berple says:
October 5, 2011 at 7:23 am
Per my comment @6:40 I concur.
Hi Zac,
The climate-models assume that every degree of warming from CO2 would lead to enough evaporation of water to quadruple the effect on heat-retention (or final temperature, I don’t recall). I understand that assumption has already been empirically demonstrated to be false, but others here would probably know more about that.
If it’s temperature (which varies with the fourth-root of heat-retention), they’re still only talking about ~3%, but 3% of about 300K would give a 9 degree (Centigrade or Kelvin, whichever) change and that is significant even considering annual variation. If it’s heat-retention, then we are talking about something a little under 2 degrees, which is not significant, but try teaching voters who are obsessed with politicians’ personal scandals that something can happen, be interesting, theoretically have some effect, and still be too minor to be worth noting.
This analysis doesn’t say that third-order variables are unimportant,
just that they first have to alter the second- or first-order variables
before they can cause large system changes, usually against negative feedback.
It’s interesting that warmistas have to cite the ice ages
to find positive feedback amplifying a third-order variable,
their favorite bogeyman-scenario.
Ironically, the ice-age lesson is the OPPOSITE one:
When conditions are even approximately right,
positive-feedback global cooling, by glaciation,
will happen EVERY time, with literally dozens of examples,
including two Snowball Earths, lasting tens of millions of years.
With warming, however, feedbacks are obviously negative,
since 75% of the last half-billion years were much warmer than today,
with no 25-million year hyper-warming Hell analogous to Snowball Earth.
Both times there were super-continents (Rodina & Pan-Gaea), mostly desert,
why wasn’t there runaway warming, especially with that high CO2 back then?
It is plain that the Null Hypothesis is low sensitivity to warming,
but high to cooling, the opposite of the Warmista Gospel,
the devotees of which are loudly chanting
‘We are the Null, we are the Null’
Joel Shore says:
Realclimate “…moderate the comments to try to keep the signal-to-noise ratio from descending too low. They do let through intelligent questions, even ones that challenge their points-of-view, but they have a low tolerance for excessive repetition of debunked contrarian talking-points.”
What a bunch of horse manure. Literally scores of commenters here have complained that their sincere, polite and relevant questions and facts have been deliberately and arbitrarily censored by RC.
Joel Shore is reality-challenged. He actually seems to believe that RC is just filtering out the “noise”. Pure cognitive dissonance. Earth to Joel: Realclimate censors opposing points of view as a means of propaganda. Wise up.
There are constant shenanigans to control journals, as can be seen here:
http://scienceblogs.com/catdynamics/upload/2009/08/how_to_publish_a_scientific_co/How%20to%20Publish%20a%20Comment.pdf
dscott says:
No…Scientists (the proper name for who you call “AGW hoaxers”) are not claiming that at all. You just made this up. It is well-understood that water vapor in the atmosphere varies with the temperature, both on timescales having to do with the temperature rise due to greenhouse gases over many decades and timescales having to do with fluctuations in global temperature such as those produced by El Nino and La Nina. In fact, it is the dependence of water vapor on temperature over these shorter timescales that gives us the most confidence that the water vapor feedback is correct. See, for example, http://www.dca.iag.usp.br/www/material/akemi/radiacao-I/Soden_2005_Science.pdf
There is no contradiction there…If there are regional changes, some places can have floods and some can have droughts. Or, the same place can have both floods and droughts in different years. In fact, a warmer atmosphere will tend to be associated with both an increase in the largest precipitation events and an increase in drying of soils due to the warmer temperature. How this plays out regionally and over time can then indeed mean both floods and droughts.
A fair point, but the important factor is not the absolute magnitude of each variable, it’s how widely each of your variables varies.
An analogy: Willis Eschenbach is standing on his front porch. How far is his head from the centre of the Earth?.
Variable 1: the Earth’s radius, plus however high Willis’s house is above that (~6.371 km)
Variable 2: Willis’s height (~1 – 6 feet depending on age)
Variable 3: the thickness of shoes he’s wearing on any given day (0-1 inches, perhaps?)
Now, according to Willis, the only relevant variable is number (1), since it’s so much larger than the others. That neglects the fact that it’s essentially constant! It is a variable though – it might vary as much as a millimetre or two per year, depending whether his house is prone to subsidence.
