A system for compatible prediction of total and merchantable volumes allowing for different definitions of tree volume
A system of equations for compatible prediction of total and merchantable volumes that allows for different definitions of tree volume was developed in this study. The use of the developed system will allow the conversion and subsequent comparison of results from forest inventories using different definitions of tree volume (e.g., including or not the top material of the tree and (or) the stump, inside or outside bark). The compatibility between taper, total volume, and volume ratio equations is ensured by properly integrating the taper equation. The diameter under the bark at any height is modeled with the Demaerschalk taper equation, and the corresponding diameter over the bark is obtained by assuming that bark thickness is also modeled with Demaerschalk’s function. The set of equations that has contemporaneous cross-equation error correlation (known as nonlinear seemingly unrelated regression equations) was fit using nonlinear joint generalized least squares regression. The predictive ability was evaluated using an independent data set. The system is consistent and performs well when applied to maritime pine ( Pinus pinaster Ait.) trees in Portugal, showing better performance than do other total volume equations for maritime pine used in the latest Portuguese national forest inventories.