Modeling the Effect of the Spatial Pattern of Airborne Lidar Returns on the Prediction and the Uncertainty of Timber Merchantable Volume

Abstract

Lidar data are regularly used to characterize forest structures. In this study, we determine the effects of three lidar attributes (density, spacing, scanning angle) on the accuracy and the uncertainty of timber merchantable volume estimates of balsam fir stands (Abies balsamea (L.) Mill.) in eastern Canada. We used lidar point clouds to compute predictor variables of the merchantable volume in a nonlinear model. The best model included the mean height of first returns, the proportion of first returns below 2 m and the canopy surface roughness index. Our analysis shows a high correlation between lidar and field data of 119 plots (pseudo-R 2 = 0.91), however, residuals were heteroscedastic. More precise parameter estimates were obtained by adding to the model a variance function of variables describing the mean height of returns and the skewness of the area distribution of triangulated lidar returns. The residual standard deviation was better estimated (3.7 m 3 ha −1 multiplied by the variance function versus 28.0 m 3 ha −1 ). We found no effect of density on the predictions (p-value = 0.74). This suggests that the height and the spatial pattern of returns, rather than the density, should be considered to better assess the uncertainty of merchantable volume estimates.

A Generalized Lidar-Based Model for Predicting the Merchantable Volume of Balsam Fir of Sites Located along a Bioclimatic Gradient in Quebec, Canada

“…The simplest model (Model 1) ignored the effects of site, growth, and the bioclimatic gradient, while the most complex model (Model 6) included all of these. All possible combinations of candidate metrics (one variable per standard group) were tested in a 3-metric model (Model 1) adapted from Yoga et al [25]. We selected this model as it has been specifically developed for balsam fir stands and was successfully tested at the Montmorency site:…”

“…The statistical analyses were carried out using the "nlme" package [29] of the R software [30]. The residual heteroscedasticity was taken into account by adding a variance function to the models following Yoga et al [25]. In that study, the variance function was comprised of variables describing the average height and the spatial distribution of returns.…”

“…In our present study, the lidar data were acquired with different settings. We, therefore, opted to omit the return spacing variable of Yoga et al [25] when accounting for the heteroscedasticity. The random error term ε jm , therefore, had the following form:…”