The shadow fraction of the canopy is an important factor in Bidirectional Reflectance Distribution Function (BRDF) and in estimating physical quantities, such as tree height and biomass. Shadows are used as a shielding ratio for direct solar irradiance, but, at shorter wavelengths, the amount of diffuse solar irradiance is greater, so the shielding ratio cannot be ignored. The shielding ratio of direct and diffuse solar irradiance is called Cast Shadow (CS) and Self Cast Shadow (SCS), respectively; however, it has been pointed out that the effect of these shadows is greater at higher resolutions, such as Sentinel-2. In addition, the Bottom Of Atmosphere (BOA) reflectance is greatly affected by shadows, because it is corrected for atmospheric effects. Therefore, the main purpose of this study is to investigate the spatial variability of CS and SCS and simulate the Sentinel-2BOA reflectance with these shadows. The target forest was a greenness season of a deciduous broadleaf forest in Thailand. First, we obtained a point cloud of the forest by Structure from Motion while using the Unmanned Aerial Vehicle. Next, we created a voxel model with CS and SCS as attributes. CS was calculated as the percentage of area where the plane that is assumed per voxel is shielded from direct solar irradiance by other voxels. SCS was calculated as the percentage of area where the hemispheric radiant environment is shielded by other voxels. Subsequently, using solar irradiance and leaf spectral reflectance data, the reflectance of each band of Sentinel-2 was simulated. Nine leaves were used to investigate the effect of leaf species on the simulation. The reflectance acquired by Sentinel-2 is not at the leaf level; however, we used this spectral reflectance data because the reflectance was simulated at the same spatial resolution as the voxel size. Voxel sizes of 20 cm, 50 cm, 100 cm, and 200 cm were used. Our result showed that (1) the spatial variability of SCS was smaller than that of CS when the sun position is fixed and the view zenith angle is changed. SCS was mostly 0.12 at different zenith angles, while the CS had a maximum value of 0.45 and a minimum value of 0.15. (2) The accuracy of the simulations was evaluated using the Root Mean Square Error (RMSE). The best RMSE is 0.020 ± 0.015 and the worst one is 0.084 ± 0.044. It was found that the error is larger in short wavelength infrared bands. (3) In this forest, the relative reflectance changed only about 1.2 times as much, as the voxel size was increased from 20 cm to 200 cm. In this study, we have simulated a single Sentinel-2 image. In the future, we will simulate multi-temporal images in order to investigate the effects of phenology and shadow changes on the reflectance that was observed by optical sensors.

中文翻译：

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利用阴影参数对泰国落叶林进行大气反射的Sentinel-2底部模拟

冠层的阴影部分是双向反射分布函数（BRDF）和估算物理量（例如树高和生物量）的重要因素。阴影被用作直接太阳辐射的屏蔽率，但是，在较短的波长下，漫射太阳辐射的量较大，因此不能忽略屏蔽率。直射和漫射太阳辐射的屏蔽率分别称为“投射阴影”（CS）和“自投射阴影”（SCS）；但是，已经指出，在更高的分辨率下（例如Sentinel-2），这些阴影的影响更大。此外，“大气底部”（BOA）反射率受阴影影响很大，因为已针对大气影响进行了校正。因此，本研究的主要目的是研究CS和SCS的空间变异性，并模拟具有这些阴影的Sentinel-2BOA反射率。目标森林是泰国落叶阔叶林的绿色季节。首先，我们在使用无人飞行器时通过Motion从“结构”获得了森林的点云。接下来，我们创建了一个以CS和SCS为属性的体素模型。CS被计算为每个体素所假定的平面被其他体素屏蔽以避免直接太阳辐射的面积的百分比。SCS计算为半球辐射环境被其他体素屏蔽的面积百分比。随后，使用太阳辐照度和叶片光谱反射率数据，模拟了Sentinel-2每个波段的反射率。使用九片叶子来研究叶子种类对模拟的影响。Sentinel-2获得的反射率不在叶片水平；但是，我们使用此光谱反射率数据是因为反射率是在与体素大小相同的空间分辨率下模拟的。使用的体素大小为20 cm，50 cm，100 cm和200 cm。我们的结果表明：（1）当太阳位置固定且视角天顶角改变时，SCS的空间变异性小于CS的空间变异性。在不同的天顶角处，SCS大部分为0.12，而CS的最大值为0.45，最小值为0.15。（2）使用均方根误差（RMSE）评估仿真的准确性。最佳RMSE为0.020±0.015，最差的为0.084±0.044。发现在短波长红外波段中误差较大。（3）在该森林中，随着体素大小从20厘米增加到200厘米，相对反射率变化仅为1.2倍。在这项研究中，我们模拟了一个Sentinel-2图像。将来，我们将模拟多时间图像，以研究物候和阴影变化对光学传感器观察到的反射率的影响。