Estimating Photon Recollision Probability from LiDAR Point Clouds

Abstract:

Physically-based radiative transfer models quantitatively predict the interactions between solar radiation and vegetation. The concept of ‘spectral invariants theory’ expresses that the vegetation canopy absorptance, transmittance and reflectance can be simply approximated by the optical properties of phytoelements (e.g., leaf or needle) and one spectrally invariant structural parameter - photon recollision probability (p), which can be interpreted as the probability that a photon will interact with the canopy again after being scattered from a phytoelement. At present, the concepts of the p-theory have been reported and examined at the shoot and canopy scales, but not yet for the crown level. In addition, the p-value was estimated indirectly, such as converted from the spherically averaged silhouette to total area ratio (STAR) or canopy transmittance measurements. We report here the first method to directly estimate photon recollision probability using terrestrial LiDAR point clouds, together with the validation of the relationship between STAR and the p-value at the crown level. The presented geometric method is data-driven and avoids explicit reconstructions of tree structures. One of the critical discoveries was that the average recollision probability can be interpreted as the local spherical openness on phytoelement surfaces, which enabled a simple visibility calculation by avoiding explicit ray tracing. We here present experiment results on synthetic crowns of needle-leaved tree species with known reference p-values. Results confirmed the validity of the p-STAR relationship at the crown level, and showed that p-values can be accurately estimated from LiDAR point clouds with a relative root measure square error of less than 10%.