A universal canopy gap fraction model for forests with various tree distributions based on Nilson's models considering directional overlaps among crowns

An accurate estimation of forest canopy gap fraction (GF) is a prerequisite for remote sensing retrievals of several associated canopy parameters e.g. leaf area index, fAPAR (fraction of photosynthetically active radiation absorbed by the canopy), clumping index, etc. A universal canopy GF model for forests is required for various tree distribution patterns on flat and slopping terrains, yet existing models so far do not possess all these abilities simultaneously. For example, the Neyman type-A model, the Poisson model, and the hypergeometric model are suitable only to forests with clumped, random, and regular tree distributions, respectively. In this regard, the suite of Nilson's canopy GF models developed for forests with various tree distributions have the potential to become universal models. For this purpose, this study attempts to overcome the following limitations of these models to make them be true universally applicable: (1) canopy GF calculated by the Nilson's models is mostly accurate for various tree distributions at nadir whereas at off-nadir, it is either underestimated for clumped tree distributions or overestimated for regular tree distributions at off-nadir; and (2) Nilson's models were developed for flat terrains and untested for sloping terrains. Herein, two Nilson's models are modified by expanding the calculation of overlaps among crowns (OAC) at nadir to the whole hemispherical space. The results show that all canopy GF simulations in the new models (New91 and New99) show higher consistency with ray-tracing results than those in original Nilson's models in all directions, highlighting the need to consider directional OAC. The modified models (especially for New99) are validated in two RAMI forest stands and a Saihanba forest stand: the relative error in canopy GF between the modified models and a ray-tracing model is less than 10 % in all forest stands. The modified models (especially New99) are suitable for various tree distributions on flat and slopping terrains and therefore increased the universality of the original Nilson's models suitable for a wide-range of remote sensing applications. New99 can be deemed as a universal canopy GF model for forests with various tree distributions.