# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## 2 Materials and Methods
### Radiative Transfer Modelling  
For this study, PRO4 SAIL-5B (PROSPECT 5B + 4 SAIL) was used which operates based on the input parameters listed in Table 2 and described in Section 2.2.2. Following the suggestion of [1], the Skyl-parameter was kept stable at 0.1. The soil brightness parameter scales the dominance of the bright and dark canopy background in the output signal. By default, standard literature soils are used for this. In this study they were replaced by the brightest and the darkest soil spectrum of the campaign, measured directly at the study fields for each date. The background signal gains more weight in the simulated reflectance for vegetation that is sparse in terms of green LAI. It is important to note that spectral signatures of senescent canopies differ from those of small plants that cover the soil only partially, although situations might result in the same low value for green LAI. For this reason, another background type is introduced that was calculated as the mean senescence signal for rip wheat crops of both seasons. All other leaf and canopy parameters were randomly drawn from uniform distributions with min and max values adjusted according to Table 2. Input parameters regulating the s-t-s-geometry uniformly covered all field scenarios. For example, the minimum SZA observed in the field was 29.14\({}^{\circ}\) and the maximum was 52.63\({}^{\circ}\). As a result, SZAs of 30\({}^{\circ}\), 35\({}^{\circ}\), 40\({}^{\circ}\), 45\({}^{\circ}\), 50\({}^{\circ}\) and 55\({}^{\circ}\) were used for generating the LUT. Variations in the OZA of \(-\)30\({}^{\circ}\), 0\({}^{\circ}\) and +30\({}^{\circ}\) took account of the three experiments of the simulated EnMAP platform tilt. For winter wheat crops it was suggested setting the leaf structure parameter N to a mean of 2.0 with a SD of 0.34 [7]. Since our study data covered the complete vegetation cycle from seeding to harvest, these values were slightly adapted to a wider range of 1.0 to 2.5. The size of each LUT (n\({}_{\text{lut}}\)) can be understood as the number of variations of the parameters (n\({}_{\text{para}}\)) multiplied by the number of variations of the s-t-s-geometry (n\({}_{\text{angles}}\)). n\({}_{\text{lut}}\) has a linear influence on the calculation time for the generation and the inversion of the LUT. On the other hand, larger LUT sizes yield more possible parameter constellations, which may improve the quality of the retrieval. Many authors suggest n\({}_{\text{para}}\) = 100,000 as the best trade-off between calculation time and inversion accuracy (e.g., [8; 12; 49]). In each of these studies, however, angles of sun and observer were fixed. As described in Table 2, n\({}_{\text{angles}}\) here needed to cover 252 different geometric constellations which would result in \begin{table}
\begin{tabular}{c c c c c c} \hline
**Model** & **Parameter** & **Description** & **Unit** & **Min** & **Max** \\ \hline PROSPECT & N & Leaf structure parameter & - & 1.0 & 2.5 \\  & LCC & Leaf Chlorophyll\({}_{\text{s+b}}\) content & mg cm\({}^{-2}\) & 0.0 & 80 \\  & LCarC & Leaf Carotenoids content & \(\mu\)g cm\({}^{-2}\) & 0.0 & 20 \\  & EWT & Leaf Equivalent Water content & cm & 0.001 & 0.05 \\  & LMA & Leaf Mass per Area & g cm\({}^{-2}\) & 0.001 & 0.02 \\  & C\({}_{\text{br}}\) & Fraction of brown leaves & - & 0.0 & 1.0 \\ \hline SAIL & LAI & Leaf Area Index & m\({}^{2}\) m\({}^{-2}\) & 0.0 & 8.0 \\  & ALIA & Average Leaf Inclination Angle & deg & 20 & 90 \\  & Hspot & Hot Spot size parameter & - & 0.01 & 0.5 \\  & Skyl & Ratio of diffuse and total & - & 0.1 & 0.1 \\  & \(\gamma\) & Soil Brightness Parameter & - & 0.0 & 1.0 \\ \hline Model & Parameter & Description & Unit & Min & Max & Divisions \\ \hline SAIL & SZA & Sun Zenith Angle & deg & 30 & 55 & 6 \\  & OZA & Observer Zenith Angle & deg & \(-\)30 & 30 & 3 \\  & rAA & relative Azimuth Angle & deg & 0 & 65 & 14 \\ \hline \end{tabular}
\end{table} 
Table 2: Overview of the PROSAIL parameter ranges for creation of the look-up-table.