Uncertainty, Emergence, and Statistics in Dendrochronology

  • Edward R. CookEmail author
  • Neil Pederson
Part of the Developments in Paleoenvironmental Research book series (DPER, volume 11)


Some fundamental concepts of dendrochronological analysis are reviewed in the context of statistically modeling the climatically related environmental signals in cross-dated tree-ring series. Significant uncertainty exists due to our incomplete mechanistic understanding of radial growth of most tree species in the natural world, one where environmental effects are unobserved, uncontrolled, and steadily changing over time. This biological uncertainty cascades into the realm of statistical uncertainty in ways that are difficult to quantify even though the latter may be well constrained by theory. Therefore, great care must be taken to apply the many well-developed and tested statistical methods of dendrochronology in ways that reduce the probability of making false inferences. This is especially true in the case of biological emergence. This is a special case of uncertainty that arises from the way in which trees as complex organisms can have properties expressed in their ring widths that are impossible to predict from a basic understanding of lower-level physiological processes. Statistical modeling must be conducted in ways that allow for the discovery of such phenomena and, at the same time, protect from the incorrect acceptance of spurious emergent properties. To reduce the probability of the latter, we argue that model verification be an important part of any dendrochronological inquiry based on statistics. Correlation and response function analysis is used to illustrate some of the concepts discussed here. The value of empirical signal strength statistics as predictors of climatic signal strength in tree rings is also investigated.


Dendrochronology Uncertainty Emergence Statistics Response functions Verification 



This chapter is a contribution to the meeting ‘Tree Rings and Climate: Sharpening the Focus,’ held at the University of Arizona, Tucson, on April 6–9, 2004. We thank the organizing committee members (Malcolm Hughes, Henry Diaz, and Tom Swetnam) for their kind support and encouragement. This chapter is based the generous long-term support of the Lamont-Doherty Tree-Ring Laboratory (TRL)by the National Science Foundation and the National Oceanic and Atmospheric Administration Office of Global Programs. The U.S. Department of Energy Global Change Education Program also supported N. Pederson in his PhD dissertation research at the Lamont TRL that contributed to this chapter. We also thank the Mohonk Preserve (Paul Huth and John Thompson) for permission to sample trees used in this study and for access to the Mohonk Lake meteorological data, and to the remarkable naturalist Daniel Smiley of Mohonk who made all of this possible. Lamont-Doherty Earth Observatory Contribution No. 7205.


  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr AC-19(6):716–723CrossRefGoogle Scholar
  2. Anchukaitis KJ, Evans MN, Kaplan A, Vaganov EA, Hughes MK, Grissino-Mayer HD, Cane MA (2006) Forward modeling of regional-scale tree-ring patterns in the southeastern United States and the recent emergence of summer drought stress. Geophys Res Lett 33(4):L04705. doi:10.1029/2005GL025050CrossRefGoogle Scholar
  3. Anderson PW (1972) More is different. Science 177:393–396CrossRefGoogle Scholar
  4. Angier N (1997) Ernst Mayr at 93. Nat Hist 106(4):8–11Google Scholar
  5. Baillie MGL, Pilcher JR (1973) A simple cross-dating program for tree-ring research. Tree-Ring Bull 33:7–14Google Scholar
