Guest Post by Willis Eschenbach
I’ve argued in a variety of posts that the usual canonical estimate of climate sensitivity, which is 3°C of warming for a doubling of CO2, is an order of magnitude too large. Today, at the urging of Steven Mosher in a thread on Lucia Liljegren’s excellent blog “The Blackboard”, I’ve taken a deeper look at the Berkeley Earth Surface Temperature (BEST) volcano forcings. It’s a curious tale, with an even more curious outcome. Here’s the graph in question:
Figure 1. BEST comparison of hindcast temperature changes due to CO2 plus volcanoes (heavy black line) with the BEST temperature data (light black lines). SOURCE
I asked Steven Mosher where the BEST folks got the data on the temperature change expected from volcanic forcing as shown in the heavy black line above … no reply. Setting that question aside, I decided to just use the data I had. So … I did what I usually do. I digitized their figure, since their underlying data wasn’t readily available. That allowed me to analyze their data, which revealed a very odd thing.
Their explanation of the black line in Figure 1 above (their Figure 5) is as follows:
A linear combination of volcanic sulfates and CO2 changes were fit to the land-surface temperature history to produce Figure 5. As we will describe in a moment, the addition of a solar activity proxy did not significantly improve the fit. The large negative excursions are associated with volcanic sulfate emissions, with the four largest eruptions having all occurred pre-1850; thus our extension to the pre-1850 data proved useful for the observation of these events. To perform the fit, we adjusted the sulfate record by applying an exponential decay with a two year half-life following emission. The choice of two-years was motivated by maximizing the fit, and is considerably longer than the 4-8 month half-life observed for sulfate total mass in the atmosphere (but plausible for reflectivity which depends on area not volume).
OK, that makes me nervous … they have used a linear regression fit to the temperature record of the lagged exponential decay, with a separately fitted time constant, of an estimate of volcanic sulfate emissions based on ice cores … OK, I’ll buy that, but at a discount. They are using the emissions from here, but although I can get close to the figure above, I cannot replicate it exactly.
I wanted to extract the volcanic data. My plan of attack was as follows. First, I would digitize the heavy black line from Figure 1 above. Then I’d match it up with the logarithm of the CO increase since 1750. Once I subtracted out the CO2 increase, the remainder would be the hindcast change in temperature resulting from the volcanic eruptions alone.
Figure 2 shows the first part of the calculation, the digitized black line from Figure 1 (CO2 + volcanoes) with the log CO2 overlaid on it in red.
Figure 2. The black line is the digitized black line from Figure 1. The red line is three times the log (base 2) of the change in CO2 plus an offset. CO2 data is from Law Dome ice cores 1750-1950, and from Mauna Loa thereafter.
I fit the CO2 curve to the data by hand and by eye, by manually adjusting the slope and the intercept of the regression, because standard regression methods don’t fit it to the top of the black line. A couple of things indicated to me that I was on the right track. First is the good fit of the log of the CO2 data to the BEST data. The second is that it turned out that the best fit is when using the standard climate sensitivity of 3°C for a doubling of CO2. Encouraged, I pressed on.
Subtracting the volcanic data from the CO2 data gives us the temperature change expected from volcanoes, as shown in Figure 3.
Note that as I mentioned above, I can get close to the temperature changes they hindcast (black line) using a lagged version of their sulfate data as they described (red line), but the match is not exact. Since the black line is what they show in Figure 1 above, and the differences are minor, I’ll continue to use the heavy black line.
Now, let’s pause here for a moment and consider what they have done, and what they have not done. What they have done is converted changes in atmospheric CO2 forcing in watts per square metre (W/m2) to a hindcast temperature change (in degrees C). They did this conversion by using the standard climate sensitivity of 3°C of warming for each doubling of CO2 (doubling gives an additional 3.7 W/m2).
They have also converted stratospheric injections of volcanic sulfates (in Teragrams) to a hindcast temperature change (in degrees C). They have done this by brute force, using a lagged model of the results of the stratospheric sulfate injections which is fit to the temperature.
