The authors present a feasibility study for using SNMR to detect an englacial channel at the Rhonegletscher. The study focuses on the challenges encountered in a low signal, high noise environment and how to still image an englacial channel. The approach uses a grid search of different glacialw water content models to try and fit the acquired data. The results are compared against a Ground penetrating radar (GPR) survey and show consistency between the two methods.

My comments relate mostly to the noise estimation and how the grid search is performed. It is mentioned that the average noise level is 70 nV for most pulse moments (P.12 L.268), but inspecting Figure 7, the largest error bar found here is ~18nV wide. In this figure, we see the forwarded data from three model scenarios having difficulties fitting the observed data within error bars. From one pulse moment to the next, the signal amplitude doubles and then drops by 35%, a difference way larger than the assigned error bars. Is the difficulty in fitting this data a product of the simplified model scenario, or could it be a product of underestimating the uncertainty affecting the initial values?  

Even with Equation 4 (P.9 L200), it is still unclear to me how the mean noise of 70nV becomes maximum 17nV in uncertainty on the model parameter e0. Please clarify.

In Figure 8b, the misfit for the models with a varying aquifer depth is shown. But unlike 8a, it seems it has not yet reached the lowest misfit, i.e., maybe an aquifer depth of 62m would be a better fit. Were the ranges chosen on previously acquired data (GPR)? If not, perhaps increasing the range here could reveal a similar parabola shape, like the one in Figure 8a.

These results of aquifer depth are later discussed (P.18 L. 359-361) as broadly consistent with the GPR profile which finds a channel at 40m. But the lowest misfit for the SNMR was with a channel at 59m depth. 

The RNC possibly distorting the signal up to 27nV is quite concerning since it is >25% of the maximum initial value seen (Figure 7). This is addressed in the conclusion, but only after stating that the RNC was the most crucial step in increasing S/N. Perhaps a more combined conclusion on RNC could highlight the usefulness and the issues with this approach. 

Additionally, since a noise record has been recorded, would it be possible to use RNC on the noise only data and examine if the transfer functions are different? If they are different, it might be a sign of signal being distorted.

When assuming 100% water it vastly reduces the aquifer thicknesses found fitting data within the threshold. But is the instrument capable of resolving a <1m thick layer at 40m to 60m depth? Perhaps add some discussion on whether this is feasible given the selected pulse moments and loop dimensions.

A question about the englacial channel. I assume the water flowing within this channel, if so, how quickly? It might reduce the signal amplitude and should be discussed if appropriate.

Minor comments:

P.5 L.108: The 16th q was not completed. Could this have helped constrain the aquifer depth in Figure 8 by increasing the depth of investigation?

P. 11 L.242: Indicate the abbreviation, i.e., “both the coincident(coi)- and separate(sep)-loop data…”

P.12 L.261: The peaks at -20Hz are not seen in noise only spectrum in Figure 5b. Are these harmonics or related to transmitting at high pulse moments? And what harmonics do you expect at this frequency?

Figure 6a: Is it expected that the separate and coincident coil shows very different initial values? Is the water content lower here or is it mainly a product of less excitation?

Figure 8: Layout of figure is a bit confusing having the upper panel be (a),(b),(e), and the lower panel being (c),(d),(f). Perhaps consider three rows with a,b and c,d and lastly e,f..

Figure 9: Consider marking the maximum observed dimension of the englacial channel according to Church et al., 2021, if feasible.

P20. L.426: a space missing between “,accumulate”

P.21 L. 464: A year is missing on the Ogier et al. reference.

In light of rapid glacier retreat and degradation of alpine permafrost, reliable observational methods for subsurface liquid water and ice contents are urgently needed. The authors present an interesting case study and a very rare application of surface nuclear magnetic resonance (SNMR) to detect and characterize an englacial channel of Rhonegletscher, Switzerland.

Although challenged by considerable and yet unknown sources of electromagnetic noise, the authors managed to derive a useable signal as well as plausible 1D models of the englacial hydrological setting by advanced data processing. Results were validated with their own colocated as well as previously acquired ground-penetrating radar measurements.