  6. Biondi F, Waikul K (2004) DENDROCLIM2002: a C++ program for statistical calibration of climate signals in tree-ring chronologies. Comput Geosci 30:303–311CrossRefGoogle Scholar
  7. Blasing TJ, Solomon AM, Duvick DN (1984) Response functions revisited. Tree-Ring Bull 44:1–15Google Scholar
  8. Box GEP, Jenkins GM (1976) Time series analysis: forecasting and control. Holden Day, San Francisco, 553 ppGoogle Scholar
  9. Briffa KR, Jones PD (1990) Basic chronology statistics and assessment. In: Cook ER, Kairiukstis LA (eds) Methods of dendrochronology: applications in the environmental sciences. International Institute for Applied Systems Analysis, Kluwer Academic Publishers, Boston, pp. 137–152Google Scholar
  10. Cook ER (1985) A time series analysis approach to tree ring standardization. PhD Dissertation, University of Arizona, Tucson, 185 ppGoogle Scholar
  11. Cook ER (1990) Bootstrap confidence intervals for red spruce ring-width chronologies and an assessment of age-related bias in recent growth trends. Can J Forest Res 20: 326–1331CrossRefGoogle Scholar
  12. Cook ER, Cole J (1991) Predicting the response of forests in eastern North America to future climatic change. Climatic Change 19:271–282CrossRefGoogle Scholar
  13. Cook ER, Johnson AH (1989) Climate change and forest decline: a review of the red spruce case. Water Air Soil Poll 48:127–140CrossRefGoogle Scholar
  14. Cook, ER, Peters K (1981) The smoothing spline: a new approach to standardizing forest interior tree-ring width series for dendroclimatic studies. Tree-Ring Bull 41: 43–53Google Scholar
  15. Cook ER, Meko DM, Stahle DW, Cleaveland MK (1999) Drought reconstructions for the continental United States. J Climate 12:1145–1162CrossRefGoogle Scholar
  16. Cook ER, Glitzenstein JS, Krusic PJ, Harcombe PA (2001) Identifying functional groups of trees in west Gulf Coast forests (USA): a tree-ring approach. Ecol Appl 11(3):883–903CrossRefGoogle Scholar
  17. Cropper JP (1982a) Comment on climate reconstructions from tree rings. In: Hughes MK, Kelly PM, Pilcher JR, LaMarche VC Jr (eds) Climate from tree rings. Cambridge University Press, Cambridge, pp 65–67Google Scholar
  18. Cropper JP (1982b) Comment on response functions. In: Hughes MK, Kelly PM, Pilcher JR, LaMarche VC Jr (eds) Climate from tree rings. Cambridge University Press, Cambridge, pp 47–50Google Scholar
  19. Cropper JP, Fritts HC (1982) Density of tree-ring grids in western North America. Tree-Ring Bull 42:3–10Google Scholar
  20. de Jong AFM, Mook WG, Becker B (1979) Confirmation of the Suess wiggles 3200–3800 BC. Nature 280:48–49CrossRefGoogle Scholar
  21. DeWitt E, Ames M (1978) Tree-ring chronologies of eastern North America. Chronology series IV, vol 1. Laboratory of Tree-Ring Research, University of Arizona, Tucson, Arizona, 42 pp + tablesGoogle Scholar
  22. D’Odorico P, Revelli R, Ridolfi L (2000) On the use of neural networks for dendroclimatic reconstructions. Geophys Res Lett 27(6):791–794CrossRefGoogle Scholar
  23. Douglass AE (1946) Precision of ring dating in tree-ring chronologies. In: Laboratory of Tree-Ring Research Bulletin 3. University of Arizona Bull 17(3):1–21Google Scholar
  24. Evans MN, Reichert BK, Kaplan A, Anchukaitis KJ, Vaganov EA, Hughes MK, Cane MA (2006) A forward modeling approach to paleoclimatic interpretation of tree-ring data. J Geophys Res-Biogeosci 111:G03008. doi:10.1029/2006JG000166CrossRefGoogle Scholar
  25. Fekedulegn BD, Colbert JJ, Hicks RR Jr, Schuckers ME (2002) Coping with multicollinearity: an example on application of principal components regression in dendroecology. Research paper NE-721. U.S. Department of Agriculture, Forest Service, Northeastern Research Station, Newtown Square, Pennsylvania, 43 ppGoogle Scholar
