Guest commentary by David Ritson
Realclimate recently gave a detailed review of the issues surrounding the Von Storch et al. (2004) Science article that purported to show that the paleo-reconstructions of Mann et al. were invalid. Part of the review centered on a comment of Wahl, Amman and myself and the response to it by Von Storch et al that appeared on April 27 in Science. The response admitted that our critique of their original results was correct but then opened up a new area of debate. As in their original 2004 article von Storch et al had used a coupled climate model (AOGCM) to simulate the temperatures of the last two thousand years. They had then generated pseudo-proxies by adding noise at selected spatial locations to the AOGCM generated temperature histories. The added noise was purportedly designed to represent non-climatic effects such as disease or insect infestation. This simulated ‘noisy’ world then can be used as a test-bed for the reconstruction methodology. A given analysis procedure is validated if it successfully recovers the original AOGCM noise free results and could be rejected if it fails to recover the original results. Of course such testing only makes sense if the simulated test world has characteristics similar to the real-world.
As discussed in the original post there were problems with their AOGCM simulations. However more importantly they had very substantially altered the character of the added noise, substantially increasing the difficulties of analysis. In technical terms they had now simply postulated that the added simulated noise be ‘red’.
Red noise in a random time series is associated with each year’s value being correlated with the value of the year before. The strength of that correlation is a measure of how ‘red’ the time series is and how much memory carries from year to year. Von Storch et al added proxy-specific noise that was highly correlated from year to year. It was characterized as AR1, or a simple Markoff process, noise with 70% of a previous years history carried over from a previous year to the next year (this a corresponds to a one year autocorrelation coefficient of 0.7). A factor of 0.7 corresponds to a decorrelation time of (1+.7)/(1-.7) or 6.3 years and reduces the effective number of independent data-points by the same factor i.e. 6.3. If the noise component of real proxy data were really so strongly red, not only the precision of results of Mann et al. (the target of the von Storch et al’s analysis) but indeed of all previous millennial paleo-reconstructions would be substantially degraded. In the past it has been generally accepted that the added noise should be only slightly red, if not white (uncorrelated). Von Storch et al. provided no rationale for why they assumed such large year to year correlations.
Based on existing real proxy data one can derive the real-world year to year correlations. Using data from the North American network of seventy sets of tree rings extending from 1400 to 1980 you obtain an actual one-year AR1 mean autocorrelation factor with a value close to 0.15 (the exact number depends on the proxy series and time period chosen but is always less than about 0.3). A value of 0.15 corresponds to a decorrelation time of 1.4 years and a reduction by the same factor of independent data points. This reduction is a factor five less severe than that associated with the value von Storch et al assumed. Had they used the more realistic value of 0.15 (or even 0.3) for their tests, they would have found little change from their earlier published results based on simulated proxies where white, not red noise with the same annual variance, had been added. These prior white noise results did not provide a basis for rejecting the Mann et al. results. Therefore we can conclude that the current new von Storch et al. simulated ‘testing’, supposedly a new basis for rejection of Mann et al. results, is likely just an artifact derived from the introduction of artificially high correlations (redness) into the new von Storch et al. calculations.