Theoretical and Applied Climatology

, Volume 107, Issue 1–2, pp 131–141 | Cite as

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

  • Bao Yang
  • Dmitry M. Sonechkin
  • Nina M. Datsenko
  • Nadezda N. Ivashchenko
  • Jingjing Liu
  • Chun Qin
Original Paper


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.

Supplementary material

704_2011_468_Fig8_ESM.jpg (22 kb)
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)

704_2011_468_MOESM1_ESM.tif (1.7 mb)
High Resolution (TIFF 1721 kb)
704_2011_468_Fig9_ESM.jpg (23 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)

704_2011_468_MOESM2_ESM.tif (1.7 mb)
High Resolution (TIFF 1736 kb)
704_2011_468_Fig10_ESM.jpg (22 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)

704_2011_468_MOESM3_ESM.tif (1.7 mb)
High Resolution (TIFF 1736 kb)
704_2011_468_MOESM4_ESM.doc (70 kb)
ESM 4(DOC 70 kb)


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Bao Yang
    • 1
  • Dmitry M. Sonechkin
    • 2
  • Nina M. Datsenko
    • 3
  • Nadezda N. Ivashchenko
    • 3
  • Jingjing Liu
    • 1
  • Chun Qin
    • 1
  1. 1.Cold and Arid Regions Environmental and Engineering Research InstituteChinese Academy of SciencesLanzhouChina
  2. 2.P.P. Shirshov Oceanology InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Hydrometeorological Research Centre of RussiaMoscowRussia

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