General comments:

This paper presents interesting results from a field survey of mountain glaciers at Colle Gnifetti using a phase-sensitive radio echo-sounder (pRES). The authors obtained the results with a layer-optimized SAR processing method, which is special in that it performs coherent summation over the synthetic aperture along an optimally estimated linear slope. The echograms from pRES revealed deeper internal reflection horizons (IRHs) that were not visible in the results from previous surveys with pulsed GPR. This data set is thus valuable for studying snow accumulation, ice flow and ice core chronologies in this area. The paper also provides valuable insights into different reflection mechanisms of the glacial IRHs at different depths by comparing radar data and ice core records. The algorithm of the tailored layer-optimized processing is an important part of the paper and aims to improve the detectability of IRHs. So, it is necessary to accurately assess the effectiveness of this algorithm in terms of the improvement in IRH detectability by comparing it with other methods that people have routinely been using in radar data processing. However, this paper does not have this kind of comparison and analysis, which is my major concern. The paper will be improved well for publication if this concern can be addressed.

Specific comments, questions, and suggestions:

1. For the across-saddle and upstream profiles, it is desirable to see an echogram for each profile that is generated by applying a moving averaging filter of the same aperture length on each trace in Fig. 5 (c) and Fig. 5 (e). This averaging is like unfocused SAR processing without along-track decimation, which is much faster than the proposed LO-SAR processing. Because the phase shift due to slope has been corrected in reference phase substruction and thus the corrected phase is constant along the slope, this averaging is also similar to the coherent integration performed in the reference by Castelletti et al. (2019), i.e., the summation is not along the slope. By comparing these two echograms with Fig. 5 (d) and Fig. 5 (f), the improvement on IRH detectability by the proposed LO_SAR can be qualitatively and quantitatively analyzed and discussed.
2. In 5.2 for discussions on slope estimation, the authors mentioned that “strong reflections spread out over several range bins, across which the raw phase tends to be stable”, and according to Fig. 5 (b), the “inclination relative to the surface is quantified during the LO-SAR processing and attains values of about 10° at both ends”. For the aperture length of 5 meters used in the processing, this inclination corresponds to only two range bins from one end of the aperture to the other end, therefore there might be no significant difference in performing the summation along the slope and not along the slope if the reflected power does not have big difference neither within two range bins. It would be helpful to demonstrate at what aperture length and at what slope angle the improvement of SNR for IRH detectability can be expected from the proposed LO-SAR.
3. The iteration range of slopes used was from −30° to 30° in steps of 0.2°, much larger than the slop range observed in the data. Some discussion about smart selection of this range may be included in section 5.2 for reducing the computation intensity of the proposed LO-SAR.
4. What was the data logger sampling rate used during data collection? 40kHz as discussed in section 5.1?

Technical corrections and suggestions:

1. In Fig. 2 (a), the two legends are hard to distinguish, consider changing one of them with dashed line. The two red line segments for antennas need to explicitly be mentioned either in the figure caption or in text.
2. In Fig. 3, missing information flow direction arrow along the line between the block for “Pre-processed mobile pRES data” and the block for “Moving median filtering of S”.
3. Revise “by the weighting the values” to “by weighting the values” at line 166 on page 8.
4. It is suggested to mark the crossover between the cross-saddle profile and the GPR profile, the crossover between the cross-saddle profile and the upstream profile towards KCC, and the crossover between the upstream profile towards KCC and the GPR profile with A, B and C respectively in Fig. 1, and according to mark those vertical white lines in Fig. 5 with A, B and C. It is much easier this way to identify these crossovers.
5. The location of the white line to the right in Fig. 5 (a) does not match with the location of the crossover between the upstream profile towards KCC and the GPR profile in Fig. 1 which is at the very end of the GPS profile.

see attached