Direct estimation of photon recollision probability using terrestrial laser scanning

Photon recollision probability p is a spectrally invariant structural parameter and a powerful tool to link canopy optical properties at any wavelengths to model reflectance, transmittance, or absorption of vegetation canopies. The concepts of the p-theory have been reported and examined at the shoot and canopy scales, but not yet for the crown level. Currently, the p-value is estimated indirectly, such as converted from the spherically averaged silhouette to total area ratio (STAR¯) or canopy transmittance measurements. In this work, we first validate the theoretical considerations of the p concept at the crown level (e.g., its relationship with STAR¯), and then provide the first method to directly estimate photon recollision probability using Terrestrial Laser Scanning (TLS) data. The proposed geometric method is data-driven and avoids explicit reconstructions of tree structures. The p-value estimated here is the average recollision probability over spatial locations. We showed that the average recollision probability can be interpreted as the local spherical openness on phytoelement (leaf or needle) surfaces, which enabled a simple visibility calculation by avoiding explicit ray tracing. The developed method was tested on synthetic crowns of needle-leaved tree species, for which the reference p-values were known. Results confirmed the validity of the p-STAR¯ relationship at the crown level, and showed that p-values can be accurately estimated from TLS point clouds with a relative root measure square error of less than 10%. This study displays the distinct advantage of TLS in delineating detailed tree crown structures and highlights its potential in studies of forest reflectance modeling.