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Eigen analysis of tree-ring records: part 3, taking heteroscedasticity and sampling effects into consideration

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Abstract

This paper reports on the further development of a new technique for standardization of tree-ring records called the eigen analysis of tree-ring records. The data are from the same sample set of 56 long-lived Qilian junipers (Sabina przewalskii Kom.) from the Dulan region in western China as was used in our previous paper (Yang et al. 2011b). To assess the heteroscedasticity of individual record deviations from the sample set regional curve (RC), we tested five different definitions of those deviations. Direct computations of eigenvectors of all relevant intrarecord covariation matrices turned out to be greatly affected by observational and computational noise; an analytic approximation of these vectors was therefore desirable. The Bessel function of the first kind and the zero order proved suitable for such an approximation, especially because the deviations were defined via subtraction of the RC from raw ring width records. Exclusion of the contributions of the first segment of the Bessel approximation, corresponding to the extremely large first eigenvalue, rendered individual record deviations from RC homoscedastic. Therefore, the routine Fourier basis became applicable to extract climate-dependent components of the residual deviations. A Fourier expansion of the Dulan chronology revealed the quasi-200-year-long solar activity cycle to be the main factor affecting Dulan tree growth.

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Acknowledgments

This study was supported by the National Basic Research Program of China (973 Program; no. 2010CB950104) and was also funded in the framework of grant no. 2009S1-38 for Sonechkin of the CAS “Visiting Professorship for Senior International Scientists”; grant no. 29082762 for Yang of the Chinese Academy of Sciences “100 Talents Project”; and grant no. 09-05-00202-a for Datsenko of the Russian Foundation for Basic Research. Thanks to Dr. Karen L. Lew who helped finish English editing.

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Authors and Affiliations

  1. Key Laboratory of Desert and Desertification, 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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Correspondence to Bao Yang.

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Fig. S1

The shapes of the first five segments of the Bessel function of the first kind and the zero order that were used for an analytic approximation of the first eigenvectors of the Dulan tree growth (JPEG 9 kb)

High-resolution image file (TIFF 982 kb)

Fig. S2

Pattern of the projections of the individual record deviations from RC on the constant term of the Fourier basis. The spread of the magnitudes of these projections within the time interval 1000–2000 AD is almost the same independent of years of separate tree lives. This shows that the value of this projection does not depend on climate variations inherent in the 553-year-long time interval being the life-span interval of any tree (JPEG 5 kb)

High-resolution image file (TIFF 960 kb)

Fig. S3

Pattern of the projections of the individual record deviations from RC on the Fourier harmonic of the 553-year period. The out-of-phase behavior of the harmonics evidences that these projections were surely not induced by climatic variations of the respective periods (JPEG 7 kb)

High-resolution image file (TIFF 960 kb)

Fig. S4

Pattern of the projections of the individual record deviations from RC on the Fourier harmonic of the 184-year period. In-phase behavior of almost all of the projections evidences, with great certainty, that these projections were induced by climatic variations of the respective periods (JPEG 6 kb)

High-resolution image file (TIFF 960 kb)

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Yang, B., Sonechkin, D.M., Datsenko, N.M. et al. Eigen analysis of tree-ring records: part 3, taking heteroscedasticity and sampling effects into consideration. Theor Appl Climatol 107, 519–530 (2012). https://doi.org/10.1007/s00704-011-0498-5

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  • DOI: https://doi.org/10.1007/s00704-011-0498-5

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