Guest Post by Willis Eschenbach
[Update: I have found the problems in my calculations. The main one was I was measuring a different system than Kiehl et al. My thanks to all who wrote in, much appreciated.]
The IPCC puts the central value for the climate sensitivity at 3°C per doubling of CO2, with lower and upper limits of 2° and 4.5°.
I’ve been investigating the implications of the canonical climate equation illustrated in Figure 1. I find it much easier to understand an equation describing the real world if I can draw a picture of it, so I made Figure 1 below.
Be clear that Figure 1 is not representing my equation. It is representing the central climate equation of mainstream climate science (see e.g. Kiehl ). Let us accept, for the purpose of this discussion, that the canonical equation shown at the bottom left of Figure 1 is a true representation of the average system over some suitably long period of time. If it is true, then what can we deduce from it?
Figure 1. A diagram of the energy flowing through the climate system, as per the current climate paradigm. I is insolation, the incoming solar radiation, and it is equal to the outgoing energy. L, the system loss, is shown symbolically as lifting over the greenhouse gases and on to space. Q is the total downwelling radiation at the top of the atmosphere. It is composed of what is a constant (in a long-term sense) amount of solar energy I plus T/S, the amount of radiation coming from the sadly misnamed “greenhouse effect”. T ≈ 288 K, I ≈ 342 W m-2. Units of energy are watts per square metre (W m-2) or zetta-joules (10^21 joules) per year (ZJ yr-1). These two units are directly inter-convertible, with one watt per square metre of constant forcing = 16.13 ZJ per year.
In the process of looking into the implications this equation, I’ve discovered something interesting that bears on this question of sensitivity.
Let me reiterate something first. There are a host of losses and feedbacks that are not individually represented in Figure 1. Per the assumptions made by Kiehl and the other scientists he cites, these losses and feedbacks average out over time, and thus they are all subsumed into the “climate sensitivity” factor. That is the assumption made by the mainstream climate scientists for this situation. So please, no comments about how I’ve forgotten the biosphere or something. This is their equation, I haven’t forgotten those kind of things. I’m simply exploring the implications of their equation.
This equation is the basis of the oft-repeated claim that if the TOA energy goes out of balance, the only way to re-establish the balance is to change the temperature. And indeed, for the system described in Figure 1, that is the only way to re-establish the balance.
What I had never realized until I drew up Figure 1 was that L, the system loss, is equal to the incoming solar I minus T/S. And it took even longer to realize the significance of my find. Why is this relationship so important?
First, it’s important because (I – Losses)/ I is the system efficiency E. Efficiency measures how much bang for the buck the greenhouse system is giving us. Figure 1 lets us relate efficiency and sensitivity as E = (T/I) / S, where T/I is a constant equal to 0.84. This means that as sensitivity increases, efficiency decreases proportionately. I had never realized they were related that way, that the efficiency E of the whole system varies as 0.84 / S, the sensitivity. I’m quite sure I don’t yet understand all the implications of that relationship.
And more to the point of this essay, what happens to the system loss L is important because the system loss can never be less than zero. As Bob Dylan said, “When you got nothin’, you got nothin’ to lose.”
And this leads to a crucial mathematical inequality. This is that T/S, temperature divided by sensitivity, can never be greater than the incoming solar I. When T/S equals I, the system is running with no losses at all, and you can’t do better than that. This is an important and, as far as I know, unremarked inequality:
I > T/S
or
Incoming Solar I (W m-2) > Temperature T (K) / Sensitivity S (K (W m-2)-1)
Rearranging terms, we see that
S > T/I
or
Sensitivity > Temperature / Incoming Solar
Now, here is the interesting part. We know the temperature T, 288 K. We know the incoming solar I, 342 W m-2. This means that to make Figure 1 system above physically possible on Earth, the climate sensitivity S must be greater than T/I = 288/342 = 0.84 degrees C temperature rise for each additional watt per square metre of forcing.
