## 3 Materials and Methods
### Description of Simulated Datasets  
The training and performance assessment of biophysical parameters retrieval from at-sensor TOA radiance is based on simulated data of surface reflectance and TOA radiance. The use of RTMs allows us to test the retrieval accuracy under controlled conditions. On the one hand, surface reflectance datasets are based on the combination of PROSPECT-4 [20] and SAIL [21] RTMs, also known as PROSAIL. PROSPECT-4 is one of the most widely used RTMs that simulates leaf optical properties. The model calculates directional-hemispherical reflectance and transmittance measured from 400 nm to 2500 nm at 1 nm spectral sampling. SAIL solves the radiative transfer equation for scattering and absorption of four upward/downward fluxes at the canopy scale. In combination with PROSPECT-4 leaf optical properties, SAIL provides top-of-canopy (TOC) reflectance in the 400-2500 nm spectral range at 1 nm sampling. On the other hand, MODTRAN5 [24; 57] was chosen to simulate the radiative transfer in the atmosphere at 15 cm\({}^{-1}\) (0.3-9 nm in the covered spectral range of 400-2500 nm). MODTRAN has been extensively used for remote sensing applications such as atmospheric correction [6; 7; 58]. It solves the RT equation with an accurate simulation of the coupled absorption/emission and scattering effects by molecules and particulate matter in a multilayered spherically symmetric atmosphere [59; 60]. With the application of the interrogation technique developed in [54], MODTRAN can generate the following output _atmospheric transfer functions_: Atmospheric path radiance (\(L_{0}\)), direct/diffuse at-surface solar irradiance (\(E_{dir/dif}\)), direct/diffuse target-to-sensor transmittance (\(T_{dir/dif}\)), and spherical albedo (\(S\)). The generation of the simulated datasets (_analysis_, _reference_ and _retrieval_) is represented in Figure 3 and further described in the paragraphs below. The first dataset (further referred to as _analysis_) functions to train an emulator that allows running a GSA to evaluate the relative contribution into TOA radiance of various leaf-canopy and atmospheric properties. Thus, this dataset combines PROSAIL and MODTRAN into a database of TOA radiance spectra. The first step was to generate the LUT of directional reflectance (\(\rho\)) derived from the combination of the PROSPECT-4 and SAIL. A set of 10,000 samples of the six input leaf-canopy variables were distributed according to a Latin Hypercube Sampling (LHS) distribution [61] (see Table 2). The hot-spot, soil brightness coefficient, and the sun-target senor geometry variables have been excluded from the analysis in order to facilitate the coupling between the vegetation and atmospheric RTMs. Simulations were carried out in the 400-2500 nm spectral range at 1 nm sampling. The second step involves generating MODTRAN simulations. The _analysis_ dataset contains 10,000 MODTRAN simulations sampled with a LHS distribution (see Table 3). These simulations were carried out in the same spectral range as PROSAIL simulations with a sampling of 15 cm\({}^{-1}\) (0.3-9 nm in the covered spectral range of 400-2500 nm). Input variables were selected so that they have an impact in the entire wavelength range (400-2500 nm) and include typical variability [8; 62; 63; 64] in: (1) the AOT\({}_{550}\); (2) the spectral dependency of the extinction coefficient, through the Angstrom exponent; (3) the phase function, through the HG asymmetry parameter; (4) the single scattering albedo; and column-integrated concentrations of (5) ozone (O3C) and (6) vapor (CUV).