Modeling volume expansion factors for temperate tree species in France

The objective of this study was to model the volume expansion factor (VEF), defined as being the ratio between the total aboveground woody volume and the stem merchantable volume of a tree, as a function of tree height and diameter at breast height. A large database (dataset #1) of detailed stem and branches volume measurements, constituted by 8192 felled trees from 19 temperate tree species, was used for calibrating the models. In addition, an independent dataset (dataset #2), constituted by 176 felled trees from 13 species, was collected for validating the models. From dataset #1, the RMSE for the prediction of the total volume varied from 0.005 to 0.476 m(3), depending on the diameter class, and the corresponding relative RMSE varied from 8.0% to 13.7%, depending on the diameter class. A 10-fold cross-validation on dataset #1 gave an average RMSE of 0.136 for the prediction of the VEF and of 0.150 m(3) for the prediction of the total volume, which was in the same order as average RMSE obtained from the whole dataset #1. Validation on dataset #2 gave satisfactory results, even for the application of VEF to other tree species: RMSE obtained for the different tree species were in the same order as RMSE obtained from calibration dataset #1, except for some particular cases. The largest errors were obtained when the model was clearly used in extrapolation, e.g., for five large-size Fraxinus (whereas dataset #1 included smaller trees) and several Quercus and Fagus from coppice-with-standards stands (whereas dataset #1 included mainly pure even-aged high-forest trees). The observed differences between species seemed consistent with the general knowledge about species-specific traits. For a given diameter at breast height, angiosperms were found to have a much larger volume of branches in comparison with the corresponding stem volume than gymnosperms. For a tree of 30 cm in diameter, the lowest values of VEF were obtained for Picea and Abies (VEF 1.3). The methodology that was developed, based on nonlinear mixed-effects modeling, is easily applicable to other definitions of VEF or biomass expansion factors