The answer may surprise you
Note: This essay is a result of an email discussion this morning, I asked Dr. Happer to condense and complete that discussion for the benefit of WUWT readers. This is one of the most enlightening calculations I’ve seen in awhile, and it is worth your time to understand it because it speaks clearly to debunk many of the claims of temperature rise in the next 100 years made by activists, such as the 6c by 2050 Joe Romm claims, when parroting Fatih Birol in Reuters:
“When I look at this data, the trend is perfectly in line with a temperature increase of 6 degrees Celsius (by 2050), which would have devastating consequences for the planet,” Fatih Birol, IEA’s chief economist told Reuters.
Graph source: IEA.org scenarios and projections
– Anthony
Guest post by Dr. William Happer
For any rational discussion of the effects of CO2 on climate, numbers are important. An average temperature increase of 1 C will be a benefit to the planet, as every past warming has been in human history. And the added CO2 will certainly increase agricultural yields substantially and make crops more resistant to drought. But in articles like “Scant Gains Made on CO2 Emissions, Energy Agency Says” by Sarah Kent in the Wall Street Journal on April 18, 2013, we see a graph with a 6 C temperature rise by 2050 – if we don’t reduce “carbon intensity.” Indeed, a 6 C temperature rise may well be cause for concern. But anyone with a little background in mathematics and physics should be able to understand how ridiculous a number like 6 C is.
The temperature change, ∆T , from the mean temperature of the present (the year 2013), if the concentration N of CO2 is not equal to the present value, N = 400 ppm, is given by the simple equation
Here ∆T2 is the temperature rise that would be produced by doubling the CO2 concentration from its present value, and ln x denotes the natural logarithm of the number x.
The proportionality of the temperature increment ∆T to ln N is widely accepted. But few know that this is a bit of a “miracle.” The logarithmic law, Eq. (1) comes from the odd fact that the average absorption cross section of infrared light by CO2 molecules decreasesvery nearly exponentially with the detuning of the infrared frequency from the 667 cm−1 center frequency of the absorption band. More details can be found in a nice recent paper by Wilson and Gea-Banacloche, Am. J. Phys. 80 306 (2012). Eq. (1) exaggerates the warming from more CO2 because it does not account of the overlapping absorption bands of water vapor and ozone, but we will use it for a “worst case” analysis.
Recalling the identity for natural logarithms,
, we write Eq. (1) as
The only solution of the equation ln x = ln y is x = y, so (2) implies that
Recent IPCC reports claim that the most probable value of the temperature rise for doubling is ∆T2 = 3 C. Substituting this value and a warming of ∆T = 6 C into Eq. (3) we find
But the rate of increase of CO2 has been pretty close to 2 ppm/year, which implies that by the year 2050 the CO2 concentration will be larger by about (50−13) years×2 ppm/ year = 74 ppm to give a total concentration of N = 474 ppm, much less than the 1600 ppm needed.
The most obvious explanation for the striking failure of most climate models to account for the pause in warming over the past decade is that the value of ∆T2 is much smaller than the IPCC value. In fact, the basic physics of the CO2 molecule makes it hard to justify a number much larger than ∆T2 = 1 C – with no feedbacks. The number 3 C comes from various positive feedback mechanisms from water vapor and clouds that were invented to make the effects of more CO2 look more frightening. But observations suggest that the feedbacks are small and may even be negative. With a more plausible value, ∆T2 = 1 C , in Eq. (3) we find that the CO2 concentration needed to raise the temperature by ∆T = 6 C is
This amount of CO2 would be more than a warming hazard. It would be a health hazard. The US upper limit for long term exposure for people in submarines or space craft is about 5000 ppm CO2 (at atmospheric pressure). To order of magnitude, it would take a time
t = 25, 600 ppm/(2 ppm/year) = 12,800 years.
(6)
to get 6 C warming, even if we had enough fossil fuel to release this much CO2.
A 6 C warming from CO2 emissions by 2050 is absurd. It is a religious slogan, a sort of “Deus vult” of the crusade to demonize CO2, but it is not science.
=============================================================
Dr. William Happer is the Cyrus Fogg Brackett Professor of Physics at Princeton University, and a long-term member of the JASON advisory group,where he pioneered the development of adaptive optics. From 1991-93, Happer served as director of the Department of Energy’s Office of Science.
