All proxies available within a given instrumental surface temperature grid box were then averaged and scaled to the same mean and decadal standard deviation as the nearest available 5\u00c2\u00b0 latitude by longitude I say to some extent because for the time being I am not adding the decadal smoothing (which will matter for one of the features in the figures below.)<\/p>\n I quickly slapped together a script to illustrate that this method is also biased under screening. Because it can be shown to have a second type of bias that exists only when there are a small number of proxies, I am showing one graph created starting 50 proxies and another with 484. Blue is used for all proxies; green for the reconstructions when we screen those proxies. Screening is done against global temperatures. The calibration period is 80 years.<\/p>\n In the graph below, red is the target value the reconstruction should match: In the following graph, I increased the numbers of proxies.<\/p>\n Notice with the bias for the blue (unscreened) result is now non-zero but small. This is CPS that scales using \u00e2\u20ac\u02dc\u00e2\u20ac\u02dcvariance matching\u00e2\u20ac\u2122\u00e2\u20ac\u2122 is biased when few proxies are used whether or not we screen. This bias vanishes as we increase the number of proxies used. In contrast, the green (screened) trace remains biased. That is because this bias does not vanish when we increase the number of proxies.<\/p>\n Because this method is used, I’ll be adding this to my other tests using “toy” temperatures calling it “method IV”. That way we can compare the relative bias for different numbers of proxies, calibration periods, screening and other analytical choices a reconstruct-o-logist might make.<\/p>\n","protected":false},"excerpt":{"rendered":" When reading Mann08, I realized I need a “method IV” in my previous graphs. In method IV, I will rescale the mean proxy value so the variance of the proxy values match the variance of the temperature during the reconstruction period. This will (to some extent) mimic the portion highlighted below. All proxies available within … Continue reading CPS with ‘variance matching’: (Will be method IV)<\/span>
\ninstrumental surface temperature grid box series over the calibration period. […] The gridded proxy data were then areally weighted, spatially averaged over the target hemisphere, and scaled to have the same mean and decadal standard deviation<\/em> (we refer to the latter as \u00e2\u20ac\u02dc\u00e2\u20ac\u02dcvariance matching\u00e2\u20ac\u2122\u00e2\u20ac\u2122) as the target hemispheric (NH or SH) mean temperature series.\n<\/p><\/blockquote>\n
\n![\"\"](\"http:\/\/rankexploits.com\/musings\/wp-content\/uploads\/2012\/07\/CPS_biasScreened_50.png\" "\\"CPS_biasScreened_50\\"")
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\nIf you examine the “blue” (unscreened) trace, you can see that it is noisy because there are only 50 proxies. More importantly, the mean value over the reconstruction period is biased high- and the bias is statistically significant. The green trace illustrates what happens if we bias selecting only those proxies that exhibited a statistically significant correlation with the target temperature during the calibration period. The bias increases.<\/p>\n<\/a><\/p>\n