**5. Discussion**

Geophysical characterization of rock glaciers and debris-covered glaciers is usually complicated by several factors: Logistically challenging and expensive transport of equipment and personnel on site, extremely rugged topographic conditions inhibiting antenna dragging on the surface, and inaccessibility of same areas, due to safety concerns [44]. In addition, despite the advances in geophysical prospection and instrumentation of the last decades with respect to the previous reference ice bottom investigations carried out on the Belvedere Glacier, recent surveys are not free of interpretation issues. Widespread scattering and high attenuation of the EM signals, often referred to as clutter, are noticed in all the 70-MHz GPR profiles. Slightly better results are obtained with a lower frequency of the GPR antenna (40 MHz vs. 70 MHz). No information is however retrieved for depths higher than 100–150 m below the glacier surface.

Many causes may have contributed to the poor quality of GPR imaging on this glacier. The absence of direct coupling with the ground, with possible centimetric variations in the height of the antenna, limits the amount of EM energy inserted in the subsurface, resulting in rapidly decreasing energy to image the reflectors with depth and laterally variable trace amplitudes. In addition, the presence of the top debris cover, characterized by extreme variability in grain size, thickness and lateral distribution, generates diffuse scattering and attenuation of the EM pulses transmitted to the underlying ice column, with respect to GPR prospections in glaciers lacking this surface layer. Pecci et al. [45] discussed the negative clutter effects on GPR data quality caused by the surface debris cover with a highly variable thickness of Calderone Glacier (Central Apennines, Italy). Intense clutter phenomena were observed also at a depth of few meters from the surface and were related to the presence of ice layers containing a high concentration of debris. As a consequence, the reflectors corresponding to the ice-bedrock interface could not be clearly and continuously detected.

Similar results were obtained on a debris-covered glacier of Italian Dolomites [22]. Most of the GPR scans pointed out the presence of intense clutter effects, due to the presence of heterometric debris at the surface. Authors were able to detect the ice-bedrock only with an acquisition adopting bistatic antennas in parallel-polarized modality. This arrangemen<sup>t</sup> was observed to be more sensitive to buried targets oriented parallel to the main axes of the antennas and relatively insensitive to depolarized scattered fields. However, moving this configuration on a rugged topography could be a logistical issue, especially when low-frequency antennas with long dipoles are adopted.

Despite these considerations, the presence of debris at the surface and the use of air-coupled antennas are common to other GPR surveys in debris-covered glaciers and rock glaciers (e.g., [24,26]) which led to satisfactory data quality. As a consequence, we hypothesize that widespread internal heterogeneities in the glacier mass may have had an additional and primary role in scattering and attenuation of the GPR signals. Beside the possible widespread presence of solid rock debris within the ice body [45], enhanced radar scattering, due to water englacial inhomogeneities is reported by several authors. Bamber [46] performed a numerical analysis to quantify the back scattering of water-filled cavities on the scale of decimeters affecting GPR results on several glaciers in Svalbard Islands. Numerical results illustrated the difficulties that may be encountered while sounding temperate glaciers possessing widespread englacial water bodies and explained the absence of bed echoes in the accumulation zone of these glaciers. GPR profiles collected by Murray et al. [47] in the ablation zone of Tsanfleuron Glacier (Swiss Alps) and Bakaninbreen Glacier (Svalbard) showed a two-layered structure, with an upper layer characterized by low returned GPR power and a lower layer of strong scattering. The thickness of these layers was observed to rapidly change along the profiles at both sites. At Tsanfleuron Glacier, the two layers were interpreted as dry ice, with a water content of 1.18%, overlapping ice containing small water bodies, up to decimeter in size, occupying 3.90% by volume. At Bakaninbreen Glacier, the upper radar layer was interpreted as cold ice with no measurable water-content and the lower layer as warm ice with a water content of 1.29%. Barrett et al. [48] modeled layers of randomly distributed scatters of decimeter-scale dimensions with an undulating upper boundary or confined to obliquely dipping planes to reproduce the scattering effects noticed on the radargrams acquired on Bakaninbreen Glacier. Numerical results supported the hypothesis that scattering originates from multiple planar sets of water-filled cavities. These features are expected to be common in glaciers surging by a thermally regulated soft bed mechanism, both at the end of the surge and into early quiescence phases. The presence of surge-type movements at the Belvedere Glacier, supporting the hypothesis of abundant water presence within the glacial mass, is well-documented in the literature [49].

As a consequence of the poor GPR data quality, ice thickness estimation was possible only in the glacier sectors characterized by the lowest ice thickness. Layering with different orientations, probably indicating the overlap of lateral morainic deposits on the bottom materials, was found to locally emphasize the bottom morphology. Only close to the terminus of the N lobe, deeper and steeper reflectors were imaged below the ice bottom. These observations sugges<sup>t</sup> that the glacier bottom is not characterized by stiff bedrock, but by a thick sequence of fine-grained glacial deposits, as already hypothesize in the study of VAW-ETH [36]. If this hypothesis is valid, the glacial deposits have an average thickness of 40 m close to the glacier front and bedrock is located at a depth of approximately 80 m (e.g., rectangle A" in Figure 5d). The thickness of the bottom deposits rapidly increases upstream if the steep dipping of bedrock is constant.

