## 2 Materials and Methods
### DART Model
#### 2.1.1 Input Parameters  
The setting of the DART parameters in our numerical experiments is presented in Table 1. To simulate the radiative transfer from the top of the atmosphere to the bottom of the atmosphere, an irradiance spectral database called \"Solar_constant\" is employed to characterize the atmospheric properties. We determine the \"sun position\" by setting the temporal parameters, and two distinct types of sun angle were considered for all the scenes: (1) scenes with a shadow condition: the temporal parameter was set at 10:00 am on the 22 nd of June (local solar time), while the solar elevation angle was 56.07\({}^{\circ}\) (Figure 1b); and (2) scenes under a sunlit condition: the temporal parameter was set at 12:00 pm on the same date, while the solar elevation angle was 83.5\({}^{\circ}\) (Figure 1c). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Module**} & \multicolumn{1}{c}{**Value**} \\ \hline \multirow{3}{*}{Atmosphere Property} & Irradiance Spectral Database & Solar\_constant \\  & Irradiance Table & TOASolar\_THKUR \\  & Irradiance Model & irradiance \\ \hline \multirow{3}{*}{Scene Property} & Location & Latitude: 23\({}^{\circ}\)25\({}^{\prime}\)48\({}^{\prime}\)N, Longitude: 113\({}^{\circ}\)15\({}^{\prime}\)36\({}^{\prime}\)F \\  & Size & Scene size: 40 m \(\times\) 50 m, Cell size: 0.5 m \(\times\) 0.5 m \(\times\) 0.5 m \\ \hline \multirow{3}{*}{Sun Position} & Shadow Condition & Elevation: 56.07, Azimuth: 82.41\({}^{\circ}\) \\  & Sunlit Condition & Elevation: 83.5\({}^{\circ}\), Azimuth: 88.67\({}^{\circ}\) \\ \hline \multirow{3}{*}{Sensor View Direction} & View Angle & Elevation: 90\({}^{\circ}\) \\  & Red Band & Central wavelength: 0.6545 μm \\ \cline{1-1}  & & Spectral bandwidth: 0.037 μm \\ \cline{1-1}  & Near-infrared Band & Central wavelength: 0.865 μm \\ \cline{1-1}  & & Spectral bandwidth: 0.028 μm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The DART model’s input parameters. Figure 1: Scene schematic: (**a**) urban scene with building height (H), street width (W), roof area (S\({}_{i}\)) and total horizontal area (S); (**b**) urban scene with sunlight under shadow conditions; and (**c**) urban scene with sunlight under sunlit conditions. Our aim is to construct a remote-sensing observation model that can be practically applied, and the sensor view direction of the Landsat series satellites is nearly vertical. Thus, only data from the nadir view direction will be analyzed in this study. All the facets and voxel array reflectance properties are assumed to be Lambertian (Table 1). The reflectance in the red and near-infrared bands was simulated using the DART model for three types of scenes: mixed scenes, vegetation-only scenes, and building-only scenes (Figure 2). The central wavelengths and widths of the red and near-infrared bands are referenced to Landsat 8/OLI (Table 1). Each scene has a constant parameter setting. The road material is designated as \"loam_sandy_brown_bright_clean_smooth_arizona\" for both the mixed and building-only scenes, and \"sandy_loam_brown\" for the vegetation-only scenes. A single building orientation and the DART model's \"repeated\" mode are set to generate an infinite repetition of the actual cityscape model, thus avoiding unnecessary complications of urban scenes. The buildings in the actual scene are simplified into four regular rectangles of equal size, and the vegetation is simplified into a uniform type and morphology, with all the buildings and vegetation distributed evenly and symmetrically throughout the scene. [PERSON] et al. [39] analyzed the reflectance of over 30 building materials from the ASTER Spectral Library ([[https://speclib.jpl.nasa.gov](https://speclib.jpl.nasa.gov)]([https://speclib.jpl.nasa.gov](https://speclib.jpl.nasa.gov)), accessed on 15 October 2024) and found that material reflectance in the range from 0.1 to 0.5 is closer to reality.