Calculations suggest that Global warming caused by the doubling of CO2 will be less than 0.6K

Guest essay by Saburo Nonogaki

It has been said that the averaged earth surface temperature would be 255K if no green-house-effect(g-h-e) gases were contained in the atmosphere, and is 288Ｋ at present where the atmosphere contains g-h-e gases. The estimation of 255K is based on the earth’s long-term radiative equilibrium and Stefan-Boltzmann’s law which states that the total amount of radiative energy from a black body at absolute temperature T is proportional to T 4.

As the earth’s long-term radiative equilibrium will be reached also in the case where the atmosphere contains g-h-e gases, we obtain the following equation under the condition that the long-term input energy from the sun remains constant.

(1–a )T 4 = constant (1)

Here, T is the averaged earth surface absolute temperature and a the ratio of radiative energy retained by the g-h-e gases in the atmosphere to the total radiative energy. By replacing T in equation (1) with 255Ｋ and 288Ｋ, we obtain the following equation.

(1–0)×2554 = (1–a )×2884 (2)

From equation (2), we obtain the value of a as follows.

a = 0.385 (3)

Jack Barrett* has reported that, in the case of 100m-thick atmosphere, the doubling of pre-industrial concentration of CO2 will result in the increase in infrared absorption by g-h-e gases by 0.5%. The reason why the increase is so small is based mainly on the saturation tendency of infrared absorption by CO2. As the re-emission of a part of energy absorbed by g-h-e gases into the universe takes place, the increase in a is less than 0.5%. According to equations (1), (2) and (3), the increase in a by less than 0.5% results in the increase in T by less than 0.6K.

As the actual thickness of the atmosphere is about 8000m at ordinary atmospheric pressure, the saturation of infrared absorption by CO2 will be almost complete and the actual increase in a caused by the doubling of CO2 concentration must be much less than 0.5% and the resulted increase in T must be also actually much less than 0.6K.

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December 24, 2014 9:07 am

wrong

December 24, 2014 9:38 am

So far, Planet Earth is saying: Right.

Harold
December 24, 2014 10:08 am

That was impressive.

December 24, 2014 10:14 am

Mosher is correct, in saying wrong, i.e. 0.6K forcing projection is wrong. CO2 feedback has nearly reached saturation point and any further warming may occur only when solar Grand Maximum returns, and that may be 60-80 years away, so in meantime Happy Christmas to all !
Vuk

December 24, 2014 11:51 am

The post does not project a 0.6K forcing, but says that 0.6k is the maximum. In other words (am I typing slowly enough?) less than 0.6k.
My understanding is that a doubling will do nothing that we can measure and hence we can not scientifically say that a doubling will do anything. Unfortunately we will all be dead by the time the doubling of CO2 happens — and with no warming that can be attributed to said CO2 rise.

Janice Moore
December 24, 2014 12:46 pm

Happy Christmas, Vukcevic.
This one’s for you….. a… er…. an allegory of how forces deep within the earth’s mantle control the climate…. er… weather… .
#(;))
“Mister Heat Miser” — “The Year Without a Santa Claus” (youtube)

December 24, 2014 2:05 pm

Ms Moore
Thank you for your kind greeting, it’ll be treasured till 7th of January.
As for the world of the web, I graph fiction with specks of the nature’s obscured reality.

Janice Moore
December 24, 2014 2:39 pm

You’re welcome (smile), Vukcevic.
Re: “nature’s obscured reality” {and I realize you and I may be on two different channels, here, heh} … While there are, indeed, subtle lessons waiting to be discovered by the discerning… science is also announced boldly by the creation: “The heavens declare … the skies proclaim… . Day after day they pour forth speech; night after night they reveal knowledge.” Psalm 19:1,2.
#(:))

Rich
December 24, 2014 10:18 am

Wrong.

December 24, 2014 11:55 am

Way to be original, Rich.

Rich
December 24, 2014 1:07 pm

Legend. This was a correction of Moshers usual poor English. There were no other replies at the time I hit the button, and now I can’t delete the post, or even reply to you, I’m having to reply to myself?

george e. smith
December 25, 2014 8:21 pm

Rich,
Did you remember to instruct Mosher on the correct usage of the apostrophe, in the possessive case ?

December 24, 2014 10:19 am

Mr. Mosher, in his typical drive-by method, showing no data, no code, no premise, no argument, no equations, nothing. He’s mimicking the “McLaughlin Report” parody by Dana Carvey on SNL.
I give permission for everyone to ignore him until such time he presents a cogent argument.
It may be wrong, but showing why would be valuable to everyone.
Merry Christmas.

December 24, 2014 10:32 am

I <3 Anthony Watts. Though your humility may never allow you to accept it, you are a hero for the greater good of all humanity.

December 24, 2014 11:13 am

Mosher is right because policy-led science is in every way superior to data-led science. Eny fule kno that.

Alan Robertson
December 24, 2014 11:25 am

Mosh was really cranky today in another thread, so I figure that he’s nursing a great big hangover from the department Christmas party.

December 24, 2014 11:36 am

“Nature admits peer review filters out controversial “champion” papers
Classical peer review is a form of scientific gatekeeping (it’s good to see that term recognized in official literature). Unpaid anonymous peer review is useful at filtering out some low quality papers, it is also effective at blocking the controversial ones which later go on to be accepted elsewhere and become cited many times, the paradigm changers.”

highflight56433
December 24, 2014 11:43 am

As in:

Cheers!

Janice Moore
December 24, 2014 12:29 pm

MERRY CHRISTMAS, AN-THONY!! #(:))

December 24, 2014 6:49 pm

Correct! In Esperanto ‘Mosher’ means move on to the next item.

Pat Smith
December 25, 2014 12:44 am

Merry Christmas to you, Mr Watts. I for one would be interested in an update on your hearing and the impact on your life over the last few months.

Leonard Weinstein
December 25, 2014 6:02 am

I agree with Mosh on his conclusion, even though he was short on detail. The post is wrong. I expanded on the subject on a later comment below. This is a case where the final answer may be correct but for all the wrong reasons.

Jimbo
December 25, 2014 6:42 am

Here is an interesting bit from Nature.

Nature – 22 December 2014
Most scientists have horror stories to tell about how a journal brutally rejected their landmark paper. Now researchers have taken a more rigorous approach to evaluating peer review, by tracking the fate of more than 1,000 papers that were submitted ten years ago to the Annals of Internal Medicine, the British Medical Journal and The Lancet.
Using subsequent citations as a proxy for quality, the team found that the journals were good at weeding out dross and publishing solid research. But they failed — quite spectacularly — to pick up the papers that went to on to garner the most citations.
“The shocking thing to me was that the top 14 papers had all been rejected, one of them twice,” says Kyle Siler, a sociologist at the University of Toronto in Canada, who led the study1. The work was published on 22 December in the Proceedings of the National Academy of Sciences…..
But the team also found that 772 of the manuscripts were ‘desk rejected’ by at least one of the journals — meaning they were not even sent out for peer review — and that 12 out of the 15 most-cited papers suffered this fate. “This raises the question: are they scared of unconventional research?” says Siler…..
http://www.nature.com/news/peer-review-reviewed-1.16629

It should come as no surprise when ‘good’ sceptical climate papers get rejected.

Guardian – 26 September 2014
some scientists would prefer … that results are announced only after they have passed peer review, ie been checked by experts and published in a reputable journal.
There are many reasons why this will no longer wash. Those days of deference to patrician authority are over, and probably for the better
. We no longer take on trust what we are told by politicians, experts and authorities. There are hazards to such scepticism, but good motivations too. Few regret that the old spoonfeeding of facts to the ignorant masses has been replaced with attempts to engage and include the public.
But science itself has changed too. Information and communications technologies mean that not only is it all but impossible to keep hot findings under wraps, but few even try. In physics in particular, researchers put their papers on publicly accessible pre-print servers before formal publication so that they can be seen and discussed, while specialist bloggers give new claims an informal but often penetrating analysis. This enriches the scientific process and means that problems that peer reviewers for journals might not notice can be spotted and debated. Peer review is imperfect anyway – a valuable check but far from infallible, and notoriously conservative.”
http://www.theguardian.com/commentisfree/2014/sep/26/scientists-gravitational-waves-science

JamesS
December 25, 2014 1:44 pm

Could be worse. He could copy Dan Ackroyd’s character from SNL’s “Point/Counterpoint” and start every comment like this:

December 25, 2014 4:09 pm

Showing why would be lost on everyone here.

george e. smith
December 25, 2014 8:25 pm

Merry Christmas to you too Anthony. The usual Christmas music, must have been a welcome new experience for you. Happy new year too.
G

December 25, 2014 10:14 pm

Steven Mosher said @ December 25, 2014 at 4:09 pm

Showing why would be lost on everyone here.

Supercilious prick!

Those days of deference to patrician authority are over, and probably for the better.

Thanks Jimbo.

Streetcred
December 27, 2014 12:13 am

Mosher is a seagull … flies in sh8ts on you and flies off … leaving a nasty mess behind. Hence the term “seagulling”.

December 24, 2014 10:32 am

There is no such things as an average earth surface temperature. Hence the equations are wrong.

ferd berple
December 24, 2014 12:04 pm

The equations may be wrong as equalities, but can typically be written correctly as inequalities. replace equal with less than or equal or greater than or equal.

December 24, 2014 11:01 am

your message was truncated by software?

December 24, 2014 11:46 am

Are you referring to this study?
http://tallbloke.wordpress.com/2014/12/24/ed-hoskins-temperature-reduction-outcomes-from-de-carbonisation/
The table below shows the likely range of warming arising from these divergent (sceptical and IPCC) views, (without feedbacks, which are questionably either negative or positive: but probably not massively positive as assumed by CAGW alarmists), that would be averted with an increase of CO2 for the full increase from 400 ppmv up to 1000 ppmv.Screen Shot 2014-08-10 at 11.33.54The results above for countries and country groups show a range for whichever scenario of only a matter of a few thousandths to a few hundredths of a degree Centigrade.

December 24, 2014 12:39 pm

well reasoned mosh.
your posts read like a transcript of the “argument clinic” by monty python.

Janice Moore
December 24, 2014 12:54 pm

lol #(:))
Thanks for the idea…

AndyG55
December 24, 2014 1:25 pm

No, that Monty Python sketch was much cleverer and far more erudite. !

Janice Moore
December 24, 2014 2:46 pm

Ah, HA! Andy G! We meet again.
(remember how mad you were at me that time I (intending it as a compliment) compared you with Buzz Lightyear v. a v. “to infinity and beyond!” (SMILE)?
Well!
To answer you: No. It wasn’t! It was MUCH duller and suitable for a mule.
Merry Christmas (almost 8am Christmas Day in Australia :))…. WAKE UP! (figured you “celebrated” in your preferred fashion last night) O Jovial and Highly Intelligent Math Professor.
Janice
#(:))

December 24, 2014 12:46 pm

[trimmed]

TYoke
December 24, 2014 1:14 pm

Mosher is as annoying as usual, but in this case I have to say he is correct.
The equations shown above do not account for the wavelength specific absorption/emission properties of the atmosphere.
In actuality, short wavelength radiation passes through relatively unhindered, while long wavelength radiation tends to be more absorbed/emitted. Hence, the idea is that the atmosphere is to some degree a one way trap for heat.
By contrast, the equations above effectively treat the incoming shortwave radiation as though it were substantially reflected at the top of the atmosphere. That doesn’t happen.

TYoke
December 24, 2014 1:43 pm

Looking at my post above, I didn’t really express my point very well.
The problem is that in the article the incoming radiation is effectively treated as though it were long wave, and thus absorbed/reflected by the atmosphere. Instead, the incoming radiation is shortwave and is transparent to the atmosphere.

Crispin in Waterloo
December 24, 2014 9:33 pm

TYoke
Increasing the CO2 concentration increases the number of molecules radiating into space while backscatter from, say, 12 km altitude is trapped before reaching the ground with 50% sent back up again. This has been modelled and modelled and the models show a temperature increase in the region of 8-16 km above the surface the heats at 3 times the rate of the surface because of all the back and forth.
That is the theory. The hotspot as it is known, is not there. Millions of measurements confirm this. Reality doesn’t agree with theory. It therefore appears that the “one way valve” mechanism which sounds like an effective heat trap, isn’t. It might not be trapping heat because the “trap” is itself increasing the effectiveness of energy loss. If it’s indeed working, the effect is undetectable.
I don’t think anyone is dead certain why, but it is not working according to theory.

Ian W
December 25, 2014 6:15 am

Crispin in Waterloo December 24, 2014 at 9:33 pm Thank you. It is extremely difficult even on this blog to get people to accept observed data over the ‘Green House Gas’ hypothesis. as you say:

The hotspot as it is known, is not there. Millions of measurements confirm this. Reality doesn’t agree with theory. It therefore appears that the “one way valve” mechanism which sounds like an effective heat trap, isn’t.

