## 3 Methods
Our matching algorithm applies an iterative approach, where after coarse shift estimation at pixel scale the matching windows are realigned before retrieving the shifts at sub-pixel scale. The sub-pixel shift is calculated by oversampling and interpolating the peak of the cross correlation matrix. The pixel spacing of the final products is 250 m for the ice sheet wide velocity map of S1, and 30 m for the regional velocity maps. Because of the special features and novelty of the S1 IW data, we provide below further information on specific procedures applied for ice velocity mapping. Precise co-registration is performed for the image pairs used for offset tracking. TOPS mode data require high accuracy for image co-registration. A small co-registration error in azimuth can introduce an azimuth phase ramp because of the azimuth variation of the Doppler centroid within the bursts. A local mismatch of the effective velocity of the radar with respect to squint and topography causes positioning errors in azimuth and range [15]. Therefore, we apply geometric co-registration, which makes use of precise orbit data and a DEM for referring the position of each pixel in repeat pass acquisitions to a pre-selected master image [24]. The refinement of the azimuth shifts by using incoherent cross correlation and enhanced spectral diversity, which is optionally applied to TOPS mode interferometry in stationary areas [25], is not applicable on moving ice masses and is not required because of the high accuracy of S1 satellite tracking. Precise orbit data (ephemerides) are routinely provided for the Sentinel satellites, making use of the Global Navigation Satellite System (GNSS) receiver data on-board. The evaluation of geolocation accuracy using precise orbit data, evaluated over a dedicated site, reveals for SLC data a slant range \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sentinel-1 IW** & **TerraSAR-X** & **ALOS PALSAR** \\ \hline Matching window size & & & \\ Pixels (LOS \(\times\) azimuth) & 144 \(\times\) 48 & 72 \(\times\) 72 & 144 \(\times\) 144 \\ \hline Sampling steps & & & \\ Pixels (LOS \(\times\) azimuth) & 40 \(\times\) 20 & 20 \(\times\) 20 & 32 \(\times\) 32 \\ \hline Velocity product, & & & \\ Grid spacing in meters & 250 \(\times\) 250 * & & \\  & 30 \(\times\) 30 * & & \\ (Easting \(\times\) Northing) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications for window size and sampling steps in offset tracking, and for grid size of velocity products. (* ice sheet wide product, * for comparison with other products). offset of \(1.27\pm 0.06\) m and an azimuth offset of \(1.96\pm 0.41\) m [26]. Because of the high geolocation accuracy with the available orbit data of S1 there is no need for using ground control points for co-registering repeat-pass image pairs. This enables precise co-registration on moving surfaces where ground control points cannot be used. It overrides the need for coast-to coast tracks for improving orbit estimates over ice sheets and the use of balance velocity estimates for ridges and ice divides as applied for adjusting the velocities retrieved from data of previous SAR missions [27,28]. Offset tracking is performed on burst level in slant range (LOS) geometry. The SLC data are oversampled by a factor of two prior to compiling the amplitude image in order to avoid aliasing. The output of the matching procedure consists of three components: the displacements in LOS and in azimuth, and the correlation coefficient. The data of the individual bursts of a track are debursted using the start azimuth time of each burst in order to form a single strip. Subsequently noise reduction is performed in three steps: (i) excluding matches with low correlation; (ii) applying spatial filtering over moving windows of \(5\times 5\) pixels to exclude outliers based on local variance; and (iii) filling small gaps at the scale of individual pixels by interpolation from surrounding displacement values.