## 2 Materials and Methods
### Parametrization and Look-Up Table (LUT) Inversion  
Look-up tables (LUT) provides a feasible approach for the inversion of RTMs [47]. LUT inversion allows performing a global search and in comparison to other inversion methods such as numerical optimisation and neural networks avoids unexpected behaviour when the canopy spectral properties are not well presented by the simulated spectra [99]. The LUT dimensions have a significant role in the retrieval accuracy of the parameters involved [27; 30; 100; 101]. Therefore, for both 2015 and 2016 datasets used in this study, 500,000 parameter combinations were randomly generated using uniform distributions [30; 57] which were then used in the forward calculation of the PROSAIL model. Furthermore, the spectral response functions of RapidEye and Sentinel-2 bands were not considered in the PROSAIL simulations. Since reflectance data were obtained from RapidEye and Sentinel-2 imagery acquired at a known date and time, three PROSAIL input parameters related to sun and sensor geometries including sensor viewing angle (12\({}^{\circ}\), 8\({}^{\circ}\)), relative azimuth angle (109\({}^{\circ}\), 126\({}^{\circ}\)), and solar zenith angle (33\({}^{\circ}\), 36\({}^{\circ}\)) were fixed based on the image specifications. Moreover, due to the minor influence of the fraction of diffuse incoming solar radiation (skyl) on canopy reflectance [102] and the lack of onsite measurements, a fixed value of 0.1 was used for this parameter [27; 35; 76]. The other input parameters were then generated randomly using 500,000 parameter sets to realise the LUTs for model inversion. The values of these model input parameters are described in Table 2.  
We interpolated the average bare soil reflectance spectra which was measured during the field campaign to the spectral bands setting of Sentinel-2 and RapidEye to present the soil optical properties. To explain the soil roughness and moisture in the island, we also varied the range of the scale \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Abbreviation in Model** & **Unit** & **Minimum Value** & **Maximum Value** \\ \hline Leaf area index & LAI & m\({}^{2}\) m\({}^{-2}\) & 0.3 & 6.6 \\ Mean leaf & ALA & Deg & 40 & 80 \\ inclination angle & & & & \\ Dry matter content & C\({}_{\text{m}}\) & g cm\({}^{-2}\) & 0.003 & 0.02 \\ Leaf structural & & N & No dimension & 1.5 & 1.9 \\ parameter & & & & \\ Leaf chlorophyll & C\({}_{\text{ab}}\) & \(\mu\)g cm\({}^{-2}\) & 10 & 60 \\ content & & & & \\ Equivalent water & & & & \\ thickness 1 & C\({}_{\text{w}}\) & g cm\({}^{-2}\) & 0.005 & 0.025 \\ Hot spot size & & hot & m m\({}^{-1}\) & 0.05 & 0.1 \\ parameter & & & & \\ Soil brightness & & scale & No dimension & 0.5 & 1.5 \\ parameter & & & & \\ \hline \hline \end{tabular}  
* The value was kept constant to its mean value (0.01) for generation of the RapidEye LUT.  
\end{table} 
Table 2: Specific ranges for model input parameters used for generation of RapidEye and Sentinel-2 look-up tables (LUTs) using the PROSAIL model. The parameters values were selected randomly (uniform distributions) within the specified ranges. parameter [98] (Table 2). Field measurements (LAI, ALA, \(\mathrm{C_{ab}}\), \(\mathrm{C_{m}}\), and \(\mathrm{C_{w}}\)) were used to define the approximate range of \"free\" model parameters [95; 103]. Limiting the parameter space has been suggested in many studies [27; 48; 104] and assists in regularisation of the ill-posed problem of model inversion [103]. For the hot spot size parameter, a range of 0.05 to 0.1 was selected [48; 105]. Furthermore, a range of 1.5 to 1.9 was used for leaf structural parameter N [27; 30], which was in agreement with the mean value (N = 1.6) used for grassland species by [96].