## Materials and Methods
### Generating the Forward Simulations  
The widely used turbid medium model, i.e., SAILH, which is corrected by the hot-spot parameter, was selected due to its ease of use and consistent performance in validation practices [60; 61]. The input parameters in the SAILH model included LAI, average leaf inclination angle (ALA), hot-spot, soil reflectance, leaf reflectance, leaf transmittance, diffuse fraction, solar zenith angle (SZA), view zenith angle (VZA), and relative azimuth angle (RAA). The leaf reflectance and transmittance values were simulated by the PROSPECT-5B model using several biochemical and biophysical parameters, including leaf mesophyll structure (N), C\({}_{\rm ab}\), C\({}_{\rm m}\), C\({}_{\rm w}\), carotenoid content (C\({}_{\rm ar}\)), and brown pigment content (C\({}_{\rm brown}\)) [62]. The PROSPECT-5B+SAILH (PROSAIL) model has been used for more than twenty years for the retrieval of vegetation biophysical properties [63; 64]. Previous studies have demonstrated that LAI, ALA, and C\({}_{\rm ab}\) have significant influences on canopy reflectance in the visible and NIR bands. However, other parameters, e.g., N, C\({}_{\rm m}\), and C\({}_{\rm w}\), are less sensitive to the canopy reflectance corresponding to the satellite bands [63; 65]. Therefore, the parameters, e.g., N, C\({}_{\rm m}\), C\({}_{\rm w}\) C\({}_{\rm ar}\), and C\({}_{\rm brown}\), in the PROSAIL model were fixed during the simulation to reduce the complexity and improve the efficiency of the LAI inversion. In this study, the soil reflectance for the PROSAIL model was acquired from field measurements. The parameters for maize, e.g., N, C\({}_{\rm m}\), C\({}_{\rm w}\) C\({}_{\rm ar}\), and C\({}_{\rm brown}\), were fixed according to LOPEX'93. ALA varied from 40\({}^{\circ}\) to 70\({}^{\circ}\) at intervals of 10\({}^{\circ}\); C\({}_{\rm ab}\) varied from 40 to 60 at intervals of 10; SZA varied from 0\({}^{\circ}\) to 85\({}^{\circ}\) at intervals of 1\({}^{\circ}\); VZA varied from 0\({}^{\circ}\) to 35\({}^{\circ}\) at intervals of 1\({}^{\circ}\); and LAI varied from 0 to 8 at intervals of 0.1 (Table 4).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sensor**} & \multicolumn{3}{c}{**HJ-1 CCD**} & \multicolumn{3}{c}{**GF-1 WFV**} & \multicolumn{3}{c}{**ZY-3 MUX**} \\ \cline{2-10}  & **Gain** & **Offset** & **\(ESU\)N**- & **Gain** & **Offset** & **\(ESU\)N**- & **Gain** & **Offset** & **\(ESU\)N**- \\ \hline Band 1 & 1.1451 & 4.6344 & 1929.81 & 0.1713 & 0.0000 & 1968.12 & 0.2509 & 0.0000 & 1958.30 \\ Band 2 & 1.1660 & 4.0982 & 1831.14 & 0.1600 & 0.0000 & 1841.69 & 0.2338 & 0.0000 & 1855.71 \\ Band 3 & 0.7647 & 3.7360 & 1549.82 & 0.1497 & 0.0000 & 1540.30 & 0.1885 & 0.0000 & 1548.72 \\ Band 4 & 0.7558 & 0.7385 & 1078.32 & 0.1435 & 0.0000 & 1069.53 & 0.2035 & 0.0000 & 1085.60 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The calibration coefficients and extraterrestrial solar irradiance values for ZY-3 MUX, GF-1 WFV, and HJ-1 CCD.  
The PROSAIL model was then run to simulate the actual satellite observations of canopy reflectance based on the spectral response curves of ZY-3 MUX, GF-1 WFV, and HJ-1 CCD, which were acquired from CRESDA [55], and of Landsat-8 OLI, which was acquired from USGS [56] (Figure 2). The reflectance simulations of each band based on each satellite spectral response can be calculated from Equation (3) [16].  
\[\rho_{s}(\lambda)=\frac{\int_{\lambda_{\text{min}}}^{\lambda_{\text{max}}}\rho_ {s}(\lambda_{i})\varphi(\lambda_{i})d\lambda}{\int_{\lambda_{\text{min}}}^{ \lambda_{\text{max}}}\varphi(\lambda_{i})d\lambda} \tag{3}\]  
where \(\rho_{s}(\lambda)\) is the simulated band reflectance of the satellite sensor, \(\lambda_{\text{min}}\) and \(\lambda_{\text{max}}\) are the lower and upper band wavelength limits, \(\rho_{s}(\lambda_{i})\) is the simulated hyperspectral reflectance for the \(i\)th wavelength, and \(\varphi(\lambda_{i})\) is the spectral response coefficient of the different sensors for the \(i\)th wavelength.