And in more familiar units, this inequality is saying that the sensitivity must be greater than 3° per doubling of CO2. This is a very curious result. This canonical climate science equation says that given Earth’s insolation I and surface temperature T, climate sensitivity could be more, but it cannot be less than three degrees C for a doubling of CO2 … but the IPCC gives the range as 2°C to 4.5°C for a doubling.
But wait, there’s more. Remember, I just calculated the minimum sensitivity (3°C per doubling of CO2). As such, it represents a system running at 100% efficiency (no losses at all). But we know that there are lots of losses in the whole natural system. For starters there is about 100 W m-2 lost to albedo reflection from clouds and the surface. Then there is the 40 W m-2 loss through the “atmospheric window”. Then there are the losses through sensible and latent heat, they total another 50 W m-2 net loss. Losses through absorption of incoming sunlight about 35 W m-2. That totals 225 W m-2 of losses. So we’re at an efficiency of E = (I – L) / I = (342-225)/342 = 33%. (This is not an atypical efficiency for a natural heat engine). Using the formula above that relates efficiency and sensitivity S = 0.84/E, if we reduce efficiency to one-third of its value, the sensitivity triples. That gives us 9°C as a reasonable climate sensitivity figure for the doubling of CO2. And that’s way out of the ballpark as far as other estimates go.
So that’s the puzzle, and I certainly don’t have the answer. As far as I can understand it, Figure 1 is an accurate representation of the canonical equation Q = T/S + ∆H. It leads to the mathematically demonstrable conclusion that given the amount of solar energy entering the system and the temperature attained by the system, the climate sensitivity must be greater than 3°C for a doubling of CO2, and is likely on the order of 9°C per doubling. This is far above the overwhelming majority of scientific studies and climate model results.
So, what’s wrong with this picture? Problems with the equation? It seems to be working fine, all necessary energy balances are satisfied, as is the canonical equation — Q does indeed equal T/S plus ∆H. It’s just that, because of this heretofore un-noticed inequality, it gives unreasonable results in the real world. Am I leaving something out? Problems with the diagram? If so, I don’t see them. What am I missing?
All answers gratefully considered. Once again, all other effects are assumed to equal out, please don’t say it’s plankton or volcanoes.
Best wishes for the New Year,
w.
“This must undoubtedly contribute to the weak CO2 greenhouse effect on Mars – the surface emission spectrum on Mars isn’t as well aligned with CO2 absorption spectrum as it is on the earth’s surface.”
Don’t think so. I think it’s because there is very little atmosphere on Mars, way below one bar. Thus, there is little heat storage by the atmosphere. Again, see here:
http://www.ilovemycarbondioxide.com/pdf/Rethinking_the_greenhouse_effect.pdf
The greenhouse effect is far over-emphasized and simple heat storage is far under-appreciated. The GHE may not even exist for the same reason that a real greenhouse doesn’t heat up when the windows and doors are open (i.e, it is canceled by convection).
@george
FYI
– albedo of the ocean at noon near the equator is close to zero. Albedo of water increases as angle of incidence declines so ice or no ice, clouds or no clouds, the earth’s albedo increases with increasing latitude
-insolation at noon near the equator in clear sky is on the order of 1300w/m2 so every percentage point increase in albedo decreases surface insolation by 13 watts. Even if we take the globally averaged (across day/night and across all latitudes) surface insolation of 325 watts in clear sky a single percentage change in average albedo will change surface insolation by 3 watts. The calculated rise in surface equlibrium temperature is 0.3C per watt.
Different climate models use different estimates for average albedo and, as far as I know, these are “constants” in that average albedo is not assumed to change in response to changing surface temperature. The range of the estimated, unchanging average albedo varies by 7% between models which means that the model boffins are using albedo as a fudge factor which can change their average surface temperatures by as much as plus or minus 3.5C depending on whether they low-ball it or high-ball it.
That’s absolutely outrageous to have a fudge factor which allows you to manufacture surface temperature deviations of 7C in a model which purports to predict average surface temperature changes on the order of 0.1C per decade.
