Mathematical model of DBH uncertainty from the shape of the wood cross-section

Abstract

We investigate the uncertainty of Diameter at Breast Height, or DBH, of woods via a simple mathematical model. Usually, the DBH is not measured directly. The measurement is done on the Girth at Breast Height (GBH), which, by definition, is the circumference of wood at 130 cm above the ground. The DBH can then be calculated, assuming that the wood cross-section is a circle. This can introduce uncertainty to the DBH due to the irregularity of the shape of the wood cross-section. In this work, we approximate the wood cross-section by an ellipse, which can be fitted to the cross-section better than the circle. However, the eccentricity of the fitted ellipse is unknown, so we treat it as a random variable. The discrepancy between the diameter of the circle with the same area as the fitted ellipse, and the diameter of the circle with the same circumference as the GBH, is calculated. Monte Carlo simulations are performed to obtain the uncertainty of the DBH.