UPDATE: Dr. Happer has contacted the author of the paper cited, and he has graciously setup a free link to it: http://comp.uark.edu/~jgeabana/gw.html
![dec11-eleven-degrees2[1]](http://wattsupwiththat.files.wordpress.com/2013/04/dec11-eleven-degrees21.jpg?resize=500%2C305&quality=83)
Richard111 says:
April 19, 2013 at 9:34 am
Thank you for the link. Lot of useful information there. I have posted the link on another forum.
Sadly I failed to find any information on the ‘heat trapping’ capability of CO2 and why this is a problem if the current levels of CO2 double.
Maybe the following link and the next pages from Clive Best is of some help:
http://clivebest.com/blog/?p=1169
Also puzzled as to why atom bomb generated C-14 has a half life of 5 years but natural C-14 has a half life of 6,000 years which is useful for carbon dating.
Different half lives: the 5 year calculated from the bomb spike is about how fast 14C (natural or not) disappears out of the atmosphere, but is not destroyed: it simply is gone into other reservoirs (oceans and plants) and/or replaced by stable carbon (12C and 13C) from the other reservoirs. The 6,000 years is for the real destruction of 14C when it radiates a beta ray (an electron) and converts into 14N. That is the base for the carbon dating.
In respnse to joeld, folkerts: just do the obvious arithmetic: CO2 levels are rising at a current rate of about 70% per hundred years. Assuming a similar rate in the future is an aggressive assumption, and gets you to 672ppm from todays 395 in 100 years. That’s 2.5X pre industrial and 1.7x today, or 1.32 doublings/0.76 doublings. The temperature rise with sensitivity of 3 degrees is 4 degrees from pre-indstrial, or 2.3 degrees from today. A six degree rise from today is just nonsense, and six degrees from pre-industrial is highly tendentious.
Face tacts – six degrees is just a scare story!
Tim Clark says:
Yes, the confounding effects of climate change do indeed play a potentially important role. However, your whole argument does not even address my point. The question is not whether sequestration increases as the concentration of CO2 in the atmosphere increases. Rather, it is whether sequestration increases linearly…i.e., whether it continues to increase at the same rate or whether it eventually starts to slow down. Since there are likely rate-limiting factors affecting sequestration other than atmospheric concentration of CO2, such a slow-down seems likely.
Richard111:
I write to try to help you and other possibly interested WUWT readers.
You may not be aware that Ferdinand Engelbeen and I have a long-standing disagreement which has been raging for over a decade. This disagreement is that I don’t know the cause of the recent rise in atmospheric CO2 concentration while he is certain the rise has an anthropogenic cause.
Hence, I think you can trust my opinion when I say that Ferdinand has an exceptional knowledge of CO2 issues. If you – or other WUWT readers -want info. on CO2 (e.g. 14C residence time, e-folding time and half-life) then I would be very, very surprised if you cannot find everything you want on his excellent web site.
Richard
richardscourtney says:
April 19, 2013 at 10:58 am
Richard, are you really so obtuse?
Of course the trend in CO2 is the difference over a full seasonal cycle, as I said before, but the seasonal cycle doesn’t cause the trend, doesn’t influence the trend and simply has nothing to do with the trend, whatever the real cause of the trend is.
With your type of reasoning, you would say that the waves and tides are the cause of any trends in sealevel.
Any change in CO2 levels should be calculated from calendar year averages or 12 month moving averages to remove the seasonal cycle. That is the only way to see the real trend not disturbed by a seasonal cycle which is of not the slightest interest in this case, it is only noise.
BTW, the measurements at the South Pole started before Mauna Loa, but as they miss a few years of continuous measurements (but still had regular flask samples), the Mauna Loa series are mostly used as longest continuous series.
Ferdinand Engelbeen says:
April 19, 2013 at 12:30 pm
Ah! Understand! The 5 years is time in the atmosphere and NOT the radioactive decay rate.
Many thanks. Off to read Clive Best.
richardscourtney says:
April 19, 2013 at 12:53 pm
Thank you Richard. I have been aware of the contretemps for some years and read with interest. My position is I believe CO2 has no effect on the climate whatsoever. 🙂
Do you know snow is reported in Soweto, South Africa, weeks before it normally appears?
http://snowreport.co.za/
Below are the 10 year slopes of the annual Mauna Loa CO2 concentrations (hopefully the formatting will not get too messed up). So the first data point tells us that from 1959-1968, the slope was 0.75 ppm/year. For 2003-2012, the rate was up to 2.00 ppm/year.
