# Antarctic Surface Ice Velocity Retrieval from MODIS-Based Mosaic of Antarctica (MOA)
## 4 Result and Analysis
### Comparisons with MEaSUREEs
The effectiveness of filter via shrinking within a 3\(\sigma\) range is obvious by comparing the distribution and statistics from each drainage in Figure 6. In both \(X\) and \(Y\) components, the difference's distribution is all symmetrically bell-shaped roughly, approximating one or multiple Gaussian distribution curves combined. Outliers that exaggerate variance are truncated off, variance decreasing to 1/2-1/8 of the primitive result. Although this method originates from the inherent statistical characteristic of data, the a priori reference dataset is needed to work out. In addition, the statistics of difference between these two velocity datasets implies that the mean and variance both reduce remarkably, but the median, which is not sensitive to extreme outliers, remains of the same order after filtering. Furthermore, the scale of complete and continuous tracking area influences the statistics, namely in the Ross and Filcher-Ronne drainages, and the tracking techniques perform better than that in the Amundsen or Wilkes Land drainage, where only localized ice stream or ice shelves are situated. To investigate the relative difference from MOA-based velocity with respect to the MEASUREs dataset, 3000 points were strewn randomly in a valid area. Figure 7 depicts these points' differences between MOA-based and MEASUREs velocity in magnitude from both tie points and random points. As shown in Figure 7a, our results are systematically biased to some extent, since it is more prone to underestimate than MEASUREs, even though the mean relative difference is constrained within 8% beyond 500 m\(\cdot\)a\({}^{-1}\). Like streamline analysis in Section 4.1, the limiting velocity detection from MOA is about 400 m\(\cdot\)a\({}^{-1}\) or so, below which the streamline can hardly maintain itself, and the confidence for the raw tracking result is relatively low. For random points, as is evident from the left panel, the underestimate pattern is severe when velocity is less than 400 m\(\cdot\)a\({}^{-1}\). Rather, it is not the case for manually selected tie points since they are evenly distributed above and below the zero reference line within a narrow range, regardless of the MEASUREs velocity. Therefore, selecting tie points with the distinct feature is more or less a matter of \"cherry-picking,\" which reminds us that the interpretation of RMSEs in Section 4.2 might be underestimated. Figure 6: Distribution of difference between MOA-based velocity and MEaSUREEs velocity, before (upper row) and after (lower row) the Butterworth filter and the 3\(\sigma\) truncation iteration, in seven drainages: (**a**) Amundsen, (**b**) Dronning Maud, (**c**) Filchner-Ronne, (**d**) Lambert, (**e**) Peninsula, (**f**) Ross, and (**g**) Wilkes Land, respectively. Note that the value of all three statistics, mean, median, and variance, drops after the operations. Figure 7: Relative difference with respect to MEaSUREEs in (**a**) 3000 randomly strewn points and (**b**) 178 manually selected tie points. The blue margins represent 95% confidence interval, and vertical dash lines represent 500 m\(\cdot\)a\({}^{-1}\). Sometimes a cluster of tracking exceptions can happen when the surface feature changes significantly between 2004 and 2009. For example, in the middle Amery Ice Shelf, intensive supraglacial ponds scattered as dense dark patches occurred in 2004, indicating that the instantaneous environment is warm enough to melt the snow and ice, but they almost disappeared entirely in 2009. As illustrated in Figure 8, the velocity field before filtering repletes with outliers in the red rectangle, and they are restored into a more smooth field afterwards. The evident contrast between the blue and black arrows in the middle part of the Amery Ice Shelf demonstrates the effectiveness of our accuracy constraint strategy. However, some of the erroneous results can still survive even after our correction strategy, since profound image variation like this not only results in failure locally but also propagates incorrect results upstream and downstream.