# An Unexpected Limit to Climate Sensitivity

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.

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Brian H
January 3, 2011 10:34 pm

Edit: “for a natural head engine”. Is that an elaborate thought experiment? 😉
The obvious conclusion of your observation is that the “head engine” is broke. The equations are in error.
My suspicion is that L is highly variable, and T/S is small and narrowly constrained.
[Typo fixed. ~dbs]

January 3, 2011 10:34 pm

This article has me thinking, but it’s late and I don’t have time to re-read it tonight. But a 9° sensitivity seems to be contradicted by observations:
Bill Illis posted an interesting chart a while back.
Then there was the late, great John L. Daly who published Dr Heinz Hug’s take on climate sensitivity.
And an older WUWT posting on Arrhenius’ 1906 paper, in which he recants the sensitivity number in his 1896 paper — the one always quoted by the warmist crowd.

January 3, 2011 10:37 pm

I have been arguing that climate sensitivity should be based on the net energy transferred to the atmosphere and the total Greenhouse Effect. Since energy causes warming that makes a lot of engineering sense.
Since the atmosphere is 33 °C warmer than the blackbody and the NET energy transferred to the atmosphere is 198 W/m2 the climate sensitivity would be 0.167 °C/(W/m2). That is roughly 0.6 °C for a doubling of CO2. Of course that doubling of CO2 would not result in that much change as that is a forcing not a change in NET energy transfers.
It is absurd that the climate is highly sensitive to small changes in energy as it has been reasonably (+/- 15 C) for millions of years.
http://theinconvenientskeptic.com/2010/11/the-energy-balance-and-the-greenhouse-effect-1-of-3/
http://theinconvenientskeptic.com/2010/12/the-energy-balance-and-the-greenhouse-effect-3-of-3/
If someone argues that convection cools the atmosphere, check out 2-of-3 as well.

crosspatch
January 3, 2011 10:38 pm

I think it still doesn’t take into consideration a large amount of heat that is released above most of the GHG and so doesn’t get 50% re-radiated back down to Earth. I am talking about condensation and freezing taking place at high altitude. Most of the stuff assumes that heat is all released at the surface and must travel through all that GHG, I don’t think it is/does.
Also, what impact would increased CO2 have on absorbing *incoming* solar IR and re-radiating half of that into space?

DeNihilist
January 3, 2011 10:48 pm

This actually seems to square with Dr. Alley’s prediction of up 21*F for a doubling of CO2. Sorry, but at this moment, I cannot remeber where I saw this post…..

January 3, 2011 10:52 pm

As I understand it, it proves that an increase in solar results in an overall increase in temperature. Therefore, a decrease in solar ‘must’ result in an overall temperature decrease, regardless of the greenhouse gas effect, as the ‘throttle’ for the engine has been reduced.
The formula does not account for the energy loss due to the absortion of CO2, which is greatly increased by the ocean during periods of cooler temperatures, entrapment in ice, etc…
Overall, I would say that the efficiency of the machine is set too high and many other varables are missing.

John Aiken
January 3, 2011 10:58 pm

The theory is based on a 2-dimensional world. (Only up and down) The real world is 3-dimensional. The radiation does not equally radiate only up and down. All the radiants above the horizon will either go out to space or redirect down. The total net back to Earth will always be well less than 50%. There are simply a lot more “Up” radiants than “Down ” radiants. All of the “Global Warming Models” are based on a 2-dimensional world and will always fail in the “Real World”.

Michael
January 3, 2011 11:17 pm

People don’t need the mainstream media anymore. They can go to the internet to get the real scoop on stories. The lies told my the MSM are easy to sift out using the internet.

Baa Humbug
January 3, 2011 11:31 pm

Willis could you please clarify the following paragraph for me…

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 metre squared of forcing.

Should that read 0.84DegC temp rise for each DOUBLING OF CO2?
I thought sensitivity was the rise in T for each doubling of CO2

crosspatch
January 3, 2011 11:34 pm

“CO2 absorbs very little in the visible frequencies.”
I wasn’t meaning visible frequencies. Solar radiation outside the atmosphere includes a lot of IR in addition to visible. This IR will be absorbed by the GHGs on the way in.

4TimesAYear
January 3, 2011 11:35 pm

There may be a problem in that we’re still working on the assumption that warming follows the CO2 increase rather than warming causing the CO2 increase….

gnarf
January 3, 2011 11:44 pm

Hello,
It seems to me S is the sensitivity to all greenhouse gaz in the atmosphere, not only CO2. If I understand correctly, your calculation shows that doubling the total amount of greenhouse gaz in atmosphere should lead to at least 9K temperature increase.
But to estimate the effect of CO2 doubling, you have to find how much a CO2 doubling would increase the total greenhouse effect. I don’t know the exact figure, but if we assume CO2 is responsible for 10% greenhouse effect, then doubling CO2 should increase overall greenhouse effect by 10%—> doubling CO2 would lead to at least 0.9K temperature increase.

Günther Kirschbaum
January 3, 2011 11:48 pm

Have you considered checking the dreaded and skewered peer-reviewed literature? Perhaps some lucky scientist got your answer by accident?

Mike McMillan
January 4, 2011 12:39 am

Efficiency at 33% would be the amount of heat going through the engine that actually gets turned into work, in this case moving the ocean around, lifting the water for t-storms, and stirring up the wind. Could that be the “losses” that you find messing up the numbers? Sorta backwards from the Physics 101 concept of loss.

Nylo
January 4, 2011 12:57 am

I have some difficulty understanding why you say that the ammount of energy re-radiated by the greenhouse gasses is equal to T/S. It doesn’t make sense to me. It means that if sensitivity happened to be really small, say zero, the ammount of energy re-radiated would be huge, we would have a very powerful greenhouse effect. Yet in an atmosphere where greenhouse gasses didn’t exist at all, the sensitivity would be zero AND the re-radiation would be zero too. Something’s really wrong there.
The smallest the sensitivity, the strongest the GHE at play? Sorry, that doesn’t make any sense.
I think that the problem in your equation is that, in “T/S”, T should not be the actual temperature but the differential of temperatures created by the GHE. In other words, T would be the actual temperature minus the no-GHE-temperature. For the Earth, I think it is estimated as 33K or so, according to wikipedia, although I have many doubts regarding that value, but that’s another story. How does that effect your calculations? Well, it reduces the minimum possible sensitivity by an order of magnitude, i.e. 0,9K/doubling instead of 9K/doubling.

JohnH
January 4, 2011 1:17 am

Do any of these models take into account the sun only shines on 1/2 the globe at any one time, if a Greenhouse gas absorbs radiation could it also radiate it more with no input.

Dave F
January 4, 2011 1:26 am

The ‘canonical’ model is wrong.
I know, impossible, but still, check Hansen 4:25.

wayne
January 4, 2011 1:27 am

John Aiken:
Well John, at last someone see the same hole in all of this ‘exact’ climate budgeting I have raised that more than once here. Colloquially it is called the dip of the horizon effect and your right, it gets surprisingly large fast with altitude. Just 2-3% of all energy in the atmosphere, evidently ignorable by most climate scientists. Maybe they will listen to you.☺
However, in Willis’s calculations above it would just lump into L as it should it that case.
Willis:
Interesting. Wonder why you, Ferenc Miskolzci (2004,2007)and Kiehl, Ramanathan (2006) & Inamdar all seem to come up with 33% (0.33? or 1/3) in those papers for that factor. Physics? Kirchhoff’s law is the only thing that I can find that exactly explains that and if that is true even albedo variances don’t matter. You seem a hop, skip & jump from verifying his paper. Maybe you can share in the Nobel one day.
9C per doubling, known by all impossible so the only other explanation is Miskolzci is correct, the long wave optical thickness doesn’t change over time and co2 concentrations. In sixty years, nada, no change! The one third factor, it hasn’t changed in one hundred years while co2 concentration has risen. In the end the effect of co2 must be zero, not small, zero. AGW has been proven wrong over and over again but most people won’t even read the papers that did it.

January 4, 2011 1:38 am

I know that I have said this before, but isn’t it time someone conducted the experiment to prove or disprove “the greenhouse gas theory”?
Because I can’t find anything that makes Fig. 1 above any more than a theory, and as a seaman I prefer to work in facts only.

chris smith
January 4, 2011 1:40 am

Co2 absorption is already saturated. Doubling co2 will have virtually no impact. Quadrupling it would have less than twice the impact as doubling etc.
I.E. It is a non linear process. So there is no point in modelling impacts of co2 increases – we are already at the max, the saturation point.

Jordan
January 4, 2011 1:41 am

Hello Willis
You will appreciate how, in control engineering, we usually work with changes from an underlying condition. The relevant parameters relate to the slope of system changes, and not so much the abolute slope from some null state.
I often see discussion about climate sensitivity from the absolute state (of no CO2), and that leads me to the same question. It was one of the first things that crossed my mind as I read your post.
Is is worthwhile looking at how your analysis would change if you were to focus on the incremental response that an assumed forced change of CO2 emissions might have on the system. As you say – not so much the instantaneous dynamic response, but the long-term equilibrium change.
I suspect all of the changes will be concerned with the “slopes” in the inside portion of your diagram. It would also tease open the assertion of amplification by feedback – that’s something which greatly troubles me for an assumed passive system.

AndrewG
January 4, 2011 1:48 am

shouldn’t you be starting with a non-atmospheric model where Solar =L to get a blackbody temperature (Which based on the Lunar Regolith is around 238K) and then applying the other terms to the difference in temp as T/S and Delta-H? or comparing between a non-atmospheric and atmospheric?
The only other thing I can think of is DeltaH acts as a damper

steveta_uk
January 4, 2011 2:02 am

As far as I can tell, everything works out from trivial algebra up to the point CO2 is mentioned.
I cannot see the logical connection between all the preceding info which looks correct, and the assumption inserted at this point that CO2 is relevant in any way. I’m not saying CO2 isn’t relevant, just there is a logical disconnect at this point.
So if there is a problem in this analysis, I think it has to lie in the sentence:
“And in more familiar units, this inequality is saying that the sensitivity must be greater than 3° per doubling of CO2”
“And in more familiar units, this inequality is saying that the sensitivity must be greater than 3° per change in unknown units of whatever is driving the so-called greenhouse effect”.

CodeTech
January 4, 2011 2:02 am

JohnH gets it right.
What about NIGHT? That’s the half of the planet that is ONLY radiating. No matter how complicated you want to make the sun side, the night side is ALL about radiating enough energy to maintain the temperature that is overwhelmingly defined by the overall gas mix and pressure.
If it gets too warm on the sun side, extra energy is radiated out even faster from the night side. End of story.

anna
January 4, 2011 2:07 am

A small question from an ignorant layman… If according to the figure Energy in = Energy out, then there should be no warming at all? I guess I am misinterpreting the figure. It would make sense if Energy out = Energy in – Energy absorbed = System loss (L)?

Laurence M. Sheehan, PE
January 4, 2011 2:07 am

There are so few CO2 molecules in Earth’s atmosphere that they could be far warmer than they are,adding heat to the atmosphere, and it wouldn’t make a significant change in atmospheric temperatures. The sun giveth (or not), and IR radiation into outer space taketh away.
Molecules of CO2 and other air molecules are NOT “black bodies”, perfect absorbers and perfect radiators of IR. It is long since the time to be treating them as such in “calculations.

TomVonk
January 4, 2011 2:22 am

Q=T/S is just a 0 dimensional model (not even 1 dimensional) .
It makes some very limited sense for a homogeneous , isothermal body in radiative equilibrium .
There is no energy transport in this “model” per definition , the temperature gradients are zero everywhere .
The real Earth is not a homogeneous isothermal body in radiative equilibrium and the 0 dimensional “model” has no relevance for its dynamics .
You just trivially found out that Q=T/S with S and T constant is wrong and can’t even begin to describe what happens when the spatially highly non homogeneous temperature and radiation fields vary .
For the real Earth S is ill defined and if it is considered as a statistical parameter , then it depends on the chosen time scale and is highly variable with other dynamical parameters (ice cover , cloudiness , albedo , ocean currents etc) .
The usual handwaving about time averages where every inconvenient (but very real !) dynamical process goes away and cancels is just the well known “and here is where the miracle happens” .

January 4, 2011 2:28 am

This whole article is negated by the fact that back radiation CANNOT cause warming of the earths surface. It is impossible under the laws of thermodynamics that a greenhouse effect could work in this way. Therefore there is no need to look at feedbacks, positive or negative as there is nothing for the feedback to feed upon.
http://www.ilovemycarbondioxide.com/
http://claesjohnson.blogspot.com/

Keith G
January 4, 2011 2:30 am

Willis, you lost me early on. My business school math isn’t enuff to keep up with you. Rather than try to figure it out I watched this video to cheer myself up. Just 2 minutes long, safe for work.

jimmi
January 4, 2011 2:39 am

Willis,
I don’t understand why your reply at 12:58 is an answer to gnarf at 11:44. He said – haven’t you calculated the sensitivity to doubling all GHG’s not just CO2?

Bas Jong
January 4, 2011 2:40 am

I see no flaw in your reasoning, so if the “canonical equation” is correct, the obvious conclusion has to be that the expression used for calculating the change of radiative forcing with the change of CO2 concentration is not valid in the real world.

Dave (UK)
January 4, 2011 3:00 am

I’m no mathematician, but given that the GHG properties of CO2 is one of diminishing returns, and that the climate ‘scientists’ claim that the 100 ppm increase in CO2 concentration over the previous 100 years caused the observed 0.7 °C temperature increase, how can they say that the next 100 ppm (2 ppm per year over the next 50 years) will result in a much larger increase of 2 – 4 °C?
Is the IPCC’s “sensitivity factor” really so dominant? Is that why the computer models are so pessimistic, or is it just more pseudo-science?

JohnL
January 4, 2011 3:08 am

Looks like the equation is based on sensible heat flows only. It has no way to take into account the latent heat effects that are 2 to 3 orders of magnitude larger (for water/water vapor).
The latent heat of the water vapor need never be released. If there is cooling the release of this energy prevents the temperature from dropping further. It provides a massive heat storage potential (flywheel effect) at the atmosphere’s gas/liquid interface. It occurs with very small temperature changes in either direction and resists any temperature change.
In this case the important variable is the change in mass of water vapor in the low atmosphere, not the change in temperature.
It is also consistent with the outgassing theories for CO2.

kai
January 4, 2011 3:10 am

I think the explanation for the value of S you derive is simply a misunderstandind: T sensitivity is not usually understood for absolute value – where a linear relation would make no sense anyway. It is defined for (more or less) small perturbation. The idea is to define delta T = S (delta Q – delta H). If you use those relations, your analysis fall appart, imho.
Not that it would make CAGW any more believable, but the basic E balance presented by its supporters really makes sense. It is the feedbacks and also the assumptions relative to the non radiative heat exchanges and thickness of the zone where they take places that are really fragile imho…

MostlyHarmless
January 4, 2011 3:15 am

Willis Eschenbach says:
January 4, 2011 at 1:03 am
I’d need a citation for that claim, crosspatch. My understanding is that at the temperature of the sun, 5K°C, very little of the radiation is in the IR. Always willing to learn, though.
About half is in the IR region, almost entirely SW IR.
http://en.wikipedia.org/wiki/File:Solar_Spectrum.png also shows SW IR absorption by water vapour, with a little by CO2. This accounts for much of the “absorbed by atmosphere” quantity on the Kiehl & Trenberth budget diagram.
I’ve been through the K&T Radiation Budget papers with a sceptical “fine toothcomb”, and was initially highly sceptical of the magnitude of the downgoing LW IR (~324 W/m²), and the apparent omission of upgoing radiation of equal magnitude. However there have been several experiments to measure the downgoing IR, and I’m satisfied on that score – they find fluxes of 300+ W/m².
The subject of upgoing vs downgoing radiation is a little more complicated, however. Logically, one would expect half of the total GHG radiation to be upwards, and half downwards, yet K&T apparently shows no such thing, with all the emission downwards. K&T have been much criticised in online blogs on this point, and I joined in that criticism. However, the radiation experiments appear to confirm their figure, with the outer envelope of the radiation spectrum following (though a little below) the relevant Planck curve. (That “little below” would appear to reinforce another criticism of K&T, that GHGs do not behave as a perfect “black body”). The spectrum is clearly an emission spectrum, showing the bands from GHGs. However,the critical point is the corresponding spectrum from 20km looking down – this is NOT an emission spectrum, but an absorption spectrum,with GHG absorption bands and the “atmospheric window” all showing up clearly. Most examples of these spectra are contained in papers with limited or no public access, but an illustration can be found at http://mensch.org/5223/IRspectra.pdf
I can offer no simple explanation for this apparent lack of “equal and upward” GHG radiation, but I’m forced to accept it – the evidence is clear. My apologies to K&T on THIS point, at least.

January 4, 2011 3:17 am

Willis: Aren’t you assuming that the forcing from Total Solar Irradiance (which includes Downward Shortwave Radiation) is the same as the forcing from the Longwave Radiation from greenhouse gases? This may hold true for land but I don’t believe it’s the same for the oceans. The oceans have their own greenhouse effect because DSR penetrates to depth while the oceans can only release heat at the surface.

January 4, 2011 3:18 am

Assume that the global temperature would be like in 1850 and the CO2 content of 280ppm. Then 280-400ppm barely gave 0.7 C and 400-650ppm (David Archers Modtranprogram) would give 0.7 C if it were not for T4 (energy radiation increases with T ^ 4) … so an increase to 650ppm would result in considerably less than 0.7 C.. Consider that two equally surfaces with 50C and 80C-radiates as if both were not -15C but 10C, average temperature is for idiots … Increased temperature differences with the same average temperature gives greatly increased cooling by radiated energy.
Therefore, the earth probably emanated roughly the same when the Sahara was forests and at least the North Pole 5-6C warmer ..
Sahara was warmer at night and colder during the day, radiating less energy with the same average temperature.
Furthermore, it appears not all atmospheric physicists bring water extremely strong thermostat, when it is available in liquid and gaseous form.
Therefore, the Earth never had a warmer than the maximum life-friendly environment.
When sun has expand all the water will be gasified cease the thermostat, in G years, man must have moved from Tellus long ago.
All about the scientific redacted CO2-threat was only the question of energy system when 4times global population have our buying power, nuclear is all reedy the cheapest, so what´s the problem?

January 4, 2011 3:28 am

Some wrong over; +50C and -80C radiates like both where +10C not -15C.
T4 is one of the strongest negative forces and whit water in liquid and gas form it will keep earth from warming catastrophe, but not cooling, because when water frees, the thermostat stops working, and albedo even cool it more.
Sorry for my bad English and hasty writing…. ;o)
//gunnar

Jens
January 4, 2011 3:34 am

Dear Willis,
I have enjoyed reading all your previous interesting posts but this one is a complete mystery. Your equations bear no resemblence to the standard formalism, for example in the reference Kiehl07. First of all, the standard equations refer to small deviations from an initial balance between ingoing and outgoing energy flux. The ‘forcing’ delta Q is a change in the balance of these fluxes which must be reestablished by a change in temperature. Only then can the system response be assumed to be linear in the temperature (change). Your loss term L confuses the picture and should not be there. The system response deltaT/S should include both the direct radiation into space from the surface (L) and the indirect radiation from molecules in higher layers of the atmosphere. Otherwise S does not correspond to the normal definition of climate sensitivity.