The ‘rasiative gases trap heat’ hypothesis is really neat, it is just not happening in reality in the way claimed despite all the clever maths. In fact it is so appealingly simple that it is difficult for some people to accept its falsification.

catweazle666
December 24, 2014 1:26 pm

Well, you would say that, wouldn’t you?
(With apologies to the late Mandy Rice-Davis)

December 25, 2014 10:19 pm

Is there anyone else here who remembers Mandy and Christine?

December 25, 2014 10:21 pm

“Well he would say that, wouldn’t he?” ☺

mpainter
December 25, 2014 10:37 pm

I do. Ended the career of Profumo. Big sensation at the time, but I don’t recall all the details.

December 25, 2014 11:28 pm

but I don’t recall all the details.

Mandy was thrown out of Heathrow airport for fiddling with the undercarriage of a Viscount… [ducking and running]

December 24, 2014 1:55 pm

What a complete argument that is, very well reasoned.

John Finn
December 24, 2014 2:57 pm

Agreed.
The author has misinterpreted Jack Barrett.

TRM
December 24, 2014 5:33 pm

We Really Ought Not Go? With Righteous Obnoxious Nutty Garbage?
It’s a Christmas puzzle in anagram style? Right Mosh? Cool, I love those. Thanks a bunch and merry Christmas to you to 🙂

Janice Moore
December 24, 2014 6:01 pm

Without a Reason, One Naturally Growls
#(:))
[With no food, two tummies growl. 8<) .mod]

TRM
December 24, 2014 6:01 pm

wrong == grown
I would say GROAN would be more appropriate for your sniping, short, unintelligent, silly habit of drive by one word comments.

Mark
December 24, 2014 6:24 pm

Indeed, the author Mosher knows better. Why, he’s an expert. Oh, wait…
Mark

Jimbo
December 25, 2014 2:36 pm

• No hotspot can be found.
• Global sea ice anomaly at ‘normal’.
• No signs of climatological trends in extreme weather caused by greenhouse gases can be found (the opposite maybe).
• Global agricultural output at record levels.
• Biosphere has greened in recent decades.
I can go on and on. I suspect ‘global warming’ ‘climastrology’ has so far been net beneficial.
PS these folks are trying on the biggest heist in eCONomic history. The internet messed up their evil plans………result: Gleick, Climategate, failed warming model projections, Wadhams’ changed Arctic ‘ice-free’ prediction et al. It’s funny looking at these people flap about despite the massive financial and media backing. Bloody useless lot, they could not organise a drunken brawl in a hard liqueur brewery.

george e. smith
December 25, 2014 8:16 pm

Well one of the original premises of this story is complete nonsense.
Namely, that sans green house gases in earth’s atmosphere, the global mean Temperature would be 255 K.
Without GHGs, there are no clouds, and no precipitation, which eventually means very little land ice or snow, which would all melt in summer and run off, never to be replaced.
Earth’s albedo would be very much lower that the 35 or so percent we now have, and the surface solar insolation would be much higher. I have done the BB calculation of the BB equilibrium Temperature, that corresponds to a TSI of 1362 W/m^2, and it is a lot higher than 288 K.
I’m not going to do it again to show you what the number is. Try doing it for yourselves.
We easily get to more than 288 K with no clouds and no other GHGs. The 255 number is obtained sans CO2 etc, but retaining the present albedo number which is an absurd proposition.
Even without any clouds, water vapor takes a lot of incoming solar radiant energy out of the input number, so you will get a lot more than 1,000 W/m^2, with the sun at the zenith.
But of course, the earth without GHGs is silly. Peter Humbug did a “model run” on his Playstation, removing every last molecule of water from the atmosphere. His model run got it all back in three months.
So you would need to get rid of the oceans first, to get rid of GHGs.

jimmi_the_dalek
December 29, 2014 1:58 am

It would have helped if the author had known where the value of 255K came from. The he would have written
(1-0.3)*255^4 = (1-a)*288^4
and gotten a different value of a.
However that would be pointless as the only way to make the equation balance is to make the emissivity and absorptivity have different values, which is not possible.
And even if you somehow get passed that, it is useless as the GHE does not depend upon radiation from the surface, but from high up in the atmosphere.
The replies to the post illustrate the principle that you can write anything on a blog and someone will believe it.
Mosher is actually over generous to just say that it is “wrong”

December 24, 2014 9:22 am

Less than 0.6K. My estimates ranged from no change at all over the equatorial doldrums to 2.4 degrees over the North Pole, averaging 0.3K globally
What then is this “Carbon Pollution”?
A sinister, evil collusion?
CO2, it is clean,
Makes for growth, makes it green,
A transfer of wealth, a solution.
http://lenbilen.com/2014/02/22/co2-the-life-giving-gas-not-carbon-pollution-a-limerick-and-explanation/

Crispin in Waterloo
December 24, 2014 9:39 pm

Lenbilen
Good point – wealth transfer. Rich countries generate new CO2 and it is distributed equally to all humanity. They can freely tap this resource and increase their production of food and fuel crops. No questions asked, no payment sought. Sorry about the promised warming. Maybe next time.

December 24, 2014 9:26 am

Ladies and Gentlemen, faites vos jeux.
I bid 0.2K or less.

December 24, 2014 11:54 am

My bid is 0.2k or more less than your bid. 🙂

dp
December 24, 2014 9:27 am

Since this 0.6ºK is not equally distributed around the world what is the impact at say, 47º latitude where I live, what is the longitudinal distribution going to look like, and how can we know with any certainty? What will be the knock-on impact on localities of these regional variations? This would be the emergent phenomena created as a result of unequal distribution of this energy that produces 0.6ºK averaged temperature around the globe.

Bruce of Newcastle
December 24, 2014 11:32 am

I get <a href="https://www.flickr.com/photos/68018872@N08/6184340351/"0.7 K using HadCET, which is at your latitude.
In practice anything less than 1 C/doubling is harmless if you do the arithmetic. At that level there aren’t enough extractable fossil fuels in the world to produce dangerous warming.

Bruce of Newcastle
December 24, 2014 11:34 am

Apology, for the link error. It should be this: 0.7 K/doubling

BernardP
December 24, 2014 9:27 am

Less than .6K is obviously enough to bring about all the climate catastrophes predicted by the IPCC and its disciples in the MSM.
A weather forecast from the future:

Roy Spencer
December 24, 2014 9:29 am

sigh…

December 24, 2014 9:32 am

Roy, you are going to have explain that sigh, for those like me who have trouble catching nuances.

Reply to  The Ghost Of Big Jim Cooley
December 24, 2014 10:40 am

I wouldn’t presume to speak for anyone but myself, but I suspect this relates:
http://www.drroyspencer.com/2009/05/global-warming-causing-carbon-dioxide-increases-a-simple-model/
Tail wagging the dog deal – climate effects CO2 – not so much the other way.
While playing at fathoming quantum effects in a lets just do some maths anyway, I have read:
http://clivebest.com/blog/?p=1169
It is thoughtful anyway.

jai mitchell
December 24, 2014 12:54 pm

I imagine that you are contemplating discussing the fact that pressure broadening of CO2 absorption spectrums in the real world environment has shown the saturation assumptions to be overstated, just as you did at the end of the “climate debate” at heartland 2012. . .

Paul Schnurr
December 24, 2014 9:29 am

The prevailing public view seems to be that as CO2 is added to the atmosphere it is as if another quilt and then another is added to your body until you are too hot when in fact it is more like quilts are being added to your lower legs only. Good analogy?

December 24, 2014 9:40 am

How about the additional quilts only being one tenth as thick as the initial one? Just a guess.

TYoke
December 24, 2014 12:38 pm

A better analogy would be measuring the temperature of a mannequin under several quilts, when a hot lamp is directed downward on the quilts.
The more quilts you use, the less the mannequin is warmed, since the quilts re-radiate the lamp heat upwards.

TYoke
December 24, 2014 12:43 pm

I should hasten to add that the real situation is a lot more complicated since the incoming radiation is on the whole much shorter wavelength than the outgoing, and therefore the wavelength specific absorption/emission properties of the quilts matter a lot to the final result.

David Socrates
December 24, 2014 12:46 pm

You need a slight modification.
There has to be a plain glass window in the quilts that permits visible light in, and blocks IR out.

I’m sure you’re familiar with how sunshine can warm your skin.

December 24, 2014 12:52 pm

Depending of course on the quilt pattern.

Janice Moore
December 24, 2014 9:30 am

Re: “pre-industrial concentration of CO2″
A scientifically inaccurate pro-AGW bias is indicated by the use of this term.
1. Native Sources of CO2 = 150 (96%) gigatons/yr; Human CO2 = 5 (4%) gtons/yr.
{at 36:34 on the following video}
2. Re: Net Native CO2 — Native sinks approximately balance native sources.
{at 37:01 on the following video}
Conclusion: Native CO2 emissions are 2 orders of magnitude greater than human (or “industrial”), thus, “approximately” means that even a small native CO2 imbalance can overwhelm all the human CO2.
That is, Jack Barrett (and or Saburo Nonogaki) would be more accurate if he/they described current CO2 levels in terms such as “current net CO2 from all sources and sinks, both native and human.”
Source: Dr. Murry Salby, Hamburg lecture (2013) – YouTube video

December 24, 2014 4:29 pm

only we have a balanced account which proves that there is a net natural sink:, where did half of all fossil fuel co2 go?

December 25, 2014 10:28 pm

My vegetable garden where it is sequestered until I make compost from the crop residues 😉

bw
December 25, 2014 2:06 am

Most estimates of biogeochemical carbon cycle fluxes are about 33 to 50 times human. i.e. humans add about 3 percent to the global biogeochemical carbon cycle.
Some newer estimates of deep ocean magmatic carbon sources are much higher than previously guessed. How much carbon resides at the ocean bottoms are more guess than estimate. Sea water at the surface contains at least 50 times more carbon than the atmosphere above the ocean surface.
Salby is basically right, fossil carbon added to the atmosphere is just diluted into a much larger carbon cycle.

gbaikie
December 24, 2014 9:33 am

But as is well known there are other factor which could warm earth other then CO2 or H20 gas.
Clouds have a warming effect. Also the ocean mixing affect air temperature.
Or if mixed entire ocean the ocean surface temperature would around 3 C. And if ocean surface temperature was 3 C and since earth ocean cover 70% of surface area and warm tropical ocean is largely causing the world to have 15 average temperature, then Earth temperature would plunge to near freezing. And not mixing and flows of surface water cause large amount warming in places like European. And there other factors which effect earth’s average surface temperature other than greenhouse gases.

Rhoda R
December 24, 2014 9:43 am

How does the fact that the earth is not a black body affect these calculations?

December 24, 2014 12:53 pm

Racist.

Harold
December 24, 2014 4:49 pm

That was better than Mosh’s answer.

December 24, 2014 3:22 pm

Massively, emissivity can vary significantly depending on the surface and is a direct multiplier in the S-B equations. Warmists keep using an emissivity of 1 for CO2 instead of the probable emissivity of 0.0017. They also assume that CO2 radiates like a black body but then ignore the fact that at its 15µm peak as a black body it would radiate at ~193°K… making Antarctica in deep winter the only place that could possibly get any radiative energy transfer from it unless one ignores the 2nd Law of Thermodynamics (which along with the 1st, they regularly do.)

December 24, 2014 7:49 pm

Of course there is no -193 K, cannot go lower than absolute zero. -193 C =+80K, still wrong, 15 micron radiation has its Planck peak at – 80 C. Be of good cheer everyone, but not too good…

george e. smith
December 25, 2014 8:38 pm

And I see that Michael Moon read your tilde as a minus sign., and didn’t even notice that his -80 deg. C is the same roughly as your 193 K.

Ivor Ward
December 24, 2014 9:45 am

0.6K(A) = 4-6K(P)
(Where A=actual and P=political)
So good to have Mosher’s thoughtful and considered opinion to take away and mull over for the Christmas holiday.

Two Labs
December 24, 2014 10:06 am

While as a statistical scientist this reeks of oversimplification, I don’t know enough about atmospheric physics to know where to attack. I suppose Mosher and Spencer could help?

December 24, 2014 1:59 pm

However, you do know that it just has to be attacked, because, well sigh, it just is wrong, because, well because, because because.

Mark
December 24, 2014 6:35 pm

Mosher has no clue – he is just a know-it-all that thinks he can learn us all some science (look up his actual background). Spencer’s opinion is apparently the opposite: warming causes CO2, i.e., there is no forcing.
Mark

chris moffatt
December 24, 2014 10:10 am

Aren’t we missing a few feedbacks here? And is the earth truly a blackbody? and does anybody care that earth has been radiating its own geologic heat to space for around 4.5gigayears regardless of incoming solar energy?

highflight56433
December 24, 2014 10:22 am

The irony is CAGW enthusiasts are claiming such catastrophic warming which would in ‘reality” reduce the use of energy from fossil fuels etc. …. they should embrace a warmer planet. Cheers!

