## 3 Results and Discussion  
Similar results are found for each three subsets generated by full random sampling and, hence, we only show results for the first subset. Figure 2 shows feature importance scores of considered predictors given by RF for commonly used sensor VIs (results for MODIS-PRI and OLI-TCTG are shown later). It is shown that for most cases, MODIS-derived VIs show similar sensitivities to those of VIs derived from OLI, while VIs derived from the Sentinel family exhibit consistent sensitivities. This \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**VI**} & \multirow{2}{*}{**Formula**} & \multicolumn{4}{c}{**Sensor**} & \multirow{2}{*}{**Reference**} \\ \cline{3-3} \cline{5-6}  & & **MODIS** & & **OLI** & & **MSI** & **OLCI** \\ \hline
**NDVI** & \(\frac{R_{\text{NIR}}-R_{\text{R}}}{R_{\text{NIR}}+R_{\text{R}}}\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & [18] \\
**EVI** & \(G_{\frac{\text{NIR}}{\text{NIR}}+\frac{C_{\text{NIR}}-C_{\text{NIR}}+C_{ \text{NIR}}+L}{R_{\text{NIR}}+C_{\text{NIR}}+C_{\text{NIR}}+L}}\)1 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & [2] \\
**MTCI** & \(\frac{R_{\text{NIR}}-R_{\text{NIR}}}{R_{\text{NIR}}-R_{\text{NIR}}}\) & & & \(\surd\) & \(\surd\) & [19] \\
**UNVI** & \(\frac{C_{\text{NIR}}+C_{\text{NIR}}+C_{\text{NIR}}}{C_{\text{NIR}}+C_{ \text{NIR}}}\) & \(\surd\) & \(\surd\) & & & [15] \\
**NIRv** & \(\frac{R_{\text{NIR}}-R_{\text{R}}}{R_{\text{NIR}}-R_{\text{NIR}}}\times R_{ \text{NIR}}\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & [16] \\
**PRI** & \(\frac{R_{\text{NIR}}-R_{\text{R}}}{R_{\text{NIR}}+R_{\text{NIR}}}\)4 & \(\surd\) & & & & [20] \\
**TCTG** & \(\mathbf{R_{\text{B2}}}\)-\(\mathbf{g}\)-\(\mathbf{C}\)-\(\mathbf{C}\)-\(\mathbf{T}\)CTG & \(\surd\) & & & [17] \\ \hline \hline \end{tabular}  
* Constant parameters for MODIS are used, with \(G=2.5\), \(C_{1}=6\), \(C_{2}=7.5\), and \(L=1\). \({}^{2}R_{\text{RE}}\) stands for red-edge band reflectance, which corresponds to bands (705 nm) and band11 (708.75 nm) of Multi-Spectral Instrument (MSI) and Ocean Land Color Instrument (OLCI), respectively. \({}^{3}C_{\text{w}}\), \(C_{\text{w}}\), \(C_{\text{w}}\), and \(C_{\text{4}}\) stand for coefficients of vegetation, soil, water, and supplementary spectra. See [11] for detailed derivation. \({}^{4}\) MODIS band4 (555 nm) is used as a reference band. \({}^{5}\) R\({}_{\text{B2}}\)-\(\mathbf{C}\) and \(\mathbf{C}\)**ef.**TCTG stand for reflectance and TCTG coefficients vectors, respectively.  
\end{table} 
Table 2: Sensor–vegetation index (VI) combinations included in this study. Commonly used VIs considered in this study include the normalized difference VI (NDVI), enhanced VI (EVI), MERIS terrestrial chlorophyll index (MTCI), universal normalized VI (UNVI), near-infrared reflectance of vegetation (NIRv), photochemical reflectance index (PRI) and tasseled cap transformation greenness (TCTG). Formula and references of the considered VIs are also listed. Figure 1: Flow diagram showing the method of global sensitivity analysis of VIs used in this study. ARTMO: automated radiative transfer models operator. is because compared to MODIS and OLI, MSI and OLCI are narrow-band sensors and have relatively similar band settings. For almost all VIs, LAI is the most influential predictor. LAI is one of the key parameters describing canopy structure. In general, LAI determines the chance that incident solar photons interact with a leaf. For photosynthetically active radiation (PAR) bands and water absorption bands, a large LAI can induce strong canopy absorption of radiation and result in very low canopy \(\rho\). For weak absorption bands, such as NIR, solar photons are strongly scattered by the leaves in a dense canopy with a large LAI, which can result in significant anisotropic canopy \(\rho\)[23]. Therefore, LAI has a large influence on canopy \(\rho\) at all bands, especially for longer wavelengths. Accordingly, all the VIs are sensitive to LAI.