Additive biomass equations for native eucalypt forest trees of temperate Australia

Biomass additivity is a desirable characteristic of a system of equations for predicting component as well as total tree biomass since it eliminates the inconsistency between the sum of predicted values for components such as stem, bark, branch and leaf and the prediction for the total tree. Besides logical consistency, a system of additive biomass equations when estimated by taking into account the inherent correlation among the biomass components has greater statistical efficiency than separately estimated equations for individual components. Using mostly small sample data from both published and unpublished sources, a system of non-linear additive biomass equations was developed for 15 native eucalypt forest tree species of temperate Australia. Diameter at breast height was used as the independent variable for all 15 species, while the combined variable of diameter and tree height was used for 14 species with height data. The system of additive equations provided more accurate biomass estimates than the common approach of separately fitting total tree and component biomass equations using log transformed data through least squares regression. Residual error variances were collectively estimated for each species by pooling small sample data across species and using indicator variables to represent the scale factor for each species in a residual variance function. This method overcame a common problem in estimating heteroscedastic error variance in non-linear biomass equations with additive error terms for small samples. From the estimated residual variance functions, approximate confidence bands containing about 95% of the observed data about the mean curve of predicted biomass were derived for all biomass components of each species. This system of additive biomass equations will prove to be useful for biomass estimation of native eucalypt forests of temperate Australia.