3.1. Point Cloud Profile and Voxel Size Determination
In total, 3,153,374 points were generated by Pix4D mapper and its average density was about 285.64 points/m. As the geolocation errors, mean, sigma, and Root Mean Square Error (RMSE) were calculated. The mean values of X, Y, and Z were 0.00 m, respectively. Sigma and RMSE values of X, Y, and Z were 2.11, 2.18, and 8.28 m, respectively. The geolocation error means the difference between the initial and computed image positions. The image geolocation errors do not correspond to the accuracy of the observed point cloud.
As mentioned in Section 2.4
, there must be at least one point in the voxel. In the case of the average density of the point cloud acquired, for voxel sizes of 10 and 20 cm, the average number of points was 0.28 and 2.2, respectively. Therefore, the voxel size was set to 20 cm.
3.2. Spatial Variation of Cast and Self Cast Shadow
shows the voxel model (colors are based on the RGB of the point cloud acquired by SfM) and the spatial distribution of CS and SCS calculated as attributes. The voxel size is 20 cm. The sun position parameter for computing CS was determined based on the Sentinel-2 image metadata file (MTD_TL.xml) used. The zenith angle and azimuth angle of the Sun are 34.2
, respectively. Figure 6
also shows the positional relationship between the sun and voxel model. The SCS only varies with roughness and density. In other words, the value of SCS does not change as the sun position changes. The CS values have five levels: 0.00, 0.25, 0.50, 0.75, and 1.00. The SCS values are a real number between 0.00 and 1.00. From Figure 6
, it can be visually seen that most of the CS value is 0.00, followed by 1.00, and most of the CS value is about 0.5.
shows the spatial variations of the CS and SCS shown in Figure 6
when observed at limited view zenith angles from −30
under the fixed view azimuth angle 290
. Spatial variation means the change in the mean value of the CS and SCS of the voxels visible from the sensor position at each zenith angle. The zenith angle was varied every 10
. The result shows that the trends in the spatial variability of CS and SCS are the same, but the amount of variability is different. Between −10
zenith angle, SCS remains almost the same, at 0.12, while the CS increased from 0.17 to 0.23. The mean value of SCS was the lowest at 0
zenith angle and highest at −20
. They are 0.12 and 0.15, respectively. On the other hand, the mean value of CS showed the lowest value of 0.15 at a zenith angle of −30
and the highest value of 0.45 at 20
. In addition, the mean value of CS is about twice as large at 20
than at −20
at the zenith angle. The smaller variability of the SCS when compared to the CS may be due to the higher forest density and smaller roughness.
3.3. Result of Simulated Sentinel-2 BOA Reflectance
The voxel model shown in Figure 6
was used to simulate the Sentinel-2 image. As an example, Figure 8
shows simulated images of bands 3, 8A, and 11 while using the Quercus ilex
spectral reflectance. The spatial resolution of band 3 is 10 m, while that one of band 8A and 11 is 20 m. The range of reflectance is 0.02 for band 3, while that one is 0.1 for band 8A and 11. The band 3 and 11 images are brighter than the Sentinel-2 image, which indicated that the reflectance of the simulated image is higher than the Sentinel-2 one. The band 8A image was similar in brightness to Sentinel-2 image. A comparison of images simulating band 8A and 11 shows that the absolute values of reflectance are different, but the trend in brightness remains the same. This is because CS and SCS are independent of wavelength. However, in reality, the trend in reflectance in Sentinel-2 images differs between band 8A and 11, because there are other factors that reduce the reflectance besides shadows.
shows the spectral reflectance profiles for the simulation results, Sentinel-2 TOA, and Sentinel-2 BOA. In this simulation, nine leaves spectral reflectances were used, as mentioned in Section 2.3.3
. Not all of the pixels shown in Figure 8
were included in the creation of the spectral reflectance profile because there were areas of exposed soil in the target forest. The number of pixels used to create that profile was 185 pixels for bands 2, 3, 4, and 8 with a spatial resolution of 10 m, and 39 pixels were used for the other bands. When comparing the Sentinel-2 TOA to the BOA, the atmospheric correction appears to be correct. It is clear from Figure 9
that the simulation results are all overestimated for the Sentinel-2 BOA reflectance in bands 11 and 12 of SWIR. In the VIS and NIR bands, depending on the type of leaf, there is a case of over or underestimation. It is also found that the trends in spectral reflectance are different, even for the same species. Table 3
shows RMSE of the simulated reflectance to the Sentinel-2 BOA reflectance per band and its mean and Standard Deviation (StD). Simulations using
had the smallest RMSE. In particular, bands 2, 3, and 4 show very small RMSE of 0.06, 0.06, and 0.05, respectively. When Quercus virginana
or Quercus lobata
were used for simuation, the RMSE was twice that of Betula papyrfera
at 0.040, but the StD was almost the same at 0.016. On the other hand,
showed the largest RMSE; however, the decreasing trend in simulated reflectance using this leaf from NIR to SWIR bands is more similar than in other leaves.
