Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study

Forests in the southwestern Amazon are rich, diverse, and dense. The region is of high ecological importance, is crucial for conservation and management of natural resources, and contains substantial carbon and biodiversity stocks. Nevertheless, few studies have developed allometric equations for this part of the Amazon, which differs ecologically from the parts of Amazonia where most allometric studies have been done. To fill this gap, we developed allometric equations to estimate the volume, biomass, and carbon in commercial trees with diameter at breast height (DBH) ≥ 50 cm in an area under forest management in the southeastern portion of Brazil’s state of Acre. We applied the Smalian formula to data collected from 223 felled trees in 20 species, and compared multiple linear and nonlinear models. The models used diameter (DBH) measured at 1.30 m height (d), length of the commercial stem (l), basic wood density (p), and carbon content (t), as independent variables. For each dependent variable (volume, biomass, or carbon) we compared models using multiple measures of goodness-of-fit, as well as graphically analyzing residuals. The best fit for estimating aboveground volume of individual stems using diameter (d) and length (l) as variables was obtained with the Spurr model (1952; logarithmic) (root mean square error (RMSE) = 1.637, R² = 0.833, mean absolute deviation (MAD) = 1.059). The best-fit equation for biomass, considering d, l, and p as the explanatory variables, was the Loetsch et al. (1973; logarithmic) model (RMSE = 1.047, R² = 0.855, MAD = 0.609). The best fit equation for carbon was the Loetsch et al. (1973; modified) model, using the explanatory variables d, l, p, and t (RMSE = 0.530, R² = 0.85, MAD = 0.304). Existing allometric equations applied to our study trees performed poorly. We showed that the use of linear and nonlinear allometric equations for volume, biomass, and carbon can reduce the errors and improve the estimation of these metrics for the harvested stems of commercial species in the southwestern Amazon.