The slope of the slope (ie the acceleration) is 0.025 ppm/yr/yr. In other words, in the 44 years from 1968-2012, the slope increased by at total of ~ 1.1 ppm/yr (From ~ 0.9 ppm/yr to ~ 2.0 ppm/yr). This linear fit has R^sq = 87%, so it explains most of the change in the slope. p=0.000, so this increase is most definitely statistically significant.
Of course, this does not allow any great certainty about the future — there are so many variables in energy use and energy efficiency. But it is very clear that the PAST trend is for CO2 to increase at an increasing rate (which should have been obvious from an “eyeball fit” that shows that the raw data curve up in general). This suggests that projecting an increase above a linear 2% increase in the CO2 concentration is not at all unreasonable. Indeed, having the increase maintain a mere 2% rate of change would require a distinct departure from past trends.
************************************
YEAR SLOPE
1968 0.75
1969 0.81
1970 0.88
1971 0.92
1972 0.98
1973 1.09
1974 1.13
1975 1.13
1976 1.13
1977 1.15
1978 1.17
1979 1.23
1980 1.31
1981 1.36
1982 1.39
1983 1.48
1984 1.53
1985 1.55
1986 1.52
1987 1.51
1988 1.56
1989 1.59
1990 1.62
1991 1.62
1992 1.56
1993 1.47
1994 1.41
1995 1.38
1996 1.35
1997 1.33
1998 1.44
1999 1.57
2000 1.66
2001 1.73
2002 1.79
2003 1.83
2004 1.85
2005 1.90
2006 1.95
2007 1.95
2008 2.00
2009 2.03
2010 2.05
2011 2.02
2012 2.00
“joeldshore says:
April 19, 2013 at 12:47 pm ”
Yes, of course. But the only RLS I know of at this time is the upper concentration cap where increasing [CO2] doesn’t induce heightened plant growth. Which, of course, is >1000 ppm.
Richard,
For your convenience, I have plotted the full MLO data with 10-year linear trends. They show an increasing slope in trend, except for 1990-2000 and as Werner Brozek showed not increasing over the past years. Thus while Joel was anyway right for the first 40 years, we indeed don’t know what the future will bring, if the economical crisis is over and developing countries catch up with the West (if the West still has some industry left…):
http://preview.tinyurl.com/chdslc8
BTW, thanks for your kind words about my knowledge, but sometimes you make it difficult to maintain my normal calmness…
Ferdinand Engelbeen:
I am responding to your post at April 19, 2013 at 1:00 pm.
I am not “obtuse”. I am realistic.
You say
And you accuse ME of being obtuse!? Unbelievable!
The “difference over a full seasonal cycle” is the residual of the seasonal variation. The trend is the imbalance between the rise and fall of atmospheric CO2 concentration in each year. That rise and fall is an order of magnitude more than its residual each year.
Furthermore, the dynamics of the rise and fall indicate that the system is NOT saturated such that some of the total (natural and anthropogenic) CO2 emission cannot be sequestered by the natural sequestration processes. The dynamics indicate that the natural sequestration processes can easily sequester ALL of the total emission.
Hence, the only question of interest is why the natural sequestration processes do not sequester all the emission when the clear evidence is that they can. And this failure to sequester all the emissions is seen as the residual of the seasonal variation which is the annual rise.
In this circumstance, ignoring the seasonal variation is to ignore the only truly quantified data we have which pertains to the cause of the trend in atmospheric CO2 concentration since 1958.
But you assert the seasonal variation “has nothing to do with the trend”. Frankly, for the reasons I have here stated, that assertion is plain daft.
And you are being ridiculous when you say to me
You are comparing apples to cricket bats.
“Should be”?
Any change “should” exclude the only information we have on causality?
Ferdinand, that kind of assertion has no place in science.
The seasonal cycle is NOT “noise”.
Imbalance in the seasonal cycle IS the annual rise in atmospheric CO2.
It can only be a result of a changing equilibrium state of the carbon cycle. And that change can be modelled in many ways which each leads to a different forecast of future atmospheric CO2 concentration.
There is no way to determine which – if any – of the possible forecasts of future atmospheric CO2 concentration is correct.
And that returns us to the subject of this thread.
