A general method for assessing the effects of uncertainty in individual-tree volume model predictions on large-area volume estimates with a subtropical forest illustration

Abstract

Forest inventory estimates of tree volume for large areas are typically calculated by adding the model predictions of volumes for individual trees at the plot level, calculating the mean over plots, and expressing the result on a per unit area basis. The uncertainty in the model predictions is generally ignored, with the result that the precision of the large-area volume estimate is optimistic. The primary study objective was to assess the performance of a Monte Carlo based approach for estimating model prediction error that had been developed for boreal and temperate forest applications when used for a subtropical forest application. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty, the nonlinear nature of the models, and heteroskedasticity. A related objective was to estimate the effects of model prediction uncertainty due to residual and parameter uncertainty on the large-area volume estimates for the Brazilian state of Santa Catarina. The primary conclusions were fourfold. First, the methodological approach worked well. Second, the effects of model residual and parameter uncertainty on large-area estimates of mean volume per unit area were negligible for the models and calibration datasets used for the study. Third, for the models currently in use in Santa Catarina, the effects of model residual and parameter uncertainty may be ignored when calculating large-area estimates of mean volume per unit area. Fourth, differences were negligible between estimates of the mean and standard error obtained using a single, nonspecific volume model and estimates obtained using both forest-type models and species-specific/species-group models.

Generic and specific stem volume models for three subtropical forest types in southern Brazil

“…Besides the fact that nonlinear models are available and provide the possibility of fitting by maximum likelihood any model for the variance (Zuur et al 2009;Picard et al 2012), the logarithmic scaling and back transforming to original scale have a long and continuing history in constructing volume and biomass allometric models (Baskerville 1972;Brown et al 1989;Chave et al 2005;Segura and Kanninen 2005;Litton and Kauffman 2008;Basuki et al 2009;Guendehou et al 2012;Breidenbach et al 2014;McRoberts and Westfall 2014;McRoberts et al 2015). In Brazil, there is a clear trend for using this kind of transformation in volume model adjustment for native forests.…”

A practical measure for determining if diameter (D) and height (H) should be combined into D2H in allometric biomass models

“…For the nonlinear regression approach, we fit models using weighted nonlinear least squares methods (nls function in R). Because the variance is heteroscedastic on the original scale, increasing with increasing diameters, we weighted the observations using a 10-step procedure modified from McRoberts et al (2015McRoberts et al ( , 2016: i) fit a nonlinear model without weights; ii) calculate the heteroscedastic residuals ( ) and predicted biomass (AGB i ) for each tree; iii) sort the pairs AGB i and ε i in ascending order with respect to AGB i ; iv) group the pairs AGB i and ε i into g groups of size 25; v) for each group, calculate the mean of AGB i (AGB ̅̅̅̅̅̅ g ) and the variance of ε i (σ g 2 ); vi) log-log transform the resulting group values; vii) fit a linear model to the log-log transformed data, predicting…”

“…Allometric biomass models are regression models that typically use tree diameter and/or tree height to predict biomass. Despite emerging new technologies such as remote sensing, empirical allometric models remain central when predicting forest biomass (Zianis and Radoglou, 2006;Vieilledent et al, 2012;McRoberts et al, 2015). Diameter at breast height (D, at 1.3 m above ground) is a basic forest inventory variable (Gschwantner et al, 2009) and is the most common predictor of tree volume or biomass (Zianis et al, 2005).…”

Height-Diameter Models for Three Subtropical Forest Types in Southern Brazil

“…Its advantage is associated, in part, with the fact that the logarithmic scale tends to correct the level of data heteroskedasticity coming from the positive correlation between the mean and variance of the dataset (Sokal;Rohlf, 1987). Loglinear models have good qualities, such as satisfactory precision and easy adjustment and are widely used models for allometric purposes (Brown;Gillespie;Lugo, 1989;Fang;Bailey, 1998;Nogueira et al, 2008;Breidenbach et al, 2014;Westfall, 2014;McRoberts et al, 2015). Although, when model parameters are estimated using data transformed to the logarithmic scale and prediction is desired on the original scale, an adjustment term must be added to the prediction to compensate for bias that accrues due to the transformation (Baskerville, 1972).…”