Retired Engineer
December 24, 2014 10:32 am

Folks, I’ve spent more than forty years in the aerospace industry, and I’ve developed ATMOSPHERIC flight vehicles that fly at altitudes well in excess of 8000m. The sensible atmosphere is about 400,000 feet thick, and spacecraft suffer atmospheric drag at much, much higher altitudes (700km IIRC). So, any calculations based on the atmosphere being 8000m thick are a bit off.
And you will certainly not be experiencing “ordinary atmospheric pressure” at 8000m. According to the Prat and Whitney “Aeronautical Vest-Pocket Handbook”, the “US Standard Atmosphere – 1962”, shows pressure at 26,000 ft to be 10.64 inches mercury, and the sea level value is 29.92 inches.
Having said that, is the author trying to say that the effects of g-h-e are only observed to 8000m? If so, on what science is that based?
I’m hoping that there is a simple explanation.

December 24, 2014 7:32 pm

He is trying to say that the actual thickness of the atmosphere doesn’t matter, only the absolute number of gas molecules in a vertical column, and that compressing the atmosphere to a layer of homogeneous pressure makes calculations of absorption simpler.

bw
December 25, 2014 1:49 am

The OP simplified Earth’s atmosphere to uniform 1 ATM surface pressure. Weight divided by density at the surface, 10100 kg per square meter divided by 1.225 kg per cubic meter is about 8200 meters.
The atmosphere is 82 times the thickness used in the Barrett calculation.

December 24, 2014 10:33 am

I mistrust all such ‘back of the envelope’ calculations. They are based on oversimplifications of oversimplifications. Similar calculations once ‘proved conclusively’ that bumblebees cannot fly. If, for simplification, one assumes that a bumblebee is a fixed-wing aircraft, then the aerodynamic lift its *fixed* wings generate is not sufficient to overcome it’s weight.
In empirical work we call such oversimplified models ‘spherical cows,’ and leave it to the mathematicians to ride herd on them.
I would rather trust laboratory measurements of the energy absorbtion of an enclosed sample of air with and without added CO2 – as a model for CLEAR DAY heat absorbtion.
Then there remain (as yet unaddressed) the issues of (1) what happens to the sunlight that does not get absorbed by the air but reaches the ground to become absorbed, converted to heat, and transferred BY CONDUCTION to the air (surely the air does not care whether it gets heated by radiation orconduction), and (2) how does convection of air heated in the lower atmosphere into the upper atmosphere (I’ve seen convection cells 15 miles tall) affect the overall heating dynamics?
In my understanding the only solar radiation that does NOT end up as atmospheric heat is the part that gets reflected into space by clouds, bodies of water, and ground albedo – NONE of which are CO2-dependant.

Dawtgtomis
December 24, 2014 10:33 am

Do any current models contain this information? I’d be curious to see the influence.

John F. Hultquist
December 24, 2014 10:37 am

I don’t think the folks in the UN, the White House, the Washington State Governor’s office, or the EU Big House give one wit about the size of this number.
I’m curious, though.
Merry Christmas and Season’s Greetings.

Janice Moore
December 24, 2014 12:34 pm

Cute. And Merry Christmas to you (again) :).

davidmhoffer
December 24, 2014 10:54 am

Mosher may have under stated the problem.
With apologies to Einstein, this isn’t right, its not even wrong.

December 24, 2014 1:44 pm

nope, Pauli: “Das ist nicht nur nicht richtig, es ist nicht einmal falsch!”
Happy Xmas.

Harold
December 24, 2014 4:52 pm

That was Pauli.

Latitude
December 24, 2014 10:59 am

and the resulted increase in T must be also actually much less than 0.6K…..
Using his method…..if you discredit all of their wonky adjustments……since CO2 rising….the increase in T was ~ .6
…so it’s a safe bet to say it will be even less that .6 accounting for saturation
and we’re there!

SMS
December 24, 2014 11:00 am

I believe Professor Richard Lindzen had a paper suggesting that the climate sensitivity was about 0.5C. Sounds close to me. It’s certainly not anywhere near Hansens 4.5C.

Ack
December 24, 2014 11:09 am

255K is pretty darned cold. Thank you green house gases!

December 24, 2014 11:13 am

Other calculations suggest that the greenhouse effect of anthropogenic CO2 is non-existent.
For an empirically based refutation of the CAGW meme see
http://www.seipub.org/des/paperInfo.aspx?ID=21810
which states
“The planetary radiative balance is maintained by the equilibrium cloud cover which is equal to the theoretical equilibrium clear sky transfer function. The Wien temperature of the all sky emission spectrum is locked closely to the thermodynamic triple point of the water assuring the maximum radiation entropy. The stability and natural fluctuations of the global average surface temperature of the heterogeneous system are ultimately determined by the phase changes of water. Many authors have proposed a greenhouse effect due to anthropogenic carbon dioxide emissions. analysis shows that The present analysis shows such an effect is impossible.”

KevinK
December 24, 2014 1:23 pm

Dr.Page, quiet please, that topic is not allowed, you run the risk of being called a bad name. And caricatured with pointy teeth and knobs on your head.
That peer-reviewed and recently published paper also states;
“In our view the greenhouse phenomenon, as it was postulated by J. Fourier (1824), estimated by S. Arrhenius (1906), first quantified by S. Manabe and R. Wetherald (1967), explained by R. Lindzen (2007), and endorsed by the National Academy of Science and the Royal Society (2014), SIMPLY (sic) DOES NOT EXIST” (bold highlighting is mine).
It was only a hypothesis this whole time, if it does not exist then the sensitivity is ZERO per doubling/halving/tripling. Not about zero, but zero.
Happy Holidays everyone, whatever your thoughts are on this topic.
Cheers, KevinK

December 24, 2014 3:35 pm

Amen… and considering that using Gas Law gives you an “accurate” number for atmospheric temperature based on density and gravity (completely ignoring the miniscule radiative modes of the gases) and considering that no one, anywhere has ever proven that so called “greenhouse gas” makes any difference. That does NOT mean water vapor (which I get tired of saying is NOT a gas and does not behave like one) as water moves a considerable amount of energy around our planet.

Steve Case
December 24, 2014 11:22 am

What’s wrong with this:
Simple arithmetic says 4.5°C isn’t possible. Here’s why.
We already have 400 ppm CO2. That represents 4 doublings since 25 ppm and 7 or 8 since 1 or 2 ppm. The question is, at what point does the logarithmic nature of CO2’s Climate Sensitivity begin? I’ve heard “Around 20 ppm”. I also know that Methane (CH4) at not quite 2 ppm is said to be a very strong Green House Gas for the simple reason it doesn’t take much to double its concentration. The obvious question is, if CH4 is logarithmic at 2 ppm then in the world of Geese, Ganders and Greenhouse Gas wouldn’t CO2 also be?
So if you go with 20 ppm and 4 doublings, 4 x 4.5° = 18° or 54% of the 33° Green House Effect. Does anyone claim CO2 is over 50% of the Green House Effect? If 2 ppm is considered, 8 x 4.5° = 36° and I think you can see why I said it’s not arithmetically possible.
The contribution percentage of CO2 to the Green House effect is said to be anywhere from 9% to 26%. If you work backwards from 26% using 20 ppm as a logarithmic beginning and a 33° for the total Green House Effect, the Climate Sensitivity of CO2 with all its feed backs can’t be over 1.7°C. If you work backwards from 9% it can only be as much as 0.6°C.
There is a rebuttal to this over at Skptcl-Scnce
Comment #53 – Glenn Tamblyn – 21 September 2010
The basic argument says climate sensitivity varies with the current climate and the physical world namely the cryosphere.
So it requires that you lower the sensitivity for lesser concentrations of CO2 and colder more ice covered climates.
As it turns out, you have to do some serious manipulations in order to make the 4.5°C work. If you lower CO2’s sensitivity down to zero at around 10 to 15 ppm you can make it fit.
So what’s wrong with all of that? I assume it’s wrong but I really haven’t seen a good answer.

December 24, 2014 4:55 pm

Methane’s effect is linear @ 2ppm.

Steve Case
December 25, 2014 6:59 pm

There must be some physics that dictate when a Green House Gas makes the transition from linear to logarithmic.

george e. smith
December 31, 2014 12:30 am

To Steve Case,
Over the period for which we have any reasonable CO2 data SPECIALLY in light of what the OCO map has now shown us, there is no credible logarithmic relationship between CO2 and temperature.
Let me put it this way.
You can plot Log (CO2 vs T; or CO2 vs T ; or CO2 vs log(T) ; and get equally good linear graphs.
There also is no VALID theoretical reason to expect a log relationship.
Bouguer’s Law, commonly misnamed as Beer’s Law, or the Beer-Lambert Law only applies to the ABSORBED component of an incident beam of EM radiation.
It DOES NOT apply to the TRANSMITTED EM radiant energy through media which are themselves radiative.
I.E. Bouguer’s law applies ONLY when the absorbed photons stay dead, and are converted to “HEAT” (adjective) ENERGY; NOT when the absorbed photon energy is re-emitted as EM radiant energy (photons) of some other (usually longer) wavelength.
And with a “logarithmic” doubling concept, going from 280 ppm to 560 ppm, is the same as going from 1 ppm to 2 ppm.
Talking about a function being logarithmic for a value within the range of 1.0 to 1.25 (Mauna Loa), is total horse feathers. Logarithmic, means logarithmic, for any real data range: period.
Ln(1+x) = x for small x And we have an x of about 0.27. 315 – 400 ppm.
So it’s indistinguishable from linear.

jjs
December 24, 2014 11:33 am

Process engineer for 40 years. We lived by the rule that “no validation”, “no moving full forward” with projects. We would have been able to run the company out of money many times over if we did what the IPCC and others are doing. Unfortunately they won’t have to worry about running the money presses out of our ink. 0.6 or 600 at this point in the discussion doesn’t really matter; it’s more the point are we going to let ourselves be lead as humans by lies or the truth?

Joe Crawford
December 24, 2014 12:12 pm

As a process engineer, have you ever seen a process where all feedbacks (forcings?) are positive as the CAGW crowd have define the Earth’s climate system? (I suspect they defined and use the term ‘forcing’ so most would not associate it with a feedback.)
As far as money, I also suspect we are not far from the point where an awful lot of ‘Climate Scientists’ are going to be looking for new jobs. I just hope the damage they have done to the reputation of (real) science hasn’t set it back too far in the public eye.

Gary Pearse
December 24, 2014 5:30 pm

If there weren’t firm negative feedbacks in the system, we wouldn’t have a record of life stretching back ~1B years in a recognizable form. Example, the Ordovician nautiloid (archimedes screw type shells some linear, some coiled) are not so different to what is in the sea today. They had to make shells so there must of been ample CO2 and lime in the seas – still alkaline, although perhaps less so than today. They must have eaten something non unlike what their present day similar types.
https://www.tonmo.com/community/pages/nautiloids/
The earth has been hit with large asteroids that wiped out many species on a number of occasions. Each time, the earth recovered to somewhere within a few degrees up or down of where we are now. We have had 9000ppm CO2 in our atmosphere during the billion years of life and it seemed to result in a lush plenty and variety of species. We’ve had snowball earths (apparently), at least numerous ice ages that the earth rebounded from, etc. It is a hundred percent certainty that the climate system restores itself from extremes and the extremes themselves, although perhaps unpleasant for many species, actually amount to deviations from some norm by ~2% of the K temperature.
Why we don’t inform our science from the top down in this case and recognize that so much of the calculations and worry are wasteful impossible fantasies. It is so simple-minded and telling of those who would take the CO2 molecule in isolation and calculate all the horrors that await. Negative feedbacks are a certainty. Get over it. Even the high temperature extremes that exist are distributed in an essentially benign way: The tropical convergent zone in the oceans does not and therefore cannot exceed ~31C. So the warming is transfered to the polar regions where a good deal of the 5-7C or so increase in these regions basically heats up -30C to -25C (Arctic, Antarctica) and fringing areas maybe to -10C (WAG). Yeah the average goes up but know one notices. Who are these people anyway?

Mark Luhman
December 24, 2014 7:25 pm

You ask the question “Who are these people anyway?” I have a simple answer there are either conmen or useful idiots. One thing I have to say is the conmen have made themselves rich and most of us poorer, to bad there are so many useful idiots, the only good thing about the present crowed of useful idiot is that the conmen have not murder as many people as they did the last time, although I think Stalin and Mao may be turning in their graves after their cons were much more difficult, they need guns to get the people to give them the peoples money. Funny in both cases were are told it for the greater good.

