Validation of models predicting modulus of elasticity in Douglas-fir trees, boles, and logs

Abstract

Acoustic tools have simplified estimation of wood modulus of elasticity (MOE). Strong relationships between acoustic velocity and MOE of logs have encouraged use of acoustics at earlier points in the value chain, culminating in the development of acoustic harvesting systems. With accurate estimates of MOE of individual trees, improvements in efficiency along the value chain and increased value recovery will result. Our aim was to quantify the accuracy of MOE estimates at three distinct points: pre-harvest (standing trees), during harvest (merchantable boles), and post-harvest (5-m logs). We hypothesised that: (1) MOE estimated from acoustic velocity and wood density would provide greatest accuracy; and (2) bole estimates with a resonance tool would be more accurate than tree estimates with a time-of-flight tool. A sample of 168 Douglas-fir (Pseudotsuga menziesii [Mirb. Franco]) trees, representing the variability in acoustic velocity of 700 standing 36–51-year-old trees, was harvested from three sites. Prior to harvest, time-of-flight and breast-height diameter were recorded. After felling, resonance velocities of boles and subsequent 5-m logs were recorded. Discs, cut from log ends, were immersed, and green wood density determined. Half the logs were processed into boards, the other half into veneer sheets, and all products (in excess of 6000) non-destructively tested for MOE. MOE of parent trees, boles, and logs was then calculated from the mean MOE of derived products. Predictive mixed-effects models of tree, bole, and log MOE were developed using data from 139 trees. Fixed effects comprised combinations of velocity squared, wood density, acoustic MOE (derived from the wave equation), diameter, height, taper, and age. Random effects comprised site, plot, and, at the log level, tree. The models were validated using data from the remaining trees and compared using multiple performance metrics. For estimating tree MOE, a model with velocity squared, wood density, and taper as predictors is recommended. For estimating MOE of boles and logs, models with velocity squared and wood density are recommended. The models have an accuracy, as determined by RMSE, of about ± 2 GPa. For accurate MOE estimation, velocity alone is insufficient. Knowledge of wood density is necessary for improved accuracy.