NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-16-43-2009 Climate spectrum estimation in the presence of timescale errors Mudelsee M. 1 2 Scholz D. 3 4 Röthlisberger R. 1 Fleitmann D. 5 6 Mangini A. 3 Wolff E. W. 1 British Antarctic Survey, Cambridge, UK Climate Risk Analysis, Hannover, Germany Heidelberg Academy of Sciences, Heidelberg, Germany Bristol Isotope Group, School of Geographical Sciences, University of Bristol, Bristol, UK Institute of Geological Sciences, University of Bern, Bern, Switzerland Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland 05 02 2009 16 1 43 56 Copyright: © 2009 M. Mudelsee et al. 2009 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/16/43/2009/npg-16-43-2009.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/16/43/2009/npg-16-43-2009.pdf

We introduce an algorithm (called REDFITmc2) for spectrum estimation in the presence of timescale errors. It is based on the Lomb-Scargle periodogram for unevenly spaced time series, in combination with the Welch's Overlapped Segment Averaging procedure, bootstrap bias correction and persistence estimation. The timescale errors are modelled parametrically and included in the simulations for determining (1) the upper levels of the spectrum of the red-noise AR(1) alternative and (2) the uncertainty of the frequency of a spectral peak. Application of REDFITmc2 to ice core and stalagmite records of palaeoclimate allowed a more realistic evaluation of spectral peaks than when ignoring this source of uncertainty. The results support qualitatively the intuition that stronger effects on the spectrum estimate (decreased detectability and increased frequency uncertainty) occur for higher frequencies. The surplus information brought by algorithm REDFITmc2 is that those effects are quantified. Regarding timescale construction, not only the fixpoints, dating errors and the functional form of the age-depth model play a role. Also the joint distribution of all time points (serial correlation, stratigraphic order) determines spectrum estimation.

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