# Improving the Retrieval of Crop Canopy Chlorophyll Content Using Vegetation Index Combinations
## 2 Materials and Methods
### Simulation of Canopy Reflectance Using the PROSAIL-D Model  
The PROSAIL-D model was derived by coupling the PROSPECT-D leaf optical properties model [56] with the 4 SAIL canopy bidirectional reflectance model [57]. The PROSAIL-D model was used to simulate MERIS observations and model the CCC based on VIs. It simulates upward and downward hemispherical radiation fluxes between 400 and 2500 nm with seven input parameters, and outputs the leaf spectral reflectance and transmittance. The 4 SAIL model is used to simulate canopy reflectance with a series of input parameters. The input parameters for the PROSAIL-D model are shown in Table 5.  
As shown in Table 5, the LCC values were set between 10 and 80 \(\upmu\)g cm\({}^{-2}\), at 10 \(\upmu\)g cm\({}^{-2}\) intervals. The leaf carotenoid content was set to 25% of the LCC due to its insensitivity to red and red-edge region reflectance. The LAI values ranged from 0.25 to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Name** & **Formula** & **Reference** \\ \hline \multirow{3}{*}{MTCI} & MERIS terrestrial chlorophyll index & \multirow{3}{*}{(B10 \(-\) B9)/(B9 \(-\) B8)} & [13] \\  & Normalized difference vegetation index & \multirow{3}{*}{(B10 \(-\) B8)/(B10 \(+\) B8)} & [55] \\  & Linearized NDVI & & 1.2 (B10 \(-\) B8)/(B10 \(+\) B8) & [22] \\ S\(-\)NDVI & Stretched NDVI & & 4/[1 \(+\) (1.2/NDVI) 2] & [51] \\ \cline{2-3} RDVI & Renormalized difference vegetation index & \multirow{3}{*}{(B10 \(-\) B8)/SQRT(B10 \(-\) B8)} & [52] \\  & Modified triangular vegetation index 2 & & 1.5 [1.2 (B10 \(-\) B5) \(-\) 2.5 (B8 \(-\) B5)]/ & \\ \cline{2-3} MTVI2 & Vegetation index 2 & \multirow{3}{*}{SQRT((2 B10 \(+\) 1) 2 \(-\) [6 B10 \(-\) 5  SQRT(B8)] \(-\) 0.5]} & [16] \\ \cline{2-3} \end{tabular}
\end{table} 
Table 4: Vegetation indices based on MERIS band settings. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameters** & **Description** & **Units** & **Range** \\ \hline \multirow{8}{*}{Leaf} & N & Leaf structure index & - & 1.5 \\  & LCC & Leaf chlorophyll content & \(\upmu\)g cm\({}^{-2}\) & 10–80; interval, 10 \\  & C\({}_{\text{m}}\) & Leaf dry matter content & g cm\({}^{-2}\) & 0.004 \\  & C\({}_{\text{b}}\) & Leaf brown pigment content & - & 0 \\  & C\({}_{\text{w}}\) & Equivalent water thickness & cm & 0.02 \\  & Car & Leaf carotenoid content & \(\upmu\)g cm\({}^{-2}\) & 25\% LCC \\  & C\({}_{\text{Ant}}\) & Leaf anthocyanin content & \(\upmu\)g cm\({}^{-2}\) & 2 \\ \hline \multirow{8}{*}{Canopy} & LAI & Leaf area index & m\({}^{2}\) m\({}^{-2}\) & 0.25, 0.5, 0.75, 1, 1, 25, 1.5 1.75, 2, 3, 4, 5, 6, 7, 8 \\  & \(\upalpha_{\text{soil}}\) & Soil reflectance & - & As in Figure 1 \\  & ALA & Average leaf angle & Degrees & [1, 0], [0, 1], [0, -1], [0, 0] [\(-\).35, \(-\).15] \\ \cline{1-1}  & hotS & Hot spot parameter & m m\({}^{-1}\) & 0.05 \\ \cline{1-1}  & skyl & Fraction of diffuse incoming & - & According to the solar zenith angle \\ \cline{1-1}  & \(\updelta\)s & Solar zenith angle & Degrees & 0, 10, 20, 30, 40, 50, 60 \\ \cline{1-1}  & \(\uptheta\)v & View zenith angle & Degrees & 0 \\ \cline{1-1}  & \(\upvarphi\) & Sun-sensor azimuth angle & Degrees & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Configuration of the input parameters in the PROSAIL-D model. 8, representing different levels of vegetation coverage. Five different leaf inclinations and five types of soil reflectance (Figure 2) were used to represent different canopy structures and soil backgrounds, respectively. The five types of soil reflectance were determined using the field-measured spectra of bare, dry soil multiplied by different brightness coefficients. The fraction of diffuse incoming solar radiation (skyl) was calculated in the PROSAIL-D model according to the solar zenith angle. The solar zenith angles were set between 0 and 60\({}^{\circ}\), at 10\({}^{\circ}\) intervals. The remaining fixed parameters were set according to either field measurements or the scientific literature [58].