Watt about doing nothing?

The latest Watts Up With That (WUWT) post is a guest post by Ed Hoskins called CO₂ by the numbers: having the courage to do nothing. The assumptions used in the post are very poorly explained, so I’m not completely sure what Ed is getting at, but it seems like he is trying to suggest that the change in surface temperature due to CO₂ increasing from 400ppm to 800ppm will be so small that we really should just do nothing.

He includes the following table. The table shows the the amount of CO₂ emitted by various countries, the percentage of the total for each country, and the change in surface temperature – a low “skeptic” value and a “high” IPCC value.

CO₂ emissions by country and resulting change in surface temperature (credit : Ed Hoskins, WUWT).

Firstly, these numbers are all very odd as current understanding is that, in the absence of feedback, a doubling of CO₂ will produce something close to a 1^oC change in surface temperatures. This is normally expressed as the forcing depends on CO₂ concentrations through
ΔF = 5.35 ln(C/C_o),
which results in a change in surface temperature through
ΔT = λ ΔF,
where – in the absence of feedback – λ = 0.27 K/Wm^-2. What I think Ed may have done is to assume the the logarithmic dependence of ΔT on C is
ΔT = ln(C).
Firstly, this isn’t defined for C = 0 and it makes it seem that most of the change happens between 0 to 400ppm and virtually nothing for changes from 400 to 800ppm. Basically, this is just simply wrong. The temperature change does not depend logarithmically on C, it depends logarithmically on the ratio of C (i.e., C/C_o). The change in temperature in going from 200 to 400ppm is – in the absence of feedbacks – the same as going from 400 to 800ppm. Essentially, Ed isn’t even close to being right.

If you don’t believe me, you can actually see this for yourself. You can go and play with the MODTRAN code. This is an infrared radiation transfer code that allows you to vary – amongst other things – the CO₂ concentrations and vary the temperature offset of the surface. You can also change the type of atmosphere. If you run the model, it will output the spectrum seen by a sensor at 70km and the measured radiative flux. For example, for a 1976 U.S. Standard atmosphere with 200ppm of CO₂, the measured radiative flux is 261.405 Wm^-2. If you increase the CO₂ concentrations to 400ppm, the flux drops to 258.579 Wm^-2 (2.826 W m^-2 lower than that for 200 ppm). You might notice that this change is smaller than that predicted (3.7 Wm^-2) by the above equation. This is simply because in the MODTRAN code, I’m changing only the CO₂ concentration. The equation above also includes some associated changes due to methane, ozone, water vapour, etc. that increases the forcing from that due to CO₂ alone, to something slightly greater. You can also see what increase in surface temperature is required so as to get the same radiative flux with 400ppm of CO₂ as with 200ppm of CO₂. The answer, according to MODTRAN, is 0.85^oC.

Remember, that this is the change due only to a doubling of CO₂ from 200ppm to 400ppm. What if we consider going from 400ppm to 800ppm. If I increase the CO₂ concentration to 800ppm, the radiative flux at 70km is 255.753 Wm^-2, 2.826 Wm^-2 smaller than when CO₂ was at 400ppm. This is precisely the same as the change when CO₂ concentrations were increased from 200 to 400ppm. To get the same radiative flux when CO₂ is at 800ppm as when CO₂ is at 400ppm, I need to increase the surface temperature by 0.925^oC, similar to that required when CO₂ changed from 200 to 400ppm.

So, basically one can use a detailed radiative transfer model to show that the change in forcing when CO₂ doubles from 200 to 400ppm is the same as when it doubles from 400 to 800ppm. One can also use this to show that to reach equilibrium (i.e., keep the radiative flux at 70km constant) requires an increase of surface temperature of about 0.9^oC. Remember that this is due only to CO₂ and does not include changes in any other forcings (due to methane, water vapour, CFCs, ….). The actual change is likely to be higher and even low estimates of the equilibrium climates sensitivity are around 2^oC for a doubling of CO₂. Ed was suggesting that the high end estimate of surface temperature change due to CO₂ going from 400 – 800ppm was 0.6^oC and for “sceptic” estimates, it would more likely be 0.07^oC. These values are lower than any sensible estimates and are – as far as I can tell – because Ed is using the wrong logarithmic relationship between temperature and CO₂ concentration. It’s not us who should have the courage to do nothing, it’s Ed was should have the courage to recognise when he doesn’t know what he’s talking about and to consider doing nothing.