As for the other variables, the most important could be either (2) or (3), depending on whether you’re taking a decadal or a daily view. On a decadal time frame, Willis grew from a baby to an adult – all the while standing on his front porch, for the sake of argument – and that change of ~5 feet is by far the dominant factor. On a daily time frame, his height is essentially constant, and so the measured distance from the centre of the Earth will depend entirely on his choice of footwear. On a yearly time frame, both are likely irrelevant – his height’s no longer changing as he’s an adult now, and the fluctuation in shoe size will average out. The most important variable on a yearly time frame might turn out to be something like changes in hairstyle, or some such.
So – how variable is the solar downwelling flux from day to day, when averaged over a week, a year, a decade or a century? What timescale of response are we looking for in climatic terms?
Joel, if you truly believe that RealClimate only censors “excessive repetition of debunked contrarian talking points”, then my respect for you just took a giant drop. That is nonsense, as even the briefest Google search will show.
RC censors a host of things because they are far too inconvenient. See my peer reviewed article here about their censorship of my reasonable, respectful, and completely scientific questions.
However, the fact that you, an otherwise sane and sober scientist, believes that RC doesn’t censor opposing scientific views shows just how deep the AGW extremists have their hooks into you … discouraging. DO YOUR HOMEWORK, you’re way, way off base on this one.
w.
Interstellar Bill wrote:
“It’s interesting that warmistas have to cite the ice ages
to find positive feedback amplifying a third-order variable,
their favorite bogeyman-scenario.”
Since I mentioned the ice age, I presume you are referring to me. I am not a Warmista, I am a skeptic. Extraordinary claims require extraordinary proof, same for both sides of any debate. The rest of your post is a “Just So” story. How do we know it will happen EVERY time? Because every time we know of, it happened!
Here is a copy of a GREAT comment from Revkin’s deny-o-meter map the other day. I give full credit to the author of the original comment. I believe the comment supports the thesis of today’s article by Willis.
“Adrian O.
State College, PA
October 2nd, 2011
11:04 pm
I am a mathematical physicist.
A year and a half ago I started to look for actual measured data, which I certainly can read, to find out what is really going on with the anthropogenic global warming.
It took about 50 hours of digging to find the actual data (which is one of the reasons, I suppose, for which so few people have seen it.)
It showed nothing unusual whatsoever.
In temperatures, sea level rise, ice, glaciers rate of melt.
When looked at historically.
All the unusual things were in “adjustments”,
10C warming imagined in the unmeasured Arctic, serious imagined warming of the unmeasured deep oceans (which does not translate, through dilation, into unusual sea level rise at the top.)
Trees with unreliable ring thickness in the last, measured, 60 years,
which are imagined to be perfectly reliable a thousand years ago.
Glaciers which, when measured, are melting at the same rate as 60 and 120 years ago. With earlier melting natural and current identical melting imagined to be man made.
Tornado and hurricane activity which, when counted, is weaker than 50 years ago.
The people obsessed with the extra 100 ppm of CO2 = 1/100 of 1% of the atmosphere put up by humans have never made a case. Other than in imagined models, which as far as real science goes, if they don’t agree with reality are junk.
In other words, there is nothing to deny in the first place.
Where exactly does that put me on that list?”
****
ferd berple says:
October 4, 2011 at 9:23 pm
The question remains: If watts per square meter is the measure of down welling GHG IR, then you should be able to get work from the IR, regardless of source.
As such, my original point stands. The watt is a unit of work. So, if GHG does in fact radiate watts of energy it MUST be capable of work.
We know we can get work from the watts radiated from the sun. So, where it the demonstration that you can get work from down-welling GHG IR? If it can’t do work, then it is nonsense to measure it in watts.
****
You can do work from DLR. Just employ a colder heat-sink (3K of outer space is fine) than the characteristic temp of the IR and you can do work from the temp difference. And the final radiational heat-sink for the earth IS outer space at 3K.
Dear Willis, – No one puts it in perspective better than you. But there’s a misprunt in your piece: you say that the downwelling radiation at the top of the atmosphere is “330 W/m2” after deducting a bit of stratospheric interference. I think you meant “230”, calculated thus:
Total solar insolation 1368 W/m2, divided by 4 and multiplied by (1 – 0.3), where 0.3 is the albedo, gives 239.4 W/m2. Knock of a bit for the strat. and you get 230. Or are you looking at gross rather than net incoming? It would probably be fairer to the usual suspects if one worked from the net incoming. That would give CO2 a slightly larger role, but still very much a third-order effect. Splendid posting, as always – Christopher
beng says:
October 5, 2011 at 10:39 am
You can do work from DLR.
