• The Dendrochronological Potential of Populus Balsamifera in Northern Alaska

      Dunwiddie, Peter W.; Edwards, Mary E.; Lost Farm, Hummock Pond Road, Nantucket, Massachusetts; College of Forest Resources, University of Washington, Seattle, Washington (Tree-Ring Society, 1984)
      Populus balsamifera grows farther north than any other tree in North America. In northern Alaska, these trees have clear annual growth rings, and reach ages over 230 years. High year-to-year variability in ring widths permitted ready crossdating. A chronology prepared using paired cores from 16 trees exhibits mean sensitivity (0.48) and standard deviation (0.50) values much higher than those obtained from most conifer species in the Arctic. First order autocorrelation (0.43) is also lower than most Arctic species. A strong correlation (r =0.47) with June temperature suggests balsam poplar may provide a good record of growing season temperature.
    • Multicollinearity within Selected Western North American Temperature and Precipitation Data Sets

      Cropper, John Philip; ProSight Corporation (Tree-Ring Society, 1984)
      This paper is concerned with examining the degree of correlation between monthly climatic variables (multicollinearity) within data sets selected for their high quality. Various methods of describing the degree of multicollinearity are discussed and subsequently applied to different combinations of climate data within each site. The results indicate that higher degrees of multicollinearity occur in shorter data sets. Data consisting of 12 monthly variables of a single parameter (temperature or precipitation) have very low degrees of multicollinearity. Data set combinations of two parameters and lagged variables, as commonly used in tree-ring response function analysis, can have significant degrees of multicollinearity. If no preventative or corrective measures are taken when using such multicollinear data, erroneous interpretations of regression results may occur.
    • Response Functions Revisited

      Blasing, T. J.; Solomon, A. M.; Duvick, D. N.; Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 57851 (Tree-Ring Society, 1984)
      The use of orthogonalized climatic variables in regression to specify treegrowth/climate relationships, commonly known as response function analysis, involves several a priori decisions and a posteriori interpretations, any of which maybe open to question. Decisions about the number of climatic variables to include, confidence limits, number of eigenvectors to allow as candidate predictors in regression, etc., can affect the response function in unpredictable ways and lead to possible errors in interpretation. To demonstrate the nature of these effects, we compared response functions for particular chronologies with the correlation function, which is simply the series of correlation coefficients between a tree-ring chronology and each of several sequential monthly climatic variables. The results indicate that response functions including high-order eigenvectors should be interpreted cautiously, and we recommend using the correlation function as an interpretive guide. Prior tree-growth variables in regression can mask climatic effects, and the correlation function can also be useful in detecting this masking. Statistical significance is more often attained in response functions than in correlation functions, possibly due to differences in the statistical testing procedures, to the statistical efficiency of eigenvectors in spending degrees of freedom, or to the filtering effects on the climatic data that result from eliminating high-order eigenvectors (noise) from the response function. These filtering effects plus the orthogonalization make response function analysis an efficient method for specifying tree-growth/climate relationships. The examples and guidelines presented here should enhance the usefulness of the method.