Climatic Change

, Volume 94, Issue 3–4, pp 233–245 | Cite as

A mathematical analysis of the divergence problem in dendroclimatology

  • Craig LoehleEmail author


Tree rings provide a primary data source for reconstructing past climates, particularly over the past 1,000 years. However, divergence has been observed in twentieth century reconstructions. Divergence occurs when trees show a positive response to warming in the calibration period but a lesser or even negative response in recent decades. The mathematical implications of divergence for reconstructing climate are explored in this study. Divergence results either because of some unique environmental factor in recent decades, because trees reach an asymptotic maximum growth rate at some temperature, or because higher temperatures reduce tree growth. If trees show a nonlinear growth response, the result is to potentially truncate any historical temperatures higher than those in the calibration period, as well as to reduce the mean and range of reconstructed values compared to actual. This produces the divergence effect. This creates a cold bias in the reconstructed record and makes it impossible to make any statements about how warm recent decades are compared to historical periods. Some suggestions are made to overcome these problems.


Tree Ring Ring Width Calibration Period Past Climate Climate Reconstruction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.National Council for Air and Stream Improvement, Inc. (NCASI)NapervilleUSA

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