Just when you think that the MBH98 Little Shop of Horrors has been fully explored, something new turns up. I’ve never spent any time on the last part of MBH98, where he does a "detection and attribution" study linking his temperature reconstruction to solar, volcanic and CO2. All these detection and attribution studies (e.g. Hegerl) richly deserve close analysis. Anyway a blogger in New Zealand has written some highly provocative analyses, which includes a close analysis of first differences, which one of our readers was wondering about. For readers who will only read articles listed in the Jesuit Index or Nature/Science, these analyses may not be for you. For readers who are interested in what’s going on with these studies, go there immediately. It’s at the felicitously named Sir Humphreys, go to Chefen. I’ve made a few snarks about signal processing approaches to things, but Chefen shows the strength of a signal processing approach in knowledgeable hands.
Here are a few teasers, but please don’t merely accept my short characterization of the results, check it out.
Chefen examined the Fourier spectra and Allen variances of the first differences in the Mann temperature reconstruction, obtaining
"a nearly perfectly straight line sloping downwards … with a slope of nearly -1. To anyone who works with signal processing that means… almost a pure noise source…. It looks whiteish with the low frequency removed, or as if some noise has been high-pass filtered.
If you do want to create your own Mann-method temperature noise signal, then just use a N(0,0.0115) distribution and add it up. It’s a fairly good approximation.)
Now for the next interesting find. Chefen did a simple check on the correlation of the temperature reconstruction to solar and to CO2, reporting:
Note at this stage that Mann outright claimed that the correlation for the CO2 data in the 20th century was much much higher than that for the solar data. Now straight away we are suspicious of that, because just looking at the graph above it is hard to say which is a better match. Indeed, if we do an actual correlation then the coefficient for the solar data is 0.804 while that for CO2 data is 0.815. That is, marginally higher for CO2 but the difference is utterly insignificant. We really have no cause for prefering one over the other and CO2 certainly does NOT dominate.
Now for the topper. Chefen gets exactly the same coefficients from random data processed according to the sum of filtered white noise described above:
Let’s take that idea a bit further, now I’ll generate a purely random data set in the following way…1. Create a normally distributed data set with the same mean and standard deviation as the difference temperature data. This is pretty much like white-noise and distributed as N(0.045,0.201).
2. High pass filter this with a cutoff frequency of 0.1/year to make the spectrum match that of the difference temperature data, which lacks power below 0.1/year.
3. Sum this data to create a noise data set that has the same characteristics as the real temperature data.
4. Calculate the correlation of this noise with the temperature data, just as we did for the solar and CO2 data.
5. Repeat this 100,000 times to get a good idea of what is going on.The correlations for with purely RANDOM data sets are tightly bunched in the range 0.80 to 0.83! The correlations for the CO2 and solar data lie completely WITHIN this range. What does this say?
It’s quite remarkable. Will his observations become more true if they are published in Nature or more formally in a journal? I don’t think so. They are either right or wrong as they stand. The journal is simply a form of endorsement and an effective means of disseminating the information to non-specialists. You have some qualified specialists, who may or may not have their own agendas, telling you that the article is worth reading. In this instance, I view myself as a qualified specialist and I’m telling you that this is worth reading. I’m not telling you that it’s necesaarily true as I haven’t replicated the simulations. But Nature referees don’t do that for you either.