A three-dimensional light transfer model based on the vertical point-quadrant method and Monte-Carlo simulation in a Fagus crenata forest canopy on Mount Naeba in Japan

We divided the canopy of a 50-year-old secondary Fagus crenata stand into an array of small three dimensional (3D) rectangular cells (termed voxels, 0.25 m × 0.25 m × 0.20 m in height), and determined the leaf area density (LAD) of all voxels using the vertical point quadrat method. The estimated LAD values showed good agreement, at both voxel and stand scales, with measured values obtained by destructive sampling and litter trapping, respectively. The 3D distribution of LAD was then imported into a ray-tracing program based on a turbid medium analogy to simulate photosynthetic photon flux density at leaf surface (PPFDleaf) within a voxel at 30-min intervals. To include finite leaf size and non-random leaf dispersion within a voxel in the light calculation, the angular dependency of the shoot silhouette to projection area ratio (SPAR), with the foliage volume the same as the voxel, was used as the light extinction coefficient in the analogy. In addition, the frequency distribution of PPFDleaf within a voxel was simulated at each interval for all leafy voxels in the canopy, by integrating a Monte-Carlo simulation of the voxel-shading fraction of a solar disc in the light calculations. The light simulation provided reasonable estimates of both the mean PPFDleaf and the frequency distribution of PPFDleaf in a voxel for evaluating canopy photosynthesis (Pcanopy), when comparing them to the measured values. Ignoring the within-voxel variation in PPFDleaf caused a 21.8% overestimation of Pcanopy during the summer period (July to September). The results demonstrate the potential importance of a detailed description of light heterogeneity in Pcanopy calculations.