Abstract
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.
Highlights
The timely and cost-effective acquisition of forest inventory data, including forest carbon, at a large scale, has long been of concern for sustainable management and planning of forest ecosystems [1,2]
A system of compatible individual tree diameter at breast height (DBH) and aboveground biomass (AGB) error-in-variable models (model system (7)) was developed using an error-in-variable modeling approach based on both the airborne light detection and ranging (LiDAR) and the field-measured datasets of individual P. crassifolia trees collected in northwestern China
The results showed that only the error-in-variable modeling approach effectively accounted for the inherent correlation between DBH and AGB and the effects of measurement errors in the independent variables on the response variable and ensured the compatible properties of the estimated tree AGB and DBH, whereas the nonlinear least squares (NLS)&DD and NLS&NDD did not
Summary
The timely and cost-effective acquisition of forest inventory data, including forest carbon, at a large scale, has long been of concern for sustainable management and planning of forest ecosystems [1,2]. Tree diameter at breast height (DBH) and biomass are the two of the most common measures of tree size in forest mensuration. Tree DBH and biomass are two essential factors in forest growth and yield modeling. Tree DBH can be measured on the ground with high accuracy, ground measurements of tree biomass are less accurate and often difficult, time-consuming, and costly. DBH is usually measured for all trees in ground-based forest inventories, experimental and permanent growth plots, but tree biomass measurements are usually obtained from an affordable number of sample trees [3]. As a result of these studies, predicting tree biomass from DBH has become a well-established technique, widely applied in forest inventory and growth and yield predictions. The collection of DBH data at a large scale can be costly and time-consuming
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