  26. Feynman RP (1999) The relation of science and religion. In: The pleasure of finding things out. Helix Books, Perseus, Cambridge, Massachusetts, pp 245–257Google Scholar
  27. Fowler A (1998) XMATCH98: an interactive tree-ring crossdating program. Occasional paper 38. University of Auckland, Department of Geography, pp 1–29Google Scholar
  28. Fritts HC (1963) Computer programs for tree-ring research. Tree-Ring Bull 25(3–4):2–7Google Scholar
  29. Fritts HC (1965) Tree-ring evidence for climatic changes in western North America. Mon Weather Rev 93(7):421–443CrossRefGoogle Scholar
  30. Fritts HC (1969) Bristlecone pine in the White Mountains of California. Growth and ring-width characteristics. Papers of the Laboratory of Tree-Ring Research 4. University of Arizona Press, Tucson, Arizona, pp 1–44Google Scholar
  31. Fritts HC (1971) Dendroclimatology and dendroecology. Quaternary Res 1(4):419–449CrossRefGoogle Scholar
  32. Fritts HC (1976) Tree rings and climate. Academic, London, 567 ppGoogle Scholar
  33. Fritts HC, Shashkin AV (1995) Modeling tree-ring structure as related to temperature, precipitation, and day length. In: Lewis TE (ed) Tree rings as indicators of ecosystem health. CRC, Boca Raton, pp 17–57Google Scholar
  34. Fritts HC, Shatz DJ (1975) Selecting and characterizing tree-ring chronologies for dendroclimatic analysis. Tree-Ring Bull 35:31–40Google Scholar
  35. Fritts HC, Vaganov EA, Sviderskaya IV, Shashkin AV (1991) Climatic variation and tree-ring structure in conifers: empirical and mechanistic models of tree-ring width, number of cells, cell size, cell-wall thickness and wood density. Climate Res 1(2):97–116CrossRefGoogle Scholar
  36. Fritts HC, Shashkin A, Downes GM (1999) A simulation model of conifer ring growth and cell structure. In: Wimmer R, Vetter RE (eds) Tree-ring analysis: biological, methodological, and environmental aspects. CABI, Oxon, UK, pp 3–32Google Scholar
  37. Ghent AW (1952) A technique for determining the year of the outside ring of dead trees. Forest Chron 28(4):85–93Google Scholar
  38. Gordon GA, LeDuc SK (1981) Verification statistics for regression models. Seventh conference on probability and statistics in atmospheric sciences, Monterey, California, USAGoogle Scholar
  39. Gray BM, Wigley TML, Pilcher JR (1981) Statistical significance and reproducibility of tree-ring response functions. Tree-Ring Bull 41:21–35Google Scholar
  40. Graumlich LJ (1993) Response of tree growth to climatic variation in the mixed conifer and deciduous forests of the upper Great Lakes region. Can J Forest Res 23:133–143CrossRefGoogle Scholar
  41. Guiot J (1991) The bootstrapped response function. Tree-Ring Bull 51:39–41Google Scholar
  42. Guiot J, Berger AL, Munaut AV (1982) Response functions. In: Hughes MK, Kelly PM, Pilcher JR, LaMarche VC (eds) Climate from tree rings. Cambridge University Press, Cambridge, UK, pp 38–45Google Scholar
  43. Guiot J, Keller T, Tessier L (1995) Relational databases in dendroclimatology and new non-linear methods to analyse the tree response to climate and pollution. In: Ohta S, Fujii T, Okada N, Hughes MK, Eckstein D (eds) Tree rings: from the past to the future. Proceedings of the international workshop on Asian and Pacific dendrochronology. Forestry and Forest Products Research Institute Scientific Meeting Report, vol 1, pp 17–23Google Scholar
  44. Guttman L (1954) Some necessary conditions for common-factor analysis. Psychometrika 19:149–161CrossRefGoogle Scholar
