## 4 Results
### Global Sensitivity Analysis Results  
A GPR emulator was first developed as approximation of the coupled PROSPECT4-SAIL-MODTRAN model given 12 input variables and 1000 samples taken from the _analysis_ dataset. GPR was used because of superior performances as opposed to other MLRAs [31; 32; 33]. This was also the case here: GPR clearly outperformed competing algorithms such as neural networks and kernel ridge regression (results not shown). Training the GPR emulator took less than 3 min. It reached an overall accuracy with RMS errors (RMSE) of 1.06 and normalized RMS errors (NRMSE) of 2.39%. When plotting the NRMSE along the spectral range, it appears that accuracies are consistent with the exception of the water absorption regions around 1400 and 1900 nm where accuracies are somewhat poorer (errors around 6%) (results not shown). This accuracy is on the same order as earlier published emulators [33; 90], and can be considered as adequate for subsequent GSA calculations. Running the GPR emulator into the GSA with 1000 samples per variable took less than 40 s. In comparison, if the same analysis would have been done by the original coupled RTMs, run-time would take on the order of several weeks. The total sensitivity GSA results shown in Figure 5 are expressed as relative contributions to output variance for each one of the input variables in the TOA spectrum (\(S_{Ti}\), expressed in %). The figure leads to the following observations:  
* Generally, the GSA results indicate that atmospheric variables had a weaker influence than vegetation variables. Regarding the atmospheric variables, clearly, the H\({}_{2}\)O content had a strong impact in discrete parts of the spectrum, in agreement with the location of H\({}_{2}\)O absorption bands. Relatively small impact bands can be found at 820 nm, while stronger impact (over 70% \(S_{Ti}\)) in the region of 900-950 nm and 1100-1150 and the largest impact bands (over 80% \(S_{Ti}\)) between 1350-1450 and between 1800-1900 nm where the H\({}_{2}\)O absorption saturates. * The aerosol optical properties (extinction, absorption and phase function) were the most dominant atmospheric variables. Particularly, the AOT\({}_{550}\) and phase function (through the Henyey-Greenstein parameter, G) had a relatively strong impact (30% \(S_{Ti}\)) in the region of 400 to 500 nm, where the scattering is higher. This impact diminishes to a few percents in the range of 500 to 1300 nm and with barely any influence after 1300 nm. According to the GSA results, the O\({}_{3}\) seemed not to have a relevant influence over the variance of the TOA radiance even at the bottom of the Chappuis absorption band (400-650 nm) where the O\({}_{3}\) absorption is higher. * Among vegetation variables, at the leaf level, chlorophyll content (Cab) was the main driver of TOA radiance in the visible range (450-750 nm) with over 60% \(S_{Ti}\), while dry matter content (Cm) was the main driver in the NIR range (750 to 1200 nm), 70%. Water content (Cw) had a negligible impact on the visible and the NIR but had a considerable impact in the SWIR (1400 to 2500 nm), with \(S_{Ti}\) up to 20%. These three variables explain more than the 60% of the variance along the visible and NIR spectral range (400-1400 nm). The leaf layer variable (N) had a rather weak influence, but it covered the whole spectral range. Among canopy variables, LAI is the most dominant variable. It has influence along the whole spectral range, but it becomes especially dominant from 1400 nm onwards. LAI especially dominates the 2000-2400 nm SWIR region with a \(S_{Ti}\) of around 80%. From a practical point of view, the GSA results suggest that it should be perfectly possible to retrieve Cab (dominant in the visible), Cw (dominant in the NIR-SWIR) and LAI (dominant in the NIR-SWIR) from TOA radiance data. When interpreting these results in view of S2 band settings (see Figure 1), we observed that atmosphere has little influence in the SWIR, B11 at 1610 nm and B12 at 2190 nm. These bands seem to be particularly appropriate for LAI retrieval.