TimTheToolMan
January 4, 2011 3:41 am

I’m with Nylo and later AndrewG on this one. Surely the T/S term must be the temperature due to greenhous gasses (~33K) and thats not the whole temperature (~288K).
If you dont think so, then could you please explain the “meaning” behind the term T/S if thats at all possible?

January 4, 2011 3:49 am

Willis,
O/T, but were you Long by Chron. or Marcq St. Hilaire?

Baa Humbug
January 4, 2011 3:55 am

Houston we have a problem.

From the left side of the chart we have…

Q = T/S + SOLAR

The canonical equation is….

Q= T/S + ΔH

Therefore…

SOLAR = ΔH
WUWT??
I also think T/S may need to be halved but I haven’t got my head around that yet.

Colin Davidson
January 4, 2011 4:13 am

A couple of observations.
1. The atmosphere is heated by two mechanisms:
A. Energy absorbed from sunlight. This occurs mainly in the upper atmosphere.
B. Energy absorbed from the surface. There are 3 components to this:
(i) Direct conduction (about one fifth). This enters the atmosphere at the surface.
(ii) Net Radiation (about the same as conduction – about one fifth). This enters the atmosphere at a highish level – it is a measure of the inefficiency of the back-radiation. ( For wavenumber 670, John Nicol has calculated that all the back radiation must be coming from the lowest 5m of atmosphere – as this will be nearly the same temperature as the surface there will be little NET absorption at this frequency. For other frequencies, where the average height of emission of the back radiation is much higher, the temperature is less and so the back radiation cannot balance the surface emissions, and there is a NET transfer of energy.)
iii) Evaporated water condensing in the atmosphere as fogs, mists, frosts and clouds (about three fifths). This is all over by around the cloud tops.
2. The energy from the surface is converted to atmospheric kinetic energy no matter what its original form or entry height. It modifies the Adiabatic Lapse Rate (9.8DegC/km) to some other value, on average taken to be 6.5DegC/km.
3. The Surface anchors the atmosphere: the atmosphere cannot heat up and maintain the lapse rate without the surface driving it. (or to put it another way, if the conditions are not sufficient to maintain the surface at a new, elevated temperature, it will cool down, dragging the atmosphere with it.) The critical sensitivity is therefore that of the Surface. (This also satisfies commonsense – we want to know the relationship of surface temperature with changes in GHG concentration, so we shouldn’t be calculating what is occurring high in the atmosphere – we need to calculate for the surface.)
4. When the surface heats up, the energy emitted as radiation increases , as does the energy emitted as evaporated water. (In contrast, if you heat the atmosphere, all you get is an increase in radiation). So the sensitivity of the surface to a change in conditions (either a change in back-radiation, or a change in insolation) is much less than the sensitivity of the atmosphere. [The change in evaporation rate is one of the big unknowns. The climate modellers use a very low figure – around 2%/DegC. It could be much higher than this, near the theoretical maximum of 7%/DegC.] If you plug in the simple numbers from the Kiehl & Trenbeth diagrams you get between 0.095 and 0.15 DegC/W/m^2 for the surface sensitivity, or between 0.35 and 0.55 DegC for a doubling of CO2. Let’s say 0.5DegC.
4. To get any higher than this AT THE SURFACE you need to make rabbits come out of hats. Specifically the static increase in Forcing at the Surface has to be much higher than the 3.7W/m^2 at the Tropopause. For example, for a 3DegC increase in surface temperature the increase in surface forcing has to be between 21 and 31W/m^2. About 15W/m^2 of this is due to increased atmospheric temperature (therefore increased back-radiation). The remaining 6 to 16 W/m^2 also has to come from increased back radiation – and there’s only one way to do that – by increasing the GHG concentrations sufficiently to lower the height of emission of the back-radiation, thus increasing its intensity.
5. Such a change could not be due to the changed CO2 concentration. Virtually all back-radiation from CO2 is coming from below 200m, the vast majority from below 20m, so in the CO2 frequencies the surface and back radiation are nearly balanced. The only way would be to greatly increase the water vapour concentration, so that the inefficient absorption bands in the water spectrum are greatly improved.
6. I guess this long ramble has merely shown that to get a high sensitivity you MUST have positive water vapour feedback, and it must be quite fierce. This is the area where I think the CO2-causes -lots-of-warming hypothesis is weak. The detail of the effect of water vapour concentration on the SURFACE conditions is in my view central to that hypothesis, but is mostly vague, lost in the models. In particular, the modellers need as high a surface sensitivity as possible (ie as low an increase in evaporation rate as possible) but the largest possible increase in atmospheric water vapour. So they have a 2%/DegC increase in evaporation rate but a 7%/DegC increase in atmospheric water vapour.
7. I think that area needs more explanation to satisfy us ancient sea-dogs. It is relevant that measurements suggest evaporation rate changes around 5%/degC.

Brett_McS
January 4, 2011 4:14 am

The elephant in the room has to be ocean heat – the rest is round-off error in comparison. One buck of that bronco (to mix metaphors) and all the delicate little atmospheric calculations come crashing down.

Richard S Courtney
January 4, 2011 4:23 am

TomVonk:
I completely agree with your post at January 4, 2011 at 2:22 am . It summarises to your statements that say;
“The real Earth is not a homogeneous isothermal body in radiative equilibrium and the 0 dimensional “model” has no relevance for its dynamics .
You just trivially found out that Q=T/S with S and T constant is wrong and can’t even begin to describe what happens when the spatially highly non homogeneous temperature and radiation fields vary .”
Energy lost by radiation from a surface is proportional to T^4. Therefore, small changes to temperature distribution over the Earth’s surface have large effect on total radiated energy loss from the total surface.
The cartoon K-T budget that Willis is assessing is so simplified that it is plain wrong to the degree of being meaningless. And all Willis’ analysis does is to illustrate that the K-T budget is plain wrong. The cartoon is a useful illustration of the GHG but it is not an analytical tool, and this is why GCMs are constructed.
Nobody is more AGW-skeptic than me, but I see no point in assessing a cartoon used for illustration purposes.
Richard

January 4, 2011 4:42 am

The system equation completely ignores cloud and dust cover, which reduce I. The diagram shows that ALL exiting radiation comes from the surface or was absorbed from below and re-radiated in the atmosphere. There is no factor for incoming energy that “bounces off” the atmosphere and back into space, or was absorbed before it got to the surface and reradiated into space.
So either the incoming arrow is drawn incorrectly, and I is a measured value at the surface, not from space, or it would seem there’s a huge factor missing.

DocMartyn
January 4, 2011 4:49 am

here is a model of the atmosphere:-
you note that the higher up the gravity well you go the lower the molecular weight of the molecules. Also note that the ‘lapse rate’ is also present.
With regard to the atmosphere, the hotter it gets then the distribution of molecules at the top of the atmosphere changes; you get more low molecular weight molecules. The molecule with the lowest molecular weight is water. Heat the atmosphere and gravity fractionation increases the number of water molecules at the top; where they can radiate heat into space.

January 4, 2011 4:56 am

Willis,
the original equation in Kiehl is differential. delta Q = lambda * delta T
You are not using differential values?

January 4, 2011 5:02 am

The missing factors!
Whats the equation that calculates the CHANGES of T/I T/S and E? The T/I is a varible factor that effects S (sensitivity). What were the T/S and E and S during MWP? LIA? Who decided to make them constants ? Were beeing fooled by the lack of time perspective and the redicoulous assumption of co2 as main driver of climate.When you add and find the true”forcings” into the histrorical changes of T/S E and S you will find the keys to complete the equation of the radiation budget of the planet. S changes! We have relations between the factors that are not linear.
Whats the forcing behind KAOS?

gary gulrud
January 4, 2011 5:03 am

The atmosphere heats the oceans by conduction alone. Back-radiation is never an issue because the emissivity of CO2 is 1/1000th that of the liquid/solid surface.
It’s elementary.

Steve Keohane
January 4, 2011 5:13 am

Another thoughtful piece Willis, thanks. I have had the nagging feeling the important factor is the amount of radiation hitting the earth’s surface, and believe crosspatch is correct wrt IR composing a large fraction of TSI. Someone else posted a reference above, here’s one I keep. http://i55.tinypic.com/zn1yt3.jpg
If CO2 is as interactive with IR as the CAGW people profess, it impacts incoming as well as outgoing, ie. blocking IR coming in. This would make CO2 self-regulating/limiting, more= more atmospheric retention of heat, but less incoming IR or heat to retain. The main problem I see with this is that most of the incoming IR is absorbed by H2O, so CO2 is hardly a player. Regardless of formulas and how things work out on paper, CO2 never lives up to high or even significant sensitivity.
Intellectually, under ideal circumstances, communism seems like a good idea. The only flaw is not taking human nature into account.

Dave Springer
January 4, 2011 5:17 am

crosspatch says:
January 3, 2011 at 10:38 pm

I think it still doesn’t take into consideration a large amount of heat that is released above most of the GHG and so doesn’t get 50% re-radiated back down to Earth. I am talking about condensation and freezing taking place at high altitude. Most of the stuff assumes that heat is all released at the surface and must travel through all that GHG, I don’t think it is/does.
Also, what impact would increased CO2 have on absorbing *incoming* solar IR and re-radiating half of that into space?

The fly in the ointment is that thermal IR cannot heat the ocean. It only heats the land. IR is absorbed by water in the first few micrometers at the surface. This doesn’t heat the body of water at all but instead increases the evaporation rate. The thermal energy is thus instantly carried away from the surface in latent heat of vaporization. Water vapor being lighter than air it carries the latent heat upward until adiabatic lapse rate causes condensation. So the IR energy never registers on a thermometer at the ocean surface but rather only registers at the cloud level. That’s why the downwelling thermal IR from CO2 doesn’t raise the surface temperature anywhere near as much as AGW boffins think it must.
Over land the downwelling IR does indeed heat the surface but since only 30% of the earth’s surface is land only 30% of the downwelling IR has any effect on surface temperature. The other 70% only shows up in the cloud layer. Then since clouds reflect up to 85% of visible sunlight the clouds radically limit daytime heating of the ocean which then lowers the evaporation rate which results in fewer clouds and it just keeps going round and round in that manner.
The bottom line appears to be, near as I can tell, is that CO2 doublings beginning from a base level of 150ppm or more (where the logarithmic curve is well established) can increase surface temperature by 1.0C and that’s it. The so-called amplification by water vapor is fictional. Moreover the surface temperature increase can only be observed over land with more of it at the higher latitudes in the winter when there is little evaporation occuring because the surface is frozen. Because there is a greater concentration of land surface in the northern hemisphere the NH will exhibit more surface temperature increase than the southern hemisphere.
There is not a single observation that contradicts anything written above. Observation only supports it.

Edward Bancroft
January 4, 2011 5:23 am

crosspatch:“so, what impact would increased CO2 have on absorbing *incoming* solar IR and re-radiating half of that into space?”
JohnH“Do any of these models take into account the sun only shines on 1/2 the globe at any one time, if a Greenhouse gas absorbs radiation could it also radiate it more with no input.”
The other thing missing from this kind of diagrammatic explanation is what happens at night when the sun is not shining. It would be instructive to start explaining the ‘greenhouse effect’ from that viewpoint, as it would show the other part of the IR-active gas dynamic, their cooling properties.

John A
January 4, 2011 5:30 am

Willis,
I think you’ve established that the Kevin Trenberth zero dimensional cartoon version of the “greenhouse effect” leads to absurd results. But that’s about it.
Fortunately you haven’t made the same terrible mistakes as your previous thermodynamics forays (eg “The Steel Greenhouse”) which comes as something of a relief.

Richard111
January 4, 2011 5:34 am

I agree with crosspatch and Dave Springer.
the M-B kinetic energy distribution curves for gases.
To claim re-radiation of half up half down of all
absorbed energy is nonsense and invalidates
all calculations.

Molon Labe
January 4, 2011 5:35 am

Re: Dave Springer @ January 4, 2011 at 5:17 am
So maybe it’s:
+CO2 => +Downwelling IR on ocean => +Evaporation => +Clouds => Global Cooling!
but then
-Temp => +Ocean CO2 absorption => -Clouds => Negative feedback => Stability

Chris Smith
January 4, 2011 5:39 am

@Willis Eschenbach
I agree with what you say (i.e. the model is for all types of forcing) but the IPCC is obsessed with CO2 increases, which seems daft since that absorption is already saturated. So it seems a bit irrelevant. Or did I miss something?
Also, CO2 is good for life on the planet. So again, it seems a bit daft to worry about having too much of it.

Frosty
January 4, 2011 5:42 am

“In the tropics, mid-day surface insolation averages about a kilowatt per square metre, and the amount reflected by clouds is on the order of 340 W/m2.
This gives us a cloud effect about five times as strong as the global average. In the tropics there is a change of 5 W/m2 in reflected energy for each 1% change in cloud cover. This allows for large swings, as I showed in my paper.”
Looking at the graph of low level tropical cloud cover http://www.climate4you.com/images/HadCRUT3%20and%20TropicalCloudCoverHIGH-MEDIUM-LOW%20ISCCP.gif
It seems there has been a decline of approximate 2% between 1985 and 1998.
If we assume the IPCC figure of 1.6 W/m² for the net anthropogenic forcing.
Would it be correct to assume there has been a tropical cloud effect at least 6 times the proposed anthropogenic forcing over the period? Can this account for the correlation in temperature rise without anthropogenic forcing?
T.I.A. much appreciated.

Dave Springer
January 4, 2011 5:47 am

Steve Keohane says:
January 4, 2011 at 5:13 am
“If CO2 is as interactive with IR as the CAGW people profess, it impacts incoming as well as outgoing, ie. blocking IR coming in.”
That’s true and it’s even truer for water vapor but very little of the sun’s energy is thermal IR. The sun presents itself as a nearly ideal 5000K blackbody continuous spectrum with peak emission at 0.5 micrometer (yellow). Emitted energy falls off rapidly on either side of the peak. CO2 absorption begins at 5 micrometers and longer. There is essentially no energy in sunlight at wavelengths that long. Energy emitted by the earth however approximates a continuous 255K blackbody spectrum with peak emission at 12 micrometers which is very near CO2 peak absorption wavelength of 15 micrometers. Water vapor however overlaps about half of CO2’s absorption peak so when and where water vapor is present (which is most of the time in most places) it negates much of CO2’s potential as an insulating greenhouse gas.

Charles Duncan
January 4, 2011 5:50 am

I’m not sure it’s fair to treat the atmosphere as a single thin layer, or to say that the up-going radiation from the atmosphere is the same as the down-going:
http://barrettbellamyclimate.com/page5.htm
I asked Jack Barrett why, and he kindly explained to me that it was because the emissions to space are from the much colder top of the atmosphere.
I guess it’s all to do with optical density and lapse rate…

Joe Lalonde
January 4, 2011 6:04 am

Willis,
I’m amazed science has yet to understand the importance of pressure fluctuations in a enclosed biosphere. The more gases building in the atmosphere, the more density to wind and the changes to the surface salt on the oceans.
Growth up mountainsides shows the expansion of the atmosphere has exerted against the ceiling of this biosphere.

Dave Springer
January 4, 2011 6:16 am

John of Kent says:
January 4, 2011 at 2:28 am
“This whole article is negated by the fact that back radiation CANNOT cause warming of the earths surface.”
Technically correct. What back radiation does is slows down the rate of cooling. Just like a layer of clothing doesn’t actually warm your body but rather slows down how fast your body loses warmth. Greenhouse gases are insulators. Insulation doesn’t supply heat it just slows down the loss of heat.

gnarf
January 4, 2011 6:20 am

So a climate sensitivity of 1 K (W m-2)-1 is exactly equivalent to a change of 3.7°C from a 3.7 W m-2 change from doubling of CO2. To convert from one to the other, you multiply or divide by 3.7.
I see what you mean. But on your drawing, S is the climate sensitivity induced by all greenhouse gas effect. Even with the exact same units (K.w-1.m2) I do not see how you can easily switch from S to Sco2 alone.
The equation works with S, but not sure why it should work with SCO2 alone, excepted on Venus maybe.

Nylo
January 4, 2011 6:21 am

S (K/Wm-2) = How much temperature increases when we increase the forcing by 1 Wm-2.
1/S = How many Wm-2 of forcing are needed for a 1K increase in temperature.
If we call E to the total energy per unit of area that GHG reradiate, i.e. E=T/S, it results that:
E=T/S -> 1/S = E/T, therefore
Watts per 1K of Temperature change = Total energy / total temperature CHANGE.
Therefore Willis, in your T/S expression, T is not the absolute temperature, but the temperature change due to GHGs, i.e. about 33K. This results in a minimum posible sensitivity which is an order of magnitude smaller than you calculated.

Nylo
January 4, 2011 6:26 am

I am quite sure to have solved Willis’ problem at 12:57 a.m. and further explained it a few minutes ago. Yet the post seems to have escaped Willis’ notice.

January 4, 2011 6:26 am

342 W/m^2 is for directly perpendicular to the sun, not at the polls. Winter in the Arctic get’s nothing. Thus the 3d aspect to the atmosphere is important, as warmed parts of the world is trying to heat the cold parts not getting heated by the sun.
Plus, he only part of the planet that is directly perpendicular to the sun and getting 342 W/m^2 is at noon, hence only a small diameter of surface gets that input, the rest of the planet gets less. Soon as night comes, there is no solar input. So again, those parts of the planet getting sun will have its heat moved into colder areas. This is why there are winds (fiction loss as well as redistrubution of heat).
Bottom line is this model is wrong because it is far too simplistic. It is modeling a flat surface equally getting the same solar input. The real world is a sphere, which has only a small percent of its surface getting solar input. Hence wind moves heat around with frontal systems. A large portion of your upwelling must be supplying this redistribution.
Take this into account and CO2 sensitivity drops to zero.

