One of the major accomplishments of the SO&P project has been the investigation of the behaviour of some of the statistical calibration techniques that have been used to generate reconstructions of past climate from networks of proxy data.
It has become clear from work undertaken within SO&P (including, but not limited to, the studies published by von Storch et al., 2004; Burger et al., 2006) that the traditional use of simple linear regression to predict Northern Hemisphere (NH) temperatures from a weighted or unweighted combination of individual proxy records, with the assumption that the error is contained wholly within the temperature data, results in a reconstruction with a biased regression coefficient such that the low-frequency variance is always underestimated. Inverting the regression equation, with the assumption that the error is contained wholly within the proxy data, results in an overestimation of the regression coefficient and of the low-frequency reconstructed temperature variability. An unbiased reconstruction can only be obtained using simple linear regression if the relative magnitudes of the proxy error and the temperature error can be determined a priori and incorporated into the calibration procedure via the use of total least squares regression. The result will lie somewhere between the traditional and the inverted regression results. Scaling the combined proxy record so that its variance matches the variance of the NH temperature series will also result in a reconstruction that lies between those obtained via the traditional and inverted regression methods, though in general it will not be unbiased.
Despite errors (Wahl et al., 2006) in the implementation of the Mann et al. (1998, 1999) method (which combines an inverted regression step with a variance-matching or rescaling step) by von Storch et al. (2004), it nevertheless seems likely that this method can also result in biased reconstructions in some, possibly realistic, cases, though the underestimate of the low-frequency variance is likely to be smaller than that found by von Storch et al. (2004).
Existing NH temperature reconstructions have been collated for use within SO&P and recalibrated against a common target time series of instrumental temperatures. Some of these were published in Science (Briffa and Osborn, 2002), in the following figure.
Though the latter versions of these multiple reconstructions provide an ad hoc attempt at compensating for the low-amplitude bias at low frequencies that might have been present in them when they were calibrated using traditional regression, they are really only indicative of the possibilities of greater millennial-scale fluctuations. More reliable reconstructions will only be possible once improved representations of both proxy and instrumental temperature errors have been developed and utilised within appropriate calibration methods.
The RegEM method (Regularized Expectation Maximization) introduced by Schneider (2001) has the capacity to take into account a priori estimates of proxy and instrumental temperature errors. Though these have not yet been adequately developed (particularly for the proxy error), we have been involved in an application of the RegEM method under the assumption of equal errors in the proxy and instrumental data (Rutherford et al., 2005). Separate analysis of this approach to generating reconstructions of past temperatures indicates that it may be less likely to result in the low-amplitude bias at low frequencies than other methods (Mann et al., 2005).
Our study using RegEM (Rutherford et al., 2005) represents an in-depth analysis of the sensitivity of climate reconstructions to proxy data networks, region and season of temperature target, and of calibration/reconstruction statistical methodology. A number of NH or quasi-NH temperature reconstructions have been developed within this study.
Here is an example of one of the reconstructions, using the RegEM method with the combined Mann et al. (1998) multi-proxy network and the Briffa/Schweingruber tree-ring density network, being used to reconstruct NH annual-mean temperature.
For all references cited here, see papers listed in the SO&P publications list and references therein.