Climate of the Past Discussions www.clim-past-discuss.net 1814-9340 1814-9359 5 3 2009 10.5194/cpd-5-1645-2009 http://www.clim-past-discuss.net/5/1645/2009/ http://www.clim-past-discuss.net/5/1645/2009/cpd-5-1645-2009.html http://www.clim-past-discuss.net/5/1645/2009/cpd-5-1645-2009.pdf 1645 1657 2009-06-16 Technical Note: Correcting for signal attenuation from noise: sharpening the focus on past climate C. M. Ammann ammann@ucar.edu M. G. Genton B. Li National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, CO 80307-3000, USA Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA Department of Statistics, Purdue University, West Lafayette, IN 47907, USA Regression-based climate reconstructions scale one or more noisy proxy records against a (generally) short instrumental data series. Based on that relationship, the indirect information is then used to estimate that particular measure of climate back in time. A well-calibrated proxy record(s), if stationary in its relationship to the target, should faithfully preserve the mean amplitude of the climatic variable. However, it is well established in the statistical literature that traditional regression parameter estimation can lead to substantial amplitude attenuation if the predictors carry significant amounts of noise. This issue is known as "Measurement Error" (Fuller, 1987; Carroll et al., 2006). Climate proxies derived from tree-rings, ice cores, lake sediments, etc., are inherently noisy and thus all regression-based reconstructions could suffer from this problem. Some recent applications attempt to ward off amplitude attenuation, but implementations are often complex (Lee et al., 2008) or require additional information, e.g. from climate models (Hegerl et al., 2006, 2007). 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