I include this graph for the general shape of the logarithmic curve. The absolute temperatures used are open to debate.
One of the points that should be better understood, and more widely known, in the climate debate, is the fact that the theoretical warming effect of any additional atmospheric CO2 becomes lower as the overall level of atmospheric CO2 increases. In mathematical terms, this is a logarithmic relationship. In vernacular parlance, it’s a “Law of Diminishing Returns”.
We can put it more simply – any doubling of the level of atmospheric CO2 has the same warming effect as any other doubling. Imagine a world with say only 200 parts per million (ppm) CO2, and we increase it to 400 ppm. That has the same warming effect (in terms of incremental temperature) as doubling from 400 ppm to 800 ppm. So the added CO2 between 400 and 800 ppm was only half as effective in warming terms as the CO2 we used to increase the level from 200 to 400.
If you draw a graph of warming against CO2 (see above), you get a curve that is steep to start with, but gradually gets flatter and flatter. It never gets totally flat (it is not, as we mathematicians like to say, asymptotic), but the gradient gets very low indeed. The more CO2 you have in the atmosphere, the less you need to worry about additional CO2.
This is not rocket science, and fortunately it is not in dispute, or not at least amongst those who know the first thing about the subject. It is one rare point of agreement between orthodox and sceptical climate scientists. For a (slightly) more technical description, see “The relationship between carbon dioxide and radiative forcing is logarithmic, and thus increased concentrations have a progressively smaller warming effect”.
While the logarithmic/diminishing-returns point is not in dispute, the actual effect of any doubling of CO2 is disputed, because it is subject to all kinds of messy real-world factors that cut across the perfect theoretical model. These include, notably, cloud cover, albedo, and consequent positive and negative feedbacks. The IPCC seems to think that the effect of a doubling is around 3 to 3½oC, while many sceptical climatologists would put it at 1o or less. But no one disputes that any doubling gives the same result, and that thus the warming effect of a given rise declines as the atmospheric CO2 level increases.
Sorry if I’ve laboured this point, but I hope now you’ll understand why I recently Tweeted: “Diminishing returns: Warmists fail to understand that the higher the level of atmospheric CO2, the less effect any additional CO2 will have”.
I wasn’t sure what response to expect, if any, but sure enough up popped the Warmist trolls, and their responses immediately proved my point — that they really did not know about diminishing returns, and they rushed to try to rubbish my Tweet. Here comes @john3ners “I suppose you’ll be coming up with evidence to support that claim?” You see — he didn’t know! Or David Tait; “And your qualifications are?”. Actually, David, a Cambridge Maths degree. But the speaker’s qualifications don’t make the statement right or wrong. The facts do that.
These same trolls are constantly accusing me of being ignorant and stupid and ignoring “the science”. Yet here their own ignorance stands revealed in all its breathtaking glory.
Or take Geoff Hickman @steppenjiff: “Quite right Rog — like when you’re already shot in the head with 3 bullets — a 4th has less impact than the 1st”. Again, his failure to understand is writ large. The state of being alive or dead is binary. You’re either one or the other. And any given shot in the head is quite likely to kill you. This is entirely inappropriate as a metaphor for radiative forcing, where the level of atmospheric CO2, the radiative forcing effect, and the mean global temperature are all infinitely variable, and are, moreover, linked by a well-understood logarithmic relationship.
So thank you to those guys, to John and David and Geoff, for rushing to prove the point that I made in my original Tweet – that these Warmists (and Warmist trolls) who claim the cloak of science, and vilify the sceptics, actually don’t know the first thing about it.
Another example — unrelated but on the same theme (and I apologise that despite some time on Google I haven’t been able to find the link) — a Guardian journalist was discussing the alarmist warnings that global temperatures could rise by 5oC by 2100, rather than the 2oC which some Warmists say is the safe limit. She (I think I recall that it was a she) had clearly been told to use both Fahrenheit and Centigrade. But she converted 2oC and 5oC as absolute temperatures, when of course she was talking about temperature increments. So she came out with 2oC as 35.6oF, and 5oC as 41oC. Correct as absolute temperatures, but nonsense as increments. She meant 3.6oF and 9oF respectively. Those who would like to be regarded as authorities on these issues need to take a little more care.