JAE says:
January 5, 2011 at 3:17 pm
“http://www.ilovemycarbondioxide.com/pdf/Rethinking_the_greenhouse_effect.pdf”
Biggest pile of crap I’ve seen in a while. That’s the first and last time I’ll bother reading anything on that website.
“Biggest pile of crap I’ve seen in a while. That’s the first and last time I’ll bother reading anything on that website.”
Well, that was informative! 🙂 Do you have any rational reason for such a strong statement?
Jon-Anders Grannes: January 5, 2011 at 12:24 am
kai: January 5, 2011 at 1:37 am
Dave Springer: January 5, 2011 at 9:16 am
Fellows, ignore my post above, it’s totally incorrect in a twist way and especially don’t want to lead any other person reading the same to be misled. When will I learn to dig in the math first before typing away.
George Smith.
“I don’t care (one iota) what ANY computer model predicts about what has happened in the past; how many of those models can predict the already recorded Temperature anomalies for all (or any) of the surface stations where GISS or HADCrut data have been gathered. Oh I forgot; the models don’t use the same grid of data points that anybody actually measures any data for.”
See AR4 chapter 9, supplemental material section Sm 9-5
This covers the proceedure used to match observations with hindcasts.
George if you want to ma
JAE says:
January 5, 2011 at 5:15 pm
The clincher was the speculation at the end that gravitational compression of the atmospheric gases accounts for the heating beyond blackbody equilibrium temperature.
Gases only heat as they are compressing. They don’t remain heated once the compression ends without something else keeping them heated. That statement was so utterly ignorant of the most basic thermodynamic principles the author must have flunked his 9th grade physical science class. I’m not saying it takes a rocket scientist to understand basic gas laws but it does require more than that author had in his brain bucket.
“The clincher was the speculation at the end that gravitational compression of the atmospheric gases accounts for the heating beyond blackbody equilibrium temperature.”
LOL. You evidently don’t understand the article at all! You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating. Siddons is arguing that such an effect is not necessary, because of the gas law, T = PV/R. V and P depend ONLY upon stored energy (kinetic and potential). Therefore, T has to, also. The article backs up this fact by showing that all planets with atmospheric pressures above 1 bar have about the same T at one bar, REGARDLESS of how much GHGs are present in the atmospheres. IOW, it is impossible to have an atmosphere at a pressure of 1 bar without the temperature being raised above the BB temp. He cites pretty powerful empirical evidence from NASA to back that up. There is NO empirical evidence for an atmospheric greenhouse effect! It is very likely, IMHO, that any warming caused by backradiation is immediatelly cancelled by convection–just like in a real greenhouse when the doors and windows are open.
JAE says:
January 5, 2011 at 3:17 pm
“Don’t think so. I think it’s because there is very little atmosphere on Mars, way below one bar. Thus, there is little heat storage by the atmosphere.”
Thermal mass alone only smooths out variations in temperature over heating and cooling cycles. It doesn’t raise or lower the average temperature.
That’s not to say the exceedingly low pressure isn’t a primary cause. I think it has more to do with lack of conductive heating of accessory (non-greenhouse) gases that happens in the earth’s much denser atmosphere. In the thin gas with nothing but CO2 molecules the absorption and re-emission is all at 15um and it quickly becomes saturated. In the the thicker earth atmosphere composed mostly of nitrogen and oxygen the excited CO2 molecule, instead of re-emitting another 15um photon instead bleeds the energy off through conductive (mechanical not radiative) means and this doesn’t result in the re-emission of a 15um photon. So the CO2 molecule is then primed to absorb another upwelling 15um photon from the surface.
That might not be quantum mechanically correct. I’m not real comfortable with it and I usually avoid QM explanations like the plague because they are seldom needed or appropriate in cold dense gases (like the Earth’s troposphere) but in the case of Mars’ far less dense troposphere a QM explanation may be apt.
Regarding planetary atmospheres, did you know that Neptune radiates 2.6 times as much heat as it receives from the sun? Its atmosphere has an internal temperature up to 5000 K, and some of the fastest winds in the solar system peaking at 600 m/s (1,300 mph). Nobody knows how it works, or where the extra heat comes from.
