Calculating the greenhouse effect
In another forum (on a planet far, far away), the following quote recently came up:
{And get's regurgitated ad nauseam to this day, thus the need to repost this authoritative and most informative article.}
….the combined effect of these greenhouse gases is to warm Earth’s atmosphere by about 33 ºC, from a chilly -18 ºC in their absence to a pleasant +15 ºC in their presence. 95% (31.35 ºC) of this warming is produced by water vapour, which is far and away the most important greenhouse gas. The other trace gases contribute 5% (1.65 ºC) of the greenhouse warming, amongst which carbon dioxide corresponds to 3.65% (1.19 ºC). The human-caused contribution corresponds to about 3% of the total carbon dioxide in the present atmosphere, the great majority of which is derived from natural sources. Therefore, the probable effect of human-injected carbon dioxide is a miniscule 0.12% of the greenhouse warming, that is a temperature rise of 0.036 ºC. Put another way, 99.88% of the greenhouse effect has nothing to do with carbon dioxide emissions from human activity8.
We’ve discussed the magnitude of the greenhouse effect before, but it might be helpful to step through this ‘back-of-the-agenda’ calculation and see what the numbers really give. (Deltoid has also had a go at some of these mis-statements).
The quote comes from a lecture by an Australian climate ‘contrarian’ and frequent contributor to the southern hemisphere op-ed pages. Where did he get this from? One might assume that reference ‘8’ was a scientific text, but one would assume wrong. It was in fact our old friend at Fox News, who may in turn have picked up his (junk)science from here. It is not clear whether this is the original source, but it’s close enough.
So, starting at the top:
- “33 ºC” is the difference between the mean surface air temperature of the planet and the blackbody radiating temperature (i.e. the temperature a blackbody would need to radiate at to be in equilibrium with the incoming solar radiation given an albedo of about 0.3). So far so good. While that is one way to assess the strength of the basic greenhouse effect, another one is measure the amount of long wave radiation from the surface that is absorbed in the atmosphere (by greenhouse gases (incl. water vapour), clouds, aerosols, etc.). That is currently about 150 W/m2 and would be zero with no greenhouse effect at all.
- “95% of this warming is caused by water vapour”. This is sourced to a couple of chaps who may have worked for Accu-Weather, but a) is misquoted – their ’90-95%’ is for both water vapour and clouds, and b) just wrong and c) irrelevant anyway.
Dealing with b) first, if you remove all water vapour and clouds you still absorb about 34% of the long wave radiation, and conversely, if you only have water vapour and clouds you absorb 85% (calculations here). Thus the effect of water vapour and clouds is between 66 and 85% – the range being due to the spectral overlaps with the other absorbers. These calculations were done with the GISS GCM radiation code, which matches line-by-line codes to about 10% – but the numbers are very similar to Ramanathan and Coakley (1978), and so probably aren’t too far off what you would get with any decent radiation code. I’ll get to ‘c)’ below…. - “The other trace gases contribute 5% … amongst which carbon dioxide corresponds to 3.65%”. That is just 100 minus 95% of course, but really it should be 15 to 34% – of which CO2 on its own is between 9 and 26% (op cit). If you were to naively estimate the total temperature contribution of the CO2 it would be between 3 and 9 ºC – but see below.
- “The human-caused contribution corresponds to about 3% of the total carbon dioxide in the present atmosphere,”. This one is blatantly false and is erroneously credited to the US Dept. of Energy in the original source (their Table 1)! The ‘3%’ number actually comes from comparing the human emissions with the gross emissions from natural sources while neglecting to consider the large natural sink. Because of the rapid cycling between the biosphere, the atmosphere and the upper ocean, that is an irrelevant comparison – kind of like comparing the interest on your bank account and your salary and expecting to be able to say something about your savings without thinking about your spending. The correct statement is that CO2 is around 30% higher than it was in the pre-industrial period, and all of that rise is due to human emissions (fossil fuel use and deforestation principally).
- “Therefore, the probable effect of human-injected carbon dioxide is a miniscule 0.12% of the greenhouse warming”. That’s just 0.03*0.0365 of course – but even that is calculated wrong (it should be 0.11% by my calculator). But from our numbers, it would be between 3 and 8%.
- “a temperature rise of 0.036 ºC”. More like 1-2.6 ºC actually, but although this gives numbers that are in the ballpark of the IPCC estimates (0.6 to 1.7 ºC warming for an increase of 30% in CO2 at equilibirum) this is not a sensible way to calculate climate sensitivty.
Why do I claim this is an irrelevant and not very sensible calculation? Firstly, it assumes linearity – all of the gases contributing according to their effects today when it is obvious that overlaps and saturation effects are large and important, and more importantly, it ignores feedbacks. The calculation above gives the impression that what you are calculating is the change of temperature that would result if you remove all the CO2. But since water vapour concentration is a feedback not a forcing, it can’t be assumed to remain constant as the planet cools. Water vapour does in fact change (roughly keeping relative humidity, as opposed to specific humidity, constant) and this has been shown in the real world as a function of volcanic cooling (Soden et al, 2002) and for longer term trends (Soden et al, 2005, discussed here), and is well reproduced in climate models.
What then is an appropriate calculation? Well, it’s simply the estimate of climate sensitivity for the present climate – how much would you expect the planet to warm if you doubled CO2? We’ve discussed this numerous times before, and in my opinion the best answer so far comes from looking at the difference between the last glacial period and the modern era – this gives a number around 3 +/- 1 ºC at doubling.
For the 30% rise in CO2 there has been so far, that would imply that would represent around 3% of the natural greenhouse effect – a good order of magnitude bigger than that suggested above. Of course, this is at equilibrium and not applicable to a transient change. If one takes into account the human-induced changes in the other GHGs (CH4, N2O, CFCs), you’d get something like double that. Given that even a 5 or 6 ºC cooling was associated with the huge ice sheets 20,000 years ago, and that 33 ºC cooling would reduce our planet to a near-snowball-like state, a potential increase of 5 to 6% of the natural greenhouse effect is not to be sniffed at… nor dismissed as irrelevent with highly misleading arithmetic.
One could make the point that my calculations are ‘just another web page’ no more and no less authoritative than the links above. In some sense that is correct (though I’d argue my sourcing is a little better!). But you will never find a peer-reviewed rebuttal of such a bizarre line of reasoning as we are dealing with here – basically because such a line of reasoning is highly unlikely to make it past peer-review itself. There are innumerable ‘proper’ references to estimates of the climate sensitivity though, and one should indeed hesitate to accept calculations like this example over the mass of peer reviewed studies.
- See more at: http://www.realclimate.org/index.php/archives/2006/01/calculating-the-greenhouse-effect/#sthash.Z8Mtowu4.dpuf
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