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.

Table showing how the required carbon dioxide concentration for 6 degrees rise in temperature varies with climate sensitivity.

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.

Carbon dioxide concentrations from Mauna Loa together with a linear increase of 2ppm per year (dash-dot line) and an exponential fit (dashed line).

If we extend the exponential fit into the future we get what is shown in the figure below.

An estimate of future carbon dioxide concentrations assuming an exponential fit to the Mauna Loa measurements.

Assuming an exponential fit of the form shown above, we reach CO2 levels in excess of 3000 ppm in just over 200 years. I accept that this is relatively simple calculation and that the fit to the Mauna Loa data has been done by eye, rather than through some proper fitting process. I also accept that this ignores many other processes (increases in methane levels, water vapour, changes in albedo), but these are also ignored by William Happer. Basically, however, using climate sensitivities consistent with a majority of existing studies suggests that a rise of 6oC would require CO2 levels of 3000 to 6000 ppm. Fitting to existing CO2 measurements from Mauna Loa suggests that CO2 levels are rising exponentially and that levels of 3000 to 6000 ppm could be reached within the next few hundred years. Again, this is a basic projection that ignores many possible aspects that could influence future warming. Unlike William Happer’s work, however, it is consistent with existing studies of climate sensitivity and is based on a fit to actual CO2 measurements. William Happer appears to have chosen, without much justification, a very low climate sensitivity and then chosen to assume that CO2 levels will rise linearly with time. Neither of these assumptions appears to be supported by existing scientific evidence so, although his calculations appear correct, his assumptions and conclusions appear completely flawed.

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