• The Smoothing Spline: A New Approach to Standardizing Forest Interior Tree-Ring Width Series for Dendroclimatic Studies

      Cook, Edward R.; Peters, Kenneth; Lamont-Doherty Geological Observatory, Palisades, New York (Tree-Ring Society, 1981)
      A new approach to removing the non-climatic variance of forest interior tree-ring width series, using the smoothing spline, is described. This method is superior to orthogonal polynomials because it makes no assumptions about the shape of the curve to be used for standardization. Also, because the spline curve can range continuously from a linear least squares fit to cubic interpolation through the data, it is far more flexible than polynomials and provides a more "natural" fit. For computing the spline, we found that specifying the Lagrange multiplier p which appears in the calculus of variation solution rather than the residual variance as suggested by Reinsche was both practical and more efficient. In effect, the smoothing spline is a one-parameter family of low-pass filters defined by p. We describe the general characteristics of these filters in the time and frequency domains and compute the response functions for several of them. The smoothing spline is an excellent tree-ring standardization method because its filtering characteristics are well defined. Its utility for dendroclimatology should be considerable since, outside of semiarid environments, sites similar to forest interiors predominate.
    • Statistical Significance and Reproducibility of Tree-Ring Response Functions

      Gray, B. M.; Wigley, T. M. L.; Pilcher, J. R.; Climatic Research Unit, University of East Anglia, Norwich, U. K.; Palaeoecology Centre, The Queen's University of Belfast, Northern Ireland (Tree-Ring Society, 1981)
      This paper is concerned with the overall significance and reproducibility of the response function. A test of significance is devised which is based on the Binomial distribution. Combined with other tests, the method is then used to compare two different response functions to examine the reproducibility of climate-chronology response. Two approaches are used: the first compares two response functions covering the same period from the same site, based on independent chronologies of the same species; the second compares the response of a single chronology over two equal non-overlapping time periods. The results suggest that the response in the examples used is statistically reproducible on a site, and statistically stable over periods of time.
    • Test of a New Method for Removing the Growth Trend from Dendrochronological Data

      Warren, W. G.; | MacWilliam, S. L.; Forintek Canada Corp., Vancouver, B.C. (Tree-Ring Society, 1981)
      Tests of the compound increment function, introduced by Warren (1980) as a means for removing the growth trend from dendrochronological data, are herein reported. In particular, the inter- and intra-site correlations of the residuals generated by the new method are compared with those generated by standard exponential fits. It is also shown that, in the presence of non-climatically induced responses, such as might arise from thinning, exponential fits can lead to spuriously high intra-site correlations. Accordingly, and because the new method's virtual elimination of negative and very low positive correlations, it appears to be the more satisfactory for portraying the growth trend.