## 4 Results and Discussions  
### Model Calibration  
Before actual model tuning, we pursued a preliminary assessment of the best cross-correlation method in _TemplateMatch_ for the PMG area, among the four available methods (i.e., NCC, OC, PC, and CCF) as reported above. The algorithm takes in input two subsequent (in time) images covering the same area (\(A\)-\(B\)), and outputs the correlation of any cell in image \(A\) with all the cells in image \(B\), belonging to a certain research region. The largest correlation of each cell in image \(A\) with a cell in image \(B\) provides a guess of the new position of the feature in image \(A\) within image \(B\) (i.e., of its displacement in time), and according to the difference in time, an estimate of the velocity. All methods use Fast Fourier Transformation, to allow detection of movement smaller than the image pixel resolution. Here, a preliminary adoption of these four methods was pursued to assess flow velocity of the PMG. This is fully reported in Chirico [33], while here we report the main findings. Preliminary application of the PC [34] and CCF [35] methods did not produce significant results in the PMG area (Figure 2). The NCC [36] method provides acceptable results, but some edge noise is still present, and the method is not optimal, given that it cannot manage well image rotations and distortions (Figure 2). The OC method [37] provides good results, with a proper signal to noise ration \(SNR\) (Figure 2). This method works on the intensity gradient of the images and so the method is fast, statistically robust, exhaustive, and invariant to image brightness. In addition, working with correlation, some weak spots of optimization are avoided. For instance, the OC method does not need an initial state, and it does not need a priori knowledge (such as,  
Figure 2: Comparison between the different methods to assess flow velocity of the PMG. e.g., NCC), and thanks to the exhaustive research, local minima do not lead to sub-optimal solutions. Accordingly, we decided to use OC methods for PMG tracking here. Further, _TemplateMatch_ behavior was tested against different spectral bands, given that the algorithm uses single bands (i.e., not RGB visible bands), which can have different resolution. We initially used visible bands (i.e., 2, 3, 4 of SENTINEL2, and 1, 2, 3 of LANDSAT). Subsequently, we tested panchromatic band of LANDSAT (band 8) which has high resolution (15 m). SENTINEL2 images have RGB bands with the same resolution as panchromatic (10 m), and _TemplateMatch_ provided here similar results for all bands. The time step (\(\Delta t\)) between two images \(A\)-\(B\) also affects the results. Given the lack of debris cover on the glacier usable for reference and the relatively high flow velocity (\(\approx\) 1 m day\({}^{-1}\) on average), a too large value of \(\Delta t\) would not be suitable, because the characteristic of the images would change too much. Crevasses can be used as target features, but crevassed zones on the glacier tend to remain the same in time, so not actual movement may be found. The largest value of \(\Delta t\) is 80 days, as reported in Table 1. Moreover, given image availability and cloud cover in the period of study (2002-2017 with LANDSAT), the lowest \(\Delta t\) here is 13 days (see Table 1). A first parameter to be chosen for model tuning is the number of templates (i.e., spacing between template centers) to set into image \(A\) and then follow in image \(B\). This parameter does not influence the results largely, but the higher the number of templates, the (exponentially) longer the computational time. A regular grid of template centers is used in this study, with density fixed, so as to investigate different areas and phenomena (e.g., a dense grid of 5 by 5 pixels is used for the analysis made on the sole front, more interesting to assess calving, and a sparser grid of 10 by 10 pixels is used to investigate the largest ablation area).