David L.
January 4, 2011 6:35 am

Willis, another excellent and thought-provoking article. As a Physical chemist, all these equations worry me. I remember back in graduate school when we were collecting vibrational structure of electronically excited diatomic molecules; my advisor would say “Why bother figuring out the theoretical quantum mechanical equations when you can just shine a laser on the molecule and nature solves the equation for you”. He is an excellent experimental chemical physicist. Most of our energy was spent on the experiments and then we’d use theory to check our results. If theory agreed that was a bonus. But if it didn’t agree, then that was usually the theory was incomplete.
It really bothers me that AGW is based primarily on observational (historical) data and computer models. Where are the experiments? I checked the literature and there doesn’t seem to be much. How hard would it be to set up a real Greenhouse modelling the major parameter of the earth and just measure what’s going on? All major factors can be controlled and manipulated. Sure we can’t control any weather patterns in the greenhouse, but we aren’t interested in weather..we are interested in the climate.
I tried this in my backyard with some glass bottles. (A similar experiment was also found on Youtube demonstrated by a fourth grader so I’m not saying this is amazing science: just the first step in thinking about what a real experiment would look like). One bottle had air, one had air and 50g water, one had 50g water and 100% CO2 (from the beer meister!) and each had a type K thermocouple attached to data logger. The air temp was 1.7C. Air alone was 7.2C. Air plus water was 12.8 and CO2 plus water was 15.3. Difference by adding water was 5.6C. Difference by switching air with 100% CO2 was only 2.5C after 2 hours of monitoring (water’s a better greenhouse gas than CO2….who would have known????) These were then moved to the shade and each cooled to 5.6C with the same rate constant (it’s the cooling of the 50g water and glass bottle so that makes sense).
My point is: why isn’t someone tapping into all that AGW research money and doing real experiments? Throw the equations and computer models away and start doing the experiments!!!! It doesn’t have to be hard…and they’ll be a lot closer to the truth than coming up with a bunch of partial and/or faulty equations.

cba
January 4, 2011 6:35 am

Willis,
I know this is not your model, but it is not any sort of a model of the Earth. There seems to be confusion between power and thermal energy, at least in the choice of variable names. The L eqn is wrong. the assumption that T is linear is wrong, the assumption that the power flow up and down is the same amount is wrong. There is not a conservation of energy at work.
To support my comments, lets check out some simple common numbers.
the toa is about 342 w/m^2 but the albedo is roughly 0.30 meaning that only about 235 w/m^2 actually enters the atmosphere to be absorbed by atmosphere and surface. the surface averages around 288K and radiates by stefan’s law about 391 w/m^2. Total power balance means that a total of around 391 w/m^2 must be hitting the Earth’s surface. we can make the crude assumption that most of the 235 w/m^2 incoming power reaches the surface. That means we are missing 391 -235 = ~155 w/m^2 which must be coming back to the surface from the blocking of the atmosphere. Note that ghgs are good for about 120 w/m^2 blocking in clear skies, leaving around 35 w/m^2 to be accounted for by our typical cloud cover IR blocking / reemission for about 60% coverage. With these, the surface is in balance. For the outgoing LWR power balance with incoming power means that what leaves the atmosphere must be a total of 235 w/m^2. For clear skies what escapes is 391 – 120 (ghgs only) = ~270 w/m^2 – which is too much were all of the sky to be clear. What balances this is the cloudy sky component that emits somewhat less than 235 w/m^2 due to the lower temperatures of the cloud tops and the weighted average comes out to 235 w/m^2 for balance.
Note that while the atmosphere in a single shell must have both conservation of energy (and hence conservation of power) AND must radiate upward and downward at the same rate, the flow of power downward will not be the same as the upward flow. For one thing, the cloud component has a different temperature bottom and top – which are radiating surfaces for thick clouds.
The atmosphere must radiate (on average) downward to the surface at a rate of ~150 w/m^2 to maintain surface T and power balance. Clear skies (~40%) permit the surface to radiate about 270w/m^2. If we take what escapes for this, 0.4 x 270 = 108w/m^2 averaged over the whole. Add in the whole average for outbound, ASSUMING the 150 w/m^2 downward provides us with 258 w/m^2 plus the top of cloud emissions for the cloudy sky 60% portion. NOTE that we’re already above the 235 w/m^2 balance point by 23 w/m^2 and we have not accounted for the cloud radiation which will have to be positive and significant.
Therefore, the assumption of T/S outbound being equal to T/S downward is absolutely wrong in the real world. The back of the envelope numbers don’t even get close.
I suppose one could say it’s what easily happens when one tries to use nonphysical models on physical situations. It has me wondering whether whoever invented this travesty ever successfully passed university physics. I’m pretty sure they never read a book on feedback control systems either. Maybe that’s why they call themselves climatologists.
The only thing useful to do with this model (kheil’s???) is to gut it completely and do something physical, such as along the lines of kheil & trenberth’s 1997 paper – while avoiding their grossly erroneous numbers that they failed to correct in their paper a decade later.

Dan Kirk-Davidoff
January 4, 2011 6:40 am

I don’t have time to track down all the issues here, but the main one is that you’ve taken an equation from Kiehl that’s expressed in terms of changes of temperature and radiative fluxe, and converted it to an equation expressed in terms of absolute temperature and radiative flux. In Kiehl, the equation is that = /sensitivity + . That equation itself is based on linearization of a differential equation expressing energy conservation. It’s no longer valid if you get rid of the &Delta’s! The equation is being used (by Kiehl) to describe a system that is not in equilibrium (it’s warming over time), so it’s unlikely that you can meaningfully derive limits based on thermodynamic efficiency in that framework. That’s why, by the way, your picture has the weird quality of having a fixed T, despite the fact that energy is leaking out of it into the lower boundary! In Kiehl’s formulation, he’s partitioning the imbalance of energy due to CO2 at the TOA (&Delta Q) into a portion that’s going into warming the system (&Delta T/S) and a portion that’s going into warming of the ocean (H).

January 4, 2011 6:40 am

For a climate realist, if the observed differences are this far from theoretical, the equations must be incorrect.
For a global warmist, if the observed differences are this far from theoretical, the earth must be incorrect.

Dan Kirk-Davidoff
January 4, 2011 6:42 am

Sorry, tried to use too much html. I meant to say, in Kiehl, the equation is (Change in Flux at TOA due to doubling CO2) = (Change in global average surface temperature)/(Climate Sensitivty) + (Flux into the Ocean).

January 4, 2011 6:46 am

3 Cheers for the model! Finally, a model that describes the difference in thermal balance between land and ocean. But we still have to address the inherent heat emanating from the Earth’s core (which I know is much lower than solar heating). It is there as a basic starting point on top of which the atmospheric and ocean thermal balance rides. We also need to know how to deal with hot spots in the ocean, which can create a regional hot spot and throw the balance point of your model off. There are clearly regions of some decent size where the water (or air to a lesser degree) are being warmed from the magma coming to the surface. While not a driver, it is a factor that (IMHO) is much greater than CO2’s GHG effects when integrated over the entire planet.

Pamela Gray
January 4, 2011 6:49 am

Hence the Monty Python-esk search for missing heat by the AGW crowd. And the absurd amounts of flung funds being used to do it.
Reminds me much of the wild Alchemy chase to find the “turn base metal into gold” formula. We all know how that turned out.
http://en.wikipedia.org/wiki/Alchemy

Francisco
January 4, 2011 6:49 am

These discussions always confirm my long-held impression that the science of the CO2 greenhouse effect on Earth is, at best, in what biologists call a “pre-embryonic stage,” and most likely not even that far. The egg seems to be there; it hasn’t yet been implanted in the uterus; we are not quite sure if it has even been truly fertilized, and the potential father could be one among many. But the boldest among us see no impediment in predicting the precise behavior and features of the adult it might one day turn into. Medieval astrology was probably more solid.

January 4, 2011 6:50 am

The basic assumption in the construction of CAGW models is that OLR is sensitive to the atmospheric concentration of CO2 and that sensitivity controls the “greenhouse effect” of other atmospheric components. The problem with these models is that it is more likely that water in the processes of evaporation/condensation and freezing/thawing is controlling the rate of energy lost to space and those processes are also controlling the atmospheric concentration of CO2. Think about how much more energy is exchanged in evaporation compared with raising atmospheric temperature.
Temperature sensitivity to CO2 and positive feedbacks are “fudge factors” that tend to make the models appear to work. Read my presentation http://www.kidswincom.net/CO2OLR.pdf and let me know if you think I have made mistakes.

Janice
January 4, 2011 6:52 am

I is presented as a constant, without any supporting evidence. The earth is a sphere, not a flat plane. The sun has variations in energy. In addition, the constant I would appear to be valid only at a point on the earth that is receiving sunlight. What happens at night to the constant I?
S is presented as some magical number that is a constant. What the hell is “S”? Sensitivity? Sensitivity to what? I have found no definition, no table of various values, supporting the notion of a universal sensitivity that can be reduced to a single simple constant.
In surveying, we were taught that if you don’t know where you started, then you don’t know where you are going. Any real science or engineering always begins with a complete list of real known quantities and measurements. As a thought experiment, this is interesting. If it was turned in as a first-year engineering homework, it would get an “F” as being irrelevant to any real problems.

tallbloke
January 4, 2011 6:56 am

Willis
“For starters there is about 100 W m-2 lost to albedo reflection from clouds and the surface.”
This is not a loss to the system, it’s an efficent part of the process of getting from ‘in’ to ‘out’.

January 4, 2011 6:57 am

Sorry for getting excited in my first comment, but overly simplistic models simply produce crude and inaccurate results (I have had too much orbital mechanics I guess).
What you have shown in your calculation is another one of those back of the envelope checks that shows the model above to be incomplete and wrong. What it means is that energy loss and sensitivity are more complex in reality than the model allows. What astounds me in these equations is how energy loss never seems to account for energy used.
Someone once commented that ocean waves, by running laterally, never expend energy. Explain that to battered coast lines. The movement of masses of air and water is energy consuming. Rising masses against gravity are energy consuming. Electrical discharge, liquefying and evaporating, etc all transfer energy. How much of this is thermal based (vs wind or gravity)? And even though you did not want it said, biology consumes a lot of energy. Biology is the act of capturing energy and holding it in a living structure before it continues on its path of entropy.
Since turning the equation around produces nonsense, it means the model is nonsense. There is so much more at work than a bunch of heated air.

Dave in Delaware
January 4, 2011 7:11 am

Willis, a couple of quick thoughts on your diagram:
1) As drawn, Figure 1 implies that T/S Up (upper right) is nominally the same as T/S down. They are not the same, nor should they be. The T/S down should contain only downwelling IR, mostly from mid to lower atmosphere. The T/S Up should represent radiant emissions from the upper atmosphere and includes the reflected radiant energy term, which is 107 of 342 total per K&T. I have not worked through your equations to see the implication, but I suggest that is a place to start.
2) The “U” Upwelling Radiation term is a misnomer – Energy losses from the surface are dominated by Convection and Latent Heat terms, with radiant energy no more than 40% (per K&T diagram) and possibly as low as 8% (per Chilingar et al “According to our estimates, convection accounts for 67%, water vapor condensation in troposphere accounts for 25%, and radiation accounts for about 8% of the total heat transfer from the Earth’s surface to troposphere.”) Again, as it relates back to my first comment, T/S Up as drawn in Fig1 includes the energy transported by Convection and Latent Heat, so would not be equal to T/S down.
3) The T/S Downwelling is dominated by IR from water vapor as noted by MostlyHarmless and others. The Evans and Puckrin (2006) measurements of IR back radiation show CO2 to be no more than 20 to 25% in low moisture winter clear conditions, and in summer with higher humidity, both the numeric value and the percentage contribution of CO2 back radiation drop significantly. Again, not sure how that plays through your math, but we should be careful to keep total “GHG” sensitivity separate from CO2 sensitivity.
I always enjoy your articles. They make me review what I think I know, and I dig back through my saved information to compare with your presentations.
While working on this, I see there are additional comments that I have not yet read through – my apology if this is a repeat of others views.
thanks,
Dave

John from CA
January 4, 2011 7:16 am

Slightly OT:
It looks like NASA has been upgrading its website and has added new features. IMO, this feature is a step in the right direction.
NASA JPL
Eyes on the Earth 3D
http://climate.nasa.gov/Eyes/eyes.html
Select Aqua and then select CO2 monthly — tilt to view to show different angles — then do the same with Water vapor last 3 days. Note: it looks like they are still working out some bugs and loading data as some of the data maps are missing.
The data indicates, distribution of CO2 and water vapor in the atmosphere are not uniform (no news there). The equation implies a uniform effect which doesn’t exist. I realize you asked to keep this focused on the supplied equation and simple but thought you’d find it interesting as it relates to sensitivity.

D Snyder
January 4, 2011 7:20 am

I’m bothered in principle by the zero dimensional approach, IN vs OUT vs STORED. Its useful for thought experiments such as this, but not real world modeling. The Earth system is a 3D system and includes transport terms/factor. What comes in and goes out don’t have to be related to each other directly – especially the outgoing part which will vary a lot location to location.
Maybe the inequality is an expression of this?

January 4, 2011 7:26 am

Can I tell you that climate sensitivity is zero? Ferenc Miskolczi determined that the optical density of the atmosphere in the infrared band where CO2 absorbs had not changed for 61 years despite constant addition of carbon dioxide to air. This means that the greenhouse absorption signature of that added carbon dioxide is missing. No absorption, no greenhouse effect, case closed. I have come to the same conclusion because the Hansen warming he announced in 1988 does not exist in satellite records. During the Hansen warming of the eighties and nineties satellite record shows only climate oscillations due to alternating El Nino and La Nina periods but no warming whatsoever for twenty years. This too means that CO2 sensitivity = zero, independently of Miskolczi’s work.

D Snyder
January 4, 2011 7:26 am

The “work” that world heat engine might produce, might be referred to as “weather”

kai
January 4, 2011 7:27 am

Yep, quite a few of other commenters have spoted the problem with your analysis, the Sensibility relationship is established for T difference (difference from an equilibrium situation, atmosphere with pre-industrial CO2 concentration for example).
Willis, you have made very very interesting contributions, I like your atmospheric engine models, with an equatorial iris a LOT, I really think you are on the right path and that H20 have a huge stabilising effect on average T, and completely control tropical average T above the oceans.
But for this post, you made a glaring error, which is a pity because it will feed your opponents at RC for example and may distract from your more interresting theories.
I would kindly suggest you post an errata or drop the subject asap, before it turn round the blogosphere as an example of skeptic science….

D Snyder
January 4, 2011 7:37 am

Another “storage” mechanism is the evaporation/melting condensation/freezing of water. These store and dump energy w/o a temperature change, & vary a lot around the globe. The simple T/I does not hold, And even including radiated heat I-Losses) gets messed up.

Wagathon
January 4, 2011 7:37 am

Let’s look at the nature of the losses due to ‘inefficiency.’ For example, a butterfly on a tree shades the trunk as the sun warms its wings and the lizard that eats it spends less energy metabolizing the warmed butterfly and uses the unspent energy to ascend to a new home higher in the rocks, ultimately raising the habitat of that specie of lizard by a few feet. So, the heat is not really lost: it has been converted into lizard elevation. But, how do we quantify this ‘loss’ to the system. And, if we can’t, is it really lost?

Scott Brim
January 4, 2011 7:49 am

Dave Springer says, “The so-called amplification by water vapor is fictional.”
I have been asking the following question for three years on this and other forums, “What specific research activities, experimental and observational, conducted within the operative climate system itself, are necessary to prove or disprove current AGW theories?”
No one, AGW skeptic or AGW warmer alike, has ever given me anything in the way of an answer to my question, or even the most minimal starting point for a more comprehensive answer to my question.

hr
January 4, 2011 8:06 am

cba says:
January 4, 2011 at 6:35 am
“…the surface averages around 288K and radiates by stefan’s law about 391 w/m^2. Total power balance means that a total of around 391 w/m^2 must be hitting the Earth’s surface. we can make the crude assumption that most of the 235 w/m^2 incoming power reaches the surface. That means we are missing 391 -235 = ~155 w/m^2 which must be coming back to the surface from the blocking of the atmosphere. ”
cba, I don’t claim expertise in this field, I’m just a learner, but to calculate the total energy hitting the surface don’t you have to include the non-radiative heat loss from the surface? Which would make the total rather more than 391W/m^2. (An additional 102W/m^2 according to Kiehl & Trenberth (1997).) Also, K & T have 168 W/m^2 solar being absorbed at the surface, rather than 235 W/m^2. Would that not add 77 + 102 = 179 to your required 155 downward longwave? hr

Gary Pearse
January 4, 2011 8:25 am

crosspatch says:
January 3, 2011 at 11:34 pm
“CO2 absorbs very little in the visible frequencies.”
“I wasn’t meaning visible frequencies. Solar radiation outside the atmosphere includes a lot of IR in addition to visible. This IR will be absorbed by the GHGs on the way in.”
Good point crosspatch. It seems sensible that the incoming IR would saturate the “adsorptive” capacity of all CO2 in the atmosphere and returning IR from the surface would simply pass on through unaffected by the already satiated CO2. This has got to be too simple for all those astrophysicists to have missed if so. Willis?

Kevin Kilty
January 4, 2011 8:35 am

It seems at this juncture that the paradox Willis proposes is resolved by the difference of differential versus absolute measures, plus a few other issues, but I would like to add a clarification of something first stated by

crosspatch says:
January 3, 2011 at 11:34 pm
“CO2 absorbs very little in the visible frequencies.”
I wasn’t meaning visible frequencies. Solar radiation outside the atmosphere includes a lot of IR in addition to visible. This IR will be absorbed by the GHGs on the way in.

Solar spectrum contains a very large amount of thermal IR, it’s true, but in the atmosphere the Earth’s surface subtends a solid angle of about a hemisphere while the sun is only a little-bitty disk a half degree in diameter, and as a result the thermal (wavelength longer than 10 micrometers, say) radiation is dominated by that emitted from the Earth’s surface, and internal to the atmosphere. That coming from the sun is pretty insignificant. Solar IR of wavelengths from 0.7 to 10 micrometers is much more significant, but CO2 doesn’t absorb any.

January 4, 2011 8:40 am

Zero hits searching this web page for Boltzmann or Wein …
One hit for Planck.
Two hits for Atmospheric Window however!
Until consideration is given to these facets of LWIR from the earth discussion on this topic is pretty well separated from that physical processes that take place in reality.
But, maybe you have to start somewhere before graduating to the stage where one comprehends radiative energy flow from a ‘black body’ is proportional to temperature to the fourth power …
.

Baa Humbug
January 4, 2011 8:42 am

For those folks who are bringing up the subject of day/night and Earth not being flat etc.
My understanding is that there is 1368Wm2 arriving at the top of atmosphere. This is divided by 4 to simulate the day/night sphere conundrum you are raising.
So I believe all that has been accounted for. How accurately I couldn’t say.

dp
January 4, 2011 8:44 am

I would have thought the energy transferred to the surface and ultimately to the oceans by falling precipitation to be a factor in the energy budget. Maybe I missed it. It is a nearly constant movement of energy when averaged. But I’m in Seattle where rain is never far from our thoughts.

CalMike
January 4, 2011 8:58 am

Looking at the diagram: why is energy “re-radiated equally upwards and downwards”? The Earth being a sphere, would there not be a slightly larger amount going “up”? That is, any re-radiation horizontally, or even slightly downwards, would tend to leave the Earth. Or is the difference too small to matter?

Scott Brim
January 4, 2011 9:11 am

Kai says, “Yep, quite a few of other commenters have spotted the problem with your analysis, the Sensibility relationship is established for T difference (difference from an equilibrium situation, atmosphere with pre-industrial CO2 concentration for example).”
Kai, could I ask you further clarify what you mean by “an equilibrium situation”?
Moreover, is there a reason to believe that an “an equilibrium situation” of some kind existed within the earth’s climate system at pre-industrial CO2 concentrations?
If so, what are the characteristics and dimensions of that “equilibrium situation”?

