## 2 Materials and Methods  
In this study, a GSA is based on a simulated dataset. The PROSAIL RTM [13] implemented in the automated radiative transfer models operator (ARTMO) graphic user interface (GUI) [14] is used to simulate canopy \(\rho\). Different combinations of leaf constituents, canopy structure, soil reflectivity, and sun-sensor geometry are given by a pre-defined look-up table (LUT) as Table 1. In general, Table 1 is adapted from previously used LUTs [3; 5; 6; 10], but small Cab values (0-10 ug/cm\({}^{2}\)) are excluded in order to avoid potential biased sensitivity resulting from unrealistic scenarios. Because the size of the LUT grows dramatically with increasing LUT variables, we use the full random sampling method provided by ARTMO GUI, which samples the LUT uniformly to generate a random subset with each variable ranging within given boundaries. The size of the subset is set to 100,000. It should be noted that full random sampling is performed three times for each sensor, and results are cross-validated to avoid a potential sampling bias. We use the ARTMO's sensor tool to simulate spaceborne-sensor-like \(\rho\) data. The ARTMO's sensor tool spectrally samples original 1 nm \(\rho\) data into broader channels according to designed spectral response functions of the selected sensor. Spectral sampling is made before model simulations to avoid potential mismatches between canopy and soil spectra range. It should be noted that the spectral convolution is conducted at reflectance level for convenience. This may induce an inconsistency between simulated and remotely sensed data, because spectral response happens at radiance level, and canopy \(\rho\) is obtained through atmosphere correction in RS situations [1]. In this study, we consider four widely used operational multi-spectral spaceborne sensors, including MODIS (Moderate Resolution Imaging Spectrometer), Landsat-8 OLI (Operational Land Imager), Sentinel-2 MSI (Multi-Spectral Instrument), and Sentinel-3 OLCI (Ocean Land Color Instrument). Seven VIs that have been used at large scales, including the normalized difference VI (NDVI), enhanced VI (EVI), MERIS terrestrial chlorophyll index (MTCI, derived from Sentinel-2 MSI and Sentinel-3 OLCI), universal normalized VI (UNVI, derived from MODIS and Landsat-8 OLI) [15], near-infrared reflectance of vegetation (NIRv, the product of NDVI and NIR R) [16], photochemical reflectance index (PRI, derived only from MODIS), and tasseled cap transformation greenness (TCTG, derived only from OLI) [17], are calculated from simulated satellite data. Sensor-VI combinations and references are listed in Table 2. Specifically, UNVI and TCTG are calculated on the basis of band-transformation. UNVI is developed on the basis of the universal pattern decomposition method (UPDM), which takes the idea of spectral unmixing, projecting the observed spectrum to spectral space defined by standard components of vegetation, soil, water, and others (typically a spectrum of yellow leaf). It should be noted that spectral response functions are used to calculate sensor-specific standard components. Once the coefficients of standard components are derived, UNVI can be calculated using the formula given in Table 2. TCTG is another band transformation-derived index. TCT transforms original spectra into orthogonal axes with physical meaning, and TCTG represents the derived vegetation greenness in an RS image. TCTG is calculated using greenness coefficients provided by [17], which are determined to make OLI keep a continuity to its predecessor, the Landsat thematic mapper (TM).