# Comprehensive Annual Ice Sheet Velocity Mapping Using Landsat-8, Sentinel-1, and RADARSAT-2 Data
## 2 Data and Methods
### Automatic Calibration Scheme  
The large amount of data processed makes it difficult to rely on manually selected ground control points for calibration of each scene as done in [22]. Here, we use a new automated calibration of the offset maps that takes advantage of the ice velocity products from prior surveys as a reference [1; 2; 3]. In our calibration workflow, offsets are first cleaned using median filtering as described in [22]. Afterward, for each offset map, the reference is extracted from prior surveys and converted into pixel displacement. The reference is then divided in 9 equally-sized sectors, i.e., 3 rows and 3 columns. In each sector, reference displacement is sorted by magnitude. The 20% lowest speeds are kept for calibration to minimize the impact of fast ice flow variation. Using 9 sectors ensures that reference pixels are spread evenly over the entire scene, which is necessary for accurate calibration. Finally the calibration is done by fitting the difference between the reference and offset map with a quadratic plane or a constant value for Sentinel-1 and Landsat-8, respectively. For Landsat-8 only, an additional step is included by filtering the elements moving slower than 100 m/yr that deviate more than 100% from the reference velocity values. This allows to remove additional noise introduced by wind-driven displacement, e.g., sastruigi, or drifting clouds. With this scheme, large regions with variable surface velocity and no low/zero-motion areas may require additional calibration because a change in speed between the reference map and the actual scene may bias the calibration. Such regions include Thwaites Glacier in West Antarctica or Larsen C Ice Shelf in the Antarctic Peninsula for example. Our solution for these areas is to concatenate the Sentinel-1 scenes into long tracks where areas of low motion are found systematically and we then use these long tracks to calibrate shorter Landsat-8 or Sentinel-1a scenes. In principle, the Landsat-8 offset maps require no additional calibration if the images are accurately geocoded. Thus, the distribution of correction we apply to the data is directly linked to the quality of the geocoding (Figure 1). We find that Landsat images are georeferenced with a precision of 0.0 \(\pm\) 0.4 pixel, or 0.2 \(\pm\) 6.0 m in both x- and y-direction, which is consistent with the geolocation accuracy derived by [28]. If not properly corrected, a geocoding error of 0.4 pixel would introduce an error in velocity measurement ranging from 137 m/year for 16-day to 5 m/year for 368-day passes. Data products are geocoded in Polar Stereographic coordinates. For Sentinel-1, the geocoding uses the GIMP digital elevation model of Greenland [29] and the BEDMAP-2 digital elevation model of Antarctica [30]. Errors on the offset maps are assumed to be 0.1 pixel in displacement by default. Typically, the errors in ice velocity are then a few tens of meters per year for the nominal repeat cycle of the sensors (see Table 1). The precision of a sensor depends on the resolution and the repeat cycle. Because sensors differ in both, their precision varies accordingly. Table 1 provides a reference only, not for the purpose of comparing the different sensors. \begin{table}
\begin{tabular}{l c c c} \hline  & **Resolution** & **Nominal Repeat** & **Ice Vel.** \\  & **Rg. \(\times\) Az. (m)** & **Cycle (days)** & **Precision (m/year)** \\ \hline Landsat-8 & 15 \(\times\) 15 & 16 & 34.2 \(\times\) 34.2 \\ Sentinel-1 & 4 \(\times\) 14 & 12 & 12.2 \(\times\) 42.6 \\ RADARSAT-2 & 17 \(\times\) 5 & 24 & 25.8 \(\times\) 7.6 \\ _ENVISAT/ASAR_ & _20 \(\times\) 4_ & 35 & _20.8 \(\times\) 4.2_ \\ _ALOS/PALSAR_ & 7 \(\times\) 3 & 46 & _5.5 \(\times\) 2.4_ \\ _RADARSAT-1_ & 17 \(\times\) 5 & 24 & _25.8 \(\times\) 7.6_ \\ \hline \end{tabular}
\end{table}