Improving quantitative structure models of trees inspired by pipe and metabolic scaling theory

We invent here in this manuscript new tree describing parameters which can be derived from a QSM. QSMs are topological ordered cylinder models of trees which describe the branching structure completely. All new invented parameters have in common, that their defining point of view looks from the direction of the tips and not from the root along the tree. The reason here is simple, diameter relations are stronger when they rely on a distance measure to the tip(s) rather than on a distance measure to the root. In the traditional branch order for example diferent sized branches are contained, but in the reverse branch order this problem is barely exiting anymore. The pipe model theory (PMT) is a theory adapted to deciduous trees, based on the allometric scaling theory. And according to the PMT the count of new growth units can serve as a proxy to predict the sapwood area at the query cylinders cross section. By multiplying this area proxy with the cylinder length we receive a proxy for the sapwood volume contained. We name the sapwood volume of the whole subbranch VesselVolume. The sapwood volume finally serves as the predictor for the basic allometry function to predict the diameter/radius of combined sap and heartwood at the query point. For validation we use QSMs produced from an open point cloud data set of tree clouds with SimpleForest software. We compare the QSM volume against the harvested reference data for 66 felled trees. We also found QSM data of TreeQSM, a competitive and broadly accepted QSM modeling tool. Our RMSE was less than 40 % of the TreeQSM RMSE. And for other error measures, the r2 adj. and the CCC, the relative improvement looked even better with reaching only 27 % and 21 % of the TreeQSM errors respectively. With the invention of this filter we improve tree volume prediction capabilities utilizing QSMs. Additionally, we run numerical tests against the West Brown Enquist (WBE) model predictions using our filtered QSMs. ### Competing Interest Statement The authors have declared no competing interest.