Olavi
December 24, 2014 11:34 am
Mike M.
December 24, 2014 11:38 am

Richard Petschauer write: “However CO2 is a strong absorber near 15 microns wavelength, and in this region the final emission level moves up into the troposphere where the temperature increases with altitude, hence more radiation around 15 microns. The effect of this is to reduce the reduction of heat leaving from 3.76 to under 3 W/m^2. ”
There is an obvious error here: in the troposphere the temperature decreases with altitude. Did you mean to say “stratosphere”? If so, do you you have any evidence that the emissions at 15 microns are mostly from the stratosphere? Can you cite ant calculations to back up your claims?
Mike M.

Leonard Weinstein
December 24, 2014 11:41 am

This analysis misses to entire point of how the atmospheric greenhouse effect works. It is the raising of the average altitude of radiation to space, not the near surface absorption/emission change that matters. this average altitude changes with CO2 for two reasons. The first is that unlike water vapor, CO2 does not condense at increasing altitude, and actually becomes more important compared to water vapor at high altitudes. The second is that the concentration of any component of the atmosphere that does not condense with increasing altitude will increase at a particular altitude for a give concentration increase, and this is most important at the higher altitudes. However, this issue does not address a separate point: the possible change in albedo due to changing cloudiness (which may increase or decrease). Thus the net effect of CO2 increase is presently a poorly understood issue, and may or may not result in significant warming. However, it is becoming clear that any warming will likely be much smaller that the CAGW supporters predicted, and may in fact be overwhelmed by natural variation.

ferd berple
December 24, 2014 12:24 pm

the raising of the average altitude of radiation to space
===================
that explanation relies upon the lapse rate, which ties in with PE/KE conversion by gravity of the vertical circulation created by warming due to the sun, which suggests that the extra 33C is a result of earth’s atmosphere, not GHG.
the earth is warmer because it has an atmosphere, energy from the sun, and vertical circulation. And would be warmer even if the atmoshpere contained only oxygen and nitogen. The thicker the atmosphere, the warmer the earth’s surface would be.

Robert B
December 24, 2014 6:05 pm

The GHE is based on the difference of the atmosphere being completely transparent and being opaque to frequencies absorbed by GHG. So 37% of the energy emitted by a 290k surface plus 63% of the energy emitted by a 210K surface equals that emitted by a 250K surface (without GHG in the atmosphere). So, roughly, 1% more that has to be emitted by the colder surface equates to 1K higher temperature of both to emit the same as a 250K surface.
That is just an indication of how a small amount of a GHG can affect the temperature. Its pure rubbish for calculating the effect of a small increase in GHG.

Leonard Weinstein
December 25, 2014 5:28 am

No Fred, it would not be warmer if the atmosphere were only N2 and O2. There would still be a lapse rate, but the surface level would be not be increased (it would be more uniform, due to wind distributing surface energy to higher latitudes). The lapse rate is a gradient not level, and some process has to determine the level. It is the average altitude of outgoing radiation to space that sets the level.

bones
December 24, 2014 2:49 pm

So what is the effective radiating altitude at present?

Leonard Weinstein
December 25, 2014 5:30 am

The present effective (average) radiating altitude in near 5 km

Robert B
December 24, 2014 4:37 pm

This analysis misses to entire point of how the atmospheric greenhouse effect is calculated. There world is much more complicated than two surfaces that are black bodies.

Mike M.
December 24, 2014 11:45 am

Yep, a simple-minded calculation by someone who does not know what he is talking about obviously trumps careful calculations by people who actually understand the physics.
The direct effect of doubled CO2 is about 1.1 K. Taking into account changes in water vapor (causing increased IR absorption and decreased lapse rate) increases that to something like 1.8 K. That seems to be pretty well established physics. The big question is how will cloud distributions and properties change as a result of that warming? No one knows and the models are incapable of providing an answer that can be trusted,
Mike M.

December 24, 2014 1:04 pm

We could assume cloud changes will be like those of the past. For instance, at each average temperature we have certain local regimes of clouds. We might assume clouds have and continue to be a stablizing influence.

Gary Pearse
December 24, 2014 5:42 pm

Mike, the answer to your question is that the earth definitely has negative feedbacks that keeps it within + or – 2% of the Kelvin temperature, no matter what CO2 does – it could be double the sensitivity you say and it would be countered by clouds as you’ve partly suggested, the enthalpy of the changes in waters state, currents, winds…. see my full reponse to someone else above:
http://wattsupwiththat.com/2014/12/24/calculations-suggest-that-global-warming-caused-by-the-doubling-of-co2-will-be-less-than-0-6k/#comment-1821300

Mike M.
December 25, 2014 7:46 am

Gary,
At the link you provided, you wrote “Negative feedbacks are a certainty”. Every climate modeller agrees with you. It is a fact that the climate system is a negative feedback system.
The dominant climate feedback is the Planck feedback: as temperature increases, radiation to space increases. The role of positive feedbacks is to make the net feedback less negatice than it would be from the Planck feedback alone.
Mike M.

mpainter
December 25, 2014 10:49 pm

It so happens that water vapor is a negative feedback. Those who say otherwise are in error.

Bruce Cobb
December 24, 2014 12:00 pm

So, the never-before seen, non-catastrophic and certainly helpful manmade CO2 warming should kick in any day now. We’ll wait…

Sleepalot
December 24, 2014 12:01 pm

Equivocation on the word “surface”.
288K is the estimated AIR temperature.
255k is the (wrongly) estimated GROUND temperature.
You cannot simply subtract one from the other – they are completely different things!

David Socrates
December 24, 2014 12:06 pm

They both are measured in the same units. Can’t you take the same thermometer you use to measure the air and stick it in the ground?

Sleepalot
December 24, 2014 2:04 pm

“They both are measured in the same units.”
So are the speed of light and the speed of sound, but don’t subtract one from t’other – it isn’t meaningful.
Temperature is a measure of heat energy content. For a given temperature, a kilo of air does not have the same heat content as a kilo of water, or a kilo of rock: they’re different things.

davidmhoffer
December 24, 2014 3:44 pm

255k is the (wrongly) estimated GROUND temperature.
No, 255K is the Effective Black Body temperature of earth. In other words, the earth as seen from space. As seen from space, the earth doesn’t have a “surface” per se. It is a ball of dirt and water surrounded by a fuzzy thing called an atmosphere. Energy emitted to space could originate as photons from the surface, from the top of atmosphere, or from anywhere in between. The sum total of the energy/sec escaping, regardless of the altitude any given photon escaped from, defined the EFFECTIVE black body temperature of earth.
288K is the estimated AIR temperature.
No, it isn’t. It is the estimated surface temperature of earth using air temps over land and water temps of the oceans. Note, I’m not saying it is a good estimate.
You cannot simply subtract one from the other – they are completely different things!
Yes you can. 33 degrees is the difference between the effective black body temperature of the earth and the estimated (such as it is) surface temperature of earth. Nothing wrong with that.
So are the speed of light and the speed of sound, but don’t subtract one from t’other – it isn’t meaningful.
Well sure it is. If you want to know how much faster light travels than sound does, how else would you do it?
Temperature is a measure of heat energy content. For a given temperature, a kilo of air does not have the same heat content as a kilo of water, or a kilo of rock: they’re different things.
You are confusing heat capacity and energy flux. Heat capacity is a measure of how much energy it takes to raise the temperature of a given mass by one degree. Temperature provides a measure of the energy radiated by a body at a given temperature (Stefan-Boltzmann Law) which is quite independent of the heat capacity. A kilo of rock and a kilo of water may have different heat capacities, but at the same temperature, they radiate the same w/m2. The one with the higher heat capacity simply cools off more slowly than the one with low heat capacity.

December 24, 2014 7:01 pm

Crispin in Waterloo
December 24, 2014 10:05 pm

Thanks davidm. All correct. I appreciate your patience too.

December 24, 2014 12:05 pm

The 255K vs 288K number is solely based on Albedo, 100% absorption and 70% emissivity.
If emissivity equals absorptivity, which it does in equilibrium, then the equilibrium number would be 278K or 5˚C, which just happens to be the average temperature of the ocean.
The whole 255K – 288K number doesn’t take into account the energy flux through the system, primarily the ocean.

December 25, 2014 12:19 pm

Genghis, 4 C is a better estimate with a nice little regulating effect to boot. 5C would require perfect efficiency, not likely, 4 C would allow for 4% loss. The neat regulating effect is the maximum density of fresh water at 4 C. While the oceans are salty, the fresh water density limits the base of the thermocline. What ever the average salinity is you will still have a stable 4 C layer. Kind of fortuitous doncha know. Early climate scientists seem to have assumed their butts off instead of figuring out that on a world 70% covered with water, you might want to start there. Leave it to Astrophysicists to screw up a wet dream.

Jim a
December 24, 2014 12:06 pm

this may be a case of so wrong, it’s right. Who knows… i cant prove it.
But i have a pretty good visual of the inputs/outputs and just by guesstimation the outcome sensitivity may be right.
However, i would like tadchem to tell me how that heat transfer ‘by conduction’ works,
Also another commenter referenced measurement in a controlled environment. Meaning, i suppose, a Bell Jar. That doesnt work, we dont live in one. We live in the opposite of a bell jar.
All energy ends in heat, All heat ends in space.. and there’s no pyrex to reflect it.

Martin Mason
December 24, 2014 12:26 pm

The surface temperature and lapse rate can be calculated without any reference to GHG radiation. Surely then, GHG radiation has no effect or is an effect not a cause. I’m going for zero as a sensitivity as many fairly good physicists have suggested (Milkosczi, G&T, Postma, N&K). The GHE/AGW hypothesis has been shown to be particularly weak.

December 24, 2014 1:34 pm

Martin, “The surface temperature and lapse rate can be calculated without any reference to GHG radiation.”
I can show that atmospheric radiation cools the oceans surface temperature by promoting evaporation.
I can also show that increased cloud coverage causes cooling and decreased coverage causes warming. It is hard to show that GHG’s do anything at all.

Joe G
December 24, 2014 12:27 pm

Global warming- it is generally warmer when the sun is shining than when it isn’t. But that isn’t anything to get alarmed about.

December 24, 2014 12:29 pm

Until there is some way to measure the impact of man, these kinds of estimates are no better than scrying the intestines of small furry animals.
If natural cycles dominate it may well soon be empirically established that CO2’s effect is insignificant.
That experiment is running as we observe, anthropogenic emissions of CO2 continue to rise, Estimated Global average temperate is standing still, possibly poised to repeat history and fall for 30 or 40 years.
If measured honestly, we will see soon enough.
Personally I doubt the utility of this AGT, GAT, WAG as these claims of trends less than the measuring error are idiotic.
White noise on an audio signal has greater information value.
However this post appears to be another refutation of the meme, utilizing that classic technique;using the claimants methods and standards, the results differ from their claims.
Failure to replicate in other words

Joe Chang
December 24, 2014 12:32 pm

Is the 255 & 288K based on a sphere of uniform temperature, with surface representing daily average? or high? Because of the T**4 relation, we cannot use a (linearly weighted) average. So we really the “typical” 24 hour temp pattern by latitude to determine the greenhouse effect, plus other factors.

December 24, 2014 12:57 pm

Merry Christmas!
Although I favor the old time religion. If it was good enough for Jesus it is good enough for me.

December 24, 2014 1:03 pm

The consensus view of climate science is that man-made global warming is caused by increased emissions of carbon dioxide which is the (misnamed in my opinion) ‘greenhouse gas effect’. We can all agree that at least total concentration levels of CO2 in the atmosphere is supposed to increase the average temperature of the planet regardless if those levels come from natural sources or from anthropogenic activities or both. This consensus view is held by both the alarmists as well as the luke-warmer types; with the disagreement coming over how much warming one should expect with increasing levels of CO2.
But this hypothesis is under increased pressure due to the fact that despite decades of higher CO2 emissions (or concentration levels) we have had not increase in temperature for 18 years or more according to even government funded data sets. (see WUWT and Lord Monckton’s many posts on the issue) Climate scientists have been at a loss to explain the “pause”.
According to the climate experts more CO2 is supposed to mean more warming, but 18 years of no warming seems to have invalidated that theory. My question is: “how long do we have to go without any rising temperatures if CO2 continues to skyrocket before we might stop and say — hey, maybe this simplistic idea that CO2 warms the planet might be wrong?”

James Abbott
December 24, 2014 1:32 pm

Its about 12 years of the pause. Monckton’s 18 years comes from his view of what RSS shows – but that’s one global data set out of 5 – and which just happens to be the one showing the least change. He is a cherry picker.

mpainter
December 24, 2014 1:39 pm

James Abbott:
Have you contacted GREENPEACE leaders to express your disapproval of the vandalization of the Nazca site in Peru? I understand that GREENPEACE (your party, James Abbott) refuses to disclose to the Peruvian authorities the names of those involved, despite the request of Peru that they do so.

