## 4 Results
### Error Estimate  
There are three main sources of error for retrieval of ice motion by means of offset tracking:  
1. The error introduced during the matching procedure used to determine the offsets of the image templates. This error is related to the degree of correlation between the templates in the different images. It depends on the co-registration of the image pairs, the template size, and on the quality of amplitude features and/or stability of speckle used for tracking. 2. Ionospheric disturbances due to fluctuations in ionospheric electron density that are causing phase gradients resulting in azimuth shifts [29]. These are clearly evident as streaks in the retrieved velocity, aligned slightly oblique to the LOS direction. 3. Geocoding error. Due to the very precise ephemeris data for S1 the error through transformation from slant range to map projection is primarily caused by height errors in the DEM used for topographic correction. The impact of ionospheric disturbances varies significantly over time and position. For C-band SAR a range of values is reported in the literature. [PERSON] _et al._[27] explain that ionospheric disturbances near the solar maximum over Greenland may generate noise in the velocity field retrieved from C-band RADARSAT-1 data with magnitudes of up to several tens of m\(\cdot\)a\({}^{-1}\). [PERSON] _et al._[29] report peak-to-peak modulation in azimuth shift in RADARSAT-1 data of Antarctica of up to 1 m, which corresponds to a displacement of 0.042 m\(\cdot\)d\({}^{-1}\). [PERSON] _et al._[28] explain that ionospheric disturbances cause maximum velocity errors of \(\pm\)6 m\(\cdot\)a\({}^{-1}\) (corresponding to \(\pm\)0.016 m\(\cdot\)d\({}^{-1}\)) for RADARSAT ice velocity retrievals over Antarctica. Because of the shorter repeat cycle for S1 _versus_ RADARSAT-1 (12 days _versus_ 24 days), the potential impact of ionosphere-induced noise on the velocity is doubled. In our data set the ionosphere variability appears as distinct streaks in several velocity maps derived from single S1 image pairs over northern Greenland with peak values equivalent to displacements of 0.25 m\(\cdot\)d\({}^{-1}\). For a large area (\(>\)200,000 pixels) in the central section of northern Greenland with low velocities, we obtain a standard error of 0.08 m\(\cdot\)d\({}^{-1}\) due to ionospheric disturbance. By averaging over multiple acquisitions, the error is reduced to 0.02 m\(\cdot\)d\({}^{-1}\). This confirms that efficient reduction of ionospheric noise is achieved through averaging of retrieval from multiple image pairs as reported by [27, 28]. The geocoding accuracy of the S1 ice velocity maps is related to the accuracy of the GIMP DEM used for topographic correction. The DEM has a reported ice-sheet wide root-mean-squared height error, relative to ICESat, of \(\pm\)10 m, ranging from close to \(\pm\)1 m over the main part of the ice sheet to \(\pm\)30 m in areas of high relief [23]. The geocoding of the 2D velocity vector retrieved in radar geometry is performed for each displacement value independently, so that DEM errors do not propagate. The DEM has a nominal date of 2007. Since that date major changes in surface elevation happened on the termini of outlet glaciers due to dynamic thinning. For estimating the possible impact of changes of surface topography due to dynamic thinning on outlet glaciers, we selected as example Jakobshavn Isbrae. The rate of surface lowering between 2007 and 2010 was 15 m\(\cdot\)a\({}^{-1}\) near the front and 8 m\(\cdot\)a\({}^{-1}\) 20 km upstream [32]. This rate of surface lowering over a period of eight years results in a change of the surface slope of 0.16 degrees, resulting in a bias of 0.5% in the magnitude of surface velocity. The lower terminus of Jakobshavn Glacier represents an extreme case in terms of dynamic thickness change [33]. For estimating the uncertainty of S1 velocities, we compare S1 velocity products with ice velocity maps retrieved from TerraSAR-X data (Figure 2).