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Resistograph, acoustic velocity, Douglas-fir, mixed-effects models
Background: Accurate estimates of wood density are needed by the forest sector to increase value along the tree-to-product value-chain. Amongst tools supporting in-situ assessments, micro-drills and acoustic hammers have become increasingly popular. Our objective was to use these tools, and other easily-obtained measures, to develop predictive wood density models for in-situ assessments of Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) trees in western North America.
Methods: Wood density estimates of 133 trees, 60–75 years-old, were benchmarked against X-ray densitometry data using linear mixed-effects models. Mean resistograph amplitude (unadjusted, adjusted, and standardised variants), and combinations of acoustic velocity, tree diameter, stand age, and site index were considered as fixed effects. Plots, comprising differing treatments, and sites were considered as random effects. Candidate models were selected based on fit statistics, and further evaluated with an independent external dataset comprising 37 Douglas-fir trees.
Results: The optimal model comprised amplitude (adjusted), site index (transformed), and the quotient of velocity and age. It had a mean absolute percentage error, MAPE, of 4.1%, mean absolute error, MAE, of 19.4 kg.m-3, a root-mean-squared-error, RMSE of 25.0 kg.m-3, and marginal R2 for fixed effects, R2marg of 0.60. With external data, MAPE was 8.7%, MAE 52.4 kg.m-3 and RMSE 59.5 kg.m-3. Fit statistics for a simpler two-variable model (standardised amplitude and transformed site index) were: MAPE 4.9%, MAE 23.2 kg.m-3, RMSE 28.0 kg.m-3, and R2marg, 0.48, and with external data MAPE was 8.5%, MAE 51.6 kg.m-3 and RMSE 59.3 kg.m-3. Thus, with external data, the simpler model produced greater accuracy than the optimal model. Amplitude, and all other single-variable models, recorded poorer levels of accuracy.
Conclusions: Micro-drilling alone, though highly significant as a predictor, is insufficient for providing accurate wood density estimates of individual trees. Site effects need to be considered too. Standardisation of mean amplitudes to z-scores makes models highly portable across a range of resistance tools and operating speeds, and therefore more practical. As noted in the literature, optimal models are not necessarily best for predicting outcomes with other datasets, therefore model evaluation with external data is critical to determining how well a model will perform in practice.