Nic Lewis has another post on Watts Up With That (WUWT) called Updated climate sensitivity estimates using aerosol-adjusted forcings and various ocean heat uptake estimates. Basically he tries various different changes in radiative forcing and ocean heat uptake rates to determine various values for the Transient Climate Response (TCR) and the Equilibrium Climate Sensitivity (ECS) and gets some surprising results.
The table below shows one of his sets of results. Firstly, his results don’t seem that surprising. The 5-95% range for the ECS (1 – 4oC) is very similar to other studies. I’m also not sure if his best guess value for the ECS is the mode or the median. The 3 numbers one might quote when describing a distribution are the mode, the median or the mean. These are skewed distributions (as can be seen from the fact that the best guess is closer to the lower side of the range than the higher) and so the mode will be smaller than the median, which will be smaller than the mean. If he is quoting the mode, then there is a greater than 50% chance that the actual value will be bigger than the “best estimate”.
In a sense I found this post quite interesting in that I learned quite a lot about how to get the TCR and the ECS. The TCR is fairly straightforward. It is given by
TCR = F2x ΔT/ΔF,
where F2x is the change in forcing resulting from a doubling of the CO2 concentration, ΔT and ΔF are the change in temperature and forcing over the time interval considered.
The ECS is similar but also includes the heating rate of the oceans, ΔQ. It is given by
ECS = F2x ΔT/(ΔF – ΔQ),
where the terms are the same as for the TCR. This makes sense. The TCR tells you the actual change in temperature at the instant at which the CO2 has doubled. The ECS includes that some of the energy is going into the ocean and hence that the ECS will be higher than the TCR and that there will be lag (i.e., ECS will be reached after TCR, obviously).
Basically, all that Nic Lewis has done is consider various estimates for the forcings and for the ocean heating rate. I thought I would quickly do a calculation of my own. Below is a figure showing the ocean heat content from Levitus et al. (2012). The total change in ocean heat content since 1955 is 2.5 x 1023J. The oceans cover 70% of the surface of the Earth, so this gives a heating rate of ΔQ = 0.4 W m-2.
The figure below shows the radiative forcing from the HADCRUT4 dataset. This seems to indicate that the change in radiative forcing since 1955 was about ΔF = 1.35 W m-2.
The next figure shows the change in global surface temperature which indicates that the change in surface temperature since 1955 is ΔT = 0.5 K.
TCR = F2x ΔT/ΔF = 1.37oC,
ECS = F2x ΔT/(ΔF-ΔQ) = 1.94oC.
These are very simple calculations with no errors estimates and everything determined by eye, but they seem reasonable. A TCR close to 1.5oC and an ECS close to 2oC. I guess, I’m not sure why what Nic Lewis has determined is all that surprising. The numbers might be a little lower than some other estimates, but not by much and the 5-95% ranges are quite consistent. I’m also not quite sure what the point of this post was. Maybe an attempt to write something moderately positive about a WUWT post.
Maybe someone who knows more than me can clarify something. I was assuming that ΔF was the change in total radiative forcing. However, looking at the form of the TCR makes me think that it should be only the change due to CO2. We want TCR = ΔT when the CO2 concentration has doubled and hence require (at that point) that ΔF = F2x. If so, CO2 levels have increased from Co = 315 ppm in 1955 to C=400 ppm today. The equation for the change in forcing due to CO2 changes is
ΔF = 5.35 ln(C/Co),
which gives (for the period 1955-2013)
ΔF = 1.28 W m-2.
The next issue is how does one determine ΔQ as this should now be the change in ocean heating due to increased CO2 only. Well, if the total change in forcing is 1.75 W m-2 and that due to CO2 is 1.27 W m-2, then we can assume that 73% of the change in ocean heating rate was due to CO2. Given that the total change is 0.4 W m-2, that due to CO2 would be ΔQCO2 = 0.29 W m-2.
If I use this to recalculate the TCR and ECS I get,
TCR = F2x ΔT/ΔF = 1.46oC,
ECS = F2x ΔT/(ΔF-ΔQ) = 1.9oC.
So the TCR is higher than before, but the ECS is about the same. Firstly, am I right about this? Secondly, was Nic Lewis using the correct values for ΔF and ΔQ?