A Preliminary System of Equations for Predicting Merchantable Whole-Tree Volume for the Decurrent Non-native Quercus rubra L. Grown in Navarra (Northern Spain)

Estimation of tree volume typically focuses on excurrent forms, with less attention given to decurrent forms. Species with decurrent form, particularly hardwoods, lack a dominant stem and have large diameter branches that can be included in the merchantable wood volume. We developed a preliminary two-equation system comprising a taper equation and a merchantable whole-tree volume (stem and branches) equation for Quercus rubra L. growing in Navarra (Northern Spain). The equation system includes the diameter at breast height and total tree height as independent variables, along with merchantable height—the height up to which the stem maintains a well-defined excurrent form—as an additional variable. After estimating the stem volume, the branch volume is estimated by subtracting the stem volume from the merchantable whole-tree volume. A second order continuous autoregressive error structure was used to correct for autocorrelation between residuals from the fitted taper equation. The equations explained 90% of the observed variability in diameter and 86% of the observed variability in merchantable whole-tree volume. Both equations have been implemented in the Cubica Navarra software for use as a system of equations. These equations are considered preliminary and will be refitted or validated as additional data becomes available from various locations.