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

Abstract

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.

Stocks of Carbon in Logs and Timber Products from Forest Management in the Southwestern Amazon

“…The number of individuals sampled was determined according to the sample size (n) for a population considered to be infinite using the formula n = t 2 * CV 2 (E%) 2 , where n = number of individuals sampled; t = tabulated value of Student's t-statistic at 5% significance with n-degrees of freedom; CV = coefficient of variation; and E% = required accuracy (10%). The number of individuals sampled per species was proportional to the relative density (individuals with DBH ≥ 50 cm ha −1 ) of the species in question [27,50]. Log volume (with bark) (V l ) values for the selected species were determined by the Smalian method, measuring the diameter along the stem at heights of 0.0 m, 0.3 m, and 1.0 m above the stump cut and every 2.0 m thereafter [50,51].…”

“…It was necessary to obtain fundamental information on biomass and carbon content in order to calculate the carbon stock in the trunk and in the wood products of the 12 species (136 felled trees), [27,32]. Biomass was calculated by multiplying the trunk volume (with bark) by the basic density of the wood (with bark), using the formula:…”

“…For those trees with DBH > 80 cm, a disk was removed at 0 m and then at intervals every 4.3 m until the total length of the commercial log was reached. For trees from 50 cm to 79.9 cm DBH, collections were made at 0 m and thereafter every 8 m until the total length of the commercial log was reached [27,34]. The 8-m log length allowed these logs to be used for sawn-wood products.…”

“…Brazilian legislation on forest management does not require estimates of carbon stocks [27]. Management activities can be regulated to maintain economic benefits, to minimize environmental damage, and to allow accurate carbon accounting.…”

“…In forest management in the Amazon, the log is the tree component harvested and removed from the management system [18,27]. The final sawn-wood products are obtained from logs in sawmills for primary preparation [31][32][33].…”