A Three-Step Proportional Weighting System of Nonlinear Biomass Equations

Nonlinear simultaneous systems of tree biomass models have been developed for various tree species around the world. To deal with the additivity property between total tree biomass and component biomass predictions, Parresol's (Parresol 2001) aggregation approach, in which a nonlinear model is specified for each of the tree components and the total tree biomass is set up as the sum of these component models, has been widely adapted. The aggregation nature of the systems requires each tree component to be estimated to obtain the total or subtotal biomass. A relatively large prediction error in any component biomass model can affect the prediction accuracy of the total or subtotal tree biomass. In this study, we used a three-step proportional weighting (3SPW) system to deal with the additivity of nonlinear biomass models, which disaggregated the model prediction of the total tree biomass into subtotals (e.g., aboveground or crown), and then the estimated biomass of the subtotals was proportionally divided into tree components (e.g., stems, branches, or foliage). Our results indicated that the 3SPW system guaranteed the stepwise additivity of total, subtotals, and tree components, as well as provided a biomass model for each subtotal and tree component. The results of model fitting and validation revealed that the 3SPW system performed as well as Parresol's aggregation systems and offers a good alternative for ensuring the additivity property of nonlinear biomass model systems.