Estimating individual tree diameters at breast height (DBH) from delineated crowns and tree heights on the basis of airborne light detection and ranging (LiDAR) data provides a good opportunity for large-scale forest inventory. Generally, ground-based measurements are more accurate, but LiDAR data and derived DBH values can be obtained over larger areas for a relatively smaller cost if a right procedure is developed. A nonlinear least squares (NLS) regression is not an appropriate approach to predict the aboveground biomass (AGB) of individual trees from the estimated DBH because both the response variable and the regressor are subject to measurement errors. In this study, a system of compatible individual tree DBH and AGB error-in-variable models was developed using error-in-variable regression techniques based on both airborne LiDAR and field-measured datasets of individual Picea crassifolia Kom. trees, collected in northwestern China. Two parameter estimation algorithms, i.e., the two-stage error-in-variable model (TSEM) and the nonlinear seemingly unrelated regression (NSUR), were proposed for estimating the parameters in the developed system of compatible individual tree DBH and AGB error-in-variable models. Moreover, two model structures were applied to estimate AGB for comparison purposes: NLS with AGB estimation depending on DBH (NLS&DD) and NLS with AGB estimation not depending on DBH (NLS&NDD). The results showed that both TSEM and NSUR led to almost the same parameter estimates for the developed system. Moreover, the developed system effectively accounted for the inherent correlation between DBH and AGB as well as for the effects of measurement errors in the DBH on the predictions of AGB, whereas NLS&DD and NLS&NDD did not. A leave-one-out cross-validation indicated that the prediction accuracy of the developed system of compatible individual tree DBH and AGB error-in-variable models with NSUR was the highest among those estimated by the four methods evaluated, but, statistically, the accuracy improvement was not significantly different from zero. The main reason might be that, except for the measurement errors, other source errors were ignored in the modeling. This study implies that, overall, the proposed method provides the potential to expand the estimations of both DBH and AGB from individual trees to stands by combining the error-in-variable modeling and LiDAR data and improve their estimation accuracies, but its application needs to be further validated by conducting a systematical uncertainty analysis of various source errors in a future study.

Reliable estimates of forest site productivity are a central element of forest management. The model of height-diameter relationship of dominant trees using algebraic difference approach (ADA) is a commonly used method to measure site productivity of natural uneven-aged stands. However, the existing models of this method do not recognize site type or sample plot specific variability in height curves; thus, it cannot be effectively used to estimate site type or sample plot-related site productivity for natural uneven-aged stands. Two primary subject-specific approaches, ADA with dummy variable (DV) (ADA + DV) and ADA with combination of dummy variable and nonlinear mixed-effects modelling (CM) (ADA + CM), were proposed for height–diameter modelling. Height–diameter models developed with ADA, ADA + DV and ADA + CM were compared using data from 4161 observations on 349 permanent sample plots of four major natural uneven-aged pure stands (Spruce, Korean Larch, Mongolian Oak, and White Birch) in northeastern China. It was found that models developed with ADA + CM provided the best performance, followed by the models with ADA + DV, and the models developed with ADA performed the worst. Random effects at the plot level were substantial, and their inclusion greatly improved the model’s accuracy. More importantly, the models developed with ADA + CM provide an effective method for quantifying site type- and sample plot-specific forest site productivity for uneven-aged pure stands.