# Modeling Shadow with Voxel-Based Trees for Sentinel-2 Reflectance Simulation in Tropical Rainforest
###### Abstract  
Satellite-based gross primary production (GPP) estimation has uncertainties due to shadow fraction caused by the geometric relationship between the complex forest structure and the Sun. The virtual forests allow shadow fraction estimation without 3D measurements, but require optimal structural parameters. In this study, we developed the reflectance simulator (Canopy-level Shadow and Reflectance Simulator, CSRS) that considers tree shadows and the method to determine the optimal canopy shape for shadow fraction estimation. The target forest is any tropical evergreen forest which accounts for 58% of tropical forests. Firstly, we analyzed the effects of canopy shape on the reflectance simulation based on virtual forests created with different canopy shapes. This result was checked by [PERSON]'s honestly significant difference (HSD) test. Secondly, the optimal canopy shape was determined by comparing the reflectance from Sentinel-2 Band 4 (red) bottom of atmosphere reflectance with those simulated from virtual forests. Finally, the shadow fraction estimated from the virtual forest was evaluated. Since the focus of this study was to derive the optimal canopy shape, unmanned aerial vehicle (UAV) structure from motion (SfM) was used to obtain the parameters other than canopy shape and to validate the estimated shadow fraction. The results showed that when the Sun zenith angle (SZA) was more than 20 deg, significant differences were observed among canopy shapes. The least root mean square error (RMSE) for reflectance simulation was 0.385 from the canopy shape of a half ellipsoid. Moreover, the half ellipsoid also showed the smallest RMSE in estimating shadow fraction (0.032), which indicated the reliability and applicability of CSRS. This study is the first attempt to determine the optimal canopy shape for estimating shadow fraction and is expected to improve the accuracy of GPP estimation in the future. virtual forest; canopy shape; geometrical optical model; sun zenith angle 202214088816 July 202216 July 202218 August 20221408816 July 202218 August 20221408816 July 202218 August 202218  
One of the methods to estimate the shadow fraction without 3D measurement is to use virtual forests. An advantage of using virtual forests is the estimation of diurnal shadows. A virtual forest is often used to develop an equation relating the physical quantity of the forest to the reflectance observed by the satellite sensor. Since the shadow fraction is closely related to the forest roughness [9], the virtual forest should be composed of tree models at level 2--which consider geometric characteristics such as canopy shape, crown width and crown depth--or higher according to the level of tree (LOT) [10]. Currently, there is an increasing number of globally available datasets on forest structure, such as tree height (TH) [11; 12; 13] and tree density [14]. Despite canopy shape also being an important parameter that determines forest surface roughness [15], it is estimated by researcher's experience or assigned by a forest category defined by the International Geosphere-Biosphere Programme (IGBP). Typically, cones and ellipsoids are used foriferous forests and broadleaf forests to represent canopy shapes, respectively, [16; 17; 18]. However, the canopy shapes for tropical rainforests with various tree species are uncertain, depending on the experience of different researchers. Therefore, it is necessary to determine the optimal canopy shape for virtual forests to estimate the shadow fraction. Moreover, in some satellite-based products, such as clumping index (CI), it has also been pointed out that we should correctly assign the canopy shape because the product is sensitive to the shadow fraction [19; 20]. The shadow fraction generated by the forest surface significantly alters the reflectance observed in the bidirectional reflectance distribution function (BRDF) [21; 22].