## Materials and Methods
### General Methodology
#### 2.3.5 Validation Metrics  
Validation was performed by comparing LAI, chlorophylls, and carotenoids estimates with the field measurements available using RMSE, bias, the \(R^{2}\) of the predicted-vs.-measured regression line and the STDB (standard deviation of the difference between estimated points and the regression line) as cost functions.  
Concerning LAI, each validation point was the average of LAI values derived from 3 hemispherical pictures taken within a 20 \(\times\) 20 m plot (see Section 2.2.1). Therefore, one LAI validation point does not necessarily only contain information about the LAI of the AVIRIS-C pixel it is associated with. Figure 4  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameters** & **Acronym** & **Values/Range** & **Step** & **Number of Values** \\ \hline Leaf Angle Distribution & LAD & spherical & & \\ Leaf Area Index (m\({}^{2}\)/m\({}^{2}\)) & LAI & 0.1–1.9 & 0.3 & 7 \\ Chlorophylls a+b content (\(\upmu\)g/cm\({}^{2}\)) & C\({}_{ab}\) & 10–60 & 10 & 6 \\ Carotenoid content (\(\upmu\)g/cm\({}^{2}\)) & Car & 2–22 & 4 & 6 \\ Dry matter content (g/cm\({}^{2}\)) & C\({}_{m}\) & 0.001–0.016 & 0.003 & 6 \\ Equivalent Water Thickness (cm) & C\({}_{m}\) & 0.001–0.021 & 0.004 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Leaf fixed and variable input parameters used for the LUT generation.  
illustrates the issue: Since the AVIRIS pixels and the grid used for DHP acquisitions have no reason to match, some DHP (dots) may have been acquired out of the pixel the final LAI has been associated with (red square). Direct comparison between pixel-estimated value and validation data can therefore be inappropriate, especially for spatially heterogeneous canopies. To address this, LAI validation points were compared to a spatially smoothed LAI inversion map. The spatial smoothing was done by computing the average LAI within a sliding window with an aperture size of 3 pixels. The aperture size was set to 3 as the LAI validation plot size (20 \(\times\) 20 m) roughly matches the AVIRIS-C pixel size (18 \(\times\) 18 m) (Figure 4).  
Biochemistry validation data were obtained at the leaf scale, for a single tree in each validation pixel. There is therefore an unavoidable uncertainty, as validation is done by comparing field data at the leaf scale (single tree) to plot biochemistry (canopy scale, multiple trees). An assumption is made that tree biochemistry does not vary much spatially, and C\({}_{ab}\) and Car estimations were directly extracted from the pixels associated to the acquisition positions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Method** & **N\({}_{bands}\)** & **VI Formula (Wavelengths in \(\upmu\)m)** & **Reference** \\ \hline \multirow{4}{*}{LAI} & RMSE INT LAI & 120 & & \\  & SAM INT LAI & 120 & & \\  & \(D_{NDVI}\) & 2 & & \\  & \(D_{MSAVI2}\) & 2 & \(\dfrac{1}{2}(2\rho_{0.800}+1-\sqrt{(2\rho_{0.800}+1)^{2}-8(\rho_{0.800}-\rho_{ 0.670})})\) & [55] \\ \hline \multirow{4}{*}{Cab} & RMSE INT CAB & 27 & \\  & SAM INT CAB & 27 & \\  & \(D_{TCARI/OSAVI}\) & 4 & \(3\dfrac{(\rho_{0.700}-\rho_{0.670})-0.2(\rho_{0.700}-\rho_{0.550})\frac{\rho_{0.700}}{\rho_{0.670}}}{1.16\frac{\rho_{0.800}-\rho_{0.670}+0.16}{\rho_{0.800}+ \rho_{0.500}+0.16}}\) & [59] \\  & \(D_{MACCIONI}\) & 3 & \(\dfrac{\rho_{0.780}-\rho_{0.710}}{\rho_{0.780}-\rho_{0.680}}\) & [60] \\  & \(D_{gNDVI}\) & 2 & \(\dfrac{\rho_{0.780}-\rho_{0.550}}{\rho_{0.780}+\rho_{0.550}}\) & [61] \\  & \(D_{GM\_94b}\) & 2 & \(\dfrac{\rho_{0.750}}{\rho_{0.550}}\) & [62] \\  & \(D_{MCARI2}\) & 3 & \(1.5\dfrac{2.5(\rho_{0.800}-\rho_{0.670})-1.3(\rho_{0.800}-\rho_{0.550}))}{ \sqrt{(2\rho_{0.800}+1)^{2}-(6\rho_{0.800}-5\sqrt{\rho_{0.670}})-0.5}}\) & [47] \\ \hline \multirow{4}{*}{Car} & RMSE INT CAR & 6 & \\  & SAM INT CAR & 6 & \\  & \(D_{R515/R570}\) & 2 & \(\dfrac{\rho_{0.515}}{\rho_{0.550}}\) & [30] \\  & \(D_{CRI}\) & 2 & \(\dfrac{1}{\rho_{0.515}}-\dfrac{1}{\rho_{0.570}}\) & [63] \\ \hline \hline \end{tabular}
\end{table}
Table 5: Spectral strategies applied for the inverse problem.