Regression estimators for aboveground biomass and its constituent parts of trees in native southern Brazilian forests

The mathematical models used applying the Nonlinear Seemingly Unrelated Regressions (NSUR) or Weighted Nonlinear Seemingly Unrelated Regressions (WNSUR) methodologies can contribute to generate acceptable and reliable estimates of total aboveground biomass and its constituent parts, which are needed to implement forest management strategies to maintain desirable and sustainable carbon stocks. The aim of this study was: 1) to fit the sample data with independent nonlinear regression models and present the results obtained from the respective statistical estimates for total biomass aboveground and the constituent parts of trees in native forest trees. 2) To fit the sample data with regression models simultaneously, that is, whose models are composed of appropriate combinations of their coefficients, in order to obtain additivity of the estimates and present better results for the total aboveground biomass and the constituent parts of the trees. 3) To apply weighting procedures to the variances of the fitted models. 4) To evaluate the error due to the regression function on forest biomass estimation. The data came from eight sites located in the states of Parana and Rio Grande do Sul, Brazil, and information was collected on diameter at 1.30 m aboveground ( DBH ), total height, biomasses of the trunk components (branches and leaves) and total aboveground biomass. Non-linear functions were independently and simultaneously fitted, using DBH and total height as independent variables in the regression models. Independent fitting of equations was performed using generalized nonlinear least squares (ENGLS) and simultaneous fitting of equations was obtained by means of NSUR. Weighting, by applying a variance structure in the two procedures, was done to solve the issue of heteroscedasticity. Numerically, the equations fitted simultaneously performed better and were more efficient than the independently fitted models, which resulted in biological inconsistency, that is, non-additivity of the biomass of constituent parts of the trees and the total biomass. Simultaneous fitting generated superior statistical and biological properties to obtain tree estimates of the of constituent parts of the trees and total aboveground biomass in native forests of southern Brazil. The smaller error due to the regression function used in the forest biomass inventory was obtained by simultaneous fitting. With these results, the procedure using simultaneous and weighted fitting of equations (WNSUR) is recommended to fit biomass equations for native forests in southern Brazil.