Estimating above-ground biomass of trees: comparing Bayesian calibration with regression technique

Abstract

The commitment to report greenhouse gas emissions requires an estimation of biomass stocks and their changes in forests. When this was first done, representative biomass functions for most common tree species were very often not available. In Germany, an estimation method based on solid volume was developed (expansion procedure). It is easy to apply because the required information is available for nearly all relevant tree species. However, the distributions of neither parameters nor prediction intervals are available. In this study, two different methods to estimate above-ground biomass for Norway spruce (Picea abies), European beech (Fagus sylvatica), and Scots pine (Pinus sylvestris) are compared. First, an approach based on information from the literature was used to predict above-ground biomass. It is basically the same method used in greenhouse gas reporting in Germany and was applied with prior and posterior parameters. Second, equations for direct estimation of biomass with standard regression techniques were developed. A sample of above-ground biomass of trees was measured in campaigns conducted previously to the third National Forest Inventory in Germany (2012). The data permitted the application of Bayesian calibration (BC) to estimate posterior distribution of the parameters for the expansion procedure. Moreover, BC enables the calculation of prediction intervals which are necessary for error estimations required for reporting. The two methods are compared with regard to predictive accuracy via cross-validation, under varying sample sizes. Our findings show that BC of the expansion procedure performs better, especially when sample size is small. We therefore encourage the use of existing knowledge together with small samples of observed biomass (e.g., for rare tree species) to gain predictive accuracy in biomass estimation.

Appendix

For practical usage in standard inventories, simplified models are presented in Table 3. An additive error term with a variance function as presented in “Estimating parameters by regression” section was used.