Accommodating heteroscedasticity in allometric biomass models

Allometric models are commonly used to predict forest biomass. These models typically take nonlinear powerlaw forms that predict individual tree aboveground biomass (AGB) as functions of diameter at breast height (D) and/or tree height (H). Because the residual variance is in most cases heteroscedastic, accommodating the heteroscedasticity (i.e., heterogeneity of variance) becomes necessary when estimating model parameters. We tested several weighting procedures and a logarithmic transformation for nonlinear allometric biomass models. We further evaluated the effectiveness of these procedures with emphasis on how they affected estimates of mean AGB per hectare and their standard errors for large forest areas. Our results revealed that some weighting procedures were more effective for accommodating heteroscedasticity than others and that effectiveness was greater for single predictor models but less for models based on both D and H. Failing to effectively accommodate heteroscedasticity produced small to moderate differences in the estimates of mean AGB per hectare and their standard errors. However, these differences were greater between model forms (models based on D and H versus models based on D only), regardless of the weighting approach. Similar consequences were observed with respect to whether model prediction uncertainty was or was not included when estimating mean AGB per hectare and standard errors. When including model prediction uncertainty, the standard errors of the estimated means increased substantially, by 44-59%. Therefore, to avoid possible negative consequences on large-area biomass estimation, we recommend: (i) testing the effectiveness of a weighting procedure when accommodating heteroscedasticity in allometric biomass models, (ii) incorporating model prediction uncertainty in the total uncertainty estimate and (iii) including H as an additional predictor variable in allometric biomass models.

Automated summary

Allometric models for predicting forest biomass often take nonlinear powerlaw forms and accommodating heteroscedasticity in the residual variance is necessary for accurate estimates. Weighting procedures and transformations were tested on biomass models, with some procedures showing more effectiveness in accommodating heteroscedasticity. Adding height as an additional predictor variable was recommended for better estimation accuracy.