Modeling Tree Crown Ratio

TL;DR: The crown ratio (the ratio of live crown length to total height) of an individual tree in a stand can be predicted from commonly measured stand and tree variables and, when extrapolated, this nonlinear model continues to be biologically reasonable.

Abstract: The crown ratio (the ratio of live crown length to total height) of an individual tree in a stand can be predicted from commonly measured stand and tree variables. For example, the ratio can be estimated using a nonlinear model combining stand basal area (BA) and initial tree diameter (DBH). The first term reflects the importance of competition on crown ratio; the second term differentiates among trees of different sizes.Biologically reasonable behavior is exhibited by the crown ratio model. The core model, with only two parameters, is very flexible; the full model, with four parameters, is capable of describing a full range of logical crown ratio growth patterns. When extrapolated, this nonlinear model continues to be biologically reasonable. In addition, the parameters are capable of theoretical interpretation.When tested on a Lake States data base of over 150 000 trees, the moan crown ratio estimation error was small, −2% for softwoods and +3% for hardwoods. Variation in weather and survey crew effects...