But what they haven’t done, as far as I could find, is to calculate the forcing due to the volcanic eruptions (in W/m2). They just fitted the sulfate data directly to the temperature data and skipped the intermediate step. Without knowing the forcing due to the eruptions, I couldn’t estimate what climate sensitivity they had used to calculate the temperature response to the volcanic eruptions.
However, there’s more than one way to skin a cat. The NASA GISS folks have an estimate of the volcanic forcing (in W/m2, column headed “StratAer” for stratospheric aerosols from volcanoes). So to investigate BEST’s climate sensitivity, I used the GISS volcanic forcings. They only cover the period 1880—2000, but I could still use them to estimate the climate sensitivity that BEST had used for the volcanic forcings. And that’s where I found the curious part. Figure 4 shows the volcanic forcing in W/m2 from NASA GISS, along with the BEST hindcast temperature response from that forcing.
Figure 4. Black line shows the BEST hindcast temperature anomaly (cooling) from the eruptions. Red line is the change in forcing, in watts per square metre (W/m2), from the eruptions. Green line shows the best fit theoretical cooling resulting from the GISS forcing. Note the different time period from the preceding figures.
As you can see, the regression (green line) of the GISS forcing gives a reasonable approximation of the BEST temperature anomaly, so again we’re on the right track. The curious part is the relative sizes. The change in temperature is just under a tenth of the change in forcing (0.08°C per W/m2).
This equates to a climate sensitivity of about 0.3°C per doubling of CO2 (0.08°C/W/m2 times 3.7 W/m2/doubling = 0.3°C/doubling)… which is a tenth of the canonical figure of three degrees per doubling of CO2.
So in their graph, in the heavy black line they have combined a climate sensitivity of 3°C per doubling for the CO2 portion, with a climate sensitivity of only 0.3°C per doubling for the volcanic portion …
Now this is indeed an odd result. There are several possible ways to explain this finding of a climate sensitivity of 0.3°C per doubling. Here are the possibilities
1. The NASA GISS folks have overestimated the forcing due to volcanoes by a factor of ten, a full order of magnitude. Possible, but very doubtful. The reduction in clear-sky sunlight following volcanic eruptions has been studied at length. We have a pretty good idea of the loss in incoming energy. We might be wrong by a factor of two, but not by a factor of ten.
2. The BEST temperature data underestimates the variation in temperature following volcanic eruptions by a full order of magnitude. Even more doubtful. The BEST temperature data is not perfect, but it is arguably the best we got.
3. The BEST data and the NASA data are both wrong, but providentially they are each wrong in the right direction to cancel each other out and give a sensitivity of three degrees per doubling. Odds are thin on that happening by chance, plus the reasons above still apply.
4. Both the NASA and BEST data are roughly correct, and the climate sensitivity actually is on the order of a tenth of what is claimed.
Me, I go for door number four, small climate sensitivity. I say the climate is buffered by a variety of homeostatic mechanisms that tend to minimize the temperature effects of changes in the forcing, as I have discussed at length in a variety of posts.
However, as always, alternative hypotheses are welcome.
Regards to everyone,
DATA: I did this on an excel spreadsheet, which is here. While it is not user-friendly, I don’t think it is actively user-aggressive … the BEST temperature data on that spreadsheet is from here. Note that curiously, the BEST folks have not removed all of the annual cycle from their temperature data, there remains about a full degree of annual swing … go figure.
[UPDATE] Richard Telford in the comments points out that what I have calculated is the instantaneous sensitivity, and he is correct.
However, as I showed in “Time Lags in the Climate System“, in a system that is driven cyclically and that picks up and loses heat via exponential gain and decay, the instantaneous sensitivity is related to the longer-term sensitivity by the relationship
where t1 is the lag, t is the length of the cycle, and s2/s1 is the size of the reduction in amplitude. Since in this case we are dealing with the BEST land-only temperatures, where the lag is short (less than a month on average) that means that the short-term sensitivity is about 64% of the longer-term sensitivity. This would make the longer-term sensitivity about 0.46°C per doubling of CO2. This is still far, far below the usual estimate of 3°C per doubling.