Nullius in Verba
January 4, 2011 9:13 am

Sorry, again I haven’t spent a lot of time thinking about this. But it looks to me like a “one-shell” pure radiative model. Climate scientists might conceivably use it in explanatory thought experiments, but I don’t think anyone uses it as an actual model of the atmosphere.
The “shells model” is a way of calculating a pure radiative greenhouse effect by treating the atmosphere as a series of concentric LW-opaque shells, each one optical depth thick. If the world absorbs W units of power, then the outermost shell must radiate W units upwards for the whole Earth to be in equilibrium. It radiates W units downwards, because radiation is isotropic and only radiative heat transfer is being considered here. Because it is radiating 2W units in total, it must be absorbing 2W units at equilibrium, which can only come from below. The next shell down is therefore radiating 2W units up, 2W units down, and absorbing W units from above. It must therefore absorb 3W units from below to maintain equilibrium. And so on.
The first shell radiate W units up/down, the second 2W units, the third 3W units, and so on, with radiated power being proportional to optical depth measured from the top of the atmosphere, and hence the temperature proportional to the fourth root of optical depth. With sufficiently many shells, there is no limit to the temperature that may theoretically be achieved. (In practice, it would stop when the surface got hot enough to radiate in the visible spectrum where the atmosphere is no longer opaque.) As the density of the atmosphere, and hence optical depth, varies exponentially with altitude, so would the temperature. If you run the numbers for Earth, the surface temperature would be something like 45 C or even 60 C (I’ve seen various estimates) and you wouldn’t get the straight line lapse rate that is actually observed. I imagine you would also get a higher temperature sensitivity, although I haven’t calculated it.
It gives completely the wrong answer, because the atmosphere isn’t pure radiative. Convection short-circuits the process once the gradient exceeds a certain fixed level, and thereafter controls the temperature profile of atmosphere (and hence the surface) totally. (I’ve written about that extensively elsewhere.) It’s simply not possible to calculate realistic greenhouse warming without incorporating this non-linear adiabatic lapse rate effect. Shell models don’t work.
Your calculation looks like a one-shell (or “up to one shell”) pure radiative model, and therefore has no chance of correctly calculating, or setting limits on, greenhouse warming. But it is an interesting demonstration that the simplistic one-shell picture you often see in popular presentations of the greenhouse effect cannot be correct. Understanding how to do this sort of calculation is essential to the debate about greenhouse mechanisms.

charlie
January 4, 2011 9:16 am

Willis,
As Dan Kirk-Davidoff says:
The main issue here is that that Kiehl used (delta T) and (delta Q).
The sensitivity in your formula is not constant over temperature because the “upwelling radiation” is proportional to T^4. The sensitivity is much larger at lower temperatures. I think the sensitivity you arrive at is some kind of average from zero K to 288 K, not the sensitivity at 288 K.

ferd berple
January 4, 2011 9:42 am

The result reminds me of mathematical proof by contradiction. Either the model is incorrect, or one of the formulas underlying the model are not correct, or you have made a mistake in the calculations.
This could be an important result because it presents a possible falsification of the GHG model. Also, it shifts the argument from Climatology to Physics.
On a side note, as an old sea dog with 20 years experience at sea in the tropics, I would say the model does not adequately represent the scale of the heat exchange between the oceans and atmosphere. The idea that the sun mostly heats the air which heats the water is from my observations false, at least in the tropics.
A large portion of the energy from the sun passes through the atmosphere, where it is absorbed by the oceans. This is released though evaporation, convection and condensation back into the atmosphere, often quite violently.

Hoser
January 4, 2011 9:43 am

KE of molecules in a coordinated direction is wind or currents. When uncoordinated, i.e. random in direction, it’s temperature. Eventually KEcoord turns into heat since turbulence eventually leads to uncoordinated motion. If KEcoord were to increase without devolving into heat, wind speeds would not be limited. Obviously, that doesn’t happen. Thus, KEcoord can be thought of as an intermediate (potentially ingnored), but also as a carrier of energy from one place to another in a more refined model. Eventually, it all turns into heat and radiates.

A Holmes
January 4, 2011 9:59 am

Hi , as a complete layman , I was just wondering wether anyone has actually doubled the amount of CO2 gas in an actual greenhouse and measured the temperature increase this creates ? Would be interesting to know how much warmer it gets .

January 4, 2011 10:12 am

New important invention:
Heatballs with 95% efficiency.
http://heatball.de/en/

Fernando
January 4, 2011 10:45 am

Charles Duncan says:
January 4, 2011 at 5:50 am
I’m not sure it’s fair to treat the atmosphere as a single thin layer,…

Willis,
If this treatment is correct. ( ideal gas )
The equations must be adjusted to two dimensions.
(k= Boltzmann)
E = 3 / 2 kT
1/2kT (i) + 1 / 2 kt (j) + 1 / 2 kt (z)
In this case the result of 33% indicates the removal of two planes.
This is the result of the first reading.

Charles Duncan
January 4, 2011 10:49 am

A Holmes suggest it would be interesting to double the CO2 in a greenhouse and measure the effect. It might be, but it would bear little resemblance to the atmosphere where warm air can freely rise…
Depending on whose model you use convection is either trivial or the major heat transfer mechanism.
I would be interested to know what data there is that links evaporation rate (of sea, puddles etc) and hence latent heat transfer with temperature. My back-of-an-envelope calculation suggests it is represents around 75W/M2 at 13°C and rises steeply with temperature.

Rod Smith
January 4, 2011 11:19 am

“I ≈ 342 W m-2.”
Where do we draw our box? What “area” are we talking about? It can’t be the earth’s surface, because the energy balance begins at TOA. However, warming the atmosphere causes it to expand (and thin!) and increases the surface area at “TOA.” My own thoughts are that this expansion would not have much influence on incoming radiation, but would increase the atmosphere’s heat loss through a larger surface.

Moritz Petersen
January 4, 2011 11:19 am

There seem to be multiple problems here:
The upward and downward radiation from the atmosphere are the same in this Model. This implies that this is a single shell model. However there are two observations that suggest a multi-shell model:
*A lot of energy is being absorbed and re-radiated multiple times within the atmosphere before it reaches space.
*The absorption through CO2 is mostly saturated, so there are hardly any changes possible in a single shell model
In a multi-shell model, however, the downward forcing would be higher than the upward forcing. So you would need two separate sensitivities for radiation onto the ground and radiation into space.
The second problem is that T and S are not linear and the change in forcing is deltaT/S
So the total downward forcing would be the integral(deltaT/S * dT) from 0 to T.

Duster
January 4, 2011 11:20 am

A Holmes says:
January 4, 2011 at 9:59 am
“Hi , as a complete layman , I was just wondering wether anyone has actually doubled the amount of CO2 gas in an actual greenhouse and measured the temperature increase this creates ? Would be interesting to know how much warmer it gets .”
A real green house operates by limiting convection. Normally, in the open, warm air near the ground surface tends to depart in small (or large) vortices at that circulate it upward and away from sun warmed surfaces. Cooler air moves in replacing the warmed air. In a green house the formation of vortices that carry away the heat is not permitted physically by the walls and roof of the enclosure. This is also why the phrase the “so-called green house effect” is often encountered when reading about climate. The energy absorption and release of the atmosphere have little in common with a real green house. Doubling the CO2 would make the plants happier though since they fix light energy into carbohydrates using CO2 and water.

January 4, 2011 11:29 am

@ Dave Springer
The fly in the ointment is that thermal IR cannot heat the ocean. It only heats the land. IR is absorbed by water in the first few micrometers at the surface. This doesn’t heat the body of water at all but instead increases the evaporation rate. The thermal energy is thus instantly carried away from the surface in latent heat of vaporization.
That seems to be nonsense to me. Shallow pools of water heated by the sun are demonstrably warmer than deeper pools with the same surface area. For particularly deep bodies, with not a lot of turbulance, you can end up with a scenario where the top couple of feet are much warmer than the lower areas.
The IR doesn’t vaporize water. IR increases molecule speed (heat.) With more heat, more water molecules evaporate certainly, _but not all particles that gain energy evaporate_. The additional heat increases molecular motion and a large amount gets distributed throughout the water body via conduction and convection.

Baa Humbug
January 4, 2011 11:30 am

Charles Duncan says:
January 4, 2011 at 10:49 am

I would be interested to know what data there is that links evaporation rate (of sea, puddles etc) and hence latent heat transfer with temperature.

Would Pan Evaporation data be useful to you? If so, google it, there are numerous papers on the subject.

Oliver Ramsay
January 4, 2011 11:37 am

_Jim says:
January 4, 2011 at 8:40 am
Zero hits searching this web page for Boltzmann or Wein …
One hit for Planck.
Two hits for Atmospheric Window however!
Until consideration is given to these facets of LWIR from the earth discussion on this topic is pretty well separated from that physical processes that take place in reality.
But, maybe you have to start somewhere before graduating to the stage where one comprehends radiative energy flow from a ‘black body’ is proportional to temperature to the fourth power …
———————-
Yes, even after your post there’s still no mention of WIEN.
There were some variations on the S-B theme.
I’m not sure if there’s another point you wanted to make.

Charles Duncan
January 4, 2011 11:37 am

The circumference of the Earth is about 40,000km, so the diameter is about 12,730km. In comparison the atmosphere is but a thin veneer, and the additional area at TOA is trivial, I believe.

January 4, 2011 11:41 am

I found it interesting when the geniuses at RC basically told me this: not only does the mythical ‘greenhouse effect’ not work in a greenhouse, but it can’t be made to work (i.e. demonstrated).

Wondering Aloud
January 4, 2011 12:12 pm

Perhaps you have discovered why the true believers are so convinced. Their equation shows catastrophic warming is inevitable, and is even worse than the models suggest. They are so sure it is fundamentally correct that it never occurs to them that observations could disprove their theory. Therefore they can go through life fudging away and ignoring inconveniet data because they “know” they are right.

beng
January 4, 2011 12:16 pm

Offhand, the amount of Watts/m2 (whatever it is) of “forcing” produced by doubling CO2 is vastly overestimated. By your sensitivity estimate (which seems reasonable), the actual W/m2 of CO2 forcing should be about 1/9th of what the IPCC says (assuming a “real” 1C rise).

Rod Smith
January 4, 2011 12:20 pm

“T/S” is a troubling term. It is not derived using mathematics and physics, but is declared valid by definition. Theoretical worlds are built through definitions (complex mathematics based upon the square root of -1 comes to mind), but does the world they are building have any validity to the real world. S is supposed to represent all of those noisy and complicated systems that haven’t been properly defined nor quantified, yet they assume that every one of these systems is largely static except for the impact from CO2. Is there any proof or even data that supports this? I haven’t seen any.

January 4, 2011 12:35 pm

I’m sorry, I am not a climate scientist and the terms you use here I’m only familiar with by seeing them here and in other blogs. But I thought that as S increases the number of degrees of temperature increase per doubling of CO2 goes down. Surely if S was so high that T/S is practically zero then we have I = F-(a very small amount), and thus there would be almost no temperature increase per doubling of CO2. This would mean that your bound of S>.84 would indicate that the temperature increase per doubling of CO2 is less than 3 degrees not more.

George E. Smith
January 4, 2011 12:45 pm

Well Willis, I don’t like your energy cartoon any more than I like Dr Trenberth’s; but yours is at least understandab;le.
The problem is that the TSI is 1366 W/m^2, and not 342; and the thermal conductivity of the earth is not infinite; so the earth is not isothermal at 288 K.
A practical result of a 1366 w/m^2 blow torch, suitably attenuated by atmospheric absorption, scattering (Raleigh and clouds) impinging on a 70% near black body oceanic absorber, and a somewhat less absorbtive solid land surface, is that local temperatures rise far above 288 K; as high as 333 K or more fro the hottest land surfaces; and as a result those surfaces cool (radiate) at a much higher rate than your 288 K isothermal earth; so the result is nothing like oyur staic infinite conductivity, non rotating earth model.
Otherwise your coolors are prettier than Trenberth’s; but still just pink elephants.

Warren in Minnesota
January 4, 2011 1:01 pm

Willis,
I do not see or understand how the derivation of E=(T/I) / S from the system efficiency E which equals (I – Losses) / I is done.

JAE
January 4, 2011 1:03 pm

Dave Springer, Jan. 4, 5:17 am says:
“The fly in the ointment is that thermal IR cannot heat the ocean. It only heats the land. IR is absorbed by water in the first few micrometers at the surface.”
That’s a good point, but it also extends to land surfaces which are moist or covered with vegetation. So maybe 85% of the Earth’s surface is not heated by thermal IR.

Keith Wallis
January 4, 2011 1:09 pm

_Jim says:
January 4, 2011 at 8:40 am
Zero hits searching this web page for Boltzmann or Wein …
One hit for Planck.
Two hits for Atmospheric Window however!
Until consideration is given to these facets of LWIR from the earth discussion on this topic is pretty well separated from that physical processes that take place in reality.
But, maybe you have to start somewhere before graduating to the stage where one comprehends radiative energy flow from a ‘black body’ is proportional to temperature to the fourth power …

Perhaps if you actually read through the article and comments, rather than lazily searching for terms you think may appear in precise terms, you’d appreciate that your snide, patronising tone is unwarranted.
There are no shortcuts to knowledge, my friend.

JAE
January 4, 2011 1:10 pm

Dave Springer, Jan 4, 6:16 says:
“Technically correct. What back radiation does is slows down the rate of cooling. Just like a layer of clothing doesn’t actually warm your body but rather slows down how fast your body loses warmth. Greenhouse gases are insulators. Insulation doesn’t supply heat it just slows down the loss of heat.”
Well, ALL the gases in the atmosphere function as “insulation,” not just the GHGs (remember, the N2 and O2 are heated by collisions/thermalization). That’s why the there is way too much emphasis on radiative effects, alone. The real reason the Earth stays warmer than it “should be” is simply heat storage of the oceans and atmosphere–and insulation by those gases.

Nullius in Verba
January 4, 2011 1:23 pm

The way water is heated by sunlight is complicated. Visible light passes through the surface layers and is absorbed deeper down, in the top few tens of metres. It then rises mainly by convection, but with some conduction (and a tiny amount of radiation) to the surface. (Assuming the water is well above freezing point – cold water does strange things because of water’s odd temperature-density properties.) The water then cools by radiation, evaporation, and conduction at the surface.
The role of downwelling IR is to slow the rate at which the surface cools, which in turn affects the temperature differential that drives convection and conduction of heat to the surface. If you have water pouring into a tank from a tap and out again through a hole in the bottom, you can increase the water level in the tank by partially blocking the hole. Putting your finger over the hole at the bottom does not pour any additional water into the tank above it, but it can still have an effect on the level there.
Interestingly, the role of convection can be studied by turning it off – there is an arrangement called a solar pond in which salt is dissolved in water in layers, with more dense/concentrated solution at the bottom and less dense/fresher water at the top. The heavier water at the bottom does not rise when heated – it does not convect. So sunlight shines through to the bottom of the pond, and can then only escape to the surface by conduction. Solar ponds can easily reach temperatures over 90 C at the bottom with only a few metres of water.
Water acts like concentric shells to radiation, but with millions of shells micrometres apart. If pure radiation was all there was to it, the greenhouse effect in water would result in boiling below the surface with only a few centimetres of water. (Water molecules inside the bulk of a body of water still radiate.) Conversely, the surface would radiate all its heat away faster than it could be replenished by radiation from below and (if we ignore conduction from the air above) would freeze! A radiation-only world would be strange indeed! Fortunately, conduction can convey heat a lot faster, reducing the gradient to mere tens of degrees C per metre, and convection reduces it further still. As with air, you cannot understand the temperature of the water surface without understanding the role of convection.

EthicallyCivil
January 4, 2011 1:46 pm

I’ve been pondering the “thermostat” hypothesis for a while and looking up at the cold clear night sky it struck me. On cold days, cloud cover warms — on warm days, it cools. On warm days T > Tcrit and the atomsphere convects, on cold days it doesn’t (even to the point of inversion layers… a cold weather phenomenon.
Thoughts all.

Dave Springer
January 4, 2011 1:58 pm

Nullius in Verba says:
January 4, 2011 at 1:23 pm
“Assuming the water is well above freezing point – cold water does strange things because of water’s odd temperature-density properties”
Seawater does nothing odd. Maximum density occurs at the freezing point which at 3.5% salinity is -1.8C.

January 4, 2011 1:59 pm

Dear Willis,
the problem is easy to solve.
The definition of the sensitivity in your simple model would be:
1/Sensitivity=dU(Greenhouse)/dT=Differential of Greenhouse Back Radiation and Temperature.
Assuming Stefan-Boltzmann Law this yields in your model (which indeed is very simple)
1/Sensitivity=4*U(Greenhouse)/T
Sensitivity>1/4*T/I=1/4*288/341K/W/m2=0.211K/W/m2
If the Radiative Forcing for 2*CO2 would be 3.7W/m2 a temperature of T>0.78 would result.
The values for the sensitivity and temperature for 2*CO2 of course only valid in this simple model.
It is just a factor 1/4 which was missing
Best regards
Rainer

harrywr2
January 4, 2011 2:03 pm

George E. Smith says:
January 4, 2011 at 12:45 pm
“The problem is that the TSI is 1366 W/m^2, and not 342”
TSI is 1366 W/m^2 if the earth is flat and orientated towards the sun.
The earth isn’t flat and only a small portion is orientated towards the sun at any given time.
To get average TSI one divides by 4.

Dave Springer
January 4, 2011 2:11 pm

JAE says:
January 4, 2011 at 1:03 pm
“That’s a good point, but it also extends to land surfaces which are moist or covered with vegetation. So maybe 85% of the Earth’s surface is not heated by thermal IR.”
Point taken. I considered it but didn’t think the complication of trying to figure out what percentage of land surface is wet and for what percentage of the time was needed to make the point.

Malcolm Miller
January 4, 2011 2:16 pm

What fascinates me about all the learned exchanges and calculation here is that most of it shows just how little understanding of what’s going on in the region of temperature/energy input and output and such we really have! No wonder the AGW is still alive and kicking – it’s proponents are CERTAIN that they’re right and need no discussion or argument – for them there is consensus and ‘the science is settled’!

Joel Shore
January 4, 2011 2:21 pm

charlie says:

As Dan Kirk-Davidoff says:
The main issue here is that that Kiehl used (delta T) and (delta Q).
The sensitivity in your formula is not constant over temperature because the “upwelling radiation” is proportional to T^4. The sensitivity is much larger at lower temperatures. I think the sensitivity you arrive at is some kind of average from zero K to 288 K, not the sensitivity at 288 K.

Moritz Petersen says:

The second problem is that T and S are not linear and the change in forcing is deltaT/S
So the total downward forcing would be the integral(deltaT/S * dT) from 0 to T.

I agree. This is what I see as a very serious problem. Not sure it is the only problem (see for example the 1st part of Moritz’s post) but this confusion of T and deltaT is a big one.

kai
January 4, 2011 2:26 pm

@Scott Brim,
sorry, wrong wording. I meant “reference situation”, around which linear relations can hopefully be derived for small enough variation.
Nothing special about pre-industrial CO2, besides the fact that I am inclined to believe the mainstream climate view there, i.e. that CO2 was relatively stable during historic era (at least after the last glaciation), and that the current CO2 increase is due to the burning of fossil fuels.
I also believe that CO2 increase is good: it makes plants grow faster, put the biosphere back in the safety zone while previous levels were dangerously low. The warming effect is probably there (good theoretical reasons to believe it’s there), but it seems small compared to natural variability, is certainly not catastrophic, maybe positive, and basically nothing to worry about. Peak oil is worrying me (a little), CAGW, not at all.
This place me firmly in the skeptic camp, although not among the rabid skeptic. I quite like the theories of Willis, as I said his analysis of tropical effects is original, well explained, and looks probable (I think there should be something like his regulating effects to maintain T within tight bounds at least at the tropics, it would explain the faint sun paradox). But this do not detract me to point glaring errors when I see them, and here the error is quite simple and would be embarassing if highlighted on other blogs…

Dave Springer
January 4, 2011 2:28 pm

kcrucible says:
January 4, 2011 at 11:29 am
“That seems to be nonsense to me. Shallow pools of water heated by the sun are demonstrably warmer than deeper pools with the same surface area. For particularly deep bodies, with not a lot of turbulance, you can end up with a scenario where the top couple of feet are much warmer than the lower areas.”
The sun isn’t heating them with thermal IR.
“The IR doesn’t vaporize water. IR increases molecule speed (heat.) With more heat, more water molecules evaporate certainly, _but not all particles that gain energy evaporate_. The additional heat increases molecular motion and a large amount gets distributed throughout the water body via conduction and convection.”
Convection only occurs when you heat water from the bottom or cool it from the top.

