Modelling knot morphology as a function of external tree and branch attributes

Existing models for describing knot morphology are typically based on polynomial functions with parameters that are often not biologically interpretable. Hence, they are difficult to integrate into tree growth simulators due to the limited possibilities for linking knot shape to external branch and tree characteristics. X-ray computed tomography (CT) images taken along the stems of 16 jack pine (Pinus banksiana Lamb.) trees and 32 black spruce (Picea mariana (Mill.) B.S.P.) trees were used to extract the three-dimensional shape of 3450 and 11 276 knots from each species, respectively. Using a nonlinear approach, we firstly fitted a model of knot geometry adapted from a Weibull function. Separate equations were used to describe both the curvature and the diameter of the knot along its pith. Combining these two equations gave an accurate representation of knot shape using only five parameters. Secondly, to facilitate the integration of the resulting model into a tree growth simulator, we extracted the parameters obtained for each knot and modelled them as functions of external branch and tree characteristics (e.g., branch diameter, insertion angle, position in the stem, tree height, and stem diameter). When fitted to a separate data set, the model residuals of the black spruce knot curvature equation were less than 2.9 mm in any part of the knot profile for 75% of the observations. The corresponding value from the diameter equation was 2.8 mm. In jack pine, these statistics increased to 5.4 mm and 3.2 mm, respectively. Overall, the ability to predict knot attributes from external tree- and branch-level variables has the potential to improve the simulation of internal stem properties.