Analysis of the Relationship between DBH and Crown Projection Area Using a New Model

Abstract

Relations of DBH-crown projection area (CPA) were studied for deciduous and coniferous trees with different models, one of which is newly derived this time. For DBH-CPA relations, a proposed power-sigmoid function was the most suitable one among four models because of its good fit and mechanistic meaning. This model contains the feature that CPA grows with the second power relation to DBH, and the increasing rate of CPA slows as DBH increases. With transformation, the power-sigmoid function for DBH-CPA relation can be applied for individual basal area (IBA)-CPA relations as single-saturate function, and these two functional models have high compatibility. Next, the differences of DBH-CPA between deciduous and coniferous tree groups were analyzed with power-sigmoid function. The initial increasing rates of CPA against DBH for each group were similar, though the CPA's increasing rate for the coniferous group tended to decrease earlier than for the deciduous group. Because the power sigmoid function has mechanistic meanings, one can separately analyze the attributes of the DBH-CPA relation: the initial increasing rate of CPA and final tree form.