Joel Shore
January 4, 2011 2:30 pm

JAE says:

Well, ALL the gases in the atmosphere function as “insulation,” not just the GHGs (remember, the N2 and O2 are heated by collisions/thermalization). That’s why the there is way too much emphasis on radiative effects, alone. The real reason the Earth stays warmer than it “should be” is simply heat storage of the oceans and atmosphere–and insulation by those gases.

The reason the emphasis is on radiative effects is because the only way that the earth / atmosphere system communicates with the sun or space is via radiation! Oceans can’t really keep the earth warmer overall. In the absence of greenhouse gases, energy balance shows that in steady-state the earth’s average temperature (or more precisely, the average of T^4 over the earth’s surface) is determined completely by its distance from the sun and its albedo. The ocean mainly serves as a heat sink that reduces the variations in temperature (e.g., during the diurnal cycle). [Although technically, the reduction of this cycle can lead to a somewhat warmer average temperature, , because the behavior of vs is such that if you have two temperature distributions with the same then the one with a larger variation will have a somewhat lower value of .]

Rod Smith
January 4, 2011 2:49 pm

“Charles Duncan says:
January 4, 2011 at 11:37 am
The circumference of the Earth is about 40,000km, so the diameter is about 12,730km. In comparison the atmosphere is but a thin veneer, and the additional area at TOA is trivial, I believe.”
Is it trivial? Climate theory assumes that all of the heating occurs in this thin veneer. Before you can dismiss the extra heat loss through radiation from a less dense, expanded atmosphere, you must first quantify its value. Skylab crashed to the earth at least two years before NASA’s planned rescue, because unanticipated atmospheric expansion caused increased drag on the lab. Calling it trivial doesn’t make it so.

George E. Smith
January 4, 2011 2:53 pm

“”””” Nullius in Verba says:
January 4, 2011 at 1:23 pm
The way water is heated by sunlight is complicated. Visible light passes through the surface layers and is absorbed deeper down, in the top few tens of metres. It then rises mainly by convection, but with some conduction (and a tiny amount of radiation) to the surface. (Assuming the water is well above freezing point – cold water does strange things because of water’s odd temperature-density properties.) The water then cools by radiation, evaporation, and conduction at the surface. “””””
Well unfortunately, that odd density temperature function ONLY applies to fresh water, and low salinity salt water. Sea water with more than 2.47% of dissolved salts, exhibits NO MAXIMUM DENSITY before it freezes. Average sea water has 3.5% salinity, so it keeps getting denser right down to its freezing point which is of the order of a couple of degrees C below zero. So the turnover phenomenon of fresh water lakes, does not happen in the ocean.
The optical absorption coefficient of sea water is well documented fro all wavelengths from the Atmospheric UV limit near 180 nm and all the way out to wavelengths of about 1 metre; but with good data to around 100 microns wavelenght which is the end of the climatically useful far infra-red region.
Specifically for sea water at around 460 nm which is close to the solar spectrum peak, the absoption coefficient is between 1 and 2 x 10^-4 cm^-1 Even if it was as high as 2 E-4, that would put the 1/e transmission dept at 50 metres, or 250 metres for a 99% extinction.
So solar energy proceeds much deeper in the deep ocean than just a few tens of metres.
I agree that the local expansion caused by the heating of deeper waters should create an upward convection gradient, that would cause heated waters to slowly carry much of that energy back towards the surface; which is warmed not so much by direct absorption in the shallows; but by upward convection.
The warming of shallow water bodies, simply reflects the fact that the bottom reflects much of the light back towards the surface. In the deeper oceans, the water behaves like a grey body with an absorptance of about 97%, which is not a bad stand in for a black body absorber, and radiator.
Sea water has strong absorption bands at around 1, 2, and 3 microns, reaching a maximum absorption coefficient of about 9,000 cm^-1 at 3.0 microns, which gives a 1/e depth of around 1.1 microns or less than 6 microns for 99% absorption.
For the longer wavelength regions of interest to atmospheric thermal radiation (surface too), from around 6.0 to around 100 microns sea water has an absorption coefficient between about 200 and 6,000 cm^-1 which gives 1/e depths of around 2-60 microns; so the downward LWIR gets absorbed in the top few hundred microns of the ocean; where it mainly promotes prompt evaporation.
You cannot simply add downward LWIR radiative fluxes to incoming solar insolation, as if they both do the same thing; they don’t, and that is one of the failings of the climatists to accept that.

Bryan
January 4, 2011 3:12 pm

Joel Shore
I think that you are quite familiar with the climate models that the IPCC rely on.
Perhaps you have one of the basic models yourself?
What would happen if one of the models was left to run with the IR radiative effects of CO2 shut down?
H2O still operating with radiative properties in the IR and the usual phase change effects still intact.
I guess that the Earth climate would be pretty much as we experience it at present.

George E. Smith
January 4, 2011 3:12 pm

“”””” harrywr2 says:
January 4, 2011 at 2:03 pm
George E. Smith says:
January 4, 2011 at 12:45 pm
“The problem is that the TSI is 1366 W/m^2, and not 342″
TSI is 1366 W/m^2 if the earth is flat and orientated towards the sun.
The earth isn’t flat and only a small portion is orientated towards the sun at any given time.
To get average TSI one divides by 4. “””””
You obviously didn’t read what I said. TSI averages around 1366 W/m^2, and varies over an eleven year cycle by about 0.1% and of course seasonally due to the small changing sun earth distance change.
Your figure of 342 W/m^2 has nothing to do with earth flatness or roundness; it has to do with a completely fictional and quite absurd assumptiuon that the sun shines on the entire earth surface 24/7/365; from pole to pole and even on Antarctica in the depths of Winter midnight.
It doesn’t do that, on either this planet or any other planet in the universe. the earth rotates, and the sun that reaches the ground (clear air) packs about 1000 W/m^2 of projected area (normal to the sun-earth line), everywhere on the sunlit half of the planet.
The resulting thermal response of the planet, is nothing at all like your fictitious non-rotating isothermal earth receiving 342 W/m^2 over its entire surfqace at all times.
The system is quite non-linear; so you simply can’t average the real Physical effects; the heating of the earth to well above 288 K during a single daytime pass of the sun, persists well beyond the following night time period; so the temperature rise during daylight hours does not simply revert to some average value over night
TSI is NOT 342 W/m^2 it is 1366 give or take a smidgeon; but it illuminates only half the earth at any one time instant; well actually slightly more than half, by at least one degree so 181/360ths of the earth.
Last time I checked 181/36 of the whole would not normally be referred to as “only a small portion”.
This is not rocket science; maybe a third grade science question for “Are You Smarter than a Fifth Grader ?” What fraction of the earth surface is in daylight at any instant of time ? Answer; about half !

Gordon Ford
January 4, 2011 3:34 pm

Willis
Missing from the cartoon is geothermal energy from radioactive decay in the earth. Energy in from space must be less than energy radiated to space. Otherwise the oceans would have boiled off long ago.

JAE
January 4, 2011 4:00 pm

Joel:
It is true that virtually all the energy in the Earth system is gained and lost only through radiation, but it seems to me that you need to think beyond radiation and also consider that the atmosphere, land and (especially) water stores a lot of heat. In order to have a troposphere that is many kilometers in depth, there has to be a LOT of stored energy in the atmosphere (kinetic AND potential). And I think that that stored energy is all you need to consider to explain the surface temperature on Earth. For gases (the atmosphere), PV = RT; so T = (the constant, R)x(PV). Both P and V of a quantity of gas depend only upon the amount of stored energy in that gas, so T must also depends on this.

Joel Shore
January 4, 2011 4:24 pm

Bryan says:

What would happen if one of the models was left to run with the IR radiative effects of CO2 shut down?
H2O still operating with radiative properties in the IR and the usual phase change effects still intact.

This recent paper addresses that issue: http://www.sciencemag.org/content/330/6002/356.abstract

stumpy
January 4, 2011 4:35 pm

The equation is wrong – firstly it assumes a linear system in equilibrium when its a non-linear chaotic system.
Surface temperature is linked to ocean temperatire, the energy traded back and forth between the two varies with albedo / cloud cover / aerosols etc… and these are related to the sea temperature and surface temperature – the result is a climate sensitvity that changes size and sign depending on the systems state at a given point i.e. the deviation from the “ideal climate”) – but this results in an unsolvable equation that results in randon chaotic fluctuations, not a nice linear system in equilibrium, so it is instead simplified to the point where the equation is of very limited use for projecting temperatures for future states where the resulting climate sensitivity is unknown (see IPCC equation above).

January 4, 2011 4:41 pm

Willis, I may be a bit late but: The circumference of the earth at the equator is 24,901.55 miles (40,075.16 kilometers). But, if you measure the earth through the poles the circumference is a bit shorter – 24,859.82 miles (40,008 km). Thus the earth is a tad wider than it is tall, giving it a slight bulge at the equator. This shape is known as an ellipsoid or more properly, geoid (earth-like).

Nullius in Verba
January 4, 2011 4:49 pm

“Well unfortunately, that odd density temperature function ONLY applies to fresh water, and low salinity salt water.”
Yes. True. I should have been a bit clearer – you’ll note of course that I didn’t actually specify whether it was salt or fresh water (I said “water” and was thinking in general physical terms), but I agree that it might have been assumed to be salt given that the oceans are the biggest part of the effect of all this on climate.
I am aware that I have an unfortunate tendency towards extremely long posts in which I am tempted to cram in all the necessary caveats and clarifications, distractingly diverting to discuss interesting but peripheral side-topics, which urges I try very hard to resist, so I normally try to keep caveats brief. They are only intended as a marker to the unwary that there is potentially more going on here than I am saying – and if you want to know more, to look it up, or to have a longer think about it. But it’s always more complicated. When sea ice melts, for example, the surface salinity can get quite low.
It doesn’t affect the main content of the comment, which was intended to be entirely about the simpler circumstances where such complications don’t apply. But I appreciate it that people are taking the time to read the comments and make improvements. My thanks.

cba
January 4, 2011 4:59 pm

hr,
my purpose wasn’t to provide a theory or accurate results beyond simply disproving the cartoon assumption Willis posted.
h2o vapor/water cycle is extremely important near the surface but gradually fades out towards the tropopause

January 4, 2011 5:13 pm

George E. Smith says January 4, 2011 at 3:12 pm:
“You obviously didn’t read what I said. TSI averages around 1366 W/m^2, and varies over an eleven year cycle by about 0.1% and of course seasonally due to the small changing sun earth distance change.
Your figure of 342 W/m^2 has nothing to do with earth flatness or roundness; it has to do with a completely fictional and quite absurd assumptiuon that the sun shines on the entire earth surface 24/7/365; from pole to pole and even on Antarctica in the depths of Winter midnight.
It doesn’t do that, on either this planet or any other planet in the universe. the earth rotates, and the sun that reaches the ground (clear air) packs about 1000 W/m^2 of projected area (normal to the sun-earth line), everywhere on the sunlit half of the planet.”
Well said George 342 W/m² is the same for the moon and would also be the same for a tennis ball in earth’s orbit. It has nothing to do with what the earth’s surface gets or receives to absorb.
I do not believe any one of the W/m² values given in these energy flow plans has been actually measured. Apart from may be the Solar Constant (S) of 1366 W/m².

David L
January 4, 2011 5:26 pm

Ken Coffman says:
January 4, 2011 at 11:41 am
I found it interesting when the geniuses at RC basically told me this: not only does the mythical ‘greenhouse effect’ not work in a greenhouse, but it can’t be made to work (i.e. demonstrated).”
So let me get this straight. Using earth as a model, CO2 alone can cause the earth’s temperature to increase to disastrous levels. No feedbacks nor feedforwards nor interactions are required. But as a single factor in a greenhouse experiment, the same CO2 will not produce the temperature effect? I guess because there aren’t all the complicated real world interactions. So if you need all those complicated real work interactions in order for CO2 to manifest itself into higher temps, then the AGW theory and supposed knowledge is even more lacking than previously thought and the initial claim that CO2 alone can cause the runaway greenhouse effect is completely wrong. Once again, they can’t have it both ways. It’s either a main effect or it’s not. It can’t be a main effect in earths atmosphere but not a main effect in a greenhouse experiment.

Kevin Kilty
January 4, 2011 6:01 pm

_Jim says:
January 4, 2011 at 8:40 am
Zero hits searching this web page for Boltzmann or Wein …
One hit for Planck.
Two hits for Atmospheric Window however!
Until consideration is given to these facets of LWIR from the earth discussion on this topic is pretty well separated from that physical processes that take place in reality.
But, maybe you have to start somewhere before graduating to the stage where one comprehends radiative energy flow from a ‘black body’ is proportional to temperature to the fourth power …

Emitted power is proportional to temperature to the fourth power in the case of a cavity radiator only when the entire spectrum is present. In the case of such a radiator “looking through” a band limited window, as that in the atmosphere, the relationship is more like temperature to the 4.6 power, with a constant of proportionality quite a lot smaller than the stefan constant.

Ian W
January 4, 2011 6:30 pm

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?
What you are missing is that S (sensitivity) is not a constant it is a variable with both negative and positive bounds. Sensitivity is dependent on other variables that are not in the simplistic equation, such as humidity, associated atmospheric heat content and albedo. As you have yourself stated in previous posts as heat content increases atmospheric sensitivity (the positive feedback) initially can assist heating then becomes a negative feedback to the extent that inbound heating is locally massively reduced.

jae
January 4, 2011 7:47 pm

David L: you are not crazy. The “atmospheric greenhouse effect” fails EXACTLY for the same reasons that the “real” greenhouse effect doesn’t work when you open the windows. Convection, sir! If CO2 had an effect, it would have to change the lapse rate. It hasn’t. The models are wrong. There is no “hot spot” at 5 km in mid-latitudes. It doesn’t get hotter in Sterling, Colorado on a clear humid July day than on an extremely dry clear day. The “atmospheric greenhouse effect” cannot be demonstrated, and is probably nonsense. But I’m still open to some proof….

jae
January 4, 2011 8:34 pm

Hey, moderators: you are withholding a comment, no? It is about [Jeff’s] failure to consider thermalization, capiche??? This is not “normal” for this site and will render this site similar to Realclimate in my eyes–i.e., totally biased and irrelevantm unless it is fixed. Please post the comment! Jeff, you need to study thermalization!
REPLY: Fixed the name per your request, I don’t see any other comments in moderation from you. OTOH we’ve been hit with a barrage of spam comments today, so possible it got lost in that. Feel free to resubmit – Anthony

jae
January 4, 2011 8:38 pm

Sorry, Anthony, I meant Jeff. He has some “splaining” to do.

Robert Wykoff
January 4, 2011 9:12 pm

If there are 3 degrees per doubling of CO2, then if you reduced the CO2 to 3ppm, the temperature of the earth would be less than the black body radiation

Darren Parker
January 4, 2011 9:41 pm

Secretly I’m a little bit naive. So i’ll need some help through this. I had heard that E=mc2 (that’s squared). So does taht mean that some energy in the system is turned into matter? Could a 6% growth in world biomass in the last few years be an absorption of the extra energy?

jorgekafkazar
January 4, 2011 10:20 pm

Nullius in Verba says: “…I am aware that I have an unfortunate tendency towards extremely long posts in which I am tempted to cram in all the necessary caveats and clarifications…”
That’s okay, Nullius. I only read the first 16 lines of a comment. A lot less than that if there are a lot of words in all caps or quote marks.

Ammonite
January 4, 2011 10:42 pm

ferd berple says: January 4, 2011 at 9:42 am
Either the model is incorrect, or one of the formulas underlying the model are not correct, or you have made a mistake in the calculations.
…or fundamental-misunderstandings/incorrect-assumptions are present in the argument above. Please, for those who are truly skeptical, when someone presents a half-page/one-line proof that AGW is false it is wise to dig a little deeper. In this case, the assumption of linearity across the entire range of temperature response is in error.
Repeating charlie: January 4, 2011 at 9:16 am
As Dan Kirk-Davidoff says:
The main issue here is that that Kiehl used (delta T) and (delta Q).
The sensitivity in your formula is not constant over temperature because the “upwelling radiation” is proportional to T^4. The sensitivity is much larger at lower temperatures. I think the sensitivity you arrive at is some kind of average from zero K to 288 K, not the sensitivity at 288 K.

stumpy
January 4, 2011 10:59 pm

A thought experiment:
If we start with a cooler sea than current (for whatever reason), there is less cloud cover / rain / storms at the equator as there is less evaporation and latent heat, the trade winds from the equator are relaxed and moisture air reaches the current desert areas of the earth, they are green. The northern and southern extremes are cold in winter as there the current warm currents have slowed, but also clearer in summer due to the lower humidity. The sun is beaming energy at a constant rate, the clear sky at the equator allows much of the incoming energy to be absorbed into the ocean, this energy is conveyed via currents to the northern and southern extremes, as the sea warms more the currents start to struggle to keep up, the seas at the equator keep warmer, the air is moister, cloud cover more common, storms more frequent, h20 and co2 increase in the atmosphere, wind patterns accelerate, soil erosion increase, more sediment is washed into the equatorial seas changing its albedo and absorption characteristics, dust changes occur and effect the atmospheric albedo due to changed wind patterns, a monsoon belt forms shading the band closet to the sun, less energy starts to come in and the oceans locally receive less energy, due to increased rainfall drier air reaches the desert areas changing them from green to yellow and changing the overall albedo of earth, meanwhile warm water is still being transported to the extreme latitudes lagging behind the cooling at the equator, the currents slow as energy at the equator reduces and the system keeps going, undulating up and down trying to find that balance, only being thrown out by small changes in TSI, millancovitch cycles, changes in cloud cover due to GCR variation etc… the results in a constantly moving unstable system were many factors all effect each other in non-linear ways – then some one has tried to convert to a ridiculously simplistic equation using mostly assumed values and we ask whats wrong? We know very little about the climate full stop.

gnarf
January 4, 2011 11:48 pm

I think I know what puzzles me with this drawing. On your drawing, you consider S as a constant, but it is a function of T. Even for a black body, S is a function of T, as T does not move lineraly with incoming radiation.
For an accurate drawing, you should consider the system in equilibrium, with all flows constant, a given temperature, and add a little deltaForcing, for which you consider T will move of deltaT and S(t+deltaT)=S(T).
I suppose the equation will be far different.
Oops, I see many commenters write the same thing with better words 🙂

Jon-Anders Grannes
January 5, 2011 12:24 am

I think the whole debate and take on this has been somewhat “politicized/radicalized” made up and set up by “parties/elements” that that have a political agenda.
On average temperature decreases by 2 degrees C every 300 meter upwards. And visa versa.
If you added 40 hPa more air to our atmosphere so that the global standard air pressure at sea level increased to 1055 hPa, instead of today’s 1013 hPa, the global temperature at any given place would increase by 2 degrees C and the global temperature would increase from 14-15 degrees C to 16-17 degrees C.
This means on average that the more column of air you have above you the warmer it gets. The atmosphere also has an isolation effect. Just like in an air tight house in cold weather with a 2000w heating and the radical difference in temperature with no isolation in the walls and 40 cm isolation in the walls.
Temperature decreases by 2 degrees C every 300 meter upwards. Fig 1 claims “Most upwelling radiation absorbed by greenhouse gases and re-radiated equally upwards and downward.”
?
Radiation goes from warm to cold. Never from cold to warm.
The window area in a house during winter isn’t colder because cold radiation from outside is coming in. It’s cold because the house “warmness” in that area is radiating out.
A fridge does not get cold because you add coldness/ cold radiation. A fridge gets cold because you radiate out the warmness inside the fridge.
So when we know that normally the air above is colder it is technically difficult for me to comprehend that the surface is warmed by cold radiation from above?
?

