Ratio estimators for aboveground biomass and its parts in subtropical forests of Brazil

Researchers on forest biomass seek to develop or find methods of simple application, whose estimators reveals the best performance and provide the additivity of the biomass parts. Tree biomass normally is obtained by scaling tree parts (stem, branches, and leaves) separately. When the biomass is modeled by parts of the tree, their sum does not match the total, which means lack of additivity in the tree biomass estimation. We aimed to test and propose a modeling technique for estimating total aboveground biomass, so that consistency between tree parts will be achieved. The techniques 'ratio estimators' and 'weighted apparently unrelated nonlinear regressions (WNSUR)' were tested using a biomass dataset with 387 trees. Data were collected in eight sites located in Parana & PRIME; and Rio Grande do Sul, Brazil, where information was collected on diameter at 1.30 m aboveground (dbh), heights (total, stem and crown), total biomass aboveground and its parts: stem, branches and leaves. All trees were identified at species level. To adjust the ratio equations, the cylinder volume (vcl), based on the mean square diameter (d2qi), was used as the independent variable and the total aboveground biomass and the respective parts: stem, branches, and leaves, as dependent variables. The occurrence of heteroscedasticity in the ratio estimators indicated that the data should be stratified into two stages, the first by dbh and the second by the slope of the ratio between the total aboveground biomass and the vcl of each tree. To group the trees in the second stage, a posteriori, a discriminant analysis was applied. The standard errors of the estimate resulted in less than 4% for the ratio estimators, while for the WNSUR they reached values larger than 40% for the total biomass aboveground and its parts. The statistics: bias, MAE, MSE and RMSE showed better performance by ratio estimators when compared to the WNSUR, for the total biomass and its parts except for the bias towards the stem. Ratio estimators naturally provide additivity to biomass parts making it possible to improve the precisions of the estimates. In future work with forest biomass and its parts, more canopy variables should be collected to improve the stratification of trees within the diameter stratum. The total volume of the trees should also be estimated, if possible, via xylometry, to approximate the ratio coefficients of the total aboveground biomass, as much as possible, to the actual values of the specific gravity of the wood.