## 3 Results
### Effects of Urban Geometry on NDVI  
To investigate the effects of H/W and \(\lambda_{\text{p}}\) on the NDVI, we computed the mean values of the NDVI\({}_{\text{mean}}\) for scenes with different H/W and \(\lambda_{\text{p}}\) but with the same material reflectance. Given the similar NDVI patterns observed in urban scenes with varying FVCs, only the NDVI\({}_{\text{mean}}\) with FVCs of 0.1 and 0.3 are presented in Figure 3.  
It is evident that buildings cause the NDVI\({}_{\text{mean}}\) to be underestimated compared to the NDVI\({}_{\text{mean}}\) for vegetation-only scenes (Figure 3). All the curved lines have a lower NDVI\({}_{\text{mean}}\) than the one corresponding to the NDVI\({}_{\text{mean}}\) with the same FVC in Table 5. Figure 3 illustrates that shadows intensify the impact of urban geometry on the NDVI, with greater vegetation cover exhibiting a heightened degree of influence from urban geometry. A significant negative correlation is observed between the \(\lambda_{\text{p}}\) and the NDVI, regardless of the sunlight condition. However, the relationship between the H/W and the NDVI is found to be significantly affected by the sunlight conditions. Under sunlit conditions, the H/W and NDVI are almost independent, whereas with shadow conditions, the effects of the H/W on the NDVI are also related to the \(\lambda_{\text{p}}\) and FVC. When \(\lambda_{\text{p}}\) = 0.1 and 0.1875, the impact of the H/W on the NDVI was minimal. When \(\lambda_{\text{p}}\) = 0.3, 0.4375, and 0.6, there is a negative correlation between the H/W and the NDVI, with this correlation increasing in  
\begin{table}
\begin{tabular}{c c} \hline \hline
**FVC** & **NDVI\({}_{\text{mean}}\)** \\ \hline
0.10 & 0.301 \\
0.15 & 0.352 \\
0.20 & 0.398 \\
0.25 & 0.441 \\
0.30 & 0.477 \\ \hline \hline \end{tabular}
\end{table}
Table 5: NDVI\({}_{\text{mean}}\) of vegetation-only scenes with different FVCs.  
line with the FVC. Thus, the NDVI may be underestimated to a greater extent in urban areas with high vegetation cover and high building density.  
Likewise, with the same FVC, the NDVI\({}_{\text{mean}}\) under shadow conditions is mostly higher than that under sunlit conditions, and it is closer to the red straight line for the scenes with shadow conditions than for the scenes under sunlit conditions (Figure 3). Generally, the NDVI with shadow conditions is higher than that under sunlit conditions. This may be because the fraction of diffuse solar irradiance reflected by adjacent pixels is a large fraction of the total irradiance onto the observed pixel under shadow conditions. The reflectance of both vegetation and buildings in the red band is lower than that in the NIR band. Thus, the scattered radiance and irradiance in the red bands is lower than in the NIR band. This makes the NDVI under shadow conditions higher than under sunlit conditions. With the increase of the H/W, the SVF decreases and reduces the NIR radiance reflected to the sky. This makes the NDVI decrease with the H/W. Thus, when the H/W, \(\lambda_{\text{p}}\), and FVC are all high, the reduced radiance within pixels due to scattering and absorption is higher than the added radiance from adjacent pixels. Then, the NDVI\({}_{\text{mean}}\) under shadow conditions is lower than that under sunlit conditions (Figure 3b,d).  
Figure 3: NDVI changes with H/W: (**a**) with shadow conditions and FVC = 0.1; (**b**) with shadow conditions and FVC = 0.3; (**c**) under sunlit conditions and FVC = 0.1; (**d**) under sunlit conditions and FVC = 0.3. The red straight lines represent the NDVI\({}_{\text{mean}}\) values of the corresponding vegetation-only scenes (Table 5).