Model error propagation in a compatible tree volume, biomass, and carbon prediction system

Abstract

Background: Individual tree attributes such as volume, biomass and carbon mass are widely known to be highly correlated. As these attributes are typically predicted from statistical models, frameworks that provide compatible relationships among these attributes are usually preferred over approaches that provide independent predictions. However, the propagation of model error can be a concern as this compatibility often relies on predictions for one attribute providing the basis for other attributes. In this study, a compatible tree volume, biomass, and carbon prediction system was evaluated to ascertain how model prediction uncertainty propagates through the system and to examine the contribution to uncertainty in population estimates. Results: Generally, the total and merchantable stem volume predictions are used to derive associated biomass values and subsequently biomass is converted to carbon. As expected, the amount of uncertainty due to the models follows volume < biomass < carbon such that the carbon attribute is the most affected by error propagation. Biomass and associated carbon in tree branches tended to have larger model uncertainty than the stem components due to smaller sample sizes and a greater proportion of unexplained variation. In this model system, direct predictions of whole tree biomass provide the biomass basis and stem and branch components are harmonized to sum to the whole tree value. Corresponding harmonized carbon content values are obtained through application of a common carbon fraction. As such, whole tree biomass and carbon tended to have less model uncertainty than the constituent components primarily due to fewer contributing sources. Conclusions: Although a wide range of outcomes are realized across the various volume, biomass, and carbon components, increases in the standard error of the population estimate due to model uncertainty were always less than 5% and usually smaller than 3%. Thus, forest inventory data users desiring population estimates of tree volume, biomass, and carbon can expect little additional uncertainty due to the prediction model system while benefitting from the implicit compatibility among attributes.