Single-station passive seismic measurements confirmed the absence of sharp acoustic impedance contrasts in the glacier subsurface. The lack of a single clear peaks with high HVSR amplification values are a key piece of evidence for the absence of ice in direct contact with stiff bedrock. The occurrence of a multi-layered subsurface, with several weak contrasts in acoustic impedance at depth, can conversely help to explain the obtained HVSR results. The progressive lowering in the frequency of f0 peak from station A to C (Figure 7) is coherent with the presence of interfaces which are progressively deeper upstream, as highlighted in the GPR results (Figure 5d). HVSR complex results are however difficult to interpret with single simplified equations (e.g., Equation (1)), due to the existence of multiple interfaces whose resonance phenomena are superimposed. The stratigraphic condition appearing from all the above considerations is also at the limit of validity of the assumptions underlying further processing and interpretation of the measured curves. Despite the challenging working environment and investigated ice mass, a comparison between past and present geophysical surveys at the Belvedere Glacier is worthy of investigation. The ice-thickness map obtained from triangulation with linear interpolation of the GPR bottom peaks (Figure 6b) is shown in Figure 9a. The map confirms the previous observations of a traditional U-shaped bottom morphology for the N lobe and of shallow ice depths and flatter bottom surface for the S lobe. A digitized version of the ice thickness map of De Visintini [35], reported in Diolaiuti et al. [39], is shown for the same area of the glacier in Figure 9b. It must be noticed that the only reflection seismic measurements on this area were performed at the confluence of the two lobes (black bold lines in Figure 9b) and no data coverage was directly available on the lobes. As a consequence, this map is the result of a more approximated data interpretation with respect to the continuous GPR profiling from which Figure 9a is derived. Despite these considerations, Figure 9c shows the difference in ice thickness between the present and past maps.

A general agreemen<sup>t</sup> in ice thickness estimation is found along the axial position of the N lobe and on a wide area of the south lobe. Visible negative values (reduction in ice thickness) are found close to the northern front, underlying the accelerating retreat and shrinkage of the glacier in recent times. A visible decrease in ice thickness is also noticed close to the confluence between the lobes. This result can be considered quite reliable given the good data coverage of both present and previous surveys close to this point. By contrast, the unrealistic increases in ice thickness close to the glacier sides are more likely due to an erroneous approximation of ice thickness in the past study, rather than to a significant increase in ice volume in these marginal sectors.

**Figure 9.** (**a**) Interpolated glacier bottom map from GPR results (2016–2018). (**b**) Reference glacier bottom map from De Visintini [35] and Diolaiuti et al. [39]. The black bold lines in (**b**) indicate the location of the only seismic reflection measurements in the area of interest. (**c**) Difference between (**a**) and (**b**) maps. The black dashed line highlights the approximate glacier perimeter in October 2016 (first GPR campaign).

An independent comparison between the glacier cross-sections obtained from the interpretation of the radar measurements of VAW-ETH [36] and the closest GPR profiles of the present study is presented in Figure 10. In this case, the adopted geophysical technique is the same, even if in different frequency bands. Both surveys should therefore have depicted the same interfaces. The ice bottom morphology presented in the previous work (black dashed lines in Figure 10b,c) is however the results of only two points of measure on each lobe (white triangles in Figure 10b,c), for both FF' and GG' sections [36] and not of continuous profiling.

Along the FF' cross-section, the 40-MHz profile 1 shows a depressed glacier topography with respect to the one of 1985. An acceptable discrepancy of around 15 m between the maximum ice bottom depth of the two surveys is noticed. Major differences in the morphology of the bottom surface are observed between the two campaigns. Recent GPR profiles outline a narrower and more asymmetric section of the N lobe, steeper on the side of the moraine hosting the Belvedere Mountain Hat. It is however interesting to notice that the reflection points related to the ray paths of two radar measurements performed on the N lobe well overlap with the recent bottom estimation from continuous GPR profiling. The lateral discrepancies can therefore be explained as the consequence of insufficient lateral data coverage of previous surveys. Similar results are found on GG' cross-section. Along this section, the topographic variations appear less marked on the N lobe. On the S lobe, profile 25 has higher topography than previous data, due to the fact that it is located almost 100 m upstream the reference GG' section trace. A good agreemen<sup>t</sup> between the present and past data is however found for the S lobe bottom. On the N lobe, the maximum depth depicted in the two surveys is the same, but the GPR profile 7 defines again a narrower ice bottom section. A wider and smoother bottom morphology was considered during the interpretation of previous radar measurements and a clear mismatch is observed between the two surveys. Differently from the original data interpretation, past radar echoes (and related ray paths) were probably originated from the deepest and narrowest axial sector of the glacial valley rather than from the lateral moraines. This comparison definitely highlights the undeniable advantages of continuous GPR profiling in maximizing data coverage and improving bottom morphology reconstruction, with respect to previous sparse and local measurements.

**Figure 10.** Comparison between the radar cross-sections of VAW-ETH [36] and the closest GPR profiles of the present study with successful glacier bottom picking. (**a**) Location of the profiles. (**b**) Section FF'. (**c**) Section GG'. The original data interpretation is shown in black (white triangles and gray rays indicate the radar measurement points and the interpreted EM ray paths as reported in [36]), while recent GPR results are shown in red for Profiles 1 and 7 (40 MHz, December 2018) and in green for Profile 25 (70 MHz, October 2016). Bold line: Topography, dashed line: Estimated ice bottom location.
