Product and Residue Biomass Equations for Individual Trees in Rotation Age Pinus radiata Stands under Three Thinning Regimes in New South Wales, Australia

Using data from 239 trees that were destructively sampled and completely weighed in the field, four systems of nonlinear additive equations were developed for the estimation of product and residue fresh and dry weight of individual trees in rotation age (28 to 42 years) Pinus radiata stands under three thinning regimes: unthinned (T0), one thinning (T1) and two thinnings (T2). To cater for all practical applications, the four systems of equations included diameter at breast height overbark (DBHOB) as the only independent variable or both DBHOB and total tree height as predictors either with or without the incorporation of dummy variables for stand types. For all systems, the property of additivity was guaranteed by placing constraints on the structural parameters of the system equations. The parameter estimates were obtained by the generalized methods of moments (GMM) following a comparison with weighted nonlinear seemingly unrelated regression (WNSUR). Based on the predicted values from the system that had DBHOB as the predictor and dummy variables for stand types, the percentage of total tree fresh weight accounted for by residues increased from 14.8% to 20.5%, from 15.6% to 22.2% and from 13.9% to 18.7% for trees in the T0, T1 and T2 stands, respectively, as DBHOB increased from 15 to 70 cm. The corresponding changes in the percentage of residue dry weight were from 15.1% to 16.1%, from 15.7% to 17.1% and from 14.9% to 15.8% for the three stand types. In addition, two systems of allocative equations were developed to allocate the predicted product and residue biomass to their respective subcomponents. The system of allocative equations for product biomass predicted that sawlogs with bark accounted for 83% to 85% of product fresh weight and 82% to 87% of product dry weight over the same range of DBHOB. The predicted allocation of total residue dry weight to stump changed little, between 12% and 13%, over the same diameter range, but it was slightly higher for trees with DBHOB between 30 and 45 cm. The predicted allocation of total residue biomass to branches increased from 18% to 65% in fresh weight and from 18% to 57% in dry weight and that to waste decreased from 71% to 27% in fresh weight and from 70% to 32% in dry weight as DBHOB increased from 15 to 70 cm. Among the five biomass components, prediction accuracy was the lowest for pulpwood and waste. The systems of additive and allocative biomass equations developed in this study provided the first example of how the two approaches could be used together for the estimation of total tree, major and sub-component biomass. They will provide forest management with an enhanced capacity to more accurately estimate product and residue biomass of rotation age trees and thus to include the production of biomass for renewable energy generation in their management systems for P. radiata plantations.