Just a small point of order. The D in DLR (DWLR) stands for down. Usually outer space you mentioned is by convention normally UP.
Willis – I like your idea of the first, second, and third order variables. However, AGW proponents are scaring us about a temperature rise of some 2 degrees K from a base temperature of 300 K. That in itself is a third-order effect and we can not safely ignore third-order variables supposedly causing it.
Peter Sørensen, you are confusing enthalpy with temperature.
DSCOTT:
I have been looking at the chats about a CO2-less atmosphere. One thing for sure, an atmosphere without CO2 would still have a great deal of water vapour in it. Think about how many times you have been told that the water vapour is a ‘feedback’ from CO2! It is like a broken record…
So it is interesting to see what the temperature would be without CO2 but still with the main greenhouse gas, water vapour. One could argue that with an increase in CO2, there will be more water vapour: RGates, argue away! He basically said we would be frozen solid without CO2, as if that was the only cause of warming available in the atmosphere. But the fact remains that water vapour appears in all bottles of gases (and is a problem) and it would similarly appear in the atmosphere of a CO2-less planet. It would provide warming, and is its own ‘forcing’ which would stabilise at some point above the black body temperature.
Willis’ point that there is only a total of 33 degrees of warming taking into consideration all feedbacks is well taken. It is not as if there is ONLY CO2 to credit for the 33 degrees. Wthout it, on a watery planet like this one, it would be plenty warm with no CO2 at all. Warmist bloggers write as if that is not the case, as if without CO2 all moisture would disappear from the atmosphere because of a cold (black body) surface. I guess they have never heard of sublimation.
If the water vapour concentration dropped, there would be fewer clouds too, so things would warm more efficiently (etc).
Willis, I checked the cartoon you modified, If you want to fix it right,
http://ourhydrogeneconomy.blogspot.com/2011/10/better-cartoon.html
Enjoy
Fred,
I agree with about 1/2 of what you write. Unfortunately, being 1/2 wrong is almost worse than being all wrong, since it makes it all seem more plausible.
Let me start with the first few things you wrote in response to me:
No, you can make a reflector that is not sensitive to direction. It is not perhaps not as efficient as point source, but it can be done.
You are correct — you can focus diffuse light. For example, you can focus the light from a diffuse fluorescent light overhead to get a brighter spot on your desk with mirrors or lenses.
But the sky is “bright” in the IR in every direction. That would be like having your entire room covered ceiling to floor with the fluorescent lights. In this case, you can’t get the light any brighter on your desk than it is to start with. If you put a mirror in to reflect more of the light from above, you will necessarily be blocking just as much light from some other fluorescent bulb.
You cannot focus light from the fluorescent bulbs any brighter than the surface of the bulb. You cannot focus light from a filament any brighter than the surface of the filament. You cannot focus light from the sun any brighter than the surface of the sun. And you cannot focus light from air molecules in the atmosphere any brighter than the original temperature of the air. So a “thermal IR collector focusing light from the cool sky cannot warm anything above the temperature of the sky. (Although you can use this principle to make a “refrigerator” by focusing on the cool sky and blocking the IR from the warm ground)
The watt is a unit of work. So, if GHG does in fact radiate watts of energy it MUST be capable of work.
First, I’ll assume we are talking Joules of work, where watts wold be the rate at which the joules of energy are being transferred.
There is a “high school” definition that “energy is the ability to do work”, but the truth is that thermal energy is only capable of doing work if there is a heat engine connected to some lower temperature reservoir, and even then the work done is limited by the temperature difference. 2 kg of room temperature water might have the same total thermal energy as 1 kg of steam, but there is no question that 1 kg of steam can do work, while the more “diffuse” energy of the cooler water cannot.
There is no requirement that 1 J of IR energy (spread out over many photons) can do the same work as 1 J of solar energy, just like there is no requirement that 1 J of thermal energy in cool water (spread out over many molecules) can do the same work as 1 J of thermal energy in steam.