You and Joel Shore each process the data – e.g. by smoothing – then fit a curve to the processed data. But many curves can be chosen and there is no way to know which – if any – is correct. However, within the seasonal variation a linear fit is as good as any other.
Hence, Happer is correct to use linear extrapolation because that fit is the only extrapolation which does not represent a prejudice concerning how atmospheric CO2 concentration change is likely to vary in future.
Richard
PS Thanks for pointing out about the Antarctic data but – as I am sure you were aware – I knew that, and I cited MLO data because it is the longest continuous data set. However, your point may be useful information for onlookers.
Ferdinand Engelbeen:
Thanks for your post at April 19, 2013 at 1:42 pm.
Unfortunately, your link does not give me access to the graph, but this is not a problem because I know what it would look like. Indeed, you say
Yes. And that demonstrates my point which I have repeatedly stated; i.e.
And I am ignoring your assertions concerning anthropogenic causality because they are not pertinent to this thread.
Richard
While I don’t doubt the way the amount of IR absorption by CO2 increases due to spectral detuning (I’ll accept the quantum mechanics expert’s opinions on that), for the life of me I can’t see why that should carry over to the average surface Temperature of the whole planet.
So I for one do not accept the supposed logarithmic relationship.
Besides, I know what a logarithm is, and if going from 280 ppm to 560 ppm of CO2 is a “doubling”, so is going from 1 ppm to 2 ppm, or one molecule of CO2 in the whole atmosphere to two molecules of CO2 in the whole atmosphere.
So maybe the theoretical relationship, can at best be claimed to be non-linear.
Unfortunately, we have no experimental data to show that logarithmic is any better than linear is.
We DO know that CO2 and Temperature do NOT even go in the same direction (always) simultaneously. And no time offset, will make them go in the same direction (always).
So something else must override any effect CO2 has.
So I agree with Prof Happer, that the 6 deg C claim is silly. I just don’t think one needs to invoke, ANY kind of CO2-Temp relationship. I can directly observe what cloud variations do to Temperature.
“””””…..Mark Bofill says:
April 19, 2013 at 9:05 am
geran says:
April 19, 2013 at 7:46 am
…
http://en.wikipedia.org/wiki/Solar_radiation
And a relevant pasting from the iink:
“Sunlight in space at the top of Earth’s atmosphere at a power of 1366 watts/m2 is composed (by total energy) of about 50% infrared light, 40% visible light, and 10% ultraviolet light.[3] At ground level this decreases to about 1120–1000 watts/m2, …
——
That’s odd. No problem with TOA 1366 W/m^2, but then I’ve always read that you have to adjust for surface area of a sphere as opposed to a disk (disk RPI, sphere 4RPI, so divide by 4), and then adjust again for albedo (1-0.3), which gives about 240 W/m^2 at the surface. Is this wrong?…..”””””
Of course it is wrong.
TSI is 1362 W/m^2 (recent NASA / NOAA assertion ). And with atmospheric scattering and absorption (clear sky) it comes down to something around 1,000 W/m^2 at the surface. If you go out in your back yard on a clear sky day, say anywhere in the USA lower 49 (sans Alaska), with a calibrated radiometer that can measure surface Irradance, and point it roughly at the sun, that is the number you will likely read on your radiometer.
If you EVER go outside in the lower 49 between say 10 AM and 2 PM on a clear sky cloudless day, and observe a surface irradiance of 240 W/m^2, and you are not in the shadow of anything overhead; then I would say, you should put your head down between your knees and kiss yourself good bye. Well I suppose it is possible that you are pointing your radiometer at a near full moon, instead of the sun. In that case, you are too stupid to understand the problem.
TSI is 1362 W/m^2, not 240 w/m^2, or even 341 W/m^2
richardscourtney says:
April 19, 2013 at 1:52 pm
Richard, we may go again over our longstanding discussion, to not much avail, except for entertaining (or boring) others here.
In summary for new readers:
– according to Richard, the seasonal cycle does show that the earth can accept a lot of CO2 in short term, thus also the (relative) tiny amounts that humans emit each year. Thus it is not necessary that humans are the cause of the increase. It may be humans. but there may be other causes.
– according to me, the seasonal cycle indeed does show what fast processes can do with CO2, as result of temperature changes. The flows involved are huge (about 90 GtC exchange with the oceans, 60 GtC with the biosphere), but the effect is very limited: about 5 ppmv (10 GtC) global change in CO2 for a global change of 1°C over a year, where oceans vs. vegetation and NH vs. SH work in countercurrent for temperature changes.
