# Calculating the greenhouse effect

• “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.

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