Predicting branch to bole volume scaling relationships from varying centroids of tree bole volume

Abstract

A novel “varying-centroid” method is presented for predicting whole-tree, aboveground stem volume (i.e., bole plus branch volume) to bole volume ratios from changes in the centroid of tree bole volume associated with branching of the bole. The method was derived from a simple fractal-like tree model based on a conceptualization of tree branching architecture by Leonardo da Vinci. The method recognizes that the centroid of bole volume (the point at which one half of bole volume is above and one half is below) is always lower than the centroid of whole-tree volume and that shifts in the centroid of bole volume should be predictably related to the size of a tree’s crown. The method assumes that branch-displaced bole volume profiles can be compared with reference bole profiles that are not significantly influenced by branching, at the centroid of bole volume, and that the magnitude of bole centroid displacement predicts the branch volume necessary to cause it. When the method was applied to hardwood trees representing diverse species, sizes, and stand conditions across Michigan, the centroid of bole volume was found to vary predictably with measurable tree crown attributes and bole plus branch wood to bole wood volume ratios were generally predicted within 10% of the true value using the new method.