  The three-dimensional structures of individual trees are important pieces of
information necessary to understand the effect of trees on urban environments.
In this study, we demonstrate a method for estimating the leaf area density
(LAD) distribution of individual trees using high-resolution airborne LiDAR.
This method improves upon the previously proposed method, which calculates LAD
based on the contact frequency between the laser beams and leaves by tracing
the paths of the laser beams. The proposed method in this study exploits the
last and intermediate pulses in addition to the first and single pulses to
capture the foliage distribution in the inner part of the crown. Each laser
beam is traced from a point derived by the last pulse to the point derived by
the first or intermediate pulse that is recorded immediately before the last
pulse. The laser beam interceptions and intersections can thus be accurately
reproduced while considering the last and intermediate pulses. We verify the
estimation accuracy of the three-dimensional LAD distribution using terrestrial
LiDAR data from a single tree (Z. serrata). The appropriate voxel size for
representing the LAD distribution from the airborne LiDAR is first determined
by comparing the distribution of voxels containing one or more airborne LiDAR
points with that containing one or more terrestrial LiDAR points. The estimated
LAD distribution with a voxel size of 1 m by 1 m by 0.5 m is subsequently
compared to the terrestrial LiDAR-derived LAD distribution. When only the first
and single pulses are used, the LAD is overestimated and underestimated in the
upper and lower part of the crown, respectively. We confirmed that using the
last and intermediate pulses improves the estimation accuracy of the entire
crown area.