Janice Moore
December 24, 2014 6:35 pm

Okay, Mr. Abbott. While I am convinced by Lord Monckton’s evidence showing over 18 years of no warming, ad argumentum, let’s say that the “global temperature” (a fiction, but, granted, again, ad argumentum, here) HAS NOT RISEN IN TWELVE YEARS….
… while human CO2 has continued to increase by leaps and bounds.
You see? Your quibble did nothing but draw attention to the fact that AGW is a ridiculous proposition. Yes, I said RIDICULOUS. And….. say….. was that the glimmer of a smile playing about your lips….. Ah, ha! … 🙂 … so you KNOW….
oh, …. Mister Abbott … now, ….. don’t smile….. dooonn’t smile…… . There! You ARE smiling! Oh, I just KNEW you were an honest fellow at heart. (smile) Now, come on down off that ledge. Here, take my hand, I’ll help you….. . Aaaand … there. Now, off we go to the WUWT café for some cheerful camaraderie with all the WUWT “Den1al1st Club”… perhaps, you could even engage M. Painter in a friendly discussion about Greenpeace, hm?
#(:))

Reg Nelson
December 25, 2014 3:57 pm

Are you suggesting that the others are any better?
Climategate has shown the dishonesty inherent in this.

mpainter
December 24, 2014 1:33 pm

Mark,
Others started asking that question years ago.
It all has to do with climate sensitivity, and this hypothetical figure has been variously derived from 0.5°K to over 8°K per doubling of CO2, according to who does the figuring, and figures never lie, do they?
Here are the facts:
The warming trend circa 1918-45 could not have been due to anthropogenic CO2 because that was at too slight a level to have any effect on temperature (at ~300 ppm).
We have now seen that a number of studies showing increased insolation circa 1980-2000 and this accounts for that warming trend. Be mindful that these studies are based on solid data, and they are irrefutable, while the AGW crowd can show _NO_ evidence whatsoever for their hypothesis except for some laboratory measurements.
I regard AGW theory as a collapsed house of cards.
To complete the joke: figures never lie but liars figure.

Doug Allen
December 24, 2014 7:56 pm

Think it’s more likely that the G H E warming from CO2, is presently masked by a similar cooling effect of the PDO which means the 1978- 1998 warming was a combination of the two, and we will return to warming maybe around 2030 when the PDO turns positive unless the AMO changes that and unless a solar grand minimum changes that and unless- darn all these unquantifiable forcing variables!

pochas
December 24, 2014 1:03 pm

On the problem of CO2 sensitivity, it is small. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.

December 24, 2014 1:13 pm

Hi Fermat. How ya been?
By the way, why the “pochas” nom de plume?

pochas
December 24, 2014 2:04 pm

I must use a medium nowadays.

Typhoon
December 24, 2014 1:20 pm

A good discussion of the absorption and emission of radiation by CO2:
http://www.scribd.com/doc/239526963/Argonne-National-Lab-Talk-Happer
Why Has Global Warming Paused?
Argonne National Laboratory
March 22, 2013
William Happer, Princeton University

James Abbott
December 24, 2014 1:28 pm

Given that we already have 0.6 K warming since about 1980, that CO2 has not yet reached even 50% above pre-industrial levels and that the system equilibrium response lags, then even on a very basic level, real world evidence suggests Saburo Nonogaki is wrong.

mpainter
December 24, 2014 1:42 pm

James Abbott
What about Nazca? Do you approve of that?

James Abbott
December 24, 2014 2:08 pm

Hello mpainter
You have a short memory. I have already said that what they did was totally wrong and re your other post on this, greenpeace is not a political party.

mpainter
December 24, 2014 3:39 pm

Wrong , James Abbott,
I have a long memory.
Now, I ask again, have you expressed your disapproval of the Nazca vandalism to GREENPEACE leadership? After all, you are a member, are you not?

Streetcred
December 27, 2014 12:24 am

… but Greenpus is a political lobbyist organisation masquerading as an environmental NGO.

Typhoon
December 24, 2014 1:47 pm

Nope. With regards to GW by CO2, the devil is in the details . . . and there are a lot of details.
See the presentation above by Happer.

davidmhoffer
December 24, 2014 3:31 pm

James Abbott December 24, 2014 at 2:58 pm
What has caused the warming if not CO2 ? Occam’s Razor applies.

What caused the MWP and the LIA? What caused the steady increase in temps from the LIA until CO2 levels started to increase in a meaningful way since about 1920? If CO2 is the simplest answer, why does the period of largest CO2 increase (the last 20 years) not correspond to the largest change in temperatures? You cannot apply Occam’s Razor to this question because CO2 increases fail to explain the behaviour of the system as a whole over time. Occam’s Razor requires that the simplest answer be valid under all conditions, and so CO2 is falsified by Occam’s Razor in this instance.

December 24, 2014 2:17 pm

That assumes that 100% of the observed warming is caused by increased CO2, which is just an assumption, it hasn’t been proven.

December 24, 2014 2:20 pm

The above was meant as a reply to James Abbott.

James Abbott
December 24, 2014 2:58 pm

What has caused the warming if not CO2 ? Occam’s Razor applies.

Mark
December 24, 2014 6:52 pm

Are you sure you know what Ockham’s razor is? It has nothing to do with simplicity… It is about the number of assumptions. AGW theory is nothing if not full of unknowns and assumptions. Heck, you can’t even spell it correctly, hardly a surprise you don’t know how to apply it.
Mark

December 24, 2014 2:32 pm

He is a prominent researcher in the field of plastics, so how can you be sure that he might be off in his small referential paper about climate change?

Crispin in Waterloo
December 24, 2014 10:16 pm

James Abbott
0.6 or 0.8 degrees since 1980… All of it by 1996, yes? Then nothing since. Is that about right? Want to quibble about a couple of years? Why didn’t it go up another 0.6 since then?
Because GHG forcing is overwhelmed by natural variation which immediately begs the question, “How much of the 0.6-0.8 was caused by natural variation? All? Most?

December 26, 2014 2:08 am

Most or all.

Scarface
December 24, 2014 1:52 pm

@Mosher, all AGW-promotors and everyone who feels invited to react
I have a null-hypothesis: a doubling of C02 will have no effect at all.
Prove me wrong. And please take into consideration all feedbacks. Otherwise I will not be impressed.

James Abbott
December 24, 2014 3:03 pm

The Ice Age oscillations prove you are wrong.

Scarface
December 24, 2014 4:58 pm

I live now and am told that a doubling of co2 will be catastrophic. Proof?

davidmhoffer
December 24, 2014 3:24 pm

Since the feedbacks are not known in their entirety, your challenge is impossible to satisfy. However, in isolation, we can understand what the direct effects are, and these can be measured in the lab.
http://www.john-daly.com/artifact.htm
I recommend that you read the zip file at the top of the page to understand the limitations of this experiment in terms of drawing any conclusions about the atmospheric air column as a whole. That said, the direct effects of doubling of CO2 are readily quantified on this scale, and are most decidedly not zero. Not being able to quantify the feedbacks, I cannot say that the sum total will be zero, but that chances that it would be are vanishingly small.

December 24, 2014 5:08 pm

Exactly, yet I’m told that the science is settled. I think we know not much yet. And given the non relation between co2 and temp during earth’s history my null-hypothesis is more likely true than not. AGW is the wrong fight to fight. Poverty and illlnesses are our greatest threats. AGW is a sinister religion, nothing more and nothing less. It certainly has nothing to do with science.

High Treason
December 24, 2014 1:56 pm

Most, if not all of the apparent greenhouse effect is from the old PV=nRT. Temperature is proportional to pressure. On all planets with an atmosphere, as you go higher(and thus lower pressures) the temperature gets predictably cooler, including Venus. Mars has a rather thin atmosphere, but is 95% CO2-why is Mars not warmer?? Venus has 92-93 x the pressure at ground level as well as more solar radiation-little wonder it is hot as hell. Jupiter also gets hotter as the pressure builds, but it gets very little solar radiation. Brainless warmists- think about it.
As most of the IR bandwidth absorption occurs in the first 20 ppm (note, plant life stalls at 150-200 ppm), there is very little potential to get warmer from doubling CO2. I would predict that at 800 ppm CO2 an increase in temperatures of 0.15 Kelvin if that. This will make no significant or even measurable effect on planet earth. Certainly will not be detrimental, probably will be good. However, if we foolishly listen to the doomsayers and their paranoid fantasies, we will destroy the technology that IS humanity’s niche in the world. If we had to rely on our physical attributes only to survive in the jungle, we would not get very far.
Could it be that the stupidity of some humans that have been allowed to breed to plague proportions renders the entire species extinct?

James Abbott
December 24, 2014 2:16 pm

Is this a joke ?
If not, how do you explain the temperature response to changing CO2 levels during the last 3 million years or so of the ice age oscillations ? There would have been almost no response according to your theory.
Also, you are completely wrong about Jupiter – the internal heat has nothing to do with solar radiation and it has no solid surface as we would recognise. Venus is hot because it closer to the Sun than Earth, has a dense atmosphere AND especially because it is almost all CO2.

Janice Moore
December 24, 2014 2:55 pm

Q: “how do you explain the temperature response to changing CO2 levels”?
A: The underlying assumption you make is in error: CO2 levels lag temperature by a quarter cycle per ice proxies (see Dr. Murry Salby’s 2013 Hamburg lecture posted by me above on this thread).

bw
December 25, 2014 2:27 am

CO2 never causes temperature changes. CO2 follows temperature changes. That’s been known from the ice core data for at least 10 years. Temperature changes from changes in planetary albedo and milankovitch cycles.

davidmhoffer
December 24, 2014 3:17 pm

High Treason December 24, 2014 at 1:56 pm
Most, if not all of the apparent greenhouse effect is from the old PV=nRT. Temperature is proportional to pressure.

An instantaneous change in P is proportional to an instantaneous change in T provided all other values are held equal. However, the vessel at equilibrium has a temperature before the change in pressure, and after the change in pressure will eventually cool down to the exact same equilibrium temperature.

Harold
December 24, 2014 4:59 pm

Mosher’s comment would be most appropriate here.

Latitude
December 24, 2014 2:03 pm

You guys do realize you only have 20 years to work with…..1980 – 2000

December 24, 2014 2:06 pm

@Mosher
I just visited Real-Science and a perfect post for you is presented there:
Stop Climate Fear Mongering – CO2 Increases Can Cause Only Minimal Warming
by William M. Gray – Professor Emeritus – Colorado State University
Please read the whole essay over there. I’m looking forward to you response.
Except when it is only one word.
If you can’t or don’t react on the substance of that essay, then YOU are wrong.
Anyway, Merry Chistmas!

Richard M
December 24, 2014 7:35 pm

The Dr. Gray essay is very interesting and would make a good post at WUWT. I suspect he is on to something and the data appears to back him up.

sleepingbear dunes
December 25, 2014 7:55 am

I totally agree. The presentation and logic were very persuasive. I certainly hope we see his essay here or at Climate etc. or anywhere else to get greater discussion of his ideas. That is what science is supposed to be all about.

December 24, 2014 2:29 pm

It’s funny how this article references another work which actually has much more dire conclusions than it itself reaches. Also, the author seems to be quite the expert…On plastics engineering.

December 24, 2014 2:31 pm

T occurs once in equation 1 but is substituted for twice which is absurd.

December 24, 2014 2:34 pm

The number which has to be matched in terms of CO2’s effect on Earth’s spectrum is the 279K +- 2.3 from perihelion to aphelion equilibrium mean temperature of a grey ball in our orbit .
There is no way the 0.3% variation in our estimated mean temperature this whole politically useful hysteria is over starting from such a crude extreme assumption as the ( 0.7 solar absorption ; 1.0 emission ) coefficients which generate the 255K meme . At the very least , one should start with the approximately 274 of an ocean blue ball leaving about 15K to be explained .
I can believe that the 0.6K ( 0.2% ) might be about right . It’s pretty close to the simple linear extrapolation of the bit we’ve see since the steam engine .
This image illustrates why we should expect damn little effect on our temperature from additional CO2 :
It shows a simulation of the effect on our spectrum as seen from 70km for 280ppm ( blue ) versus 560ppm ( red ) CO2 . The little bits of blue showing thru are the total change in the spectrum . And our temperature will be that temperature for which the dot product of that temperature’s Planck spectrum with that observed spectrum equals the dot product of the Sun’s spectrum with that observed spectrum .
I trust you and yours are having a copacetic and productive NH winter solstice correlated holiday month .
( See my current news letter , http://cosy.com/CoSy/CoSy/NL20141222.html , mostly about progress on my 4th.CoSy APL in Forth computing environment . )

davidmhoffer
December 24, 2014 6:24 pm

It shows a simulation of the effect on our spectrum as seen from 70km for 280ppm
It isn’t about what you can “see” from 70km. It is about what altitude (on average) you are seeing it escape from. See Leonard Weinstein’s comment upthread.

