Mann 07 Part 4 – Actual Proxy Autocorrelation
Posted by Jeff Condon on August 14, 2010
I hope this is the last post for a while on Mann07 variance loss. The difference between this post and my originals is simply the use of pseudoproxies created from models plus noise rather than just using a single straight line. Mann provided 100 pseudoproxy curves on his website from his 07 work, by adding noise he demonstrated that there was no significant variance loss in the CPS method. Unfortunately, he couldn’t seem to justify an autocorrelation rho greater than 0.32, wheras I found an autocorrelation range which included values both lower and higher than his.
As we’ll see, this does make a difference.
For this post, I created 10000 pseudoproxies with 75% noise and 25% signal. The noise has the same autocorrelation histogram as actual proxies taken from Mann08 – shown above. We’ve discussed CPS here so many times I’ll just present the result.
In this example having 25% noise, I used a correlation threshold of 0.4 which retained 51 percent of the noisy proxies, throwing the rest away. If you’re new to CPS that’s what it does, it throws away data which doesn’t match temperature – basically a sophisticated way to get rid of data which doesn’t do what you want. The result, is variance loss in the historic portion of the record.
There is an interesting clue we can take from this result. Because we are using temperature-like curves from models, we can get an idea of the true signal to noise ratio in actual proxy data used. In Mann08, they retain only 40 percent of the proxies with a correlation threshold of 0.1. I’m retaining 50% with a s/n ratio of 25% at a much higher correlation threshold of 0.4 .
We adopted as our ‘‘standard’’ case SNR = 0.4 (86% noise, r = 0.37) which represents a signal-to-noise ratio than is either roughly equal to or lower than that estimated for actual proxy networks (e.g., the MXD or MBH98 proxy networks; see Auxiliary Material, section 5), making it anappropriately conservative standard for evaluating realworld proxy reconstructions.
We can see from this little bit of informatino that a SNR of 0.4 is hardly conservative.
If I set a threshold of 0.13 using this data with a SNR of 0.25 I retain 96% of proxies and produce a plot with almost zero variance loss — which you would expect because we are using basically all the data.
Now I may go back next week and adjust the S/N until we get to a 40 percent retention but now I will be away from blogland until Monday having fun. The code for this was modified from the other CPS posts and needs cleaning up of the comments for presenting here, that will also have to wait unfortunately. You’ve seen it enough times anyway, click the hockey stick posts link above for an example.
The main point is though, that if we have any higher autocorrelation proxies in the mix, these proxies are scaled in the CPS method to reduce the historic signal. This happens because higher autocorrelation of proxies have artificial noise trends that take over the correlation value and create the de-weighting effect we can see in the historic signal. The reason M07 had no trouble with variance loss – proving the ‘robustness of reconstructions’ was that he didn’t use a high enough S/N and his methods used proxies with too low an autocorrelation. Mann 07 is therefore incorrect.
Darn, I just realized there has to be at least one more post.