## 5 Results
### Radiometric Cross-Calibration  
As offsets have been subtracted during the generation of the radiometrically-corrected products, the results obtained through linear fits forced to the zero intercept, I0, referred to hereinafter as the result of the cross-calibration, were chosen. Just as a reference, the free-intercept (F\({}_{i}\)) results are included; however, the R\({}^{2}\) coefficient does not greatly differ from the I0 outcomes, and a similar amount of variability is explained by the linear fit, except for B1. A scatterplot of RapidEye radiances and FASat-C adjusted DN samples and cross-calibration results are provided in Figure 7 and Table 5, respectively.  
The degree of dispersion around the best-fit line is considered to be mainly a consequence of the angular anisotropic effects of reflectance; this factor has neither been studied nor corrected for, since it is out of the scope of this work. The absolute radiometric parameters estimated during pre-flight calibration are provided in Table 5. Relative differences between Pre-Flight (Pre-F) and I0 estimated gains are detailed, as well (\(\Delta_{\text{Gain}}\)).  
Considering the equation of FASat-C radiance, relative percentage differences have been calculated using the inverse value of the respective per-band gains. Absolute gains of Bands 1, 2 and 3 have shown an increase of 5.71%, 3.55% and 2.78% in radiance units per DN, respectively, while B4 presents a decrease of \(-\)10.88%.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Band**} & \multirow{2}{*}{**n**} & \multicolumn{3}{c}{**Free Intercept (F\({}_{i}\))**} & \multicolumn{3}{c}{**Zero Intercept (I0)**} & \multicolumn{3}{c}{**Pre-Flight Calibration (Pre-F)**} \\ \cline{3-10}  & & **Gain** & **Offset** & **R\({}^{2}\)** & **Gain** & **R\({}^{2}\)** & **Gain** & **Pre-F\({}^{-1}\)** & \(\Delta_{\text{Gain}}\) (I0\({}_{\text{Gain}}\)–Pre-F\({}^{-1}\))** \\ \hline B1 & 127 & 0.9941 & 26.266 & 0.8418 & 1.1357 & 0.8248 & 1.0708 & 5.71\% \\ B2 & 125 & 0.9691 & 12.787 & 0.9284 & 1.0230 & 0.9255 & 0.9867 & 3.55\% \\ B3 & 128 & 0.8631 & \(-\)4.605 & 0.9391 & 0.8476 & 0.9388 & 0.8239 & 2.78\% \\ B4 & 129 & 0.5741 & \(-\)1.696 & 0.9260 & 0.5688 & 0.9259 & 0.63068 & \(-\)10.88\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: FASat-C radiometric calibration parameters estimated over Frenchman Flat.  
Figure 7: Cross-calibration of FASat-C NAOMI-1 with respect to RapidEye MSI. RapidEye radiances are plotted against FASat-C adjusted DN. Linear fit parameters and R\({}^{2}\) are detailed in Table 5.  
To assess the influence of the size of the calibration sample on the estimated gains, 32 samples of 10 \(\times\) 10 pixels each were collected on the same regions that were catalogued as uniform and highly correlated. An average relative difference of 0.16% with respect to the gains estimated with the 5 \(\times\) 5-pixels samples was obtained. These gains were applied to the evaluation samples, causing an average difference of 0.04% in the RMSE values of absolute errors.  
A study about the dependence on sample size (i.e., 5 \(\times\) 5 pixels vs. 10 \(\times\) 10 pixels) of the per-band coefficients of the I\({}_{0}\) models showed an average decrease of 25.2% in the coefficients for all bands; reducing the goodness of fit of the linear models when the largest sample size is chosen. However, it must be emphasized that the relative differences between both I\({}_{0}\) gain sets have low impact on the calculated radiances/reflectances. These results demonstrate the importance of calibrating satellite sensors with a CEOS-WGCV endorsed site and the potential of LISA to define specific calibration regions, as shown in [PERSON] et al. (2013); [PERSON] et al. (2015).