## 3 Materials and Methods
### Description of Simulated Datasets
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Model Variables** & **Units** & **Minimum** & **Maximum** \\ \hline \hline \multicolumn{4}{c}{**Leaf variables (PROSPECT-4)**} \\ N & Leaf structure index & \multicolumn{2}{c}{unitless} & 1.3 & 2.5 \\ Cw & Leaf water content & [g/cm\({}^{2}\)] or [cm] & 0.002 & 0.05 \\ Cab & Leaf chlorophyll content & [ug/cm\({}^{2}\)] & 1 & 70 \\ Cm & Leaf dry matter content & [g/cm\({}^{2}\)] & 0.002 & 0.05 \\ \hline \multicolumn{4}{c}{**Canopy variables (SAIL)**} \\ LAI & Leaf area index & [m\({}^{2}\)/m\({}^{2}\)] & 0.1 & 7 \\ LAD & Leaf angle distribution & [\({}^{\circ}\)] & 0 & 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range of vegetation input variables for the PROSAIL LUTs according to Latin Hypercube sampling. SAIL fixed variables: hot spot: 0.01; solar zenith angle: 30\({}^{\circ}\); observer zenith angle: 0\({}^{\circ}\). Figure 3: Schematic representation of synthetic datasets based on PROSAIL and MODTRAN simulations. The red-dashed and green lines identify the datasets used respectively for Global Sensitivity Analysis and Biophysical parameters retrieval. The surface (PROSAIL) and the atmospheric (MODTRAN) simulations were randomly one-to-one combined (10'000 simulations) and propagated to TOA radiance following Equation (1) with the Lambertian and homogeneous surface assumption:  
\[L=L_{0}+\frac{E_{tot}T_{tot}\rho}{\pi(1-S\rho)} \tag{1}\]  
where \(T_{tot}=T_{dir}+T_{dif}\) is the total target-to-sensor transmittance and \(T_{tot}=E_{dir}\cos\theta_{il}+E_{dif}\) is the total at-surface irradiance for a solar zenith angle \(\theta_{il}\). Here, the 1 nm sampling surface reflectance (\(\rho\)) was interpolated by cubic splines to the MODTRAN wavelength grid. For the sake of simplicity, the spectral dependency of all terms in the Equation (1) has been omitted. A random subset of 1000 cases is then used to train an emulator for further GSA calculation. The second dataset (further referred to as _reference_) aims at representing realistic S2 observations over land surfaces for broad atmospheric conditions and is used for validation. The _reference_ dataset is divided into three subsets to validate the retrieval strategies under three different scenarios (see Figure 3): (1) retrieval from an ideal surface reflectance data, (2) retrieval from TOA radiance, and (3) retrieval from surface reflectance after a non-perfect atmospheric correction. The first subset (_reference_toc) corresponds to a reference surface reflectance dataset composed of a random subset of 5000 samples extracted from the _analysis_ dataset previously described in Table 2. This scenario should be taken as the ideal case, since there are no radiometric perturbances due to atmospheric scattering and absorption. This surface reflectance data is combined with other 5000 MODTRAN simulations to create the second subset of reference TOA radiance (_reference_toa_). This second scenario refers to the goal of this paper i.e., to validate the performance of retrieving biophysical variables directly from TOA radiance. In this case, MODTRAN simulations were run with varying conditions of CWV, O3C, AOT\({}_{550}\) and aerosol type with an LHS distribution (see Table 4) and in the same spectral range and sampling as in the _analysis_ dataset. With respect the aerosol type, the following 9 models were included: MODTRAN's rural, urban and navy-maritime (with 3 air mass values identifying coastal to strong land influence), and OPAC's continental (clean, average and polluted) and urban [62]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Model Variables** & **Units** & **Minimum** & **Maximum** \\ \hline O3C & O\({}_{3}\) column concentration & [amt-cm] & 0.25 & 0.35 \\ CWV & Column Water Vapour & g\(\cdot\)cm\({}^{-2}\) & 0.4 & 4.5 \\ AOT\({}_{550}\) & Aerosol Optical Thickness at 550 nm & unitless & 0.05 & 0.5 \\  & Aerosol type & 9 types (see text above) & \\ \hline \hline \end{tabular}
\end{table}