# Mapping Surface Flow Velocity of Glaciers at Regional Scale Using a Multiple Sensors Approach
## 3 Results
### Uncertainties Analysis  
#### 3.3.1 Sensor Precision  
For each repeat cycle and each pixel of Landsat and Sentinel time-averaged maps, we calculate the filtered average surface velocities and its standard deviation as described previously in Section 2.4. The weights applied to the standard deviation and average calculations have no effect here as each mosaic is computed with the same repeat cycle and sensor. As output values are provided separately for x- and y-component, we combine them by taking the norm. The statistics presented in this section are calculated over the entire study regions (European Alps, Cordillera Blanca, New Zealand), hence over areas larger than the mosaics presented in Figures 1-3 in Section 3.1 (see Figures S2 and S3). Figure 4A represents the cumulative distribution of the standard deviations (per pixel) of ice-free areas for different repeat cycle lengths. We assume that the 50 th percentile of the standard deviation distributions (the median value of the distribution) represents the nominal precision that can be achieved for each cycle (Figure 4C). For comparison, we also calculated the mean of the distribution, which is about 1 m/year larger than the value of the median, hence do not impair our error analysis. Note that precision in glacierized areas is probably larger (less precise) than in ice-free zones because the surface texture is different and changes (e.g., snow precipitation, surface melt) can occur more rapidly, therefore causing more decorrelation. As glacier motion can changed rapidly over short time scale, the standard deviation over the glacier-covered areas does not necessarily represent the sensor precision but, more likely, natural fluctuations of the surface displacement. Nevertheless, we believe that our analysis on stable ground is valid to compare sensors precision and still provide insights on the capability of each sensor to map slow-moving mountain glaciers. As expected, the precision on ice speed measurement increases with time separation between two acquisitions (at the expense of temporal resolution). Typically, precision for Sentinel-2 is about 52 m/year for a repeat cycle of five days and changes exponentially to 16.5, 7.8, 4.0, 3.5, 1.6 and 1.1 m/year for 10, 30, 60, 90, 335 and 390 days, respectively. For Landsat 8, we also found that the nominal precision is about two times larger than for Sentinel-2. Thus, displacement derived from Landsat repeat cycles of 16, 64, 96, 336 and 400 days can be mapped with a precision of about 41, 9.9, 7.2, 2 and 1.9 m/year, respectively. Hypothesizing that these values depends only on image correlation, we can calculate the sub-pixel image matching precision as \(mp=(\sigma_{cycle}/365.25)\times(c/ps)\), where \(\sigma_{cycle}\) is the standard deviation of a given cycle, \(c\) is the cycle length and \(ps\) the pixel size. We found that our correlation algorithm has a sub-pixel precision of about 0.1 pixel, which matches our earlier assumption for the calculation of the weights (Figure 4D) and is similar to [29; 35]. For Sentinel-2, correlation tends to perform better for short repeat cycles (about 0.06 to 0.09 pixel matching precision) than for long repeat cycles (about 0.13-0.16 pixel matching precision), which is expected as change in surface texture will be larger for longer cycles. This relationship between the precision and the cycle length is however not as clear for Landsat 7/8 (Figure 4D). In the case of the Mont Blanc massif, we also analyzed the weighted standard deviation obtained in the ablation and accumulation zones computed for the time-averaged maps of the glacier surface velocity, which contain all repeat cycles. Ablation and accumulation zones may have different surface textures impacting the correlation algorithm. We used the altitude of the equilibrium line (ELA) from [36] located around 3000 \(\pm\) 100 m.s.l. in the French Alps to distinguish the ablation and accumulation zones.