December 25, 2014 11:49 am

Yes , I point out it’s a “simulation” . But I assume that it is showing the expected perturbations from the observed . If the underlying curve is not observational , does someone have a link to the Earth’s observed absorptivity=emissivity spectrum ? I must admit I am at a loss to understand Give me a full spectrum and I’ll give you its implied ( and experimentally testable ) equilibrium temperature .
As DonB points out , alarmists are now trying to contend that the second order effect of the change in altitude , and therefore temperature , at which CO2 is emitting as the supposed cause of catastrophe . Realistically , I think that simulation shows the magnitude such effects are likely to have .

December 24, 2014 3:17 pm

Every now and then papers or posts appear here which merely serve to embarrass serious sceptics. Challenging well established physical principles just gives the climate establishment more ammo to fire contemptuously at their opposition. And the feeble supportive comments which follow just add to the cringe factor.
There may be -and in my opinion there are – good reasons why CO2 sensitivity is very low – but this sort of thing isn’t one of them.

MikeB
December 27, 2014 9:32 am

Quite so

December 24, 2014 3:37 pm

Recent estimates from IPCC (2007) say this value (the Climate Sensitivity) is likely to be between 2 and 4.5°C. But Sherwood Idso in 1998 calculated the Climate Sensitivity to be 0.4°C, and more recently Richard Lindzen at 0.5°C. Roy Spencer calculated 1.3°C in 2011.
See Carbon Dioxide and Global Warming (C. D. Idso and K. E. Idso. co2science.org, 1998), at http://www.co2science.org/about/position/globalwarming.php
See Taking Greenhouse Warming Seriously, at http://www-eaps.mit.edu/faculty/lindzen/PublicationsRSL.html
See Global Warming 101 (Roy Spencer, Ph. D., Principal Research Scientist at the University of Alabama in Huntsville – UAH), at http://www.drroyspencer.com/global-warming-101/
See Weak Warming of the Oceans 1955-2010 Implies Low Climate Sensitivity (May 12, 2011. Roy Spencer, at http://www.drroyspencer.com/2011/05/weak-warming-of-the-oceans-1955-2010-implies-low-climate-sensitivity/
See More Musings from the Greenhouse (February 19, 2012. Roy Spencer, Ph. D., Principal Research Scientist at the University of Alabama in Huntsville – UAH), at http://www.drroyspencer.com/2012/02/more-musings-from-the-greenhouse/

December 24, 2014 3:44 pm

The direct link to Lindzen’s Taking Greenhouse Warming Seriously (.pdf, 968 KB) , is at
at http://www-eaps.mit.edu/faculty/lindzen/230_TakingGr.pdf

December 24, 2014 3:39 pm

Rubbish! The 255k temperature has been picked because it is the estimated mean temperature of the moon. No other reason. Equations have been built around this assumption and make a mockery of science! Anyone with half a brain will realise that as the moon reflects a 1/3 less sunlight than the earth (albedo) that the 255k figure for earth without an atmosphere is idiotic! Dress up your equations however you like!
Second, I also don’t need to use complex equations to show by the greenhouse con men’s own theory that (assuming we accept their premise, which I don’t, but let’s play along) CO2 is spent. Simply take their 33K premise and the percentage of that amount that CO2 is supposed responsible for and after you have lampooned the “between 9% and 26%” figure that is cited for being so spread apart a bus could fit through it, draw a graph for the low figure and the high figure expressing the percentage of 33K in kelvin. That number will represent 0ppm of CO2. Now plot 280ppm (1860 levels) and the increase in temperature and today. Draw a line through the points! Anyone who can’t be bothered to do this should go back to selling snake oil until they’re thrown in jail!

davidmhoffer
December 24, 2014 3:52 pm

Rubbish! The 255k temperature has been picked because it is the estimated mean temperature of the moon.
Rubbish! The estimated mean temperature of the moon is 271K. That is NOT where the 255K number comes from.

December 24, 2014 5:35 pm

David , That’s real interesting to me because it’s within 3% of the 278.7 orbital gray body temperature , much closer than other estimates I’ve heard . I’d appreciate a reference .
That implies a ratio of about 1.11 between the Moon’s emissivity in the IR versus its absorptivity over the Solar spectrum .

Anything is possible
December 24, 2014 5:40 pm

Instead of using estimated mean temperatures if the Moon, why not use the actual measured temperatures?
http://www.diviner.ucla.edu/science.shtml
Hmm…. 206K – AT THE EQUATOR!
Looks like those estimated mean temperatures are a pile of donkey-doos.

davidmhoffer
December 24, 2014 6:01 pm

Bob Armstrong;
That implies a ratio of about 1.11 between the Moon’s emissivity in the IR versus its absorptivity over the Solar spectrum .
>>>>>>>>>>>>>>
Albedo of Earth is about 0.3 and the moon is about 0.1 Slight variations in temp estimates depending on reference. Willis did a rather thorough write up on it a while back:
Anything is possible – suggest you read this as well. The problem is one of how you average a temperature that swings wildly to equate to SB Law.
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/

richard verney
December 25, 2014 3:51 am

davidmhoffer (December 24, 2014 at 6:01 pm) links to an article regarding the Moon.
In a ddition to bearing in mind the very different and significant rotational spped of the Moon which has a substantial bearing on its temperature, It is well worth repeating the comment made by Bryan on that post and the guilty little secret:
Bryan (January 9, 2012 at 1:15 am)
The SB equation is misused by IPCC style Climate Science.
The Moon is a perfect example of this.
1. why after 14 Earth days does the dark side never reach absolute zero but stays some 90K above?
2.why after 14 Earth days does the Sunlit side never reach its predicted radiative max but stays well below it.
The guilty little secret of IPCC Moon Science is that to get anywhere near realistic temperature figures they have to include a substantial contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.
The guilty little secret of IPCC Earth Science is that they refuse to include a ANY contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.
If they did so they would find little use for the so called greenhouse effect.

davidmhoffer
December 25, 2014 5:14 am

Richard Verney;
1. why after 14 Earth days does the dark side never reach absolute zero but stays some 90K above?
Because the moon has a heat capacity and would take a lot longer than 14 days to reach absolute zero.

December 25, 2014 11:26 am

David , certainly your ( .9 solar absorption ; 1.0 emission ) producing your 271K matches the requirements for radiative balance . Does anybody have an measured absorptivity=emissivity averaged spectrum for the moon ? How temperature dependent is it ?
Whatever physical data are measured , they must be reconciled with the spectral data and energy balance with the Sun .

richard verney
December 26, 2014 4:03 am

davidmhoffer
December 25, 2014 at 5:14 am
////////////////////
I am aware of your point. See Bryan’s comment : “The guilty little secret of IPCC Moon Science is that to get anywhere near realistic temperature figures they have to include a substantial contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.”
But of course, planet Earth with its huge heat storage reservoirs (the oceans) and it significantly faster speed of rotation (which keeps the oceans well heated) is not similarly so treated. As bryan notes: “The guilty little secret of IPCC Earth Science is that they refuse to include a ANY contribution from a GROUND HEAT FLUX in addition to the radiative fluxes.”
Bryan goes on to conclude: “If they did so [ie., treat the Earth in the same manner as they treat the Moon] they would find little use for the so called greenhouse effect.”
David, it is worth looking at how quickly the surface of the moon cools soon as the sun dips below the horizon. It drops off a cliff. Very different to planet Earth with its huge storage heates (the oceans).

Bruce Cobb
December 24, 2014 3:53 pm

James Abbott
December 24, 2014 at 2:58 pm

What has caused the warming if not CO2 ? Occam’s Razor applies.

Wow, that’s a blast from the past. You must have dug that one up out of the old pile of dumbest Warmist arguments. Sorry, but the null hypothesis remains that climate change is natural. So far, despite Warmists’ most fervent efforts and wishes, no manmade fingerprint has been determined. Their last great hope appears to be that “the warming” has magically vanished into the deep oceans. And they call themselves “scientists”.

davidmhoffer
December 24, 2014 4:05 pm

+1
My own response got dumped in the wrong part of the thread, so not to steal your thunder, but here it is again:
davidmhoffer December 24, 2014 at 3:31 pm
James Abbott December 24, 2014 at 2:58 pm
What has caused the warming if not CO2 ? Occam’s Razor applies.

What caused the MWP and the LIA? What caused the steady increase in temps from the LIA until CO2 levels started to increase in a meaningful way since about 1920? If CO2 is the simplest answer, why does the period of largest CO2 increase (the last 20 years) not correspond to the largest change in temperatures? You cannot apply Occam’s Razor to this question because CO2 increases fail to explain the behaviour of the system as a whole over time. Occam’s Razor requires that the simplest answer be valid under all conditions, and so CO2 is falsified by Occam’s Razor in this instance.

December 24, 2014 4:53 pm

Close, but no cigar. . You got the mechanism, emission from a higher level of the atmosphere with all the emission from lower down being trapped, but except for the CO2 Q branch (in the center of the 15 um band) the level at which the atmosphere emits to space is well within the troposphere where temperature decreases with altitude. Even at much higher CO2 concentrations emission to space from the troposphere will be considerable.
Eli suspects that you may have neglected decreasing atmospheric density with altitude.

December 25, 2014 4:45 am

Eli, Decreasing density would just make it that much more difficult to cool the upper atmosphere. You do get an inverted spike with increasing CO2 at 15 microns. That is probably due to CO2 temperature being so low that is has limited degrees of freedom as it nears is triple point. CO2 concentrations are not high enough for it to precipitate out, but that doesn’t mean it radiant properties can change.
In any case, this approach is similar to Kimoto’s which indicates the actual “surface” isn’t like to respond to the full CO2 impact estimates. Some surface where evaporation and convection are less involved could, but the moist atmospheric boundary layer isn’t likely to let the majority of the surface behave like an ideal GHG model.

Mike M.
December 25, 2014 7:49 am

Thanks, Richard. I will look at that article. But I suspect that Eli is right.
Mike M.

December 25, 2014 4:30 pm

Richard, and Captain D, the spike is the Q branch and in that band, the absorption is so strong that emissions from the troposphere are trapped, and only emission from CO2 in the stratosphere can escape into space. However, the Q branch covers only a small part of the 15 um CO2 spectrum.
The height of the spike identifies the temperature of the level of the stratosphere that the emission is taking place from. You can see this in the Chicago MODTRAN applet. To make things clearer set everything except the CO2 mixing ratio to zero and vary the CO2. In the tropics the Q branch spike emits to space from about 35 km where the temperature is ~245 K.
The thermal structure of the atmosphere is controlled by the lapse rate and the absorption of oxygen and ozone in the UV and does not change much as CO2 concentrations increases. What does change is the width of the CO2 15 um absorption increases (play with MODTRAN). That means that with increasing CO2 a decreasing amount of energy reaches space (or 70 km, but Eli repeats himself).
To maintain thermal equilibrium increasing amounts of energy have to reach space in other regions of the spectrum, and that turns out to be in the so called atmospheric windows, where increased blackbody radiation from warming surface can be generated. Note that in Chicago MODTRAN the temperature of the ground is fixed. Best- Eli

Mike M.
December 25, 2014 7:59 pm

I’ve looked at Richard’s article. It does not seems unreasonable and certainly does not make as basic an error as Eli suggests. But it does seem to be a somewhat crude form of the radiative transfer calculations done in climate models. So I see no reason to trust his result over the well established result.
Mike M.

December 26, 2014 5:03 pm

Eli, what I was referring to was the limit at 245K (-28C) and below. You can 10xCO2 at that temperature and get virtually no change in OLR. That would mean advection pole ward as well as convection upward would be negative feedbacks as they approaches 245K. Ozone and traces of water vapor kick in at the poles to limit minimum temperatures to around 184k which is the Turbopause temperature ~100km.