  45. Hatcher MJ, Tofts C (2004) Reductionism isn’t functional. Unpublished paper. Trusted Systems Laboratory, HP Laboratories, Bristol. Google Scholar
  46. Heikkenen HJ (1984) Tree-ring patterns: a key-year technique for cross-dating. J Forest 82:302–305Google Scholar
  47. Holmes RL (1983) Computer-assisted quality control in tree-ring dating and measurement. Tree-Ring Bull 43:69–78Google Scholar
  48. Huber B (1943) Über die Sicherheit jahrringchronologische Datierung (On the accuracy of dendrochronological dating). Holz als Roh und Werkstoff, 6(10/12):263–268CrossRefGoogle Scholar
  49. Hurvich CM, Tsay CL (1989) Regression and time series modeling in small samples. Biometrika 76:297–307CrossRefGoogle Scholar
  50. Huth P (2005) Personal communication on an updated history of gypsy moth defoliation in Ulster County, New York. Daniel Smiley Research Center, Mohonk Preserve, Mohonk Lake, New Paltz, New YorkGoogle Scholar
  51. Jolliffe IT (1973) Discarding variables in a principal component analysis II: real data. Appl Stat 22:21–31CrossRefGoogle Scholar
  52. Jones RH (1985) Time series analysis—time domain. In: Murphy AH, Katz RW (eds) Probability, statistics and decision making in the atmospheric sciences. Westview, Boulder, Colorado, pp 223–259Google Scholar
  53. Kaiser HF (1960) The application of electronic computers to factor analysis. Educ Psychol Meas 20:141–151CrossRefGoogle Scholar
  54. Kozlowski TT, Kramer PJ, Pallardy SG (1991) The physiological ecology of woody plants. Academic, London, 657 ppGoogle Scholar
  55. LaMarche VC Jr, Harlan TP (1973) Accuracy of tree-ring dating of bristlecone pine for calibration of the radiocarbon time scale. J Geophys Res 78(36):8849–8858CrossRefGoogle Scholar
  56. Laughlin RB (2005) A different universe: remaking physics from the bottom down. Basic Books, New YorkGoogle Scholar
  57. Laughlin RB, Pines D (2000) The theory of everything. Proc Natl Acad Sci USA 97:28–31CrossRefGoogle Scholar
  58. Linick TW, Suess HE, Becker B (1985) La Jolla measurements of radiocarbon on south German oak tree ring chronologies. Radiocarbon 27(1):20–30Google Scholar
  59. Mitchell JM Jr, Dzerdzeevskii B, Flohn H, Hofmeyr WL, Lamb HH, Rao KN, Walléen CC (1966) Climatic change. WMO technical note no 79Google Scholar
  60. Morrison DF (1976) Multivariate statistical methods, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  61. Ni F, Cavazos T, Hughes MK, Comrie AC, Funkhouser G (2002) Cool-season precipitation in the southwestern USA since AD 1000: comparison of linear and nonlinear techniques for reconstruction. Int J Climatol 22:1645–1662CrossRefGoogle Scholar
  62. Pederson N, Cook ER, Jacoby GC, Peteet DM, Griffin KL (2004) The influence of winter temperatures on the annual radial growth of six northern range margin tree species. Dendrochronologia 22:7–29CrossRefGoogle Scholar
  63. Pilcher JR, Baillie MGL, Schmidt B, Becker B (1984) A 7272-year tree-ring chronology for western Europe. Nature 312(5990):150–152CrossRefGoogle Scholar
  64. Preisendorfer RW (1988) Principal component analysis in meteorology and oceanography. Elsevier Science, Amsterdam, 426 ppGoogle Scholar
  65. Preisendorfer RW, Zwiers FW, Barnett TP (1981) Foundations of principal components selection rules. SIO reference series 81-4, Scripps Institution of Oceanography, La Jolla, California, USA, 192 ppGoogle Scholar
  66. Read J, Busby JR (1990) Comparative responses to temperature of the major canopy species of Tasmanian cool temperate rainforest and their ecological significance. II. Net photosynthesis and climate analysis. Aust J Bot 38:185–205CrossRefGoogle Scholar
