A global and local allometric pantropical model - Paz-Pellat, Fernando (Instituto de Ecología, A.C., 2021)
The development of generalized allometric models that allow estimations that are comparable with local models is a great challenge for estimating aerial biomass in tropical forests. The estimates of the parametrized allometric models in the logarithmic space (transformation to logarithmic format) minimizing the squared error of estimation requires the estimation of correction factors for the inverse transformation to the arithmetic space. Additionally, if the objective is the minimization of biases (mean relative error MRE and mean absolute error MAE), then the absolute estimation error can be minimized. In this work, classic allometric models were used, based on the relationship between biomass (B) and normal diameter (D), total height (H) and wood density (ρ), to review the relationships between their parameters. To analyze the proposed allometric relationships, a pantropical public database (4 004 data, 58 sampling sites) was used. The analyzes showed that for global models (all sites) and local (each site) the linear regression model of the relationship B versus ρD2H resulted in the best model (root mean square error or RMSE metric), for which was used as a reference standard. The models parametrized in the logarithmic space for the global estimates resulted with estimation errors greater than the model B = av0 (D2H) with av0 as a linear function with ρ. The estimation of av0 was performed by minimizing the absolute error, resulting in the lowest estimation bias errors (MRE and MAE), with RMSE values comparable to the quadratic error minimization process. For local estimates using allometric models at the site level, the model was used with only av0 (minimization of the absolute error) and changing the correction factor from the simple estimator to that of ratio estimator, resulting in a prediction model with an estimation error comparable to the nonlinear regressions and surpassing the classic allometry models. Since there is no information on aerial biomass in normal forest inventories, the estimation of the ratio correction factor was empirically parameterized by a multivariate linear regression process of data measured in the field, with results comparable to having measurements of aerial biomass on the field.