## 4 BRDF Archetype Construction  
The MODIS multiangle reflectivity observation data carried on Aqua/Terra in the past five years were used to construct the BRFD archetype database in the Hefei area. The MODIS reflectance observation data after atmospheric correction and cloud mask are substituted into the semiempirical kernel-driven BRDF model mentioned above to obtain the corresponding model parameters. According to the physical meaning of the model, invalid data with model parameters greater than 1 and less than 0 are eliminated, and the BRDF model parameters of the Hefei area are obtained. According to Formula (12), AFX can also be obtained. To determine the optimal number of BRDF archetypes in the Hefei area, the data are divided into 2\(\sim\)10 categories according to the AFX value through the iterative self-organizing data analysis techniques algorithm (ISODATA), and the corresponding fit root mean square error (fit-RMSE) is calculated. Figure 7 shows the corresponding fit-RMSE when the number of BRDF archetypes is set to 2 10. The solar zenith angle is set to 45\({}^{\circ}\), and the observation zenith angle is selected as 5 angles (\(0^{\circ},15^{\circ},30^{\circ},45^{\circ},60^{\circ}\)). The fit-RMSE at each angle reaches a minimum value when the number of archetypes is eight, and when the observed zenith angle is 0\({}^{\circ}\), the minimum fit-RMSE is 0.294. The fit-RMSE is greatly affected by the observed zenith angle. When the observed zenith angle exceeds 45\({}^{\circ}\), the fitting error is as high as 0.06. In summary, the number of prototypes in the BRDF archetype database is finally selected as 8. Next, the fitting errors of 8 BRDF archetypes are discussed. Figure 8 shows the fit-RMSE of each archetype when the number of BRDF archetypes is 8. The left y-axis in the figure corresponds to the fit-RMSE, and the right y-axis corresponds to the average AFX value. The gray solid line in the figure is the change curve of AFX. In general, the fit-RMSE increases with increasing zenith angle. The fit-RMSE of the class 8 BRDF archetype is at least 0.0221 when the zenith angle is 0\({}^{\circ}\), while the fit-RMSE of class 1 is at most 0.0817  
Figure 5: The spectral response of FY-2G visible channel and MODIS red band. Figure 6: Fitting curve is the corresponding reflectance of FY-2G visible band and MODIS red band. when the zenith angle is 45\({}^{\circ}\). The figure shows that when the AFX is small (approximately 0.7000), the BRDF archetype fit-RMSE is the largest. According to the previous analysis, eight BRDF archetypes can be selected to summarize the bidirectional reflection distribution pattern of the surface in Hefei for MODIS multiangle observation data. Through the ISODATA clustering analysis algorithm, the eight BRDF archetypes in the Hefei area from five years of MODIS red band multiangle observation data were established. Table 2 shows the mean and range of AFX and the model parameter values corresponding to each BRDF archetype. Figure 9 shows the shape of the BRDF archetypes with the view zenith angle when the solar zenith angle is 45\({}^{\circ}\), in which Figure 9a shows the changing trend of the principle plane (PP), and Figure 9b shows the changing trend of the cross-principle plane. The BRDF in Figure 9 is the result of normalizing the isotropic scattering coefficient when assuming \(f_{iso}=0.5\). As the AFX value increases, the shape of the BRDF changes from dome-shaped to bowl-shaped, and the \(f_{vol}\) coefficient increases, while the \(f_{geo}\) coefficient gradually decreases. This means that with increasing AFX, the geometrical optics effect is gradually weakened, and the volume scattering effect is gradually enhanced.