On the Use of Upper Stem Diameters to Localize a Segmented Taper Equation to New Trees

Abstract

Upper stem diameter measurements on trees can be used to localize an existing stem taper equation to individual trees and hence improve the tree-level accuracy of stem taper models. Two approaches of localizing taper equations were evaluated on the Max and Burkhart (1976) taper model: (1) an algebraic constraint (AC) approach where some of the parameters of the taper equation are constrained algebraically so that the taper equation predicts the observed dbh and upper stem diameter(s) and (2) an empirical Bayes random effects prediction (EB) approach where the observed upper stem diameter(s) is/are used to predict the tree-specific taper model parameters for a given tree. Radiata pine (Pinus radiata D. Don) over bark stem sections data from sites across New Zealand and similar data from loblolly pine (Pinus taeda L.) trees from sites across southern United States were used in the analysis. Seventy percent of the trees in each data set were used to fit a random parameter Max and Burkhart (1976) taper equation and the remaining 30% used to validate the model, identify a single upper stem diameter that gave the most accurate localized taper model, and determine the better localizing approach between AC and EB. The AC and EB approaches, with the best localizing upper stem diameter, were tested on additional independent data sets that were not part of the split data sets. Upper stem diameters measured at 60% of total height resulted in the lowest prediction error localized models, with the EB approach generally performing better than the AC approach. Compared to the prediction error from using nonlocalized models, overall model prediction error due to the best localized model was 1 to 3 absolute percentage points smaller with most reductions in prediction error occurring in the portion of the tree bole above 50% of total height.