Bryan
January 5, 2011 1:00 am

Bryan says, Joel Shore;
What would happen if one of the models was left to run with the IR radiative effects of CO2 shut down?
H2O still operating with radiative properties in the IR and the usual phase change effects still intact.
Joel replied; “This recent paper addresses that issue:”….
http://www.sciencemag.org/content/330/6002/356.abstract
Unfortunately it is behind a pay wall and written by the “usual suspects”.
I cannot tell therefor if their prediction of the end of all human life is justified.
Common sense tells me that the consequences of such a minor change would be negligable.

kai
January 5, 2011 1:37 am

Jon-Anders Grannes said: “So when we know that normally the air above is colder it is technically difficult for me to comprehend that the surface is warmed by cold radiation from above?”
That’s not too difficult to get, once you build the correct mental picture:
Figure 2 cases, and consider only radiative transfer:
a) a body B at T1 in a medium M1 at T2<T1
b) same body B at T1 in a medium M2 at T3<T2.
Do you concur that the body B will get colder more quick in case (a) than in case (b)? If yes, you have understood why atmospheric greenhouse effect does not violate thermodynamics, and why radiation must indeed occur from a cold body to a warm body (only less so than from warm to cold):
A photon coming out of the body at T1 does not know the temperature of the surrounding medium. For him, only molecular energy levels of body B count, he does not see the surrounding before it is emitted and afterward, too late to come back to body B 😉
But so does the photons emitted by the surrounding medium: they care only about the temperature of the medium that emit them.
So in case (a) and (b), body B emit the same amount of radiation toward the outside. But the outside medium M1, being at higher temp T2, emit more radiation in all direction (including body B), than medium M2 at temp T3. So body B gets colder in (b), not because it radiate more, but because it absorb less from the surrounding medium. when B is at the same T as tis surrounding, B temperature does not change anymore, even if it radiate the same, because at this point it absorb exactly the same energy as it radiates.
So in this case, the colder atmosphere really radiates back to the warmer ground, but of course not as much as the ground radiates up. Ground is thus not really heated, it just get colder more slow, and the less cold the surround medium is, the slower the ground will get colder.

Nullius in Verba
January 5, 2011 2:33 am

“Radiation goes from warm to cold. Never from cold to warm.”
Radiation goes from anything above absolute zero, outwards – irrespective of the temperature of its surroundings. But warm radiates more than cold, so the net energy transfer between warm and cold is always from warm to cold.
“A fridge gets cold because you radiate out the warmness inside the fridge.”
A fridge gets cold because gases get hot when they’re compressed and they cool when they’re allowed to expand, just like air that rises or falls in the atmosphere.
“So when we know that normally the air above is colder it is technically difficult for me to comprehend that the surface is warmed by cold radiation from above?”
It isn’t. But if radiation was the only thing that mattered, it would be the case that that the surface would cool less quickly with a merely cold sky above it rather than one at close to absolute zero. When you wear clothes, the cloth is cooler than your skin, but is nevertheless warmer than the snowy-white landscape of knee-deep global warming that surrounds you. Clothes don’t generate any heat, and there is no net transfer of heat from cool cloth to warm you, but they still keep you warm.
But as I’ve said elsewhere, this argument about back-radiation is all an annoying distraction, because it isn’t how the greenhouse effect really works anyway. Climate scientists use a completely different model for calculations – they just use this pure radiative model in simple explanations. It’s like physicists saying that objects all fall at 9.8 m/s^2 under gravity, and applying this theory to the fall of feathers when explaining to the general public. The physicists already know perfectly well that feather fall doesn’t work that way. But huge amounts of sceptic time are wasted by people doing the equivalent of applying 9.8 m/s^2 to the fall of various objects and complaining that it doesn’t fit. The equations when extrapolated to extremes end up predicting ridiculous results.
The basic problem here is that they haven’t bothered to explain it properly.

Rabe
January 5, 2011 4:01 am

Dave Springer:

Maximum density [of water] occurs at the freezing point

since when? See Table 8a-1: Density of water molecules at various temperatures…
http://www.physicalgeography.net/fundamentals/8a.html

Dave Springer
January 5, 2011 4:59 am

Nullius in Verba says:
January 4, 2011 at 4:49 pm

“Well unfortunately, that odd density temperature function ONLY applies to fresh water, and low salinity salt water.”

“Yes. True. I should have been a bit clearer – you’ll note of course that I didn’t actually specify whether it was salt or fresh water (I said “water” and was thinking in general physical terms), but I agree that it might have been assumed to be salt given that the oceans are the biggest part of the effect of all this on climate.”
No. False. What you should do is admit you made a mistake. Seawater density increases constantly until it freezes and the freezing temperature is about 2 degrees C below zero. Not knowing that led you to say that the deep ocean temperature is 3C because that’s the point of grestest density.

Dave Springer
January 5, 2011 5:03 am

Rabe says:
January 5, 2011 at 4:01 am

Dave Springer:
Maximum density [of water] occurs at the freezing point

“since when? See Table 8a-1: Density of water molecules at various temperatures…”
I was referring to seawater and its since always. Salinity changes the temperature/density relationship. At 3.5% salinity (that of the global ocean) density increases all the way to the freezing and the freezing temperature is -1.8C.

Dave Springer
January 5, 2011 5:13 am

JAE says:
January 4, 2011 at 1:10 pm
“Well, ALL the gases in the atmosphere function as “insulation,” not just the GHGs (remember, the N2 and O2 are heated by collisions/thermalization).”
No they DO NOT act as insulators. They are buffers. They reduce the temperature differential between day and night and nothing more.

Dave Springer
January 5, 2011 5:28 am

Graph of temperature vs. density of seawater
I’m gobsmacked at how many times this must be repeated. Seawater increases in density all the way to the freezing point. In this respect it is quite unlike fresh water.
Ninety percent of the global ocean lies below the thermocline at nearly a nearly constant temperature of 3C. It isn’t because that’s the maximum density of seawater. Maximum density is at -1.8C. It’s 3C because that’s the average temperature of the surface waters when the average is taken over the entire course of a glacial/interglacial period (100,000+ years). Over that length of time convection and conduction are sufficient to equalize the temperature of the deep waters with the surface waters. If there is any other possible cause for the measured temperature of the ocean below the thermocline I’ve yet to hear it.

Joel Shore
January 5, 2011 5:39 am

Bryan says:

Unfortunately it is behind a pay wall and written by the “usual suspects”.
I cannot tell therefor if their prediction of the end of all human life is justified.
Common sense tells me that the consequences of such a minor change would be negligable.

You should be able to find a copy of Science at any reasonable local library. The basic picture is that CO2 alone provides about 20% of the radiative greenhouse effect (with the other non-condensable greenhouse gases providing another 5%). Water vapor and clouds (condensed water vapor) provide the other 75% with the division being water vapor ~50% and clouds ~25%. However, if you remove the non-condensable greenhouse gases, then the resulting cooling causes the amount of water vapor in the atmosphere to plummet because of the strong dependence of the saturation pressure on the temperature.
“Common sense” is not always a very good guide when talking about things that one really hasn’t developed much intuition for.
JAE says:

And I think that that stored energy is all you need to consider to explain the surface temperature on Earth. For gases (the atmosphere), PV = RT; so T = (the constant, R)x(PV). Both P and V of a quantity of gas depend only upon the amount of stored energy in that gas, so T must also depends on this.

It is quite a jump from writing down the ideal gas law (pV = nRT), which involves 4 variables, to explaining how this constrains the surface temperature. I have never seen anyone successfully make that jump…and I predict it would be quite difficult to do so, since it seems impossible to violate the constraint of energy balance for very long.
If the earth’s surface were warmer than energy balance predicts (in the absence of IR-active gases in the atmosphere) then it would emit more radiation than it receives and it would cool down. It is as simple as that. There are ways to get around that, e.g., by having constant gravitational collapse…but I would doubt you would want to make the argument that the earth or its atmosphere are undergoing continuous gravitational collapse!

mkelly
January 5, 2011 5:52 am

On subjects like this it seems to me that some basics of heat transfer should be available to new comers etc so they can start to grasp the questions surrounding the discussion.
Such as for heat to be transferrd there must be two basic requirements.
1. a path
Without out these two regardless of the mechanism no heat is transferred.
I know folks can look up much themselves,but maybe a section on the site where they can quickly go to get info maybe be helpful.

Dave Springer
January 5, 2011 6:08 am

Bryan says:
January 5, 2011 at 1:00 am
Bryan says, Joel Shore;
“What would happen if one of the models was left to run with the IR radiative effects of CO2 shut down?”
“H2O still operating with radiative properties in the IR and the usual phase change effects still intact.”
Not sure who said what re Joel and Bryan.
What would happen is commonly referred to as “Snowball Earth” which has happened several times in the earth’s history. The water cycle shuts down. The earth’s average surface temperature without greenhouse gases is way below freezing. CO2 with sufficient partial pressure raises (through its effect as an insulator) the surface temperature above freezing which in turn starts the water cycle. Once the water cycle is started water vapor takes over as the primary greenhouse gas raising the temperature even more until there are enough albedo-lowering clouds to prevent any further warming of the surface.
If CO2 were suddenly absent water vapor would continue to keep the surface warmer than freezing for a while but eventually the ice would win, the water cycle would be shut down, and average temperature would plunge below that of the moon (moon’s average temperature is -23C) because snow and ice has a far higher albedo than lunar regolith.
Indeed it is commonly believed that CO2 build-up during a Snowball Earth episode is what eventually melts the frozen surface. When the earth is covered with ice and snow the water cycle isn’t the only thing that shuts down. The carbon cycle shuts down as well. Volcanism continues and over the course of millions of years CO2 being belched out of volcanoes accumulates in the atmosphere. On a frozen earth there is nothing to remove CO2 from the atmosphere. No plants, no chemistry, no liquid water on the surface to absorb any of it. Eventually it reaches a high enough partial pressure to defeat the ice and the melt is rapid.
At a CO2 partial pressure of 280ppm (presumably the average over the last few million years) any minor perturbation is enough for snow and ice to start building further and further downward from the poles. A mere 3 degree cyclical change in axial tilt which does nothing more than increase/decrease the temperature difference between winters and summers is enough to start and stop interglacial/glacial periods.
The only “tipping point” we’re near today is tipping back from interglacial to glacial. Wanting to reduce or limit atmospheric CO2 is the same as wanting to push the planet over the edge back into a full blown ice age that will persist for 100,000 years and cover everything north of Washington, DC with a glacier that’s a mile thick. It’s insane.

Bryan
January 5, 2011 7:24 am

Dave Springer
…..”What would happen is commonly referred to as “Snowball Earth”…….
……”If CO2 were suddenly absent water vapor would continue to keep the surface warmer than freezing for a while but eventually the ice would win, the water cycle would be shut down”……
There are about 40 H2O molecules to each CO2 molecule on average.
In addition to having even more radiative possibilities in the IR, water also has two phase changes at atmospheric temperatures.
The absence of a CO2 radiative component would mean that the Earth Surface would be warmer during daylight.
In my hypothetical atmosphere CO2 would still be there but would not radiate at around 15um.
Vegetation and so on would behave as the temperature dictated.
The question was addressed to Joel Shore because I suspect he has access to a model and I was wondering if such a run had been attempted and what the outcome was.

Rabe
January 5, 2011 8:05 am

Dave Springer, thanks for the graph, regarding the water, your point. But I won’t buy the CO2 cycle without seeing it experimentally confirmed.
BTW, I like most of your explanations here.

David L.
January 5, 2011 8:09 am

Too much detail too fast. If you can’t get close to the observables with a few basic robust factors, there’s no chance to explain it further. All this worry about thermoclines, tropospheres, back raditation, etc. will not solve the problem as to whether there’s AGW due to CO2 or not. If one needs to employ these arguments, then there isn’t an argument. Look how complicated the human body is. But you don’t need a detailed dissection of human anatomy to know that the more calories you eat and the less you work out, the heavier you become. Sure you can talk about the ATP cycle and metabolising glucose and the role of vitamins and burning energy in muscle tissue and storage in fat tissue, etc. But really adding food calories above the burning rate explains a lot of what’s going on. You start there and dig deeper as needed. The fact that AGW needs to pull in all this detail to try and patch together a story tells me that they don’t have a clue what’s going on with the climate. Not a clue at all.

Nullius in Verba
January 5, 2011 8:44 am

Dave, Springer,
“No. False. What you should do is admit you made a mistake. Seawater density increases constantly until it freezes and the freezing temperature is about 2 degrees C below zero. Not knowing that led you to say that the deep ocean temperature is 3C because that’s the point of grestest density.

Deary, deary me. Well, I do try to be careful about what I write, but nobody’s perfect. Let’s see…
Could you take a look at my comment here and quote for me the exact text where I say:
a) the water in question is seawater;
b) that seawater density does not increase all the way to freezing point;
c) the deep ocean temperature is 3C;
d) the deep ocean temperature is what it is because that is the point of “grestest” density?
I’m particularly interested in the answer to part a), because my intention at the time was to talk about water generally, without specifying salt or fresh. I’m interested to know what I said that made you so certain that I was only referring to salt water, so I can avoid the error in future. Thanks in advance.
If everybody here had to apologise for all their errors, all the threads would be about twice as long. I shall look out for your response with interest.

January 5, 2011 8:54 am

@ Dave Springer

““That seems to be nonsense to me. Shallow pools of water heated by the sun are demonstrably warmer than deeper pools with the same surface area. For particularly deep bodies, with not a lot of turbulance, you can end up with a scenario where the top couple of feet are much warmer than the lower areas.”
The sun isn’t heating them with thermal IR.

Heat diffuses through the entire portion via conduction and brownian motion, in addition to the non-IR heating element (visible light -> IR.) So yes, some IR is heating the water.
According to your theory, I can point a heat lamp at a bathtub and the water will remain room temp.

Dave Springer
January 5, 2011 9:16 am

Jon-Anders Grannes says:
January 5, 2011 at 12:24 am
“This means on average that the more column of air you have above you the warmer it gets.”
That depends on the gases present and the radiative spectrum at that level in the atmosphere. In more of the atmosphere than not (by column feet) temperature increases with altitude.
See here:
http://www.srh.noaa.gov/jetstream//atmos/atmprofile.htm
If you understand why the stratosphere temperature increases with altitude almost as quickly as the troposphere decreases with altitude you’ll then understand why increasing partial pressure of N2 and O2 at the surface won’t raise or lower average surface temperature. All it will do is reduce the temperature differential between day and night via increased thermal mass.

sky
January 5, 2011 10:13 am

As long as climate science relies on cartoonish conceptions of thermal energy fluxes largely through radiative means, puerile misconceptions of how surface temperatures are elevated above nominal blackbody levels will run wild.
Although radiation provides the only escape for energy to space, the TOA balance is not the core issue at the surface, where moist convection is the principal means of thermal energy transfer to the atmosphere on an oceanic planet. Colin Davidson (Jan 4, 4:13am) summarizes the physical problem very well. I only add the observation that the “inert” bulk constituents of the atmosphere, once thermalized by convection and by molecular collisions with GHGs, provide (along with clouds) what little “thermal inertia” the atmosphere posseses; it is very small compared to that of the oceans.
The GHGs act as a dispersant rather than a store of thermal energy, with outward as well as backward radiation at every level. Despite Kiel and Trenberth’s propagandistic portrayal of backradiation as the principal source of thermal energy at the surface, it is simply part of a nearly null-net radiative exchange with the insolation-warmed surface, with the latter invariably stronger on climatic scales. It’s the surface that warms the atmosphere, not the other way around.
What the presence of any atmosphere does is provide a gaseous envelope into which thermal energy from the thermalized surface can conduct and convect, thereby buffering the temperature differential between the surface and space. Since all matter at temperatures above zero K radiates, regardless of the composition of the atmosphere there will always be backradiation that effectively retards radiative cooling of the surface. The density of the atmosphere, which is a factor in its enthalpy, and the surface heat capacitance are what really matters. Mars, with ~16 times more CO2 molecules between its surface and space, but less than one percent of Earth’s atmospheric density, shows very little “greenhouse effect.” It’s not a matter of radiative algebra.
That’s all, folks!

JAE
January 5, 2011 10:37 am

Joel Shore at 5:39 am says:
“It is quite a jump from writing down the ideal gas law (pV = nRT), which involves 4 variables, to explaining how this constrains the surface temperature. I have never seen anyone successfully make that jump…and I predict it would be quite difficult to do so, since it seems impossible to violate the constraint of energy balance for very long. ”

JAE
January 5, 2011 11:09 am
Bryan
January 5, 2011 11:10 am

Dave Springer and Joel Shore
How come with your “snowball” earth concern you had not noticed that increased CO2 follows increasing temperature.
It is a lagging factor not a causal one.
This fact is now generally acknowledged and is a current feature article in of all places Skeptical Science.
While agreeing this is the case they make some convoluted attempt to show its still the ever guilty CO2s fault.
The BBC tonight were at the usual spin saying the record cold December is due .to Global Warming.
Cold is hot,up is down,black is white,effect is cause,lagging is leading.

George E. Smith
January 5, 2011 11:10 am

“”””” kcrucible says:
January 5, 2011 at 8:54 am
@ Dave Springer
““That seems to be nonsense to me. Shallow pools of water heated by the sun are demonstrably warmer than deeper pools with the same surface area. For particularly deep bodies, with not a lot of turbulance, you can end up with a scenario where the top couple of feet are much warmer than the lower areas.”
The sun isn’t heating them with thermal IR.
Heat diffuses through the entire portion via conduction and brownian motion, in addition to the non-IR heating element (visible light -> IR.) So yes, some IR is heating the water.
According to your theory, I can point a heat lamp at a bathtub and the water will remain room temp. “””””
Well I doubt that much “heat” is transported by Brownian Motion; which is the observed eratic motion of small airborne particles like dust or pollens; that is well known to be the result of such particles being sufficiently small and low in mass, that they are capable of registering even a single molecular collision with air ; rather than responding blankly to just the average of those random molecular collisions. And as for this :- “”””” According to your theory, I can point a heat lamp at a bathtub and the water will remain room temp. “””””
Well not exactly; a “Heat Lamp” actually emits EM radiations that the human body (because of its water content) actually recognises as “heat”; those being wavelengths in the range from about 750 nm to about 4.0 microns, right in the range where “heat lamps” emit much of their energy.
BUT ! we are talking about the ocean (or surface) being warmed by a LWIR Thermal Radiation source (the atmosphere) that has a mean Temperature of about 288K (+15 deg C or +59 deg F), and emits about 390 W/m^2 in a spectrum centered at about 10.1 microns, and ranging from about 5.0 to 80.0 microns for 98% of its energy emissions. A very good laboratory source approximation to the real atmopsheric source, would be an ordinary sixteen ounce or about 250 ml bottle of drinking water. Your “heat lamp” on the other hand could be emitting as much as 4 megaWatts per square metre, in a spectrum centered at 1.0 micorns rather than ten microns. Humans cannot even sense 10 micron radiation as being “heat”; in fact we have to jump through hoops to detect it at all.
Try heating your bathtub, using a real LWIR radiation source such as a bottle of drinking water.

Dave Springer
January 5, 2011 11:12 am

Bryan says:
January 5, 2011 at 7:24 am

In my hypothetical atmosphere CO2 would still be there but would not radiate at around 15um.
Vegetation and so on would behave as the temperature dictated.
The question was addressed to Joel Shore because I suspect he has access to a model and I was wondering if such a run had been attempted and what the outcome was.

