A simple area-based model for predicting airborne LiDAR first returns from stem diameter distributions: an example study in an uneven-aged, mixed temperate forest

Tree size distributions are of fundamental importance in forestry. Airborne laser scanning (i.e., light detection and ranging, LiDAR) provides high-resolution information on canopy structure and may have potential as a tool for mapping and monitoring tree stem diameter distributions across forest landscapes. We present an area-based allometric model (with three levels of species specificity) that links ground-based plot data to the height distribution of LiDAR first returns, demonstrating the approach with survey data from a mixed, uneven-aged forest in central Ontario, Canada. Our model translates stem diameters into estimates of exposed crown area within 1m height intervals; we then compared those estimates with the height distribution of LiDAR first returns. This basic approach gave reasonable goodness of fits (root mean squared error = 32%), but accuracy was improved by adding mechanistic features (root mean squared error = 17%) to adjust crown shapes and crown permeability and allow for crown overlap and gaps. The model showed no bias in predicting LiDAR returns in the mid to upper canopy (18-30 m) but tended to underestimate the returns from the understory level (2-8 m) and overestimate returns from the ground level and lower canopy (8-18 m). Our model represents an important contribution towards the remote mapping of tree size distributions by showing that LiDAR first returns can be accurately predicted from standard plot data via the inclusion of a few fundamental canopy properties.