A mathematical framework to describe the effect of beam incidence angle on metrics derived from airborne LiDAR: The case of forest canopies approaching turbid medium behaviour

Airborne laser scanning (LiDAR) is used in forest inventories to quantify stand structure with three-dimensional point clouds. However, the 3D distribution of the point clouds depends not only on stand structure, but also on scan angle, because the probability for an oblique beam to be reflected by the canopy increases with the distance it must travel through the canopy. Thus, the canopy appears to increase in density as the incidence angle increases, all else being equal. The resulting variation between and within datasets can induce bias in LiDAR metrics derived from the vertical distribution of points. In this study, we modelled the effect of scan angle on the vertical structure of the point clouds to predict the bias of metrics derived from points sampled off-nadir. Comparison with paired observations from different flightlines (off- and at-nadir observations of the same point) demonstrated that the model accurately reproduced the bias of metrics calculated for a northern hardwood forest with relatively continuous canopy. Thus, the model could be used to correct the bias of LiDAR metrics, and provides a mathematical framework that could be used to inform the selection of maximum incidence angle in LiDAR surveys, considering the trade-off between decreasing acquisition costs and obtaining unbiased measurements.