Zeroing out the non-condensing greenhouses gases results in average surface temperature decline to -20C in the first decade using GISS ModelE AR5. Lacis did it, published the results, and discusses it below:
http://pielkeclimatesci.wordpress.com/2010/11/03/guest-post-co2-the-thermostat-that-controls-earth%E2%80%99s-temperature-by-andy-lacis/
I have no argument with it. Where I think the model boffins go wrong is that the so-called thermostat has a floor temperature set by non-condensing greenhouse gases (consistent with the model above) but where the ceiling temperature is set by cloud cover not by greenhouse gases where increasing surface temperature causes more clouds which then raises planetary albedo which then limits further surface warming. This is not how clouds are modelled and therein lies the major flaw in the vaunted global circulation models.

George E. Smith
January 5, 2011 11:34 am

“”””” Joel Shore says:
January 5, 2011 at 5:39 am
Bryan says:
Unfortunately it is behind a pay wall and written by the “usual suspects”.
I cannot tell therefor if their prediction of the end of all human life is justified.
Common sense tells me that the consequences of such a minor change would be negligable.
You should be able to find a copy of Science at any reasonable local library. The basic picture is that CO2 alone provides about 20% of the radiative greenhouse effect (with the other non-condensable greenhouse gases providing another 5%). Water vapor and clouds (condensed water vapor) provide the other 75% with the division being water vapor ~50% and clouds ~25%. However, if you remove the non-condensable greenhouse gases, then the resulting cooling causes the amount of water vapor in the atmosphere to plummet because of the strong dependence of the saturation pressure on the temperature. “””””
But Joel, if your “plummeting” water vapor scenario is correct; and remember that even ice sublimes when the atmospheric humidity is very low (see the “Snows Of Kilimanjaro”); then with the atmosphere devoid of H2O, we presumably would no longer have what NASA recently asserted was an average global cloud cover of 61%; so we would have a significantly smaller cloud albedo contibution; and absent H2O vapor in the air, we would get less near IR (0.75-4.0 microns) absorption of incoming solar energy, so the ground level solar insolation would skyrocket; and since 70% of the ground is the oceans; and even a higher percentage than that in the more tropical regions; the ocean storage of solar energy would blossom, and the near surface absorption of that 0.75 to 4.0 micron solar energy, would tend to warm the near surface layers, and we would not be wanting for water vapor in the atmosphere for very long.
Your snowball earth sans NCGHGs scenario, is a product of the nonsensical belief that the TSI is 432 W/m^2 instead of 1366 W/m^2.
Given the lousy thermal conductivity of planet earth; the planet surface responds to the instantaneous solar energy input; not to the global annual average insolation.
There are plenty of locations on this planet, whose Temperatures routinely fall below 255 K; the supposed BB equilibrium Temperature sans the GHG effect; and those locations continue to accumulate plenty of snow; which allegedly falls from the sky; and they have plenty of clouds; and all the CO2 that man has polluted the air with have failed to raise those Temperatures above the “water ignition point”. For some reason the air gets plenty of water even at Temperatures below 255K; so why isn’t the CO2 lifting the Temperature in those regions. I thought global warming was most prominent in the polar regions; so why is it still so cold there ?

George E. Smith
January 5, 2011 11:50 am

“”””” Jon-Anders Grannes says:
January 5, 2011 at 12:24 am
?
Radiation goes from warm to cold. Never from cold to warm. “””””
Well (EM) Radiation doesn’t know anything about Temperature; which is entirely a property of MATTER, so Radiation acn go pretty much anywhere it wants to.
That includes the roughly 3 K (spectrum) background radiation from the “Big Bang” having no trouble landing on the 6,000 K surface Temperature of the sun.
EM Radiation is NOT “heat”. And the second Law of Thermodynamics applies to cyclic machines; a la Clausius: ‘No cyclic machine can have no other effect than to transport heat from a source at one Temperature, to a sink at a higher Temperature.’

Joel Shore
January 5, 2011 12:12 pm

Bryan says:

How come with your “snowball” earth concern you had not noticed that increased CO2 follows increasing temperature.
It is a lagging factor not a causal one.

Chickens are also a “lagging factor” of chicken eggs. However, that does not mean that they are not a cause of chicken eggs. Causality can work both ways…and we in fact know that CO2 has radiative effects that can be calculated quite accurately (even if the feedbacks introduce considerably more uncertainty as to its final effects).
It is true that in the absence of humans rapidly liberating the carbon stored for eons in fossil fuels, there had to be some sort of trigger for the increase of greenhouse gases in the atmosphere…and during the glacial-interglacial cycles, that trigger was provided by the Milankovitch oscillations in the earth’s orbit and the resulting warmings this caused that then led to the release of CO2 into the atmosphere. However, the timing is such that the CO2 can still be responsible for a considerable fraction of the warming (and seems necessary to explain the synchronization of the two hemispheres). Estimates of the forcings involved suggest that CO2 was responsible for about 1/3 of the warming between the last glacial maximum (LGM) and now, with all the greenhouse gases together pushing that number up to about 40%.

Joel Shore
January 5, 2011 12:26 pm

George E. Smith says:

But Joel, if your “plummeting” water vapor scenario is correct; and remember that even ice sublimes when the atmospheric humidity is very low (see the “Snows Of Kilimanjaro”); then with the atmosphere devoid of H2O, we presumably would no longer have what NASA recently asserted was an average global cloud cover of 61%; so we would have a significantly smaller cloud albedo contibution; and absent H2O vapor in the air, we would get less near IR (0.75-4.0 microns) absorption of incoming solar energy, so the ground level solar insolation would skyrocket; …

Skyrocket? I think that is a little strong. At any rate, what mainly matters is the top-of-the-atmosphere energy balance (because of the strong mixing by convection and latent heat in the troposphere), which won’t be affected considerably by exactly where the absorption occurs.
And, do you have evidence that any of these effects were left out of the models? Surely, they modeled how clouds will change. (The estimates that I have seen on clouds is that they currently raise the earth’s albedo from about 12% to about 30%.) However, there are also changes in albedo due to the increase of ice.

Your snowball earth sans NCGHGs scenario, is a product of the nonsensical belief that the TSI is 432 W/m^2 instead of 1366 W/m^2.
Given the lousy thermal conductivity of planet earth; the planet surface responds to the instantaneous solar energy input; not to the global annual average insolation.

George: Things are modeled at various degrees of approximation. For a simple energy balance model, one looks at the average insolation over the surface. However, the full-blown GCMs don’t make this approximation. They have the diurnal cycle and the albedo effects of clouds and so forth. Try googling “climate models diurnal cycle”.

There are plenty of locations on this planet, whose Temperatures routinely fall below 255 K; the supposed BB equilibrium Temperature sans the GHG effect; and those locations continue to accumulate plenty of snow; which allegedly falls from the sky; and they have plenty of clouds; and all the CO2 that man has polluted the air with have failed to raise those Temperatures above the “water ignition point”.

And, do you have any evidence that climate models predict that they will? Again, George, you are just making nonsensical complaints. You are creating strawmen that have no basis in reality. The models don’t actually predict what you seem to think they say will happen.

For some reason the air gets plenty of water even at Temperatures below 255K; so why isn’t the CO2 lifting the Temperature in those regions. I thought global warming was most prominent in the polar regions; so why is it still so cold there ?

I’ve lost you here. The prediction is that an increase in the greenhouse effect will manifest itself more strongly near the poles. It is not that the poles will be warmer than tropic regions. Again, George, you are just creating strawmen of your own devising.

Dave Springer
January 5, 2011 1:09 pm

sky says:
January 5, 2011 at 10:13 am
“The density of the atmosphere, which is a factor in its enthalpy, and the surface heat capacitance are what really matters. Mars, with ~16 times more CO2 molecules between its surface and space, but less than one percent of Earth’s atmospheric density, shows very little “greenhouse effect.””
The usual answer to the weak greenhouse effect on Mars is lack of anything for CO2 to thermalize by conduction. On the earth where the atmosphere is 100 times thicker when a CO2 molecule is excited by 15um IR it immediately bumps into a molecule of nitrogen or oxygen and transfers part of the energy to those molecules. The so-called back radiation comes primarily from conductively heated nitrogen and oxygen. On Mars there’s very little conductive heat exchange going on because the separation between molecules is far greater. CO2 there absorbs and holds what little heat it can and the rest is lost to space.

wayne
January 5, 2011 1:10 pm

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
All of you are so close to the answer but in various aspects leaving out critical points here and there that confuse the discussion.
All should be wary of the atmosphere. It does some non-intuitive tricks on you. I’ll try to explain what I see you may be missing that would put you all parallel.
Does everyone think PV = nRT holds in the lower atmosphere, I do. So Dave, Jon-Anders is correct in his statement, the lower you go with more pressure the higher the temperature, walla, the lapse rate without getting into which gases are present.
But you have another effect happening at the same time, due to gravity. The higher pressure when lower in altitude has many more molecules per volume at an also elevated temperature so to equalize the temperature the molecules must slow to a degree. This creates a molecular velocity gradient that *will* try to equalize but curiously can never be really reached but it really is just an change in the conductivity vertically in addition to the radiative gradient due to the temperature difference. All molecules will also try to equalize their velocities between vertical shells. To me that is the one prime relation underlying general thermodynamics, the velocity of the molecules.
But in a paper defining the “standard atmosphere 1976” there is a plot, no numbers, of molecular velocity with altitude and the velocity is going up markedly with altitude. So the velocity equalization would be DOWNWARD, Not what I expected. That would mean there is a certain amount of energy tendency downward against the temperature gradient. Seems to violate t.d. principles but there it is. In this case to me it’s merely a decrease or even negative conductivity with altitude. Looked in isolation its warmth moving downward, not the net flow, but it would decrease it.
At some factor there is a ‘net mean molecular velocity gradient’ also imprinted in the atmosphere when looking at various altitude levels in relation to each other.
Any of you see that area I’m speaking of. It’s left out of all discussions I read. That is one other factor that is not radiative in nature in the migration of energy upward.
Not being *that* good in t.d., I can seem to follow this thought much deeper, maybe you can. Maybe it’s just another factor best tossed out the window and inappropriately ignored.

Rocky H.
January 5, 2011 2:01 pm

George E. Smith’s explanation (January 5, 2011 at 5:39 am) was easy for me to understand. But Joel Shore’s answer comes across as gibberish in places.
For example, he talks about the energy balance ”which won’t be affected considerably by exactly where the absorption occurs.” Won’t be affected considerably by exactly… ? What does that mean?
And he criticises using the word skyrocket, when he himself uses the word plummeting. It seems Mr. Shore has an axe to grind here, specially when he says Mr. Smith is just “making nonsensical complaints”. I think Mr. Smith’s explanation was good, and it wasn’t a complaint.
Mr. Shore’s comments suggest that GCM’s make good predictions. But from what Ive read they don’t. Good predictions are the real test of models. But models can’t predict with any accuracy. Maybe that’s why Mr. Shore is so testy.
The more I read this site the less I believe there’s any climate problem.

Dave Springer
January 5, 2011 2:19 pm

@sky (con’t)
I can’t say I’m completely satisfied by the above explanation for weak greenhouse effect on Mars. So as usual in such cases I dug a little deeper. In the search for contributing factors I took a look at typical night time minimum surface temperatures. Both Vikings measured -107C (160K) at night. Since the peak emission frequency shifts with changing temperature I wanted to see if that shifts the peak spectral energy away from CO2 absorption wavelengths.
A blackbody at 160K has a peak emission wavelength of 18um. See:
http://www.spectralcalc.com/blackbody_calculator/blackbody.php
CO2 absorption bands are 2, 3, 4, and 15um. The night time surface on Mars thus radiates practically no energy in the 2um to 5um range and (compared to the earth) diminished energy in the 15um region. 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.

George E. Smith
January 5, 2011 2:45 pm

“”””” Joel Shore says:
January 5, 2011 at 12:26 pm
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.
I merely pointed out that on a real planet like earth, that rotates. the FULL solar energy input acts on the regions that currently are in sunlight; not some isotherrmal blackbody calculation for an infinite thermal conductivity body might experience.
So clouds only raise earth’s albedo from about 12% to about 30%; well that’s hardly anything we would notice is it; it’s not like a 1/100th of a degree Temperature rise; excuse me Temperature anomaly would do to increase the frequency and severity of hurricanes, and tornadoes.
As for the albedo contribution of ice. Take a guess Joel; c’mon I know you can do it; Why do you think there is all that ice in the polar regions; I mean we don’t have ANY ice to speak of in the tropics where most of the sunlight is; so just how much solar energy is going to be rejected from the earth surface because of that polar ice. If clouds only increase albedo from 12% to 30%; hardly worth mentioning; why would anybody mention ice albedo.
Who cares a whit Joel about the top of the atmosphere energy balance ? The vast majority of earth’s energy is stored and captured in the oceans, directly from solar spectrum sunlight. And that happens to be in the general neighborhood of where humans and other living things tend to congregate and thrive. And the total integrated sum of all of that energy is ADVERSELY affected by each and every single H2O molecule in the atmosphere, no matter where geographically or altitudinally, nor in any way dependent on the phase of that H2O sample. It ALWAYS reduces the ground level total solar energy input to the earth; no IFS ANDS OR BUTS. Whether condensed, or in vapor form, no matter whether you just exhaled it, or whether it is waiting for a 200 year old CO2 companion to exit the atmosphere with; WATER ALWAYS reduces the total energy received by the earth from the principal energy source; the sun.
And it is that surface energy which ultimately determines the thermal transport processes which eventually escort some of that energy to the upper atmosphere to be lost to space. Most of the thermal radiation from earth originates at the surface; and a good bit of it escapes without ever paying any attention to conditions at the top of the atmosphere; and additional radiation losses pass through one or more atmospheric absorption/emission cycles before escape; but that energy starts mostly at the surface. True direct solar heating of the upper atmosphere can result in somewhat prompt loss to space; that’s a significant part of the solar energy input that never makes it to the surface because of H2O; and of course also to Ozone; well even CO2 that arch enemy of all living things, contributes to cooling the earth by capturing some small percentage of the near infra-Red solar radiation and preventing it from reaching the surface.
I would recommend Joel that you should apply for research grants to study what is actually happening on a real planet like the earth for instance; and stop paying attention to the output of some supercomputer’s backwards looking Global Circulation Model. Do they have any Global Climate Models; well besides Trenberth’s isothermal energy balance cartoon ?
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.
If you don’t think that a change in albedo from 30% down to 12% due to cloud loss would cause earth’s surface insolation to “skyrocket”, then Joel, I think I might have to re-evaluate my impression of your expertise.
Now a half a degree (C) possible (who knows) increase in mean global surface Temperature over the last 150 years; would in my book, NOT be described as a “Skyrocket” change; but the effect of clouds dropping the albedo from 30% to 12% (your figures) would fit the bill for me.

George E. Smith
January 5, 2011 3:14 pm

“”””” I’ve lost you here. The prediction is that an increase in the greenhouse effect will manifest itself more strongly near the poles. It is not that the poles will be warmer than tropic regions. Again, George, you are just creating strawmen of your own devising. “””””
The above from Joel.
I don’t have a problem with the assertion that the poles should warm faster than the tropics. After all the polar temperatures can be so low, that thermal radiation rates are a factor of as much as six lower than the rates for places at earth’s mean Temperature of (supposedly) 288 K So the polar regiosna re near useless for cooling this planet because of those low emission rates. Then because of those same lower Temperatures, the spectrum of that weak polar thermal radiation is moved to longer wavelengths, so that eventually at the coldest places, the spectral peak can sit right on the 15 micron absorption band of CO2 and hence maximise the GHG capture effect of CO2 at the poles.
Conversely in the highest Temperature tropical desert regions; where surface Temperatures of 333K or higher are seen; the thermal emission rates can be 1.8-2.0 times the global mean rates, and more than ten times the puny polar rates.
And moreover, because of those higher source Temperatures in the tropics, the emitted LWIR spectrum moves even further away from the 15 micron CO2 band making CO2 even less effective in its greenhouse effect. And for an encore, the peak of the tropical desert surface emission spectrum moves even further into the middle of the atmospheric window, that is largely due to H2O absorption band spectra; but since water vapor is largely absent over those same d3eserts; there’s not much to impede the exit of the peak of the LWIR emissions from hot deserts. They are the most efficient (radiative) coolers on the planet.
Yes I know that convection and evaporation and other thermal processes are responsible for most of the energy transport in the atmosphere; come to think of it; just what role does CO2 in the atmosphere play in interrupting conduction and convection and evaporative cooling processes from the earth surface ?
I wonder why everybody makes such a fuss over the greenhouse gas phenomenon of CO2 and methane; when it is well known that Electro-magnetic radiation is but a small part of the earth’s energy transport processes; and CO2 has no impact at all on the most prevalent energy transport physical processes.
But as to the initial paragraph of your puzzlement Joel.
Is it NOT true; that you are a disciple of the theory that CO2 is a greenhouse gas which acts as a “kindling wood” (my words) to magically kick off the previously dormant H2O evaporation process; which leads to H2O (which is NOT a greenhouse gas; since it condenses); AMPLIFYING the LWIR absorption by CO2 in a positive feedback loop ? And without that CO2, well there simply would be no H2O in the atmosphere so earth would be a frozen ice ball at around 255 K Temperature. That’s what that was all about; that so puzzled you.

JAE
January 5, 2011 3:17 pm

“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).

Dave Springer
January 5, 2011 3:21 pm

@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.

Dave Springer
January 5, 2011 4:31 pm

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.

JAE
January 5, 2011 5:15 pm

“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?

wayne
January 5, 2011 7:08 pm

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.

stevenmosher
January 5, 2011 9:06 pm

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

Dave Springer
January 6, 2011 4:46 am

JAE says:
January 5, 2011 at 5:15 pm

“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?

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.

jae
January 6, 2011 5:31 am

“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.

Dave Springer
January 6, 2011 6:13 am

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.

Nullius in Verba
January 6, 2011 9:19 am

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.

Joel Shore
January 6, 2011 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.
I merely pointed out that on a real planet like earth, that rotates. the FULL solar energy input acts on the regions that currently are in sunlight; not some isotherrmal blackbody calculation for an infinite thermal conductivity body might experience.

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.

Who cares a whit Joel about the top of the atmosphere energy balance ? The vast majority of earth’s energy is stored and captured in the oceans, directly from solar spectrum sunlight. And that happens to be in the general neighborhood of where humans and other living things tend to congregate and thrive.

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).]

Joel Shore
January 6, 2011 10:10 am

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.

Joel Shore
January 6, 2011 10:31 am

jae says:

LOL. You evidently don’t understand the article at all!

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!

wayne
January 6, 2011 12:35 pm

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://www.americanthinker.com/2010/02/the_hidden_flaw_in_greenhouse.html
http://www.ilovemycarbondioxide.com/pdf/Rethinking_the_greenhouse_effect.pdf

Dave Springer
January 6, 2011 12:57 pm

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.

Dave Springer
January 6, 2011 1:12 pm

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.

Dave Springer
January 6, 2011 2:28 pm

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.

Dave Springer
January 6, 2011 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”
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.

Dave Springer
January 6, 2011 3:03 pm

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

George E. Smith
January 6, 2011 3:27 pm

“”””” 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

Dave Springer
January 6, 2011 3:34 pm

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.