When a point cloud is missing, it affects the results of the CS and SCS calculations. It is pointed out that if the point cloud is incomplete, points that belong to the shade component are identified as the sunlit component [27
]. In UAV-SfM, the main causes of point cloud missing are shadows and occlusions [40
]. In this regard, as mentioned in Section 2.3.1
, this study was cloudy at the time of photography, so it can be inferred that there are no significant shadows in those images. Leaf shaking also affects the SfM algorithm and causes noise in the point clouds [40
]; however, we did not perform noise reduction for the point cloud. Because there was scant wind, the swaying, if any, was likely to be a few centimeters in size. Moreover, the minimum voxel size in this study was 20 cm, so the impact was considered to be small. In the case of outliers, the effect was expected to increase as the voxel size was increased. However, the effect of outliers was also considered to be small because the relative reflectance changed very small, as shown in Table 4
. In addition, because the georeferencing was performed based on the GPS log data installed in the UAV, the absolute error has not been calculated. If the error is larger than the voxel size, then it may affect the simulation results. Although this study collected images from a single camera angle, it has been reported that combining multiple angles provides a more comprehensive point cloud acquisition [41
The spatial variability of the CS and SCS was clearly different, as shown in Figure 7
. When compared to CS, SCS has a smaller variation with respect to the observation angle. This is because the sun position is used in the calculation of the CS, but not in the calculation of the SCS. These differences in spatial variability are related to structural parameters, such as forest density and roughness. Therefore, a multi-angle satellite would be expected to be able to estimate the variation of these shadows. CS and SCS are the shielding ratios for direct and diffuse solar irradiance, respectively, as shown in Equation (5
). Therefore, the radiance is affected by both CS and SCS in the short-wavelength bands. On the other hand, the radiance is affected by only CS in the long-wavelength bands, because diffuse solar irradiance is reduced. A Second-generation GLobal Imager (SGLI) product provides the shadow index (SDI) that indicates the shadow content within a pixel as a new vegetation characteristic [42
]. Because SDI uses the SWIR band, it means that value is CS. Because SGLI is also capable of multi-angle observations, it is expected to estimate structural parameters from the SDI obtained at each observation angle. On the other hand, since multi-directional observation is not possible with Sentinel-2 and Landsat, one can only extract the parameters of the forest structure by using the shadow changes due to changes in solar altitude. However, with multi-temporal images, reflectance changes not only due to shadows, but also due to changes in phenology [43
]. Therefore, the challenge for the future is to understand the impact of shadows and phenology on the annual change in reflectance rates.
The best RMSE was 2 ± 1.5% when the reflectance was simulated using Betula papyrfera
, as shown in Table 3
. This result is comparable to the accuracy of Rengarajan and Schott. [45
] when they used the Digital Image and Remote Sensing Image Generation tool to simulate the NIR band reflectance of Landsat-8 surface reflectance product. Usually, at short wavelengths, the simulation error is expected to be larger due to the influence of path-radiance. On the other hand, at long wavelengths, the simulation error is smaller because of its negligible impact. However, the present results are the opposite, as shown in Figure 9
and Table 3
. That is, the reflectance simulated in bands 11 and 12 were overestimated. The simulation method proposed in this study has four wavelength-dependent elements. They are SMARTS, Sen2Cor, the spectral reflectance of the leaves, and the water content of that one. The atmospheric conditions at the date of the Sentinel-2 image used were fine, so the parameters used for SMARTS and Sen2Cor were also standard value. In addition, the similarity of the spectral reflectance shapes of Sentinel-2TOA and BOA shown in Figure 9
suggests the atmospheric effect is small. Gueymard. [38
] has calculated the absolute spectral difference between SMARTS and MODTRAN4 irradiance predictions under air mass 1.5 and standard atmospheric conditions. The result showed that the absolute spectral differences were within 5% for all wavelengths. In addition, Li et al. [46
] validated the Sentinel-2BOA reflectance generated using Sen2Cor using the solar spectrum-vector (6SV) code. The results showed that the BOA reflectance was overestimated over 6SV in all bands. The reflectances of nine different leaves types were used in the simulations in this study, but all of them were overestimated in bands 11 and 12. Therefore, the spectral reflectance used was also not considered to be the cause of the overestimation. Seelig et al. [47
] reported a large decrease in reflectance in SWIR as compared to VIS and NIR as the relative water content of leaves increased. In the leaves they studied, even a 20% difference in relative water content changed the reflectance by about 0.05 in the SWIR band. Although there was no precipitation before or after the date acquired by Sentinel-2, the water content of the leaves used in the simulation was lower than that of the target forest, which may be the reason for the overestimation in SWIR bands.
As the voxel size increased from 20 cm to 200 cm, the relative average reflectance increased by the same ratio in all bands (Table 4
). The reason for that is the increased voxel size reduces the roughness of the three-dimensional (3D) model and the effect of CS and CSC was decreased. This finding was expected to estimate errors, even when a bigger voxel size was used for reducing the computational cost. However, this trend may change, depending on the type of forest. In the future, we need to create forests with different densities and roughnesses to further investigate the impact of voxel size on the simulation.
The main model limitation of this simulation was that all leaf orientations were assumed to be perpendicular to the XY plane, as described in Section 2.4.2
. This assumption is expected to lead to a reduction in simulation accuracy in the case of rougher forests, such as coniferous forests. The distribution of leaf inclination angles also has a direct effect on the fraction of solar radiation that is shielded [48
]. Therefore, it is necessary to use the point cloud in the voxel in order to estimate the orientation of the leaves. Furthermore, all of the voxels are assumed to be leaves. In reality, however, the voxels include branches, forest floor, and other objects with different reflectance. To solve this problem, voxels need to be classified according to each object and each reflectance be assigned.