Mann 07 Pseudoproxies Part 2
Posted by Jeff Id on July 19, 2010
The Mann 07 paper uses synthetic temperature proxies to demonstrate that the methods don’t create artificial hockey sticks. I’ve maintained here, that they most certainly do create artificial hockey sticks and that calling the papers science is more than a slight stretch. What I’ve learned over the last few days is that Mann07 is a situation where CPS and RegEM don’t show signal variance loss in the historic portion of the hockey stick. The math of M07 is correct!!
Yup, you heard it here first, M07 is right and CPS and RegEM will not create signal distortions of any magnitude from these pseudoproxies.
An important table from the SI SupplementaryInfo shows the noise levels and type of noise used in each of Mann’s experiments.
There are a couple of important columns for this discussion, SNR or signal to noise ratio, percentage of noise, and the rho column which is the autoregressive component. This basically can be thought of as how fast the noise component can change. A rho value of zero means that the noise can change instantly from one point to the next without having any dependence on the last value. Rho can vary from zero to one, a higher value means that the more recent point has some dependence on the previous value. If you imagine a pan of water, you could measure its temp and then heat it with a stove burner but if you measure every second, the measurement you take at second #2 is going to be similar to second #1. However if you measure every several hours hours, randomly turning the burner on and off, the temps will vary wildly and independently of the previous measurement temp. The dependence on the previous temp is autocorrelation.
The significance of white noise is that statistically nearly impossible to generate a trend from it. Whereas if we have autocorrelation (redness) in the noise the signal can walk creating the potential for locally induced trends after these standard paleo sorting methods are used.
You can see in the table above M07′s model r (first column – r) he used dataset A with a signal to noise of 0.4 which he refers to as 86% (does anyone know how this 86% number is computed?). Anyway, I found the column averages of dataset A from experiment a and r above and calculated an r amplitude ratio of 0.4 matching well with the table. I then fit an arima (1,0,0) model to the data and found that the noise had an average autocorrelation of 0.31 confirming the 0.32 rho from the table above. Mann wrote out the AR math himself rather than using stock functions so I wanted to check it .
I then generated 10,000 artifical noise proxies having rho of 0.32 and added in a signal, using CPS I tried to extract that signal to verify its distortion. The important part of the next figure is not through the absolute value of the vertical scale, but by the distortion in the horizontal iso-temperature lines. The deviations from linearity represents the magnitude of the distortion which is created by the CPS preferential proxy sorting method.
As you can see, the amount of amplification of the signal is absolutely minimal. CPS and therefore RegEM can extract the ‘signal’ undistorted from this data, Mann is right. I consider M07′s results completely verified from that aspect. This plot looks one heck of a lot different than my previous CPS work which used a higher AR coefficient in the proxies and got the extreme distortions shown in the figure below.
Now Mann is of the opinion that demonstrations exactly like this last graph above, are disingenuous because they have excessive redness and therefore don’t accurately represent proxy data. Perhaps though, it isn’t the other guy who’s got their thumb on the scale.
From M08 which was a CPS and RegEM hockey stick paper, 1208 series were used of which 484 preferred series were kept in creation of the hockey stick. I ran an ARMA fit to each of the proxies in this paper. Although several series wouldn’t converge due to very high redness, the vast majority did, allowing the creation of this histogram plot of the rho’s.
The red line is Mann’s 0.32 value whereas the average value of this histogram of rho’s was actually 0.44. I found that by using his 484 series which passed the uniquely magical sorting of M08, this average didn’t change. It’s almost certain that 0.32 is too low a value for annual proxy data but an average of 0.44 isn’t that different right?
I don’t think this is about the ‘average’ rho though. I think its about extremes and the rho in the calibration period. Now I wonder what this reconstruction will look like if we take out the high rho proxies, or use only high rho proxies.
In the meantime, you can see from the isotemperature line figure above that pulling any signal you want from this data will be extremely difficult. Since I can pull any signal we can imagine from the ‘actual’ proxy data of M08, as shown in the hockey stick cps part one post above and here, we know that M07 doesn’t resolve point of variance loss in any way whatsoever.
Stay tuned for the exciting pseudoproxy extravaganza, part 3. We’ll look at some of the pseudoproxies in M07 and compare them to M08, also I’m interested in the redness of the infilled blade pasted on the end of each series. — now doesn’t that sound fun?