# Sensitivity of Common Vegetation Indices to the Canopy Structure of Field Crops
## Materials and Methods
### PROSAIL Simulations  
We studied the sensitivity of the VIs to canopy structure (MTA and LAI) using the PROSAIL canopy reflectance model. The model is a combination of the leaf optical reflectance model PROSPECT-5 [39] and the canopy reflectance model SAILH [40; 41]. The PROSPECT-5 model simulates leaf reflectance and transmittance from six input parameters: leaf chlorophyll a and b content (\(C_{ab}\)), leaf carotenoid content (\(C_{Car}\)), leaf dry matter content (\(C_{m}\)), leaf water content (\(C_{w}\)), leaf brown pigment content (\(C_{bp}\)), and the mesophyll structure parameter \(N\). The SAILH sub-model simulates canopy reflectance using LAI, MTA, hot spot size parameter, soil reflectance, solar zenith angle, sensor view angle, sensor azimuth angle and the fraction of incident diffuse sky radiation. The leaf inclination angle distribution is characterized from the leaf mean tilt angle to generate an ellipsoidal leaf angle distribution [42].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Formula** & **References** \\ \hline NDVI & \(\frac{R_{800}-R_{680}}{R_{800}+R_{680}}\) & [23] \\ \hline EVI & \(\frac{2.5(R_{800}-R_{680})}{R_{800}+6R_{680}-7.5R_{470}+1}\) & [27] \\ \hline EVI2 & \(\frac{2.5(R_{800}-R_{680})}{1+R_{800}+2.4R_{680}}\) & [28] \\ \hline OSAVI & \(\frac{R_{800}-R_{680}}{R_{800}+R_{680}+0.16}\) & [29] \\ \hline MTVI2 & \(\frac{1.5[1.2(R_{800}-R_{550})-2.5(R_{680}-R_{550})]}{\sqrt{(2R_{800}+1)^{2} -\left(6R_{800}-5\sqrt{R_{680}}\right)-0.5}}\) & [30] \\ \hline WDRVI & \(\frac{aR_{800}-R_{680}}{aR_{800}+R_{680}}+\frac{1-\alpha}{1+\alpha}\), \(\alpha=0.1\) & [31; 32] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Vegetation indices used in this study.  
Figure 1: The soil reflectance used for PROSAIL simulations.  
First, to illustrate the effects of LAI and MTA on VIs, we varied the MTA between 15 and 75 degrees, set the LAI value to 1, 3 and 5, and set all other parameters to values characteristic of healthy green vegetation: \(C_{ab}=40\)\(\mu\)g cm\({}^{-2}\), \(C_{Car}=8\)\(\mu\)g cm\({}^{-2}\), \(C_{w}=0.001-0.02\) cm. Other parameters were fixed to values taken from the literature: \(C_{m}=0.005\) g cm\({}^{-2}\) (the average value of the six species [43; 44; 45; 46]), \(N=1.55\) (the average value of various crops [27]), \(C_{bp}=0\) (assuming the leaves were green during the measurements), and the hot spot parameter was set to 0.01 (this parameter has no practical influence on the results as the view direction was far from the hot spot because of low sun). The fraction of diffuse radiation was calculated using the 6S atmosphere radiative transfer model [47] from actual observation geometry and nearby sun photometer measurements. The parameters describing the illumination and view geometry in the model were set to coincide with the airborne spectroscopy imagery acquisition: solar zenith angle 49.4\({}^{\circ}\), sensor zenith angle 9\({}^{\circ}\), and azimuth angle 90\({}^{\circ}\).  
Next, we generated 100,000 parameter combinations by uniformly sampling the variation ranges of \(C_{ab}\), \(C_{w}\), LAI and MTA within the measured (for field-measured parameters) or natural variation range (for parameters for which this information was available). According to measurements [20], \(C_{ab}\) varied between 25 and 100 \(\mu\)g cm\({}^{-2}\), LAI between one and five, and MTA between 15 and 70 degrees (MTA = 15, 30, 40, 50, 60 and 70\({}^{\circ}\)). \(C_{w}\) varied in a wide natural range of the parameter, between 0.001 and 0.020 cm; \(C_{car}\) was linked to \(C_{ab}\) as 1:5 based on the LOPEX93 dataset [48].