– the seasonal change of 5 ppmv/°C is caused by fast processes: leaves growth an decay and ocean surface warming and cooling. Both are fast but limited in capacity. Thus it is not obvious that the extra release of CO2 by humans is captured by oceans or trees, as these processes are mainly temperature dependent, if there is no extra pressure in the atmosphere to do that work.
– any extra CO2 above the old time equilibrium will cause an extra uptake by plants and oceans. But that is not a doubling for a doubling of CO2 in the atmosphere. Currently the extra uptake is about 2 ppmv/year while the extra CO2 is already 100 ppmv above the temperature controlled equilibrium.
– humans currently emit about 4 ppmv/year CO2. That is about twice the observed increase and about twice the year by year variation in increase rate. Thus nature is a net sink over the past 50+ years from about 1 ppmv/year in the 1960’s to 2 ppmv/year in the latest years, not a net source.
– while the seasonal fluxes completely dwarf the human input, the latter is a one-way addition and the seasonal fluxes near completely compensate each other with slighlty more sinks than sources.
Thus in my informed opinion, supported by all available data, humans are the sole cause of the increase in the atmosphere, except for a small contribution of the temperature increase since the LIA (in the order of 8 ppmv/°C).
See further for more detailed arguments:
http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html#The_mass_balance
The effect of the increase of CO2 on temperature is a complete different topic and is the main topic of what Dr. Happer wrote…
As a corollary to my previous post (above), if you have learned from your life experience, that you can, on average, jump a horizontal distance, given a running start; 0f say 4 metres, or 12 feet, I would strongly discourage you from always trying to jump across every gap you come to, given the assurance that those gaps, on average, are only 3.5 metres or 11 feet wide.
But on average, you ought to make it across.
Ferdinand:
If you agree then I am willing to let your comment at April 19, 2013 at 2:46 pm be the ‘final word’ on this thread concerning our discussion of Happer’s use of linear extrapolation of atmospheric CO2 concentration.
I think our different views are clear for onlookers to assess, and continued discussion is likely to only be repetition.
Richard
richard telford says: April 19, 2013 at 1:32 am
“………Without strong intervention, it is much more likely that the increase in CO2 concentrations per year will continue to rise (tokyoboy April 19, 2013 at 12:42 am – don’t just eyeball the data, calculate the slope – it is superlinear).”
No, it’s not eyeballing. Please place your ruler on the 1992-2012 portion of the graph:
http://junksciencearchive.com/MSU_Temps/MaunaLoaCO2.png
“Richard111 says:
April 19, 2013 at 1:50 am
You might find this helpful.
http://www.ilovemycarbondioxide.com/pdf/Understanding_the_Atmosphere_Effect.pdf
I sure did. Thank you Richard, that is most insightful on a detailed level. It makes the notion of a major controlling influence of CO2 on temperature even more preposterous than I thought it was. That’s saying a lot.
Thanks again.
Nicely done. But while you prove that 6 degree rise is ridiculous you fail to give a reason why there is a standstill at all. It is not just a slowing down of warming but a complete standstill that cannot be explained by any formula that contains carbon dioxide in it. And empirical observations show that the current standstill is not the only one. Satellite temperature data indicate that since 1979 there have been two temperature standstills. The first one was from 1979 to early 1997. It overlapped with an active ENSO oscillation. As I described in my book in 2010, there were five El Nino peaks during that period but global temperature remained constant for 18 years. But in standard temperature graphs that standstill was wiped out and a fake warming called “late twentieth century warming” substituted for it. I have been complaining about that, and lo and behold, all three standard temperature sources (GISSTEMP, HadCRUT & NCDC) changed their eighties and nineties last fall to eliminate that fake warming! That nice red triangle that NOAA shows should now have a horizontal 18 year step carved into it. The second standstill started at the beginning of the 21st century, according to the satellites, and is still going strong. This leaves only a very short period of the satellite era for any warming at all. It includes the super El Nino of 1998 which brought so much warm water across the ocean that it created a step warming. In four years, global temperature rose by a third of a degree Celsius and then stopped. There has not been any warming since. This, and not any imaginary greenhouse warming, is responsible for the very warm first decade of our century. Hansen places nine out of ten warmest years into this period and later, implying that global warming did that. That is complete nonsense because it is quite impossible for any step warming to