I don’t think a physical intuition honed on the inner planets is likely to carry across to the atmosphere’s of the outer planets. Looking for connections like this is too much like numerology – the brain is too good at picking out patterns in noise.
George E. Smith says:
Well, given that I was describing what was shown using a GCM and you were objecting to the result, it is quite relevant to talk about what is and is not included in the model and what it predicts. It makes no sense to object to simplifications that were not in fact made, which is what most of your post consisted of.
George, there is a reason why scientists in certain fields focus on certain quantities and that is because they turn out to be the most relevant. Even if you want to understand what happens to the temperature at the surface of the earth, the way to do that is not be computing the radiative balance at the surface, because convective and latent heat effects play a very important role in determining the vertical temperature structure of the atmosphere. It turns out that the best way to figure out what will happen at the surface is to figure out how the top-of-the-atmosphere energy balance is affected and couple that to an understanding of what the vertical temperature structure of the atmosphere is (which, as I said, is determined in large part by the convective and latent heat effects). [Also, the fact that the oceans capture most of the solar energy does not in any way mean that the top-of-the-atmosphere energy balance is the wrong quantity to look at. It is still the right quantity to consider. Looking at the top-of-the-atmosphere energy balance doesn’t mean that you are ignoring things that occur at the surface. It just means that you are looking at how those things affect the balance of the radiation from the sun that enter the atmosphere and the radiation from the earth/atmosphere system that leaves the atmosphere.]
In particular, the book “Global Warming: The Hard Science” by L.D. Danny Harvey calculates two quantities:
(1) How much temperature change occurs at the surface if we have a radiative perturbation of 10 W/m^2 between the surface and the rest of the atmosphere.
(2) How much temperature change occurs at the surface if we have a radiative perturbation of 10 W/m^2 at the top-of-the-atmosphere (i.e., between the earth-atmosphere system and space).
For the energy flows that actually occur in the atmosphere, it turns out that the latter perturbation results in a temperature change at the surface that is many times the former. [I forget what the exact factor is, but I think it is something like 20-30 times more effect for (2) than (1).]
Just to clarify the last paragraph of my last post: The reason why the perturbation described by (1) has so little effect on the final surface temperature is that the energy flows between the earth’s surface and the atmosphere adjust to almost completely cancel out the radiative perturbation that was applied. Because the surface and atmosphere are so strongly coupled (i.e., there’s lots of energy flowing back and forth), this cancellation is almost complete.
jae says:
In fact, he apparently understands it better than you do, which is why he has drawn the correct conclusion about that article: that it is a bunch of garbage. It is basically just some non-sensical ramblings linked with some empirical data which is supposedly supposed to back up the nonsense but doesn’t really.
It is sort of strange that you find that “article” at all compelling. I guess people will believe what they want to believe. In our universe, conservation of energy holds…Perhaps in yours, you think it can be violated at will be simply waving around the ideal gas law! Whatever!
JAE, thank you very much for the links. The top link contains a graph that I found month’s ago but could never relocate the actual paper again, vanished. It’s the graph with six planets and Titan… do you also know where that very original paper is? That’s what I can’t seem to relocate and is much of the basis of my comments of late.
Something is very fishy in current climate science thinking, both sides to a degree, but few seem to mathematically explain it unambiguously. But you especially seem close. You know, the pressure, the lapse rates, etc. I do know it’s the ignorance of emissivities and therefore absorptivities that lies at the bottom of this answer, mathematically that is. Feynman would have loved this problem!
Many try to explain through cloud cover but since clouds being white absorb less, reflect most, they also emit less equally except when clouds turn dark in storms and the emission and absorption change appropriately. The surface will be warmer but the upper troposphere and low stratosphere will be equally colder. Internal variance but no change of the planet as a whole.
I could be very wrong but still think the correct basic physics will answer the base questions. No high mumbo-jumbo.