The manuscript is well structured and written with commendable scientific rigour reflected, among other things, by a discussion of alternative plausible models given the measurement uncertainty as well as a dedicated subsection to discuss the limitations of the approach presented.

I believe that the practical considerations and data processing steps presented here make a valuable contribution for researchers and practitioners applying SNMR in particular in, but not limited to, the emerging field of cryogeophysics.

The authors are kindly asked to consider the comments below in (minor) revisions of their exciting paper and excuse the delay in my review.

Kind regards

Florian Wagner

RWTH Aachen University

General comments



1. State of the art: The authors rightfully state that application of SNMR in cryogeophysical settings is very rare and hence only a few studies are cited in the introduction together with some GPR studies. However, the cryogeophysical community has made substantial progress in recent years in quantifying subsurface liquid water and ice contents with other geophysical methods (e.g., electrical resistivity tomography, seismic refraction, spectral induced polarization, etc.) also developing joint inversions to directly estimate water content by a combination of these methods. I feel the paper would benefit from acknowledging a few of these developments and properly placing the potential advantages and limitations of SNMR measurements in the overall effort of quantifying subsurface liquid water content with cryogeophysical methods.



2. Inversion approaches: The main inversion is based on a grid search for the 1D water content distribution. Prior to this step, a least-squares inversion is conducted to fit the decay curves. I feel that these two inversions need to be separated more clearly. In particular, I find it confusing that for the first inversion a model vector is defined, but not for the actual inversion for layer thicknesses and water contents.



3. Noise discussion: The authors are very transparent about the poor data quality. However, the reader is kept left wondering where this noise comes from and how much is attributed to the (too close?) placing of the loops. Is it possible that the site is actually not that noisy, but the approach to estimate noise is not ideal? Also, care should be taken when comparing noise to other studies. For example, a link is made to a study in Denmark (Larsen and Behroozmand, 2016) where the magnitude of noise is compared on the basis of the RMS data misfit. To my understanding, the RMS misfit is a poor indicator for observational noise, as it can be dependent (and thus "tweaked") by the noise estimates, the quality of the forward model, the complexity of the subsurface parameterization, the inversion approach with its settings, and many other settings. In short, a "good" RMS misfit can also be obtained for a data set of poor quality or am I missing something here?



4. Linguistic consistency: The authors currently mix British (e.g., "colours") and American English (e.g., "discretization"). Please choose one consistently throughout the paper. Additionally, I recommend to use the same term if the same thing is meant. For instance, "Earth's magnetic field" vs. "Earth's geomagnetic field" are both used in the paper. Choose one (or use the introduced B_earth symbol).

Line-specific comments

- L10: Maybe reformulate to "... consistent with simultaneously and previously acquired ground-penetrating radar measurements." (also to avoid the not yet introduced GPR abbreviation)

- L26 vs. L31: See general comment #4.

- L70, L91: The SNMR manufacturer is cited twice (with a URL and a not properly formatted (?) citation in L91), whereas other manufacturers (e.g., Leica or Senors & Software) do not have a reference. I think manufacturers could be simply mentioned without website links, except for the loop recommendation in the manual, which needs to be properly formatted.

- L131-133: What is the despiking based on? A bit more information would be helpful here.

- L141: Is the closer loop not helpful at all? Or could it be used to estimate the attenuation of the signal and hence the "objectivity" of the noise estimate somehow?

- L148: What exactly is meant by "best results"?

- Table 1: Comma missing in the lower right between -2π and 2π.

- L174: Use square brackets for the model vector here for better readability and consistency with the initial values in L179.

- Caption of Fig. 4 contains a mix of British and American English (see general comment #4)

- L232, L238: I think the introduction of an additional model vector here makes sense to avoid these repititions.

- L263: "provides" -> "provide" because this is referring to the "results", i.e. plural?

- L380: Could some of these noise sources be listed / discussed here?

- L416 (and elsewhere): No hyphen between model and parameter needed.

- Both "Mueller-Petke" and "Müller-Petke" appear in the reference list.