An Unexpected Limit to Climate Sensitivity

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?

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.

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.

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

“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.

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.

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

Hello Willis
Interesting comments again.
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.

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.

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)?

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” .

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.
read these sites for more information.
http://www.ilovemycarbondioxide.com/
http://claesjohnson.blogspot.com/

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.

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.

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?

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.

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.

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?

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.

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.

here is a model of the atmosphere:-
http://upload.wikimedia.org/wikipedia/commons/3/3c/Crude_Oil_Distillation.png
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.

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?

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.

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.

I agree with crosspatch and Dave Springer.
Tom Vonk made a post some while back about
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.

@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.

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.

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.

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.

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.

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).

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).

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

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.

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

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?

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

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.

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.

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?

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.

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”?

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.

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 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.

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.

@ 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.

_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.

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).

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).

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.

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.

_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.

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.

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.

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.

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’!

@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…

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 .]

“”””” 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.

“”””” 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 !

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.

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).

“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.

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: 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….

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

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?

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.

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 🙂

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.

“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.

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.
Man up and admit you made a mistake.

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.

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!

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.

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.

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.
Man up and admit you made a mistake.”
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.

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.

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. ”
Please read: http://www.buzzle.com/articles/how-hot-is-venus.html

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.

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.

“”””” 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.’

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.

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.

@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.

“”””” 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.

@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.

“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?

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

“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.

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.

Just to clarify the last paragraph of my last post: The reason why the perturbation described by (1) has so little effect on the final surface temperature is that the energy flows between the earth’s surface and the atmosphere adjust to almost completely cancel out the radiative perturbation that was applied. Because the surface and atmosphere are so strongly coupled (i.e., there’s lots of energy flowing back and forth), this cancellation is almost complete.

JAE, thank you very much for the links. The top link contains a graph that I found month’s ago but could never relocate the actual paper again, vanished. It’s the graph with six planets and Titan… do you also know where that very original paper is? That’s what I can’t seem to relocate and is much of the basis of my comments of late.
Something is very fishy in current climate science thinking, both sides to a degree, but few seem to mathematically explain it unambiguously. But you especially seem close. You know, the pressure, the lapse rates, etc. I do know it’s the ignorance of emissivities and therefore absorptivities that lies at the bottom of this answer, mathematically that is. Feynman would have loved this problem!
Many try to explain through cloud cover but since clouds being white absorb less, reflect most, they also emit less equally except when clouds turn dark in storms and the emission and absorption change appropriately. The surface will be warmer but the upper troposphere and low stratosphere will be equally colder. Internal variance but no change of the planet as a whole.
I could be very wrong but still think the correct basic physics will answer the base questions. No high mumbo-jumbo.
(sorry for my own jumbo above)
Alan Siddons
http://climaterealists.com/index.php?id=5526
http://climaterealists.com/attachments/database/RadiativeNonEquilbrium_BHermalyn_Final.pdf
http://www.americanthinker.com/2010/02/the_hidden_flaw_in_greenhouse.html
http://www.ilovemycarbondioxide.com/pdf/Rethinking_the_greenhouse_effect.pdf