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Eigen analysis of tree-ring records: part 2, posing the eigen problem

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Abstract

The technique of expanding meteorological fields on eigenvectors of the field covariation matrix is popular. In this paper, we propose for the first time to use a mathematically similar technique to solve the main problem of dendrochronology: classifying variations in tree-ring records as either age- and microenvironment-dependent or climate-induced. Applying this technique to a sample of very long-lived Qilian junipers (Sabina przewalskii Kom.) from the Dulan region in western China, we demonstrate that the ring-width variations projected on the first eigenvector are age-dependent, but those projected on several of the first subsequent vectors are mainly climate-induced. In particular, the second and third projections capture multi-centennial climatic variations, and the variations projected on the fourth through seventh eigenvectors show periodic variations that are probably induced by the 178-year solar cycle. The projections on the smallest eigenvectors seem to be negligible.

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Acknowledgments

The authors thank two anonymous reviewers for their thoughtful and constructive comments. This study is supported by the CAS Visiting Professorship for Senior International Scientists (grant no. 2009S1-38), the National Basic Research Program of China (973 Program) (no. 2010CB950104), and the CAS Strategic Priority Research Program (no. XDA05080801). Meanwhile, the study was funded by the NNSF (grant no. 07-05-92121-a) and RFBR (grant no. 09-05-00202-a for Datsenko) and the CAS 100 Talents Project (grant no. 29082762 for Yang). Thanks are extended to Anda Divine for English editing.

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Authors and Affiliations

  1. Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 320 Donggang West Road, 730000, Lanzhou, China

    Bao Yang, Jingjing Liu & Chun Qin

  2. P.P. Shirshov Oceanology Institute, Russian Academy of Sciences, Nakhimowskii Prospect 36, 117997, Moscow, Russia

    Dmitry M. Sonechkin

  3. Hydrometeorological Research Centre of Russia, Bolshoy Predtechensky Lane 9/11, 123242, Moscow, Russia

    Nina M. Datsenko & Nadezda N. Ivashchenko

Authors
  1. Bao Yang
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  2. Dmitry M. Sonechkin
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  3. Nina M. Datsenko
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  4. Nadezda N. Ivashchenko
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  5. Jingjing Liu
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  6. Chun Qin
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Corresponding author

Correspondence to Bao Yang.

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Figure S1

Chronologies of the Dulan ring-width extra sample reconstructed using only one principal component from PC(1) through PC(5). (JPEG 21 kb)

High Resolution (TIFF 1721 kb)

Figure S2

Chronologies of the Dulan ring-width extra sample reconstructed using only one principal component from PC(6) through PC(10). (JPEG 23 kb)

High Resolution (TIFF 1736 kb)

Figure S3

Chronologies of the Dulan ring-width extra sample reconstructed using only one principal component from PC(11) through PC(15). (JPEG 22 kb)

High Resolution (TIFF 1736 kb)

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Yang, B., Sonechkin, D.M., Datsenko, N.M. et al. Eigen analysis of tree-ring records: part 2, posing the eigen problem. Theor Appl Climatol 107, 131–141 (2012). https://doi.org/10.1007/s00704-011-0468-y

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