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). Here we explain the cause of the problem and propose an easy, generally applicable, data-driven strategy to effectively correct for attenuation (Fuller, 1987; Carroll et al., 2006), even at annual resolution. The impact is illustrated in the context of a Northern Hemisphere mean temperature reconstruction. An inescapable trade-off for achieving an unbiased reconstruction is an increase in variance, but for many climate applications the change in mean is a core interest.
Bibliographical noteKAUST Repository Item: Exported on 2020-04-23
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors are grateful for support by
Linda Mearns and the WCIAS-Program (C.M.A), D. Nychka and
IMAGe (B.L.) and NSF grants in Collaborations in Mathematical
Geosciences, ATM-0724828 (C.M.A. and B.L.), DMS-1007686
(B.L.) and ATM-0620624 (M.G.G.). The research of M.G.G. was
also partially supported by Award No. KUS-C1-016-04 made by
King Abdullah University of Science and Technology (KAUST).
Additionally, detailed reviews by A. Moberg, E. Zorita, P. Brohan,
B. Christiansen, K. Anchukaitis and one anonymous reviewer were
very helpful to more effectively target this contribution and highlighting
the need for future evaluation of the method under different
noise conditions. The National Center for Atmospheric Research is
sponsored by the National Science Foundation and operated by the
University Corporation for Atmospheric Research.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Global and Planetary Change