## 3 Results
### Sea-Ice Concentration Uncertainties  
#### 3.3.1 MODIS Ice Tie-Point Threshold  
The MODIS SIC uncertainties (Equations (5)-(7)) become large if the ice tie-point is close to the water tie-point. This can even lead to uncertainties which are larger than 1 in single cases. We consider a MODIS SIC with an uncertainty of 0.3 (i.e., 30%) as the upper boundary for a meaningful SIC. This is much larger than what one would accept as uncertainty for the final merged dataset. However, because the uncertainty of the merged SIC gets reduced we accept higher uncertainties for the MODIS SIC because they still can provide valuable spatial variability. As the water tie-point is fixed, we need to identify an ice tie-point threshold above which meaningful SIC cannot be derived any more. To find this threshold, we investigate the uncertainties for all 997 MODIS granules for which we have Sentinel-2 scenes. We show the mean and the 99 th percentile of the uncertainties for each granule in Figure 12. The parameters are shown for IST thresholds between 265 and 270 K, where ice tie-point values above the respective threshold are discarded. We learn from Figure 12 that the highest threshold, 270 K, would yield mean uncertainties above 0.3 in 69 cases, corresponding to 6.9% of all cases. A threshold of 266.5 K or lower would have to be chosen to discard all granules with a mean uncertainty above 0.3. The time-series of the 99 th percentile (Figure 12c) shows that the 99 th percentile of the uncertainties exceeds our sanity threshold of 0.3 for 113 granules in May (44.7% of the May granules), and for 169 granules before May (22.7% of the granules before May) when applying a threshold of 269 K or higher. A threshold of 266.5 K yields 99 th percentile values of above 0.3 for 32 granules before May (4.3% of all granules before May) and for 31 granules in May (12.3% of the May granules). The mean uncertainty does not show a trend until the end of April and then increase slightly, regardless of the threshold which is chosen. Except for some outliers, the mean uncertainties do not depend strongly on which threshold is chosen. This changes towards the end of the time-series, when the higher thresholds exhibit a higher variability. The final threshold will be a compromise between reducing the uncertainty as far as possible and, at the same time, keeping as many pixels as possible. Therefore, we also investigated how many pixels would be discarded by each threshold (Figure 12d). We present the fraction of discarded pixels which would be discarded additionally to the pixels that are discarded by the highest threshold anyway. All percentages are absolute values, i.e., an increase of 10% means an increase from, for example, 50% to 60%, not from 50% to 50.5%. Figure 12d shows that applying the lowest threshold, 265 K, would result in discarding up to 30.0% more pixels relative to the number which is discarded by the highest threshold of 270 K. However, on average (see Table 4), only 1.2% of the pixels would be discarded additionally by the lowest threshold. As expected, the number of additionally discarded \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Merged** & **MODIS** & **AMSR2** & **S2 (Thin)** & **S2 (Thick)** \\ \hline \(\mu\) & 0.987 & 0.887 & 0.988 & 0.959 & 0.902 \\ \(\Delta_{thin}\) & \(-\)0.028 & 0.072 & \(-\)0.028 & N/A & N/A \\ \(\Delta_{thick}\) & \(-\)0.085 & 0.015 & \(-\)0.085 & N/A & N/A \\ \(RMSD_{thin}\) & 0.135 & 0.156 & 0.120 & N/A & N/A \\ \(RMSD_{thick}\) & 0.199 & 0.163 & 0.198 & N/A & N/A \\ \(OWE\left[\text{km}^{2}\right]\) & 771 & 2760 & 182 & 878 & 2313 \\ \hline \end{tabular}
\end{table} 
Table 3: Like Table 2, but for the data from Figure 11. All datasets are available for 11,350 out of 11,881 pixels, which yields a surface area of 11,350 km\({}^{2}\). pixels increases strongly in May due to the enhanced presence of clouds. This shows that our retrieval is expected to perform less reliably in May than in the other months, but we can be confident that the performance will be stable at least until the end of April.