(sorry for my own jumbo above)
Alan Siddons
http://climaterealists.com/index.php?id=5526
http://climaterealists.com/attachments/database/RadiativeNonEquilbrium_BHermalyn_Final.pdf
http://www.americanthinker.com/2010/02/the_hidden_flaw_in_greenhouse.html
http://www.ilovemycarbondioxide.com/pdf/Rethinking_the_greenhouse_effect.pdf
Wayne writes:
“they also emit less equally except when clouds turn dark in storms and the emission and absorption change appropriately.”
Only the bottoms of the clouds get dark and that’s only because of limited light. The tops of those storm clouds are as white as driven snow (at least in the daytime). Surely you’ve seen satellite photos of hurricanes. White as a cotton ball on top but looking up from the bottom they’re quite dark.
Joel Shore says:
January 6, 2011 at 10:05 am
re; TOA energy balance.
It would be nice but they don’t know WTF the number is on the outgoing side. They can’t pin down average albedo better than plus or minus about 4%. All they know is that it isn’t constant yet they stick a constant in the GCM and adjust as necessary to get the results they want. Incoming energy is a piece of cake unless of course there are unexpected things happening like spectral distribution changes (there are, discovered just last year) or GCR variations causing big structural changes (probably are).
So if you don’t know the TOA outgoing radiation better than the nearest 0.2 kilowatts per square meter what good is it to start at the top and work down? There’s a phrase for that in the computing world – Garbage In, Garbage Out. If the data is bad the model won’t produce valid results even if the model is perfect. And we all know the models are a “travesty” thanks to a private candid admission from Trenberth that went embarrassingly public 14 months ago.
Nullius in Verba says:
January 6, 2011 at 9:19 am
“Regarding planetary atmospheres, did you know that Neptune radiates 2.6 times as much heat as it receives from the sun?”
Sure. Doesn’t everyone?
“Its atmosphere has an internal temperature up to 5000 K, and some of the fastest winds in the solar system peaking at 600 m/s (1,300 mph).”
Not the internal atmosphere. That’s frigid. The mantle is thought to reach 2000K-5000K. The outer atmosphere is pretty hot at 5000K or so but so is the earth’s and every other planet’s. It’s a pretty meaningless figure as it is so thin at that point it’s almost vacuum – it wouldn’t melt a snowflake in a million years and no thermometer could actually measure it because any real thermometer would lose heat faster than the thin atmosphere could supply it.
“Nobody knows how it works, or where the extra heat comes from.”
Keep in mind 2.6 times almost nothing is still almost nothing. Neptune gets about 1 watt per square meter and emits 2.6 watts. Probably a combination of heat of formation, radioactive decay, bleeding gravitational energy, and maybe some chemical reactions we don’t know about in the hideously high pressure mantle. Or maybe the mantle is rich in dilithium crystals and the Klingons or Romulans have an antimatter power generation plant down there. That would be my bet.
jae says:
January 6, 2011 at 5:31 am
“LOL. You evidently don’t understand the article at all! You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating. Siddons is arguing that such an effect is not necessary”
Evidently you don’t understand it’s no mere coincidence that Siddons rhymes with morons. He hasn’t produced a single notable thing in his life in any area of science, engineering, or mathamatics. No patents and no articles in any trade journals. This is my last word on him. The few minutes I spent finding out he’s a lunatic quoted in a handful of blogs saying stupid things is a few minutes I’ll never get back.
jae says:
January 6, 2011 at 5:31 am
“You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating.”
You are confused. It isn’t “extra” heating. If two rocks sit out in the sun all day and you throw a blanket over one of them at night you’ll find that the rock with the blanket over it is warmer in the morning. Did that rock get “extra” heating? LOL
“”””” Dave Springer says:
January 6, 2011 at 3:00 pm
jae says:
January 6, 2011 at 5:31 am
“LOL. You evidently don’t understand the article at all! You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating. Siddons is arguing that such an effect is not necessary” “””””
Dave, Been there; Done that !! Welcome to the club.
George
jae says:
January 6, 2011 at 5:31 am
“You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating.”
