## 2 Modeling of UAV Observations
### The Coupling Model for Crop Parameter Inversion  
#### 2.3.1 Coupling of Models  
For modeling the UAV observations, we replace the built-in surface BRDF (Bidirectional Reflectance Distribution Function) model in UNL-VRTM with the PROSAIL model. Then, the process of atmospheric correction and the process from the biochemical content to the spectral reflectance are integrated into a unified model. The coupling model can be specifically described by the following equation:  
\[M_{\lambda}(\mu_{\mathrm{s}},\mu_{\mathrm{v}},\phi)=\mathbf{U}\big{(}\lambda,\mu_{ \mathrm{s}},\mu_{\mathrm{v}},\phi,x_{\mathrm{air}},P\big{(}x_{\mathrm{crop}} \big{)}\big{)} \tag{2}\]  
where \(M\) denotes the coupling model, \(\mathbf{U}\) represents the UNL-VRTM model, and \(P\) refers to the PROSAIL model. The \(x_{\mathrm{air}}\) and \(x_{\mathrm{crop}}\) represent the atmospheric and crop parameters, respectively. The diagram of the coupling model is shown in Figure 1. The inputs of the coupling model include the crop physiological parameters, canopy structure parameters, and atmospheric parameters. The output of the coupling model is the intensity of radiation. The downwelling radiation after gas absorption, Rayleigh scattering, and aerosol scattering, simulated by UNL-VRTM, is shown in Figure 2, in which the assumption of \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Model**} & **Parameter** & \multirow{2}{*}{**Parameter Description**} & \multirow{2}{*}{**Common Value**} & \multirow{2}{*}{**Search Range**} & \multirow{2}{*}{**Unit**} \\  & **Symbols** & & & & \\ \hline \multirow{4}{*}{PROSPECT} & N & Leaf structure parameter & 1.3 & 1.2–2.8 & – \\  & Cab & Chlorophyll a and b content & 50 & 20–70 & \(\mu\)g:cm\({}^{-2}\) \\  & Car & Carotenoids content & 8 & 6–12 & \(\mu\)g:cm\({}^{-2}\) \\  & Cw & Equivalent water thickness & 0.004 & 0.004–0.05 & cm \\  & Cm & Leaf mass per unit leaf area & 0.012 & 0.003–0.027 & g:cm\({}^{-2}\) \\ \hline \multirow{4}{*}{SAIL} & LAI & Leaf area index & 1.4 & 1–7 & – \\  & ALA & Average leaf angle & 15 & 0–90 & Degrees (\({}^{\circ}\)) \\ \cline{1-1}  & Hspot & Hot spot & 0.01 & 0.01–1.0 & – \\ \hline \multicolumn{2}{c}{Psoil} & Soil coefficient & 0.1 & 0.1–1.0 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main input parameters of the PROSAIL model. Figure 1: Diagram of the coupling model (where \(\mu_{\mathrm{s}}\) and \(\mu_{\mathrm{v}}\) are cosine of solar zenith angle and cosine of view zenith angle, respectively, and \(\phi\) is relative azimuth angle. )Lambertian surface is adopted, and the surface reflectance is set to 0.2. Moreover, urban aerosol types are selected and different aerosol loadings, of which the AOD (Aerosol optical depth) changes from 0.2 to 1.0, are considered. It can be seen from Figure 2 that the radiation gradually increased with the increase in AOD on the whole, mainly caused by aerosol scattering. However, the radiation is nearly equal regardless of the AOD in the near-infrared bands (such as 1320-1410 nm and 1800-2200 nm). For the intensity of radiation, it is found that the contribution of AOD has about a 3.0-20% difference with the increase in AOD, indicating that the value of AOD is an important input variable of the UNL-VRTM model. Based on the values listed in Table 2, the spectral reflectance between 400 nm and 2500 nm, simulated by the PROSAIL model and the coupling model, is shown in Figure 3.  
From Figure 3, the reflectance of the coupling model is smaller than the vegetation canopy reflectance simulated by the PROSAIL model at all spectral wavelengths. The decrease in reflectance at wavelengths larger than 750 nm is mainly due to aerosol absorption, and in the blue spectrum (400-450 nm) it is because of the contribution of Rayleigh scattering.