Estimation of individual knot volumes by mixed-effects modelling

Abstract

We present a new method to estimate individual knot volumes based on a knot geometry model coupled with observations on branch characteristics. X-ray computer tomography and image analysis were used to measure the volume and geometry of 424 knots of Sitka spruce (Picea sitchensis (Bong.) Carrière). Knot geometry can be described mathematically by deriving functions for relative vertical position, diameter, and slope dependent on radial position in the stem. These functions were parameterized using “seemingly unrelated regression” and mixed-modelling techniques. This provided a base model for typical knots. To estimate individual knot volume, we used available data for branch diameter and insertion angle to obtain conditional predictions. We imputed the most likely knot trajectory, as relative vertical position cannot be measured on branches. The model explained up to 96% of the variability in knot volume by incorporating the branch measurements, in contrast to the 43% explained using the typical knot model. Knot volume assessment based only on conditional predictions of diameter and marginal predictions of vertical position also accounted for 96% of the variability. Therefore, measurements of branch diameter alone would be enough to obtain highly precise predictions of individual knot volume. This estimator is a first step towards a knot model to be used for the management of Sitka spruce in Great Britain.