Guest post by J Storrs Hall

This is a reply and extension to Pat Frank’s “Earth Abides” post (sorry, couldn’t resist) which appeared here recently. The post features an intriguing interpretation of the temperature record to deduce climate sensitivity to CO2. I thought I would try to recreate it and see where it took me. First I got the HadSST records from http://www.cru.uea.ac.uk/cru/data/temperature/.

I generally prefer to use sea-surface temperatures when looking at global trends for several reasons:

they have a lower variance, indicating a better stability to short-term perturbations

the surface water temperature is measured directly, eliminating some of the definitional issues of surface air temperature

SST’s are free of siting issues, UHI, land use, and other local human climate effects

The seas are 70% of Earth’s surface and its major heat reservoir. Temperatures can go up and down on land like a wagging tail, but the oceans are the dog.

So let’s take the SST record and fit a sinusoid to it. However, a linear fit to the secular rise simply can’t be right. It would retrodict an ice age right at the peak of the Roman Empire. Since things in nature are much more often cyclical, I tried fitting another sinusoid to the secular rise, using all the HadSST data back to 1850:

Here we have the data as dots, decadal smoothing in blue, and the fitted sum of cosines in red. (Decadal smoothing means that I convolved the data with a Gaussian with a 5-year standard deviation.) The red curve is simply the sum of two cosines, one of period 62.7 years, the other 259.9. Just how good a match is it for the data? Ignoring intra-decadal variability (weather, not climate!), let’s plot the decadally-smoothed residual:

Something very unusual happened around 1950 — that’s nearly an 8-sigma excursion. And I haven’t the slightest clue what it was. (There was a major mode shift in the PDO about that time; it was also the era of atmospheric nuclear weapon testing … and there was probably a drop in the number of pirates.) If you look at the actual data you’ll see that 1945 marks the only really drastic discontinuity in the entire record — so I feel reasonably comfortable saying that something unusual happened then. Given that the fit was so good outside the “1950 notch”, I did the fit treating the notch as an outlier (yellow line) for an even better fit (especially to recent temperatures). (That means, of course, that the model isn’t just the fit but the fit with an exception for the notch.) The red lines are one standard deviation, the magenta two. But outside of the notch, this model — a tiny one, 6 parameters — fits the decadal average SST to within 0.05 degrees for 160 years.

Here are the variances, again with the notch taken out (We take the notch out because it makes all the series correlated, so the variances wouldn’t sum. Since we explicitly say the model can’t explain the notch, we’ll concentrate on where it does match the data.):

Raw SST data 0.0687 Model fit curves 0.0534 Residual to fit 0.0153 Data – smoothed (decadal variability) 0.0145 Smoothed – fit (model error) 0.000513

In other words, decadal variability (weather!) accounts for 21% of the variance of the raw temperature series, the model accounts for 78%, leaving about 1% unaccounted for. (There’s still a tiny amount of correlation.)

But this kind of messes up the notion that there was a V-shaped piecewise linear structure to the residual across the twentieth century: the data much more clearly show a straight line with a dip than falling and rising linear trends. Yet Frank’s graph looked a lot more like the trends — what happened?

The key to the puzzle is that his data were (or included?) land temperatures, the CRUtemp data. Let’s plot that too, also as a residual to our fit curve:

Lo and behold, there really is a linear rise above the sinusoid in the land data — which isn’t there in the SST data. In other words, the divergence since 1950 is more a land-water difference than a CO2-no CO2 one. Sorry to rain on the parade, but I can’t really buy the climate sensitivity deduction. As mentioned, there are several possible explanations for the difference. We can add another one, even assuming the land temperature measurements are perfectly accurate: cloud feedbacks may operate differently over land and ocean.

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