## 3 Data and Methods
### Surface Velocity  
The surface velocity was computed here by comparing satellite images taken in different days. This comparison was made by means of ImGRAFT--Image Georectification And Feature Tracking ([[http://imgraft.glaciology.net/home](http://imgraft.glaciology.net/home)]([http://imgraft.glaciology.net/home](http://imgraft.glaciology.net/home)), accessed on 21 December 2021), an open source toolbox, developed by [PERSON] and [PERSON] in MATLAB code ([PERSON], 2019). _TemplateMatch_ is a function of ImGRAFT, used to investigate the shift between two images, based upon Orientation-Correlation techniques. The two images are defined as image \(A\) (the first taken) and image \(B\) (most recent one). This function allows to create a velocity field on the entire area of the glacier. This is different from classic feature tracking, which computes velocity values only on reference points. Calibration and validation of the method are specific for every glacier and in general for every spatial body. Thus, these steps are not yet automatic, and supervision has an important role.  
Even if the image pixel size is in the order of magnitude of meters, the displacements computed by ImGRAFT _TemplateMatch_ may be in the order of centimeters.  
Highest mean correlation is normally used as a goodness of fit parameter. However, only validation against field measurements or supervision on image classification can define the accuracy of the estimated displacement and the magnitude of noise.  
In addition to supervised classification, to avoid false matches or outliers (e.g., cloud cover), four indexes are computed in the code: (i) mean correlation index (\(C_{AVE}\), mean of the largest correlation matrix for each match), (ii) mean Signal to Noise Ratio (\(SNR_{AVE}\)), (iii) the percentage of valid cells (\(C_{\%}\), cells with \(SNR<2\) are automatically discarded), and (iv) the \(SNR\) corrected with the number of valid cells (\(SNR_{COR}\), here we took \(SNR_{COR}\geq 10\), see e.g., ([PERSON], 2019)). The \(SNR_{AVE}\) is the ratio between signal and noise typical of the signal analyses, defined as:  
\[SNR_{AVE}=C_{AVE}/C_{NOISE} \tag{1}\]  
where \(C_{AVE}\) is the mean correlation coefficient between template \(A\) and \(B\) (\(-1\) to \(+1\), cells with \(C\leq 0.6\) are automatically discarded). \(C_{NOISE}\) is the module of the average of the correlation coefficients, across the whole search region, and it is an estimate of the noise level. Here, we applied a filter for velocity values based on thresholds, namely:  
1. \(V_{5,max}\leq 5\) m day\({}^{-1}\) on the entire glaciers (whenever necessary, this was raised to \(7\) m day\({}^{-1}\));
2. \(V_{5,max}\leq 4\) m day\({}^{-1}\) and no West ward components in the ablation area;3. \(V_{S,max}\leq 2\) m day\({}^{-1}\) and flow direction only towards East in the front area, covering approximately the last 4 km.  
Such thresholds, based upon observation of the velocity fields over the many images, were used to remove coarse noise and errors and (too) large movements detected, as sometimes observed over large time windows.  
Across glacier tracks are used here. Some tracks overlap those of [PERSON] et al. [27], and others cover the glacier area and front, with a denser scheme. The field measurements in [27] are used to benchmark our results.