  67. Rencher AC, Pun FC (1980) Inflation of R 2 in best subset regression. Technometrics 22:49–53CrossRefGoogle Scholar
  68. Schulman E (1956) Dendroclimatic changes in semiarid America. University of Arizona Press, Tucson, 142 ppGoogle Scholar
  69. Schweingruber FH, Bräker OU, Schär E (1987) Temperature information from a European dendroclimatological sampling network. Dendrochronologia 5:9–33Google Scholar
  70. Schweingruber FH, Eckstein D, Serre-Bachet F, Bräker OU (1990) Identification, presentation and interpretation of event years and pointer years in dendrochronology. Dendrochronologia 8:9–38Google Scholar
  71. Shashkin AV, Vaganov EA (1993) Simulation model of climatically determined variability of conifers’ annual increment (on the example of common pine in the steppe zone). Russ J Ecol 24:275–280Google Scholar
  72. Smiley D, Huth P (1982) Gypsy moth defoliation in vicinity of Mohonk Lake 1956–1981. Unpublished research report. Mohonk Preserve, IncGoogle Scholar
  73. Snee RD (1977) Validation of regression models: methods and examples. Technometrics 19:415–428CrossRefGoogle Scholar
  74. Stokes MA, Smiley TL (1968) An introduction to tree-ring dating. University of Chicago Press, Chicago, Illinois, 73 ppGoogle Scholar
  75. Suess HE (1965) Secular variations of the cosmic-ray-produced carbon-14 in the atmosphere and their interpretation. J Geophys Res 70:5937–5952CrossRefGoogle Scholar
  76. Trumbore S, Gaudinski JB, Hanson PJ, Southon JR (2002) Quantifying ecosystem-atmosphere carbon exchange with a 14C label. Eos 83:265, 267–268CrossRefGoogle Scholar
  77. Tukey JW (1977) Exploratory data analysis. Addison-Wesley, London, 688 ppGoogle Scholar
  78. Twain M (1924) Mark Twain’s autobiography, vol 1. Harper & Brothers, New York, 368 ppGoogle Scholar
  79. Vaganov EA, Hughes MK, Kirdyanov AV, Schweingruber FH, Silkin PP (1999) Influence of snowfall and melt timing on tree growth in subarctic Eurasia. Nature 400:149–151CrossRefGoogle Scholar
  80. Vaganov EA, Hughes MK, Shashkin AV (2006) Growth dynamics of tree rings: images of past and future environments. Springer-Verlag, Berlin, Heidelberg, New YorkGoogle Scholar
  81. Visser H, Molenaar J (1988) Kalman filter analysis in dendroclimatology. Biometrics 44(4):929–940CrossRefGoogle Scholar
  82. Wigley TML, Briffa KR, Jones PD (1984) On the average value of correlated time series, with applications in dendroclimatology and hydrometeorology. J Clim Appl Meteorol 23:201–213CrossRefGoogle Scholar
  83. Wigley TML, Jones PD, Briffa KR (1987) Cross-dating methods in dendrochronology. J Archaeol Sci 14:51–64CrossRefGoogle Scholar
  84. Woodhouse CA (1999) Artificial neural networks and dendroclimatic reconstructions: an example from the Front Range, Colorado, USA. Holocene 9(5):521–529CrossRefGoogle Scholar
  85. Yamaguchi DK (1991) A simple method for cross-dating increment cores from living trees. Can J Forest Res 21:414–416CrossRefGoogle Scholar
  86. Yamaguchi DK (1994) More on estimating the statistical significance of cross-dating positions for ‘floating’ tree-ring series. Can J Forest Res 24(2):427–429CrossRefGoogle Scholar
  87. Yamaguchi DK, Allen GA (1992) A new computer program for estimating the statistical significance of cross-dating positions for ‘floating’ tree-ring series. Can J Forest Res 22(9):1215–1221CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Tree-Ring LaboratoryLamont-Doherty Earth ObservatoryPalisadesUSA
  2. 2.Department of Biological SciencesEastern Kentucky UniversityRichmondUSA

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