Dave Springer
January 6, 2011 3:59 pm

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:

Principle of operation
A practical vacuum flask is a bottle made of metal, glass, foam, plastic with hollow walls; the narrow region between the inner and outer wall is evacuated of air. It can also be considered to be two thin-walled bottles nested one inside the other and sealed together at their necks. Using vacuum as an insulator avoids heat transfer by conduction or convection. Radiative heat loss can be minimized by applying a reflective coating to surfaces: Dewar used silver. The contents of the flask reach thermal equilibrium with the inner wall; the wall is thin, with low thermal capacity, so does not exchange much heat with the contents, affecting their temperature little. At the temperatures for which vacuum flasks are used (usually below the boiling point of water), and with the use of reflective coatings, there is little infrared (radiative) transfer.

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.

George E. Smith
January 6, 2011 3:59 pm

“”””” 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.
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.

George E. Smith
January 6, 2011 4:06 pm

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

Dave Springer
January 6, 2011 4:15 pm

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.

Nullius in Verba
January 6, 2011 4:34 pm

“CO2 is an insulator not a heater. Write that down and pass the note along to anyone else who just doesn’t get it.”
CO2 is a thermostat, not an insulator.
LOL.

Alasdair Fairbairn
January 6, 2011 4:37 pm

I always thought that climate sensivity was the derivative of the Stefan-Boltzmann equation and equal to 0.21. Merely dividing T by I [Global temperature by insolation] ignores the Albedo and Emissivity elements. Not to mention the Boltzmann constant. Thus I suspect your figure of 0.84 could be wrong.
Mind you I appear to be approaching the problem from a very different perspective; so may be misinterpreting. [still need to look at your paper in more detail].
One interesting aspect I have noted is that on the current perceived values of Albedo and Emissivity of 0.3 & 0.612 respectively, the ratio of 0.49 determines the equilibrium temperature; for constant Insolation. Thus should this rise then the planet cools and visa versa.
It also puzzles me why we are all chasing temperature measurements when we should be looking at Albedo and Emissivity. After all it is these two elements that determine the temperature not the other way round.
I do concede, however, that this would be a very difficult task.
In fact the Warmists should be delighted with the recent cold patch ;as it has been very busy COOLING the earth with all that Albedo cluttering up our roads.
Is that not what they want?

David L
January 6, 2011 5:36 pm

Nullius in Verba says:
January 6, 2011 at 4:34 pm
“CO2 is an insulator not a heater. Write that down and pass the note along to anyone else who just doesn’t get it.”
CO2 is a thermostat, not an insulator.
LOL.
Anyone that thinks CO2 is an insulator needs to look up the definition of an insulator. A vacuum (which is the absence of matter) insulates because there is no ability of thermal conduction. Fiberglass and other materials insulate because the have low thermal conductivities. The last time I read about CO2 it adsorbs energy quite well in the IR. That’s exactly what you don’t want in an insulator.

wayne
January 6, 2011 10:44 pm

Dave says: CO2 is an insulator not a heater. Write that down and pass the note along to anyone else who just doesn’t get it.
Sorry Dave, CO2 is a superb conductor, not an insulator and *especially* at temps where IR is near it’s absorption/emission bands. Have you bought any CO2 filled multi-layer glass panes lately? I hear you can have them installed basically for free thanks to friendly utility company sponsored discounts (their sales are hurting a bit lately with high energy costs). Or, you could just open the windows this winter.

Nylo
January 7, 2011 5:21 am

Is Willis Eschenbach out there? No responses since January 4th. Preparing a new story which somehow continues this one, I guess?

Joel Shore
January 7, 2011 8:08 am

Dave Springer says:

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.

I don’t think albedo is a constant in the models. In fact, in the Lacis et al. paper that I linked to, it is one of the things that changes when they remove CO2. I agree that it is one of the things that can effectively be tuned but I think that is by adjusting other parameters. The +/-4% sounds high to me (where did that come from)…Do you mean +/-4% as in it could be anywhere from 26% to 34% or do you mean that it is +/- 0.04 times the central estimate of ~30%?

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.

I’m not sure where you get your 0.2 kilowatts per square meter number…and I also disagree with your claim that if you don’t know values of certain things perfectly then it means the model will give total garbage. In fact, I might expect that if you only know the albedo to 4% then perhaps you would get similar error because of that in your climate sensitivity calculation. Surely, the error bars around climate sensitivity are a lot greater than that from other uncertainties. (I did a web search and did find one paper that investigated the affect of tuning the albedo to one data set or another for the NCAR Community Model and reported “a small but statistically significant difference in the model’s equilibrium climate sensitivity”. Unfortunately, I could only find the abstract so I couldn’t see what that meant quantitatively, but given the spread in climate sensitivity between different models, I doubt that is a particularly large source of uncertainty.)
There is no doubt that significant uncertainties exist in climate modeling. However, that does not mean the models are garbage. It seems only in a politically-charged atmosphere, as exists in this case because so many people don’t like the policy implications of the science, that people seem to adopt a black-white view that the models are either perfect or useless. In the real world, models are always wrong and yet often still very useful.

And we all know the models are a “travesty” thanks to a private candid admission from Trenberth that went embarrassingly public 14 months ago.

That is not what Trenberth was actually saying.

jim hardy
January 7, 2011 9:40 am

Mr Eschenbach:
I applaud your common sense approach. You have an intuitive grasp of feedback systems. That clouds and storms are relatively quick is what keeps system stable, stability requires that feedback be faster than the process being controlled. Slow ocean and quick atmosphere is why it works.
If i’m correct in thinking that ocean heat is the bulk of climate heat, there’s one more beauty to the natural balance you propose. I’ll use the analogy of a control system because that’s what i am familiar with.
To be stable a thermostat needs to sense temperature fairly near the heat source, at least timewise, else the process will get ahead of the thermostat and divergent oscillation will result..
To that end industrial controls often have a sensor wrapped right around the heating element. This gives a little bit of “feed-forward” or “anticipation” which counteracts the natural delays in the process (thermal inertias).
You have picked up on this with your use of thunderstorms to improve the convection process, which is what determines lapse rate which in turn determines surface temperature.
I point out that tropical cyclones, being close to the heat source(tropical oceans) of earth’s heat engine, provide that feedforward. A hurricane moves about 5.2 X 10^19 from the ocean surface to the stratosphere [see http://www.aoml.noaa.gov/hrd/tcfaq/D7.html about the middle of article]. A hundred hurricane-days i think would amount to 5.2 zetajoules, which is a significant chunk of your delta-h. A typical season might have twice that many hurricane days just in the Atlantic, twenty named storms at ten days apiece.
I believe tropical cyclones are Mother Nature’s feed-forward mechanism and it is you who have made this clear to laymen such as myself. Thank you.
Your closed loop control system approach to climate is the right one. See my comment on your Thermostat paper, it’s the last one on the 2009 post at WUWT.
Water vapor is faster than CO2 and that’s why it’ll win.
Sincerely,
old jim hardy (retired power plant engineer who’s moved a lot of heat in his day)

jim hardy
January 7, 2011 9:44 am

Oops! Make that “A hurricane moves about 5.2 X 10^19 JOULES/DAY”
sorry, i was checking my units..

Dave Springer
January 7, 2011 5:51 pm

jim hardy says:
January 7, 2011 at 9:40 am
“If i’m correct in thinking that ocean heat is the bulk of climate heat”
You betcha! All divers know that 33 feet of water is equal to 1 atmosphere. The global ocean averages 12,000 feet deep. Take 71% of that to account for land surface and we get the ocean with a mass of over 250 atmospheres. Water has a specific heat 4 times that of dry air so the final number (close enough for government work) is:
The global ocean has 1000 times the heat capacity of the atmosphere.
You’ve heard of the tail wagging the dog? Well, a tail is around 1-2% the weight of the dog. The atmosphere has only 0.1% the thermal mass of the oceans.
The top 1200 feet is pretty much the only part of the ocean with a temperature that ever exceeds 3C. Everything below that, or 90% of the thermal mass, is 3C. Factoring in the average temperature of the top 1200 feet gives us a global average ocean temperature of 4C.
I gots me a couple questions for the climate boffins. How come the ocean is so dang cold? Is that the real global average temperature when you factor in 100,000 years of ice age along with 10,000 years of years of interglacial?

Dave Springer
January 7, 2011 6:05 pm

Note to climate boffins: Please don’t try to tell me the ocean is 3C below 1200 feet because that’s where water reaches its maximum density. OCEAN water is a 3.5% saline solution which has a freezing point of -1.8C and continues to get denser all the way to the freezing point. See:
http://www.nature.com/nature/journal/v428/n6978/fig_tab/428031a_F1.html

Dave Springer
January 7, 2011 6:37 pm

Joel Shore says:
January 7, 2011 at 8:08 am
“I don’t think albedo is a constant in the models. In fact, in the Lacis et al. paper that I linked to, it is one of the things that changes when they remove CO2.”
It changes for snow/ice but it’s a constant otherwise.
See GISS GCM ModelE description and reference manual:
http://www.giss.nasa.gov/tools/modelE/modelE.html

Dave Springer
January 7, 2011 7:19 pm

@Joel (continued)
“I’m not sure where you get your 0.2 kilowatts per square meter number…”
Sorry. Didn’t state that right. TOA incoming and outgoing are approximately equal at 1366w/m2 (the solar constant).
If earth’s average albedo has an error bar of +-5% then the amount of energy at TOA that is reflected and thus never makes to the surface to warm the ocean has an error range of 136 watts. I guess I rounded the wrong way. Should have said they don’t know how much insolation is reflected except to the nearest 1oo watts.
“I doubt that is a particularly large source of uncertainty.”
Plus or minus 68 watts/m2 at the surface isn’t particularly large? Anthropogenic CO2 (and equivalents) they say cause an additional 2W/m2 at the surface. If the uncertainty in global average albedo is taken into account that would be 2W/m2 plus or minus 50 watts. Seems pretty significant to me.
“people seem to adopt a black-white view that the models are either perfect or useless”
Not me. I’m of the opinion that a model that is wrong is worse than useless – it inspires potentially disastrous decisions in the real world like bridges collapsing, airplanes crashing, and a million other things that involve death and destruction. Maybe even something as bad making a decision to limit greenhouse gases because it might get too warm and instead your efforts bring on an ice age. That’s called “learning the hard way” that your model is broken.
“And we all know the models are a “travesty” thanks to a private candid admission from Trenberth that went embarrassingly public 14 months ago.”
“That is not what Trenberth was actually saying.”
Actually it was. He said they couldn’t explain the lack of significant warming in the past decade. The GCMs predicted warming. He couldn’t explain why it predicted warming that didn’t happen and that was a travesty. It was an indictment of the model.

January 8, 2011 10:13 am

dave springer says:

It changes for snow/ice but it’s a constant otherwise.
See GISS GCM ModelE description and reference manual:
http://www.giss.nasa.gov/tools/modelE/modelE.html

I don’t see where it says that. And, are you sure that you don’t just mean surface albedo (i.e., not including clouds)? I think at least some models now have different albedos for different vegetation and can track changes in vegetation. I am not sure if GISS Model E does this.

Plus or minus 68 watts/m2 at the surface isn’t particularly large? Anthropogenic CO2 (and equivalents) they say cause an additional 2W/m2 at the surface. If the uncertainty in global average albedo is taken into account that would be 2W/m2 plus or minus 50 watts. Seems pretty significant to me.

Yow! Lots of errors here. First, it makes no sense to multiply the total solar constant by 5% and then compare it to the forcing due to CO2. They have to both be measure as W/m^2 of earth’s surface. I.e., the solar constant has to be divided by 4. So, that brings us down to +/- 17 W/m^2. Second, you still haven’t justified where you got the +/-5% number and particular whether your source really meant the albedo could be any where from 25% to 35% or rather if they meant a 5% error in the 30% value (i.e., it could be 28.5% or could be 31.5%). Maybe your interpretation is correct but if the latter one is correct, then your number is further reduced to +/- 5 W/m^2.
Third, you are mixing up changes vs absolute values. If, in the modeling that I had done (including 13 years of working for industry), I always had to have my model within a certain accuracy in predicting something in order to predict a change on that order as I varied a parameter then I would have been unable to do very much in many cases.
In other words, it is not necessary to have all the absolute numbers for all of the energy flows known to a W/m^2 in order to predict how a change in forcing by 1 W/m^2 should roughly change things. In particular, the climate models are always compared to control runs in order to figure out how much warming a certain change produces. That is why the paper that I referenced found that tuning to one measurement vs. another for the model’s albedo only made a small difference in the climate sensitivity that the model predicted.

Not me. I’m of the opinion that a model that is wrong is worse than useless – it inspires potentially disastrous decisions in the real world like bridges collapsing, airplanes crashing, and a million other things that involve death and destruction. Maybe even something as bad making a decision to limit greenhouse gases because it might get too warm and instead your efforts bring on an ice age.

Well, then if you are never willing to accept a model or prediction as long as the model is not 100% correct, you might as well just simplify this and state your positions thusly: “I do not believe in making decisions based on science at all. I am so dead-set against policies to reduce carbon dioxide emissions that there are no circumstances under which I would support them” because that is the honest characterization of your position given that the models will ALWAYS be imperfect. You are demanding absolute certainty in an uncertain world.
By the way, the one point that you (at least implicitly) make in your statement that I do sort of agree with: One thing that makes geoengineering a questionable strategy is that they are much more reliant on the models being absolutely accurate. I.e., the models can already tell us that the perturbation that we are producing through greenhouse gas emissions is dangerous and should be mitigated by reducing our perturbation but I don’t think they are yet accurate enough to tell us exactly what sort of “counter-perturbation” we might want to make (through shooting aerosols into the stratosphere for instance) to counter the effects and not introduce new problems!

Actually it was. He said they couldn’t explain the lack of significant warming in the past decade. The GCMs predicted warming. He couldn’t explain why it predicted warming that didn’t happen and that was a travesty. It was an indictment of the model.

If that was really the point that he was making then he was simply misinformed since the GCMs clearly show similar periods of temperatures being steady. It is simply a facet of any system having a slow (approximately) linear trend with superimposed fluctuations and measuring trends over time periods where the underlying trend cannot accurately be determined.
Since I don’t think Trenberth is misinformed and since he wrote a paper that spelled out in more detail what he found to be a problem, I think that we can safely say that wasn’t really the issue that he had. Rather, he wanted to really be able to nail down energy flows to the point where we could understand the details of what was happening during these fluctuations, i.e., is the heat going into the oceans (and how deep?), are there fluctuations in the albedo, … Trenberth was expressing the frustration that we still aren’t able to measure these flows to the accuracy that allows us to answer these questions.

bobrgeologist
January 8, 2011 11:49 am

My opinion on clilmate change is naturally long term based on the slow pace of geologic events. It is believed that plate tectonics had a hand in the glacial environment we are in today when 50 million years ago the Indian plate impacted southern Asia, closing the Tethys seaway. Thereby disrupting a long standing equatorial warm ocean current that in the Mesozoic Era produced a dominant reptilian fauna, keeping even our polar areas quite warm. Recent core drilling in the Arctic Ocean evidenced temperatures as high as 23 deg C into early Tertiary times. The temperature of the Arctic today is 0 deg C. The past 50 my show a steadily declining temperature. 32 million yrs ago the Antarctic continent iced up. 14 my ago the Arctic Ocean froze over. 1 3/4 my ago the first Pleistoce Ice Ages began with several with 10,000 year periods of Ice. The past 5 have been approximately 100,000 yrs duration with variable interglacials. The present interglacial (Holocene) began melting 14,000 yrs ago but this warming was interrupted by a 1,300 year cold spell (Youngerf Dryas) and it required 6,000 yrs to melt. There is nothing unusual in our climate today despite Dr. Mann’s phoney “hockey stick” graph that omitted the Middle Ages warm period and the following Little Ice Age and compounded the mythical warming beginning with the Industrial Revolution around 1850 AD when human use of carbon based fuels began in earnest, for the blade. All of these fabrications were of enormous concern to the AGW crowd. We have a world financial disaster brewing because of political and environmental support for this false POLICY. But my crowning concern is this mass distraction from the real geologic situation, the Pleistocene Ice Ages as long as we have polar ice caps.

bobrgeologist
January 8, 2011 12:26 pm

My moderation
Considering that our planet has been in the grip of the Pleistocene Ice Ages for over
a million years and in that time, the northern hemisphere has been subject to 5 major continental glaciations. The present Interglacial (Holocene) still has ice in our
polar regions. As long these conditions endure, it is counterproductive to use heroic measures to preserve the status quo and enormously expensive. If we do not warm up a few degrees we will be back in the ice sooner or later.

Joel Shore
January 8, 2011 6:58 pm

Just to clarify, that post by “wrt104” was actually mine…Just logged into someone else’s WORDPRESS account.

Dave Springer
January 10, 2011 8:59 am

wrt104 says:
January 8, 2011 at 10:13 am
dave springer says:
It changes for snow/ice but it’s a constant otherwise.
See GISS GCM ModelE description and reference manual:
http://www.giss.nasa.gov/tools/modelE/modelE.html
“I don’t see where it says that.”
Rather than giving you a fish I’m going to teach you how to fish. Search the manual for the word “albedo”. Let me know what you find.

Dave Springer
January 10, 2011 9:09 am

wayne says:
January 6, 2011 at 10:44 pm

Dave says: CO2 is an insulator not a heater. Write that down and pass the note along to anyone else who just doesn’t get it.
Sorry Dave, CO2 is a superb conductor, not an insulator and *especially* at temps where IR is near it’s absorption/emission bands. Have you bought any CO2 filled multi-layer glass panes lately? I hear you can have them installed basically for free thanks to friendly utility company sponsored discounts (their sales are hurting a bit lately with high energy costs). Or, you could just open the windows this winter.

Prove it and get a Nobel prize for overturning basic thermodynamic properties of gases established by experiment 150 years ago.

Dave Springer
January 10, 2011 9:18 am

David L.
An insulator restricts the flow of energy across a boundary. It can do it by restricting conduction, convection, radiation, or all three.
It’s you who needs to learn what an insulator does and how it works. CO2 is an insulator and it works via impeding long wave infrared radiation energy flow from surface to space while doing nothing to impede the flow of short wave energy from sun to surface. It isn’t rocket science and was demonstrated experimentally 150 years ago. Maybe you should reproduce Tyndall’s experiments and try to prove him wrong. You’d be the first to do it.

Joel Shore
January 10, 2011 4:22 pm

Dave Springer says:

Rather than giving you a fish I’m going to teach you how to fish. Search the manual for the word “albedo”. Let me know what you find.

The only reference I find to the word “albedo” is this paragraph under Sea Ice Model:

Snow can be compacted into ice by accumulating over a maximum thickness, or by rain or surface melting. Surface melting is kept track of since it is used to estimate melt pond formation for the albedo calculation. No specific snow-ice formation is yet included.

Am I missing something?

jae
January 11, 2011 5:40 pm

Hey Springer, if you still “have your ears on:”
“jae says:
January 6, 2011 at 5:31 am
“You, and nearly everyone else, are arguing that a “greenhouse effect” explains that extra heating.”
Been skiing, so not paying much attention. Just in case you are still looking at this, YOU STILL DON’T GET THE POINT! There is NO greenhouse effect!!!!

Joel Shore
January 12, 2011 2:15 pm

jae says:

Just in case you are still looking at this, YOU STILL DON’T GET THE POINT! There is NO greenhouse effect!!!!

Well, maybe not in jae’s universe there isn’t, but there is in the actual universe that the rest of us inhabit. But, hey, continue to marginalize yourself by arguing scientifically-ridiculous things if you want to!