Background: Individual tree taper and volume equations are essential for forest management. They provide estimates of volume that are incorporated into plot level volume equations and growth and yield models to estimate volumes per hectare in forest crops. Moreover, taper equations allow forest managers to estimate the dimensions of logs that can be cut from stems in their forests when they have measured diameters at breast height outside bark (dbhobs) and heights of trees in inventories. Compatible taper and volume equations have the property that the same individual tree volume can be estimated either from the tree volume equation or by integrating the taper equation. Durable eucalypt species such as Eucalyptus globoidea Blakely have especially valuable heartwood, so managers require estimates of the volumes and shapes of heartwood zones within trees. Simple overall wood taper and volume equations would therefore be inadequate.

Methods: 74 Eucalyptus globoidea trees were destructively sampled in eight trials throughout New Zealand. Tree ages were 7 to 29 years old, the diameters at breast height (dbhs) were 11 to 67.6 cm, and the heights were 7.2 to 35.4 m. All trees were felled, and lengths and taper diameters outside bark were measured. Discs were cut at irregular intervals along the stems to measure heartwood and sapwood's taper diameters. Heartwood and sapwood components were identified by applying methyl orange dye and quantified using image analysis. In this study, compatibility was extended so that sums of estimated volumes of separate components of stems, bark, sapwood and heartwood would equal overall tree volume estimates. In addition, taper equations were made for outside bark, inside bark and heartwood that were compatible with their respective volume equations. Parameters of five volume equations for the whole stem, whole wood, bark, sapwood, and heartwood were simultaneously estimated. Compatible taper equations for the whole stem, stem wood and heartwood were estimated to be compatible with the volume equations, creating a fully compatible system. Different model variants were tested using dbhob and tree height as independent variables and heartwood ratio, diameter and height as additional independent variables. Three techniques were used to obtain heartwood-related measurements: the electric resistance tomograph PiCUS TreeTronic scan simulation, increment core simulation and measurements from the bottom stump parts of felled trees. The main goal was to create compatibility between all volume and taper equations using primary predictor inputs. Another purpose was to improve the prediction of the heartwood volume and taper using additional independent variables.

Results: For model with two independent variables (dbh, tree height), root mean squared error (RMSE) of volume models were: heartwood (0.13 m3), sapwood (0.06 m3), wood inside bark (0.15 m3), bark (0.11 m3), wood including bark (0.14 m3). RMSE of taper models predicting diameter were: heartwood (2.57 cm), wood inside bark (2.35 cm), and wood including bark (2.47 cm). For models with three independent variables (dbh, tree height, heartwood ratio), the best RMSE results were obtained from increment core simulation for heartwood volume 0.11 m3 and heartwood taper 2.59 cm. For models with four independent variables (dbh, tree height, heartwood ratio and diameter), the best RMSE results were for heartwood volume 0.07 m3 and heartwood taper 2.14 cm. For models with five independent variables (dbh, tree height, heartwood ratio, heartwood diameter and height), the best RMSE results were for heartwood volume 0.07 m3 and heartwood taper 1.96 cm.

Conclusions: A compatible system of multiple taper and volume equations was created by simultaneously fitting parameters with minimal bias and precision levels of ± 0.06-0.15 m3 for volume equations and ± 2.35 to 2.57 cm for taper equations for a model with individual tree dbhob and height as independent variables. By using the additional independent variables (heartwood ratio, diameter and height), heartwood volume and taper predictions were improved by up to: ± 0.02 m3 (models with three independent variables), ± 0.06 m3/ ± 0.43 cm (models with four independent variables), ± 0.06 m3/ ± 0.61 cm (models with five independent variables). Leave-one-out cross-validation of the fitted models yielded very similar levels of precision and bias to those encountered when fitting models with the entire dataset.

The taper and volume equations were incorporated into an interactive tool to provide volume and taper estimates of durable Eucalyptus globoidea trees for forest managers. The interactive tool produces complex taper and volume information for all stem components using the independent variables as model inputs. Connecting all tree stem wood and bark components’ taper and volume and ensuring their compatibility is novel in forest mensuration. Moreover, future development and improvements for similar projects are suggested.