The most recent Watts Up With That post is a guest post by Dr William Happer and is about Numeracy in climate discussions – how long will it take to get a 6oC rise in temperature?. This is supposedly based on a claim – made by Joe Romm – that the data is consistent with a 6oC increase in global surface temperatures by 2050. I don’t know if anyone has actually made this claim and – to me – this does seems a bit extreme. This has already been discussed over at HotWhopper but I thought I would add my own 2 cents worth.
Anyway, the post considers how the temperature change, ΔT, depends on CO2 concentrations, N, and on the climate sensitivity, ΔT2. Climate sensitivity is the change in temperature given a doubling of CO2. Given that our current CO2 levels are about 400 ppm, we can write
ΔT = ΔT2/ln2 eN/400.
This can be rewritten to show what concentration would be required in order for a change in temperature of ΔT :
N = 400 x 2ΔT/ΔT2.
The post then goes on to claim that climate sensitivity is probably about 1o C and hence a 6oC rise in temperatures would require a CO2 concentration of 25600 ppm. Well, according to Skeptical Science climate sensitivity is probably between 2 and 3oC. Also, as I discussed in an yesterdays’s post, WUWT has had a couple of posts recently discussing work that suggests that climate sensitivity is between 1.5 and 2oC. So there seems to be no evidence, at this stage, to support a climate sensitivity of 1oC. What happens if we consider values that are more consistent with current studies? This is shown in the table below. As you can see, there is quite a strong dependence and for climate sensitivities that are more consistent with current studies, the required CO2 concentration is between 1600 and 3200 ppm, much lower than that suggested by William Happer.
William Happer than goes on to say that CO2 concentrations are rising linearly and so to reach 25600 ppm would take 12800 years, hence we have nothing to be concerned about. Is there any validity to this claim? I downloaded the CO2 measurements for Mauna Loa from the Earth Systems Research Laboratory site. I plotted these and then tried to determine, by eye, a best-fit function. This is shown below and the best fit that I could see is an exponential function of the form
N = No e1.5 (N – No)/No .
I’ve also included (dashed-dot line) the linear increase (since 1958) of 2 ppm per year suggested by William Happer. This doesn’t appear to be a particularly good fit at all.
If we extend the exponential fit into the future we get what is shown in the figure below.