December 27, 2014 6:41 pm

Captain Dallas, take a look at this from arXiv, it may cover some of your issues. The take home is various ways of making the simple one dimensional model discussed here more realistic by including such things as rotation, heat capacity of the oceans, albedo variation, etc.
Bottom line is that without IR absorbing gases in the atmosphere, the upper limit of the Earth’s surface temperature is 255 K. That is an upper limit.

george e. smith
December 28, 2014 10:01 pm

Taking TSI as 1362 W m^-2, and sigma = 5.67051E-8 W m^-2 K^-4 ; a perfectly conducting isothermal, perfectly spherical black body, has an equilibrium Temperature of 278.37 K
But Earth is not perfectly thermal conducting, nor is it anywhere nearly isothermal, having a surface Temperature extreme range of about 150 deg. C and typically 120 deg. C
Because it is not infinitely thermally conducting, heat cannot propagate instantly to the dark side, to get equal BB radiant emittance all over the entire surface, so the sunlit half of the sphere has to run at higher Temperatures than 273.37 K in order to get rid of all that incident solar energy.
A 255 K spherical isothermal black body would require a TSI of 959.05 W m^-2, or a grey body with a total emissivity of 0.704 , or an albedo of 0.296.
If you remove all the green house molecules from the atmosphere, which includes H2O, you get no clouds, and albedo isn’t nearly 0.296. The moon has an albedo of around 0.118 but it doesn’t have any surface areas with a reflectance as low as 2-3% like Earth’s oceans have for 70 % of its surface area.
So I think Eli is incorrect in saying that 255 K is the upper bound on the effective BB temperature of earth, sans GHMs.

Donb
December 24, 2014 5:06 pm

EXPLANATION
The article (and various comments) are correct in that IR absorption by CO2 is essentially saturated, except for slight broadening of the bands. But that is NOT the mechanism by which extra CO2 produces warming.
Each IR photon emitted from the surface is absorbed and emitted (as a separate photon) several times on the upward path to escape to space. Eventually the photon is at sufficient altitude that few CO2 molecules lie between it and space and it likely will escape rather than be absorbed. That height is called the emission height, and varies around the Earth, generally in the upper troposphere, but sometimes the stratosphere. But the RATE at which a CO2 will emit an IR photon depends on the temperature to the fourth power. And the atmosphere gets colder with altitude. (This makes the rate of IR emission very sensitive to temperature.) So more CO2 added to the atmosphere forces the last CO2 emission to space to occur from greater heights. And because it is colder there, the rate of IR loss to space slows down.
When the RATE of heat loss from an object slows down, the object heats up. (Think of donning an overcoat on a cold day. The rate at which you lose heat slows down and you get warmer, until a new equilibrium is reached.) Similarly, as the atmosphere heats, the emission height grows warmer until the rate of IR emission from CO2 counter-balances the incoming solar energy. This produces a new thermal equilibrium, but with the Earth’s surface and atmosphere at a higher temperature.

December 24, 2014 5:37 pm

Is part of your problem that half of the photons are emitted back towards the surface? I means, besides the problems with the equations? That would bring you to 1.2, which is at least closer to normally accepted values.

Richard M
December 24, 2014 7:42 pm

I’ve had a question relative to this claim. While it makes sense that more CO2 would block outgoing radiation, we also have the situation that more CO2 will increase the number of radiated photons. How do these effects balance out? If it is even then the emission height will not increase.

Donb
December 24, 2014 8:28 pm

Outgoing IR photons mostly originate initially from the surface where solar irradiation impinges. A CO2 molecule absorbs a photon, which increases the molecule’s energy, which then may transfer that energy to other molecules (e.g. O2 and N2) or re-emit a photon. The CO2 molecules do not by themselves increase the number of photons. Increased H2O and CO2 do increase the number of IR photons directed back to the surface for re-emission (sort of a closed cycle). This occurs because the more times CO2 or H2O absorb and reemit a photon in the process of upward escape, the more likely some of those will be directed back to the surface. This is a consequence of the outgoing heat (IR) being delayed in the atmosphere before escape. But the energy escaping from the top of the atmosphere (the only way the Earth can lose it, ignoring minor surface retention by e.g. plants) depends upon the solar incoming energy, whatever the number of CO2 or H2O molecules present.
Incoming solar photons have relatively low abundance of IR wavelength, but those are absorbed by CO2 and H2O.
The “issue” with how much warming CO2 can produce lies not in the process I describe, but in feedback factors that increase or decrease the CO2 effect, e.g., does increasing temperature produce more clouds that reflect more incoming solar to space, but also may increase the greenhouse effect of more moisture in the atmosphere.

Phil.
December 25, 2014 5:23 pm

Actually the rate of emission depends on the Einstein coefficient of the excited state not T^4.

stevek
December 24, 2014 5:53 pm

I’m not a physcists and my last physics class was high school.
However my thoughts on the matter are that heat tends to escape. If there is a way for heat to get out it will.

perplexed
December 24, 2014 10:34 pm

Equation 1 in the original post, at best, makes no sense as a model of a dynamic process and at worst is just flat out wrong. It looks like the “constant” on the right hand side of the equation is supposed to be the incoming solar radiation (which is presumed to not change). That part is fine. But if the right hand side is heat or energy, the left hand side has to have the same units. Yet, as far as I can tell, it has units of temperature [if the “a” is simply a proportion of “energy over energy” that would make (1-a) dimensionless since the “1” has to be of the same dimension as “a” to carry out a subtraction operation]. Conversely, if the constant on the right hand side is expressed in Kelvin, then the equation makes no sense because it permits no changes in temperature, yet is used to calculate the value of “a” given a presumed change in temperature.
I THINK the original poster begins with the assumption that the net outgoing radiation has to equal the net incoming radiation (presumed constant), sets the net outgoing radiation to the radiation emitted from the surface (proportional to T^4) minus the radiation reflected back by the atmosphere, but then illogically expresses the reflected energy as a percentage of the energy emitted from the surface. The problem, as I see it, is that “a” is not a variable that directly changes as a function of surface temperature (the specific temperature of the radiating gas molecule, maybe, but not surface temperature). You can arbitrarily express is as a percentage of surface temperature, just as you can arbitrarily set it as as a percentage of the volume of tea I drink during the day, but neither has any physical meaning. Stated differently, when you multiply T^4 through the (1-a) you don’t get anything that physically makes sense for the variable aT^4.It doesn’t represent anything except for a contrived, arbitrary expression of retained radiation as a fraction of surface radiation. Thus. you can’t just plug in a couple temperatures into equation 1 and solve for “a”.

garymount
December 27, 2014 1:07 am

Your comment has caused me to study the Stefan-Boltzmann Law finally once and for all. The equation (1) appears to me to be formed correctly, and “a” is essentially the buffer or difference or retained heat compared to a black body without an atmosphere, more or less.
I have not read the referenced document to Barrett yet so can’t comment on the rest of this authors calculations.
I am more interested in writing computer climate models, and have spent the last few years studying the Math and related technologies.

Robert Clemenzi
December 24, 2014 11:48 pm

As the actual thickness of the atmosphere is about 8000m at ordinary atmospheric pressure, the saturation of infrared absorption by CO2 will be almost complete …

That is complete nonsense. Infrared absorption by CO2 will never be saturated in the Earth’s atmosphere. Use any HITRAN model you want (I wrote my own, just to be sure), CO2 must be more than 10 times the total size of the Earth’s atmosphere before it is saturated. To be clear – >10,000,000 ppm – a number not possible by simply burning fossil fuels. (There simply is not enough oxygen to produce that much CO2.)
If some claim is based on the saturation of CO2, then the claim is wrong.

December 25, 2014 12:23 pm

That’s nonsense . If CO2 is not effectively , eg , .95 saturated within a couple of hundred meters of the surface , then it is inconsequential as a “greenhouse gas” .
Neat knotion that a gas can be 10 million parts per million before being “saturated” .
And , interestingly , I’ve seen figures that the original atmosphere was on the order of 300,000ppm ( 30% ) CO2 before green life and shell forming creatures exploded releasing all the O2 we animals require , depositing the strata of fossil fuels and limestone , and exhausting the CO2 down to levels which just bounce along the minimum required for green life .

Robert Clemenzi
December 26, 2014 11:46 pm

There are 2 different definitions of “saturated” – one is the effect at a single wavelength. For a significant part of the CO2 spectrum, the most of the available energy is absorbed within a few hundred meters. As a result, CO2 is an important greenhouse gas.
The other definition considers the entire spectrum. When that is done, CO2 is not saturated. This is because there are some frequencies that are not currently saturated. As a result, adding more CO2 will saturate some frequencies that are currently absorbing only about 50% of the available energy, and other frequencies that are currently absorbing next to nothing will begin to absorb a bit more. This part of the absorption spectrum is referred to as the “wings” of the absorption bands. For the current wings to become saturated, the amount of CO2 in the atmosphere must be more than 10 times the total amount of gas (oxygen and nitrogen) currently in the atmosphere – thus >10,000,000 ppm ! This is pretty settled physics, not controversial.
Limestone is an interesting substance, for every 2 molecules of CO2 removed from the atmosphere, one molecule on oxygen (O2) is required. This oxygen could come from either the atmosphere or the oceans, but there is no way that I know of that the creation of limestone can increase the amount of oxygen in the atmosphere.

richard verney
December 25, 2014 3:24 am

There are a number of comments that suggest that half the photons re-radiated by CO2 molecuels go back down to the surface.
But is that not, as a matter of geometry, an exaggeration?
I have not looked at the geometry of the sherical shape that makes up Earth’s atmosphere, but my immediate visualisation is that some photons reradiated will be radiated sideways, or at a grazing angle of say somewhat less than 5deg to the surface. Such photons that are radiated at higher altidues surely will never hit the surface.
Is not the correct position that somewhat less than half of re-radiated photons find their way upwards to TOA and thence to space, somewhat less than half find their way top the surface, and some small percentage remain forever locked in the atmosphere neither making it to space nor to the surface.
No doubt the effect is relatively small, but even small effects become significant when one is looking at a balanced or imbalanced budget.

December 25, 2014 4:38 am

I have also always been bothered by the ignoring of 3 dimensional geometry in “climate science”. The ignoring of the globe as a rotating sphere really gets my goat.
On top of that, I think that many explain the “CO2 absorbs a proton” thing without mentioning that the molecule will most likely bump into another non-CO2 molecule (nitrogen or oxygen most likely) before it can radiate the energy. BUT, even if it does radiate said photon, why will the photon go all the way to the surface or all the way into space without hitting another CO2 molecule?? Would a photon somehow “know” that it is not supposed to be absorbed again? How would that work?

davidmhoffer
December 25, 2014 5:05 am

BUT, even if it does radiate said photon, why will the photon go all the way to the surface or all the way into space without hitting another CO2 molecule?? Would a photon somehow “know” that it is not supposed to be absorbed again? How would that work?
It doesn’t “know” and if it impacts another CO2 molecules while going up or down, it does get absorbed again. That’s the whole point. That it must be absorbed and re-emitted many many times before it gets high enough to see a free path to space.

December 25, 2014 5:53 am

“…That it must be absorbed and re-emitted many many times …”
Since the CO2 molecule is much more likely to bump into a nitrogen or oxygen molecule before it can radiate the photon, and since it has many chances to do so as you point out — then the energy must go to the non-CO2 molecules almost immediately and so convection dominates the whole process in the lower atmosphere (troposphere). So, radiation does not inhibit convection, it enhances it all else being equal.
This does not look like the “team’s greenhouse effect” at all. It looks like the model that the physicist Maxwell described so very long ago. Conduction and convection drives the weather machine and CO2 does very little on net if anything.

Mike M.
December 25, 2014 7:06 pm

markstoval wrote: ” the ignoring of 3 dimensional geometry in “climate science”. The ignoring of the globe as a rotating sphere really gets my goat”. What gets my goat is know-nothings like markstoval spouting this sort of ignorant nonsense.
Mike M.

davidmhoffer
December 25, 2014 5:10 am

But is that not, as a matter of geometry, an exaggeration?
The 1/2 up and 1/2 down is a simplification in order to explain the basic concept. Obviously in the real application, some portion are emitted at all angles, and depending on how far they travel, an angle “slightly down” or even “sideways” could become “up” at the end if the path is long enough.

December 25, 2014 5:55 am

@ davidmhoffer
There seams to be a lot of “simplification” in climate “science”. A whole lot of “simplification”. Over simplification in fact.

Donb
December 25, 2014 8:14 am

EXPLANATION
On some of the comments above: Photon emission by CO2 (or H2O) is random, up, down, or sideways. It is a “statistical walk” for a photon to eventually escape to space. Most emissions are within the troposphere where the Earth’s surface appears almost flat. But by comments expressed above, there is a preference for net upward motion. When a CO2 (or H2O) molecule absorbs an IR photon and gains energy, that energy can be distributed several ways. It can increase energy of the molecular bonds (think bond motion, of which there are several possibilities, depending on the molecule); it can collide with another molecule (likely N2 or O2) and transfer some of that energy; it can emit an IR photon and lose energy. If #s 1 or 2 occur, the molecule may not have sufficient energy to emit a photon (photon energies are quantized; i.e. they can only occur in specific energy levels). But, another molecule can strike the molecule that has lost energy and give it sufficient energy to now emit an IR photon. In this way energy of an absorbed IR photon is distributed through the atmosphere and delayed in reaching space.
By the overcoat analogy, slowing heat loss causes the planet to warm.

davidmhoffer
December 25, 2014 10:30 am

markstoval December 25, 2014 at 5:55 am
@ davidmhoffer
There seams to be a lot of “simplification” in climate “science”. A whole lot of “simplification”. Over simplification in fact.