You are confused. It isn’t “extra” heating. If two rocks sit out in the sun all day and you throw a blanket over one of them at night you’ll find that the rock with the blanket over it is warmer than the rock without the blanket in the morning. Did that rock get “extra” heating? LOL
Thought I’d better clarify by adding the bit in italics just in case a reader might think I meant that the blanketed rock was warmer in the morning that it was when the blanket was put over it at night.
CO2 is an insulator not a heater. Write that down and pass the note along to anyone else who just doesn’t get it.
A Thought Experiment to illustrate how CO2 works as an insulator.
First of all we need to know how the vacuum flask (thermos bottle) invented by Scottish physicist James Dewar in 1892 works:
Okie dokie. So much for that. Most of you probably already knew that.
Now for the thought experiment lets replace the silver coating with a one way mirror that lets light into the bottle but doesn’t let any light (which includes infrared radiation) out of the bottle.
Let’s fill a regular vacuum flask and our one-way mirrored vacuum flask with a tasty cold beverage. Make mine a Mexican Martini please. Now we’ll set both bottles out in the full afternoon sun and forget about them until after sunset.
When we go to consume our refreshing cold beverage in the evening will one of them be warmer than the other and if so which one and why?
Anyone who can get this right should have no problem understanding how CO2 works in the atmosphere.
“”””” Joel Shore says:
January 6, 2011 at 10:05 am
George E. Smith says:
Joel, absolutely nowhere in my post did I refer to what any computer models do or do not predict, project, or otherwise indicate. I don’t care what they get in the way of output from those models; since none of it seems to have happened so-far. “””””
Joel, I have no wish to cosntantly assault you with endless minutiae; so the appended above simply defines your response I am referring to.
So I have often talked about RADIATION, and BB approximations to real radiative phenomena.
Others; and YOU often refer to conduction, convection, evaporation, condensation, circulation, freezing etc etc, as other perhaps even more significant thermal energy redistribution processes; and although I too have mentioned those; I don’t dwell a lot on those (nor ignore them.)
And specifically Dr Chris de Freitas of the University of Auckland who is a well known Kiwi AGW skeptic, has even here at WUWT noted that such non radiative processes are important atmospheric energy transport processes.
He teaches Geography and Climatology; and I believe his specialty is micro-climate; namely what goes on down there at the cm to few decimetre range; the place where plants grow; particularly agricultural plants. NZ is a well known Agriculture heavy country; that turns out thousands of agricultural scientists to help feed the world’s hungry.
Well so what; so I don’t mention those important energy transport processes any more than I have to to convince the doubters like you, that I am not completely ignoring them.
So why is that; why do I not mention those clearly important processes very often, but focus on Radiative matters ??
C’mon Joel; give it you best shot; I know you can guess why I do that.
For a hint; Cite your list (in your esteemed opinion (which I value)); of the ten most important”Peer Reviewed” papers on “The Green House Gas ” Impact on Atmospheric Convective Energy Transport; or on Atmospheric Conductive Energy Transport; or on Evaporative Atmospheric Energy Transport, or on Atmospheric Precipitation Energy Transport; or any other important but ignored by me, Non-Radiative Atmospheric Energy Transport Mechanism.
I put it to you Joel; that the so-called Greenhouse effect, of which CO2 is the most evident and sinister participant in, and of almost total man made origin, is a PURELY RADIATION PHYSICS PHENOMENON, and has no invlovement whatsoever with any other means of atmospheric energy transport.
There; now I have let the cat out of the bag; I don’t ignore those other processes; I think about them all the time; it’s just that they have nothing to do with the coming greenhouse gas catastrophic thermal runaway, and global ice melting, and sea level rise disaster. That’s why I stay mostly with RADIATION ! How simple is that.
As usual, Willis has stirred up quite an interesting discussion thread. Maybe not the way he wanted it to go; but what the hey.
Just keep launching those suckers anyway Willis; we’ll sail them in some direction or other.
George
While we’re thinking about our thought experiment with vacuum flasks let’s fill them up just after dark and drink them just before sunrise. Will there be any temperature difference between the two liquids after sitting in the dark all night? Explain what you expect to find.