Development of a System of Compatible Individual Tree Diameter and Aboveground Biomass Prediction Models Using Error-In-Variable Regression and Airborne LiDAR Data

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.

Airborne LIDAR-Derived Aboveground Biomass Estimates Using a Hierarchical Bayesian Approach

“…For obtaining the absolute vegetation heights, we must remove the influence of the terrain. Thus, we obtained the digital elevation model from the ground-classified LIDAR point cloud data using a progressive morphological filter and, in this study, with a grid cell size of 0.5 m [3]. We also eliminated the noise using a Gaussian smoothing filter to obtain a more accurate crown projection area [3].…”

“…Thus, we obtained the digital elevation model from the ground-classified LIDAR point cloud data using a progressive morphological filter and, in this study, with a grid cell size of 0.5 m [3]. We also eliminated the noise using a Gaussian smoothing filter to obtain a more accurate crown projection area [3]. We used the local maxima algorithm to find the individual tree crown tops, and used the region growing method to obtain the tree crown boundary, the crown projection area was calculated according to the determined tree crown boundary.…”

“…Diameter at breast height (DBH) and aboveground biomass (AGB) are two important measurements of individual trees, widely used in yield estimations and forest growth [3]. Tree DBH is an easy measuring factor with high accuracy-all DBH data are measured.…”

“…The LIDAR system has been used to measure the forest vegetation structure and has been applied to measure forest variables since the mid-1980s [11]. These variables, including tree height, stem volume, crown projection area, diameter at breast height, and other variables, are significantly connected to the forest biomass [3,11,12]. Using these LIDAR variables, individual tree DBH and aboveground biomass can be estimated by developing DBH and AGB models, respectively [3,12,13].…”

“…These variables, including tree height, stem volume, crown projection area, diameter at breast height, and other variables, are significantly connected to the forest biomass [3,11,12]. Using these LIDAR variables, individual tree DBH and aboveground biomass can be estimated by developing DBH and AGB models, respectively [3,12,13]. With some studies also using LIDAR data to predict timber volume and discern age class, LIDAR data have been widely used in forestry over the past two decades.…”