## 3 Results
### Validation
For shadow areas, the irradiance from adjacent pixels cannot be neglected, and the NIR band is scattered heavier than the red band, as evidenced by the reflectance in the near-infrared band being always greater than that in the red band (Figure 9a); thus, the estimated NDVI in shadow areas under these illumination conditions may be higher. This means that the NDVI of the pixels in shadow areas is overestimated to some extent. Figure 9: Ground component pixels of the scene under sunlit and shadow conditions: (**a**) reflectance in the red and near-infrared bands; (**b**) sum and difference of reflectance in the red and near-infrared bands; and (**c**) schematic diagram of sampled pixels (inside the white boxes). Figure 10 provides a more illustrative representation of this phenomenon. In scenes with shadow conditions, the NDVI is relatively high in the shaded region caused by buildings (Figure 10a-c). The NDVI of the shaded region at the periphery of the building complex is found to be higher than that of the shaded region within the building complex, and the NDVI of vegetation within the shaded region is slightly higher than in the sunlit vegetation pixels (Figure 10b,c). Irrespective of the time of the day, the NDVI of the building pixels is approximately zero, whereas the NDVIs of the corresponding pixels in vegetation-only scenes are markedly higher than that of the building pixels in mixed scenes (Figure 10). The entire scene is treated as a single pixel, with the signal received by a spectro-radiometer representing the sum of the component signals within the target pixel. This allows us to define the mean NDVI of the urban mixed scene as the NDVI of the pixel. This explains the experimental result (Section 3.1) that for a certain H/W, an elevated building density (i.e., an expanded area where NDVI is proximate to zero) is associated with a diminished NDVI, and shadow may reduce the bias of NDVI estimates in urban areas. Our conclusion was also validated with satellite data provided by [PERSON] and [PERSON] et al. (2017). A similar conclusion was obtained with linear spectral mixing models by [PERSON] et al. (2018), despite the fact that this conclusion was derived from a mixed pixel comprising three components, i.e., soil, vegetation, and the projection of vegetation on soil. In our scenes, the presence of buildings is also considered. This further suggests that the presence of shadows increases the NDVI, both for the mixed pixels consisting of simple soil and vegetation and for mixed pixels in urban areas. As illustrated in Figure 10, the NDVIs of the urban mixed pixels are predominantly influenced by the shaded area and the building area within the pixels. In Section 3.1, at a  
Figure 10: NDVI derived in the DART model for four types of scenes: (**a**) vegetation-only scene with shadow conditions; (**b**) mixed scene with heterogeneous buildings and shadow conditions; (**c**) mixed scene with homogenous buildings and shadow conditions; (**d**) vegetation-only scene under sunlit conditions; (**e**) mixed scene with heterogeneous buildings under sunlit conditions; and (**f**) mixed scene with homogenous buildings under sunlit conditions. low building density (\(\lambda_{\text{p}}\) = 0.1, 0.1875), the NDVI values of the mixed scenes observed at 10 am demonstrate an increase with the H/W, whereas those observed at 12 pm exhibit no correlation with the H/W. This suggests that shadows exert a predominant influence on the NDVI when buildings are open. At high building densities (\(\lambda_{\text{p}}\) = 0.3, 0.4375, 0.6), regardless of the time of day when mixed scenes are observed, the NDVI decreases despite the fact that the H/W is increasing at this time, which is likely to be due to the reduced NIR reflectance when the SVF decreases as the H/W increases. Urban FVC estimation accuracy is inevitably affected by the misestimation of the NDVI in urban mixed pixels due to shadows and building areas. The systematic study of biomass estimation by means of vegetation indices conducted by [PERSON] et al.