A multivariate, nonparametric stem-curve prediction method

Abstract

The paper presents a general method for predicting the stem curve, volume, and merchantable height of a tree if breast height diameter (DBH) is measured, or if DBH and total height (H) as well as diameters at any heights are measured. Estimates for prediction variances are obtained both for diameters and volumes. The approach is multivariate and nonparametric. At the estimation stage, a multivariate model is developed for the total height and a fixed set of diameters: four diameters at absolute heights below breast height and eight diameters at relative distances between the breast height and the top of the tree. The expected values and variances of the dimensions and the correlations between dimensions are expressed as functions of DBH. These functions were estimated using smoothing splines. The model is applied by predicting unobserved dimensions from the observed dimensions using a linear predictor. If total height is not measured, then prediction is done using an approach based on two-point distributions. Correlation of total heights of different trees in the same stand is also modeled, and with this model, measured total heights in a stand can be used to predict unmeasured total heights. The approach provides both a detailed analysis of variation and covariation of stem curves and a practical prediction method.