You asked a question and I answered it. If you want the “full” explanation, you’re not going to get it in a blog post. You’ll have to learn some calculus and read some text book, big fat thick ones. If you want something in between, start with these:
http://wattsupwiththat.com/2011/05/07/visualizing-the-greenhouse-effect-light-and-heat/
http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/
http://wattsupwiththat.com/2011/02/28/visualizing-the-greenhouse-effect-atmospheric-windows/

December 25, 2014 3:38 pm

“You’ll have to learn some calculus and read some text book”
My, my, Does that mean I have to repay the salary I got for teaching calculus those years? And what big, bad, scary textbook will treat the 3-d, dynamic, chaotic system fully? Hmmm?
PS: I suspect the grammar error was just a typo and not karma. (no, really I do)

December 25, 2014 3:44 pm

@Donb
“By the overcoat analogy, slowing heat loss causes the planet to warm.”
Oh my god. You typed that swill on Christmas day for god’s sake.
An overcoat can cool people in the desert by keeping the sun off of them. Ever notice how the desert people cover up with their clothes?
An overcoat will not help warm a dead man whose body does not give off its own heat — just like the earth’s heat does not come from inside. (there is a big ball of fire in the sky ya know)
What we have here is more over simplification that is evidence of not a thing. But thanks for proving my point about too much simplification.

davidmhoffer
December 25, 2014 6:13 pm

Mark Stoval;
PS: I suspect the grammar error was just a typo and not karma. (no, really I do)
Then why draw attention to it?
I agreed with you on photons not knowing if they had already been absorbed or not, I agreed with you on the geometry issue you raised, I pointed out that the purpose was to illustrate a point, and when you complained about that I pointed you to some pretty good articles on the subject and suggested that the level of detail you were insisting on could not be dealt with in a blog post. Yet still you complain. Did you even read the articles I suggested?
just like the earth’s heat does not come from inside. (there is a big ball of fire in the sky ya know)
Well actually, for the purposes of discussion of the greenhouse effect, the heat does come from the “inside”. It goes through the atmosphere as SW from the Sun from outside the atmosphere, gets absorbed by the Earth, and re-emitted from inside the atmosphere. But if you’d bothered to read the articles I pointed you at, you’d know that.
Some people are trying to help you, and BTW, we’re skeptics, not warmists nor alarmists. So before you start p*ssing on us for trying to help answer your questions, consider that you could put your math skills to work and consider that the physics we’re trying to explain in this rather limited forum might well be genuine.

george e. smith
December 25, 2014 9:32 pm

Well We actually have experimental; well observational proof, that at least half will head downwards towards the surface.
At sunset, when the lower limb of the sun touches the visual horizon, the sun is already completely below the geometric horizon, due to atmospheric refraction. So a photon emitted perpendicular to the local earth radius, will actually refract downwards, by a bit more than one half of a degree.
Consequently, only the upwards 179 degree full cone angle, will head to space, and the downward 181 degree full cone angle will head down towards the surface.
But the upward escape direction is still favored, because in that direction lies lower density, and lower temperature, and both of those lead to less broadening of the GHG absorption lines, so an ever narrowing bandwidth can get reabsorbed, heading up.
But heading down, leads to ever broadening spectral absorption, and each reabsorption results in another up / down split, so less radiation would reach the ground, compared to the fraction that escapes to space.
And it is the molecular kinetic energy (velocity) that gets traded between GHG and non GHG molecules in collisions. Those collisions may cause termination of the GHG photon absorption excited state, but the emitted photon must be of the same or nearly the same frequency, as the absorbed one. It is after all a molecular resonance phenomenon.

richard verney
December 26, 2014 5:17 am

I agree with the the point that you make regarding the atmosphere acting like a lens and the consequent dispersion of vissible light, but since the refracted angle varies with wavelength, is the effect of that slightly less as you go into the IR waveband?
The more material point made is that regarding loweer density and lower temperatures favouring an upward flow.

george e. smith
December 26, 2014 10:23 pm

Well Richard, the original reticence on your part, to accept a 50:50 split up / down, was based on not accepting a planar thin atmosphere model, which would imply a 50:50 split, as the atmospherically emitted photons are necessarily isotropic in original angular distribution. On that issue, a renowned Nobel Prize Physicist, once told me (over a beer in a friend’s garden) that the no matter how small a region on an idealized spherical earth you choose, the curvature is exactly the same.
So the reality of the curvature of an iso-density lamina of the atmosphere, has to be recognized. It is a fairly standard problem in graded refractive index propagation of EM waves or optical rays in the geometrical optics simplification.
In the case of air, the refractive index is quite small, but it is not equal to one, and it is wavelength dependent. However, in the LWIR region, the index is practically constant over the whole BB envelope of the earth LWIR emission spectrum, and it is also density dependent.
Since the atmospheric gases are IR inactive (excluding GHGs), at leas as far as atomic or molecular resonance lines, there should be no anomalous dispersion edges, anywhere in the LWIR spectrum of interest to GHG climate issues. So the index will decline at longer wavelengths, but negligibly so. The dispersion is always steeper at shorter wavelengths, until you cross a resonance edge, where you get an anomalous dispersion .
So even though the effect is small, it isn’t zero, and optical rays will refract away from the zenith, when travelling upwards.
The effect of atmospheric refraction , causes a significant change in the visible region in the apparent angular velocity of distant stars. Near the zenith, the apparent angular velocity of a star is less than the actual angular velocity of the earth, since the star is displaced towards the zenith.
It seems to me, that the sidereal day is something like 86,164.09 seconds. I don’t know why that number comes to mind, but it does. As result, of the refraction, a telescope clock drive has to run slower than sidereal by something like 12-16 seconds per day, to track a star across the zenith.
It would be a smaller discrepancy for the LWIR region.
In any case, geometrically, more photons start down, than up, but the line broadening gradient favors the escape route, because of the multiple absorptions.
GHGs are such a small part of the atmosphere, they have virtually no effect on the atmospheric refractive index. Well water might be enough to show an effect, but CO2 won’t affect the index measurably.
I actually built a quartz crystal controlled clock drive for a small telescope, that used a special GT cut quartz crystal, running at something like 492 kHz (high for a GT) that divided by 2^13 and produced roughly 60 Herz two phase square waves to drive a 1200 RPM 6 pole synchronous motor (1/2 inch diameter: aka size 5). A worm reduction followed by a hypoid spiral reduction produced a one rev per siderial day plus about 26 seconds, for the refraction. That was capable of tracking a star for about six hours across the zenith, to less than one arc second deviation.
I think the crystal frequency was 492.718 kHz

December 25, 2014 5:02 am

Well, considering how long it’s taken for the average temperature anomaly to hit 0.600 maybe you’re onto something
http://www.wunderground.com/blog/joshuah/comment.html?entrynum=4

alleagra
December 25, 2014 5:29 am

Steven Mosher – this is not the British Daily Mail or The Guardian where such comments are regularly on display – as if anyone could give a **** regarding someone’s unsupported opinion.

Alan McIntire
December 25, 2014 6:36 am

I got roughly the same results by accepting what I read that a doubling of CO2 would result in a 3.7 increase in wattage flux per square meter, and plugging in the figures.
The Stefan-
Boltzmann equation for a blackbody goes
T(degrees Kelvin) = S(constant)*(watts/square meter)^0.25. Our
first step is to find that S constant.
Doing a google search, I find 1000 K implies a blackbody flux of 56790
watts/square meter.
1000K = S* (56790 watts/square meter)^ 0.25. Click on your
calculator and use the scientific view. Plug in 56790
X^Y
0.25
=
and you get 15.43718 Divide 1000K by 15.43718 and you get S =
64.77867
We now know
T(kelvin) = 64.77867 ( watts/square meter)^0.25.
For a blackbody, climate sensitivity would be
1/4 dT/ dS
For a surface temperature of 288 K, this amounts to
(1/4)( 288K/342 watts) = 0.21 K/watt
or an increase of about 0.777 K for a doubling.
Of course, that additional wattage would not be added to the rays direct from the sun, bu from Trenberth’s figures, to the 390 watts the earth’s surface gets.
1/4(288K/390 wats) gives a sensitivity of 0.185 K per watt increase.
Also, from Trenberth’s figures, theres an additional 100 watts going into the latent heat of vaporizaion of water and into convection. Using those figures,
1/4(288K/490 watts) gives a sensitivity of only 0.147 K per watt increase. Of course
the earth is a graybody, not a blackbody.
Assuming an emissivity of 0.8, If we divide that
0.147 K./watt by 0.8 emissivity, we get the same 0.7 K incrrase for 3.8 additional watts that Saburu Nonogaki got.

December 25, 2014 12:07 pm

Alan, I hate to tell you this but the Trenberth et al. series of Earth energy budgets all have a number of errors and overly optimistic assumptions. One of the worst is their “fixed” atmospheric window value of 40 Wm-2, The actual surface window is closer to 20 Wm-2 and the 40 Wm-2 would be more accurate for a surface above the atmospheric boundary layer.
http://judithcurry.com/2012/11/05/uncertainty-in-observations-of-the-earths-energy-balance/
That imposes a bit of a limit on CO2 impact at the real “surface” due to water vapor creating an “effective” saturation. There is no real saturation, but it does throw early calculations off quite a bit.

Sun Spot
December 25, 2014 1:02 pm

As Mosher is a graduate English major I assume he is indicating a problem with the grammatical construction of the article, I highly doubt he was referring to the science.

Mark T
December 27, 2014 5:30 pm

His follow up comment, as well, indicates we would likely not be able to understand the language in his explanation, either.
Mark

Donb
December 25, 2014 1:30 pm

EXPLANATION
Alan McIntire,
I don’t follow exactly what you did above, but HERE IS A CALCULATION FOR THE EARTH’S ENERGY BALANCE using temperature units.
The rate of energy radiated by an object (e.g. the Earth) equals q*T^4, where T is temperature and q is the Stefan-Boltzman constant = 5.67 * 10^-8 (units W/m^2 per K^-4)
Solar radiation heats the Earth as S*(1-a)/4, where S is the solar constant (~1365 W/m^2) and a is Earth’s albedo, variable but around 0.3. We divide by 4 to convert from the plane geometry of the Sun impinging on the Earth to the spherical Earth’s surface area (correcting for day/night and the angle of the Sun’s rays striking Earth’ surface).
Because the energy the Earth receives is in equilibrium with the energy lost by radiation, we set these two relations equal to each other.
q*T^4 = S*(1-a)/4
If we assume the Earth acted as a black body and had no atmosphere or albedo (a=0) and solve for T, this would give the Earth’s effective black-body temperature. (This is an artificial temperature, because the Earth has an atmosphere, an albedo, and surface materials that do not radiate like a black body, but at a lower emissivity. More on that below.)
Solving this equation for T gives 278 K.
If we assume the Earth has an atmosphere with a=0.3, but otherwise behaves like a black-body, solving for T gives 255 K. This assumption is akin the actual Earth condition, in that the Earth has an atmosphere and does reflect about 30% of incoming solar radiation.
The actual average (global) temperature of Earth’s surface is about 288 K. Comparing this temperature to the two “black-body” analog temperatures above indicates that a greenhouse effect has raised the global temperature by either 288-255 =33 K (for a=0.3), or by 278-288 = 10 K (for a=0).
The concept of emissivity of a body is how effectively a body radiates heat compared to a black-body, defined as having emissivity (e) equal 1.0. The average of Earth’s surface has an emissivity of ~0.96.
Considering that the Earth does have an albedo (a=0.3), but surface materials that radiate only 96% as efficiently (e=0.96) as a black body, that Earth surface would have to rise in temperature above that of a black-body by a modest amount (4%*255K =10K), until energy equilibrium was reached.
The difference between the Earth’s measured surface temperature (~288K) and Earth’s black-body temperature (however one wishes to define it above –255K, 265K, or 278K), is the greenhouse effect. The most reasonable greenhouse temperature rise is probably 288-265=23C, as that calculation represents the actual Earth albedo and the emissivity of actual Earth surface materials. But under all reasonable scenarios, the actual temperature is higher than it would be without a greenhouse effect produced in the atmosphere.
However, you will note the sensitivity such a calculation has on the value of albedo, a. A one percent change in a is worth some 3.4 watts in TOP solar insolation, equivalent to about a degree-C.
Exactly what produces that greenhouse effect is another issue.

bob boder
December 25, 2014 4:57 pm

The ocean

Alan McIntire