be caused by the greenhouse effect. Those temperatures are high simply because they sit on top of that step warming of oceanic origin. He also cheats when he uses the 2010 El Nino peak temperature for defining global temperature. The mean temperature of an ENSO oscillation is the average temperature of an El Nino peak and its adjacent La Nina valley. The La Nina of 2008 is the one nearest to the El Nino of 2010 and their average lines up perfectly with the standstill temperature of our century. That La Nina, by the way, is the one that confounded Trenberth in that well-known Climategate email. There was no other warming during the entire satellite era that began in 1979. This of course is something entirely impossible to explain with any kind of carbon dioxide warming. But Ferenc Miskolczi can easily explain it. Using NOAA weather balloon database that goes back to 1948 he studied the absorption of infrared radiation by the atmosphere and discovered that absorption had been constant for 61 years. At the same time carbon dioxide went up by 21.6 percent. This substantial addition of carbon dioxide had no effect whatsoever on the absorption of IR by the atmosphere. And no absorption means no greenhouse effect, case closed. That is why there is a standstill now and why there was one in the eighties and nineties, and also before. With this track record it becomes extremely likely that there has been no greenhouse warming at all any time in the past and that any warming we do know of has a natural cause. It is also clear that all predictions of warming based on use of the greenhouse theory have been wrong. It follows that any laws and regulations passed as a result of such false predictions were passed under false premises and have to be nullified.
Michael D Smith says:
You have unfortunately just revealed the fact that you are unable to distinguish real science from scientific-sounding gibberish.
The Romm piece specifically denies that 6C by 2050 was ever claimed. Why is so much effort being put into debunking a typo?
davidmhoffer says:
April 19, 2013 at 11:57 am
Yeah – looks like he ran away – and after accusing you of doing so. Whoda thunkit.
tjfolkerts says:
April 19, 2013 at 1:26 pm
The slope of the slope (ie the acceleration) is 0.025 ppm/yr/yr.
——————————————————-
But you didn’t actually plug those values in and see the effect, did you? As Ret pointed out your acceleration works out to a 70% increase per century. The only way to achieve even the most generous 5.1C rise by 2100 that Joel was claiming (Romm is all over the map and consistently references 6C so the 5.1C is, well, not his claim) is to assume a sensitivity of 6C per doubling or a magic additional increase from CH4, CFC’s, and, presumably, unicorn farts.
The problem with that 6C assumption is that the temp increase to date from pre-industrial levels is consistent with a far lower number than that. 3C is really the outside upper limit based on data we already have. The fact that Joel wants to believe that the carbon sinks are going to saturate real soon now makes me suspect he doesn’t truck much with inductive reasoning. Perhaps he also frets about whether the sun will rise every morning. We’ve heard these concerns about saturating sinks for years now and we’ve seen absolutely no evidence of it. Until he can provide something more compelling than an appeal to authority I remain confident that the sun will still rise in the morning and plant food will continue to be produced at an ever slowly increasing rate for a little while longer.
(sarc) I have this sudden desire to spout some scientific sounding gibberish. I can’t help it. Really. (/sarc)
How does a CO2 molecule, somewhere up in the middle troposphere, KNOW that it is only allowed to absorb upwelling radiation photons from the surface and must ignore all the other photons coming at it from all around in the atmosphere?
Well, it can’t know. It will absorb a suitable photon when it is good and ready, the direction it arrived from is irrelevant. It will then emit a photon in any direction. Again when it is good and ready.
Thus the temperature profile up the atmosphere, set by gravity, will direct the flow of photons in the 15 micron band up through the atmosphere. The flow rate of that specific IR band has been slowed somewhat, but there has been minimal loss of the ‘bulk’ of photons, not much heat transfer into the atmosphere. And back down on the surface the ‘back radiation’ from the lower CO2 molecules has reduced the surface emission in 15 micron band, reduced not stopped, which again is not a heating effect. So the surface at 15C, radiating a total of 390W/m^2 had some 8% of the IR reduced by some fraction. If that fraction went into heating the air, so what? The air loses temperature at a much, much higher rate. See here: http://www.milfordweather.org.uk/atmospheric.php
My local air temperature dropped over 9 degrees in just 12 hours. Calculate that loss of energy in a metre square column of air and then see how energy was replaced by 4% of 390W/m^2. No contest.
End of gibberish,