Addendum – 27 May 2013
Just in case you don’t get as far as the comments, the answer, unsurprisingly, to the question I pose in the title is No. I did not properly understand what one of the terms in the equation actually was. For posterity, however, I will leave my post as I wrote it. I found it quite an interesting exercise and have certainly learned quite a lot about climate sensitivity while trying to work all this out. Nothing wrong with being wrong – IMO.
As you may have noticed, I’ve become interested in the various climate sensitivities. The two that are typically considered are the transient climate response (TCR) and the equilibrium climate sensitivity (ECS). I explain these in the post linked to earlier, so won’t repeat it here.
There has been a recent paper by Otto et al. (2013) called Energy budget constraints on climate response. It’s received quite a lot of attention because it is predicting a lower TCR than many earlier studies. Not by a huge amount, but rather than a best estimate of 1.8oC their study suggests that it is closer to 1.3oC. This could be significant because this is an estimate for the change in temperature at the instant in time at which the CO2 concentrations have doubled (the actual definition is a little more complicated, but this is essentially what it represents). Hence, it is possible that the surface temperatures may rise more slowly than expected.
So, I’ve finally downloaded the paper and given it a quick read and am starting to wonder if they are simply wrong. What worries me though is that in my experience when you consider the results of a paper published by a number of high-profile scientists to be wrong, it’s much more likely that you are the one who is wrong. So, I more than happy for someone else to correct my thinking here and I’m writing this with an awareness that there is a good chance that I’m the one who is mistaken.
So, why do I think Otto et al. (2013) is wrong? I’m going to focus only on their calculation of the TCR. To estimate the TCR they use
where F2x is the change in forcing due to a doubling of the CO2 concentration. They use a value of 3.44 W m-2. The other terms are the change in global mean temperature, ΔT, and the change in radiative forcing, ΔF. They go on to say :
For ΔT, we use the HadCRUT4 ensemble data set of surface temperatures averaged globally and by decade. …. For ΔF, we use the multi-model average of the CMIP5 ensemble of climate simulations with emissions that follow a medium-to-low representative concentration pathway.
So, they use the HADCRUT4 data set to determine ΔT, the change in surface temperature. They then use the multi-model average of the CMIP5 ensemble of climate simulations to determine the change in radiative forcing, ΔF. I have no issue with their choice of ΔT, but their choice of ΔF seems wrong. They seem to have used the total change in radiative forcing. The TCR is the change in temperature due to a doubling of CO2. The change in forcing due to a doubling of CO2 is estimated to be 3.44 W m-2. Therefore, the TCR will equal ΔT when ΔF = F2x = 3.44 W m-2. Consequently, it seems that ΔF should only be the change in forcing due to CO2, not the total change in radiative forcing. By using the total change in radiative forcing, they’re estimating the climate sensitivity due to a change in forcing of 3.44 W m-2 not the climate sensitivity due to a doubling of CO2. In other words, ΔF could equal 3.44 W m-2 before the CO2 concentration has doubled and hence their assumptions will underestimate the TCR.
Firstly, it’s possible that I’m wrong or have mis-interpreted the Otto et al. (2013) paper. Also the change in forcing due to CO2 in recent times is quite close to the total change in forcing (depending on the time interval the change due to CO2 seems to be between 75% and 90% of the total change) so maybe their estimate is okay. One can, however, do a quick check. To estimate the change due to CO2 one can use
ΔFCO2 = 5.35 ln (C/Co).
Since 1970, the CO2 concentration has increased from 325ppm to 400ppm. This gives ΔF = 1.11 W m-2. The forcing used by Otto et al. (2013) for this period was ΔF = 1.21 +- 0.52 W m-2 and the temperature change was ΔT = 0.48 K. This gives a best estimate according to Otto et al. (2013) of 1.36 K while I would argue it should be 1.5 K (although I accept that I’ve ignored errors in my calculation).
So, I really would be keen if someone could let me know if I’m getting this horribly wrong. I also accept that the difference might be small, but given that people seem excited by a change in TCR of a few tenths of a degree this may still be significant. Again, I would be surprised if a group of established scientists could have made such a basic mistake, so I am assuming that their calculation is correct and I’m just misunderstanding what they’re doing or misunderstanding how the ECS and TCR are calculated.