## 5 Results
### Preliminary Evaluation Results  
#### 5.4.1 Per-Band Bias Errors  
For the evaluation of both sets of calibration coefficients, the number of remaining samples after outlier filtering was 286, 293, 295 and 293, for B1, B2, B3 and B4, respectively. This evaluation is just a preliminary exploration of the results obtained applying coefficients I\({}_{0}\) and Pre-F, mainly due to the fact that there is no land cover diversity in the area covered by both sensors. Hence, a validation must be considered over heterogeneous zones with the presence of different types of vegetation, soils, etc., in the form of large uniform patches. Under these circumstances, the evaluation of the estimated gains over a broader range of reflectances for each FASat-C band would be feasible. In order to allow the comparison of both calibration parameters sets (Pre-F and I\({}_{0}\)), per-sample bias errors were calculated with respect to RapidEye radiances and reflectances. Table 6 summarizes the main descriptive statistics for all FASat-C bands, such as Mean Bias Error (MBE), among others. The mean bias error of the evaluation samples was obtained as follows:  
\[\text{MBE}=\ \frac{1}{n}\sum_{i=1}^{n}\left(R-F\right)_{i} \tag{9}\]  
where \(n\) is the number of evaluation samples; \(R\) and \(F\) are the magnitudes derived from the common samples collected by RapidEye and FASat-C, respectively (radiance or reflectance). When compared to RapidEye, the use of Pre-F gains led to an underestimation of at-sensor radiances for B1, B2 and B3, and an overestimation for B4. The cross-calibration produced less biased results, and the best agreements were obtained for B1 and B2. The cross-calibration  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Band**} & \multirow{2}{*}{**Cal**} & \multicolumn{6}{c}{**Radiance**} & \multicolumn{6}{c}{**Reflectance**} \\ \cline{3-13}  & & **MBE** & **St Dv** & **Median** & **Max** & **Min** & **MBE** & **St Dv** & **Median** & **Max** & **Min** \\ \hline \multirow{2}{*}{**B1**} & Pre-F & 9.03 & 2.43 & 9.26 & 16.48 & 4.70 & 0.015 & 0.004 & 0.016 & 0.028 & 0.008 \\  & I\({}_{0}\) & 0.17 & 2.79 & \(-\)0.29 & 8.11 & \(-\)5.45 & 0.000 & 0.005  
reduced the B1 MBE from 9.03 down to 0.17 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\) and the B2 MBE from 7.573 down to 1.67 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\). For B3, the mean bias error decreased from 8.17 down to 3.36 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\), while for B4, it changed from \(-10.37\)-3.4 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\). In spite of the high variability observed in the sample, particularly for B1 and B2, for which the standard deviations are higher than MBE, a considerable decrease in the magnitude of MBE and maximum bias errors was achieved once I0 gains are utilized. In Figure 8, the bias error per sample is shown as a function of TOA reflectance, either for pre-flight or for cross-calibration. For B1 (Figure 8a), after cross-calibration, the range of bias errors shifted from 4.7-16.5 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\) to \(-5.45\)-8.1 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\), corresponding the highest bias errors to samples of \(\sim\)0.15 and \(\sim\)0.22 reflectance units. Radiances equivalent to reflectances higher than 0.25 are mainly overestimated; nevertheless, the biases for all samples have been substantially reduced. For B2 (Figure 8b), after cross-calibration, underestimation has lessened if compared to the results obtained after applying the Pre-F gain. With Pre-F gain, the bias errors were in the range of 1.12-17.1 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\); after applying the I0 gain, the range of bias error changed to \(-5.48\)-8.95 \(\mathrm{W\cdot m^{-2}\cdot sr^{-1}\cdot\mu m^{-1}}\), meaning that the improvement is more noticeable for higher reflectance samples. The range has been reduced, along with the MBE and dispersion, which shows the good performance of the updated parameter.