the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Jun 2023
Precision measurement of the index of refraction of deep glacial ice at radio frequencies at Summit Station, Greenland
Abstract. Glacial ice is used as a target material for the detection of ultra-high energy neutrinos, by measuring the radio signals that are emitted when those neutrinos interact in the ice. Thanks to the large attenuation length at radio frequencies, these signals can be detected over distances of several kilometers. One experiment taking advantage of this is the Radio Neutrino Observatory Greenland (RNO-G), currently under construction at Summit Station, near the apex of the Greenland ice sheet. These experiments require a thorough understanding of the dielectric properties of ice at radio frequencies. Towards this goal, calibration campaigns have been undertaken at Summit, during which we recorded radio reflections off internal layers in the ice sheet. Using data from the nearby GISP2 and GRIP ice cores, we show that these reflectors can be associated with features in the ice conductivity profiles; we use this connection to determine the index of refraction of the bulk ice as n = 1.778 ± 0.006.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2023-745', TJ Young, 31 Jul 2023
Please see attached PDF. I enjoyed reviewing your manuscript!
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AC1: 'Reply on RC1', Christoph Welling, 13 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-745/egusphere-2023-745-AC1-supplement.pdf
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RC3: 'Reply on AC1', TJ Young, 24 Oct 2023
Thank you for the point-by-point response to my initial review to your manuscript. As I am shortly heading off on fieldwork, I thought that it would be useful to provide a final reply to this discussion, to say that—in short—I am happy with the manuscript and would suggest that the authors address the (very) few remaining comments that are all minor in the attached response.
I am looking forward to seeing this manuscript published, when I return from fieldwork next year!
T.J. Young
University of St Andrews-
AC3: 'Reply on RC3', Christoph Welling, 24 Nov 2023
Thank you for your comments.
a) The frequency band was chosen this is where RNO-G is most sensitive. We are happy to include statements about the effects of frequency on the measurements and to make it clearer that the setup is (almost) the same as in Aguilar et al.
b) This was already stated as an assumption, but we are happy to point it out more clearly.
c) We will add a sentence to point that (and why) we decided to limit out measurements to the upper 850 meters earlier in the manuscript.
L 86: We are happy to add that information. Though it is worth pointing out that at depths deeper than a few hundred meters, the change in signal travel time due to the horizontal antenna separation becomes negligible rather quickly.
L 176: The misunderstanding about the two measurements on n here was due to a bad edit by us, when we added the paragraph about birefringence. Line 176 was supposed to refer to the uncertainty calculations in line 170, but the two got separated by that paragraph. We rephrased this to make it clear again what line 176 was supposed to refer to.
Citation: https://doi.org/10.5194/egusphere-2023-745-AC3
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AC3: 'Reply on RC3', Christoph Welling, 24 Nov 2023
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RC3: 'Reply on AC1', TJ Young, 24 Oct 2023
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AC1: 'Reply on RC1', Christoph Welling, 13 Aug 2023
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RC2: 'Comment on egusphere-2023-745', Anonymous Referee #2, 08 Aug 2023
Welling et al estimate bulk index of refraction (n) of glacier ice at the GISP2 location. They use existing conductivity measurements from an ice core and find best cross-correlation between those and radar-detected internal layers, which yields the bulk index of refraction estimate for this particular site.
The paper is very focused on estimating n at this particular location, motivated by neutrino detection, and as such the results might be only relevant to the RNO-G collaboration.
To make this paper relevant to other communities it could include discussion on existing techniques on estimating n, and the values and errors that have been derived elsewhere and from different techniques. This would put the result here in some broader context and make it clear how novel this paper is. At the moment there is a claim of the estimate of n here being the most precise for Greenland at the moment (line 45) but no support is given to this claim.As far as I can tell, the approach for estimating n does not differ from that of Winter et al. If that is the case. If that is not the case, and I apologize if I missed something, it would be good to highlight the improvements/differences.
Uncertainty - supposedly there is some error that comes in during the cross-correlation that comes from the assumption that peaks in conductivity change correspond to radar-detected internal layers. This often holds, but sometimes it does not, potentially affecting the error estimate. Is that something you can quantify?
There is no discussion of the location of how the location of the firn/ice boundary was assessed, past which n is assumed constant. Did you have density data available?
Related to this, some discussion on the assumption of constant n below firn layer seems important given the particular application of neutrino detection in mind. As stated in the introduction the accurate knowledge of n is absolutely key, and I wonder how small variation of n below the firn layer matter in this case.The authors motivate their work by assessing the error on 1% of n, but don't discuss what is the typical error on n, indeed their result is much less than 1% away from other values (e.g. Winter et al). So I wonder if using 1% error as motivation isn't just overstating the need for more precise knowledge of n.
I don't think the authors actually compare the radar-detected internal reflections to a quantity that is equivalent to the rate of change of conductivity with depth. More on that below.
I would like to know how much this estimate of n, and in particular the estimated error, helps reduce the area of sky that needs to be monitored, as opposed to using known values of n and the respective range/errors. I think including this would make it clear whether/how relevant is this paper even to the RNO-G collaboration itself.
In line and Minor comments:
Fig 1 and 5 - It would be better to make all lines thin for better visibility of detail
Fig 1 - How did you determine the noise level? In the green transparent curve (attenuator) it seems that there are still peaks present at the same locations as in the red curve (no attenuator) where red is not shaded.
45 - do you mean precise or accurate? How did you assess that? There is no discussion/overview of existing techniques and results and uncertainties.
60-64 - I don't understand this part, can you give a range for how much the area of the error ellipse increases for 1% error on n, instead of "significantly"?
115- incomplete sentence
124- method of
130-136 - I don't see how the procedure described here, taking a difference between raw and smoothed signal and calculating a rms over some window is equivalent to taking a derivative. I might have missed something in the text (providing an actual formula would be much clearer) but it would be to clarify how it is that the authors are actually comparing differences of conductivity rather than conductivity itself.
147 - past 1500m the signals seem to decorrelate
176 - what is meant by "this"?
184 - What is meant by "this measurement?"
Fig 4 - the dashing obscures detail, better make blue line solid too, same for Fig 2a and orange dashed line - make it thin and solid
Citation: https://doi.org/10.5194/egusphere-2023-745-RC2 -
AC2: 'Reply on RC2', Christoph Welling, 17 Oct 2023
He would like to thank you for these comments and suggestions.
It is true that this publication is very focused on the particular site of Summit Station. We provide references to other index of refraction measurements in the introduction. Unfortunately, most of those do not discuss measurement uncertainties, as the index of refraction measurement was mainly a means to another end. We could add a more thorough discussion on differences between measurements by different groups, though these will likely reflect more on the variability between different locations than the measurements themselves.
If our claim that our measurement is (to our knowledge) the most accurate for Greenland is deemed to overstate things, we can remove it.
The method used in this publication is very resilient to radar reflections from sources other than changes in conductivity or changes in conductivity not leading to radio echos. These cases will result in a smaller maximum correlation compared to the other values for n, but does not affect the position of the correlation maximum. While we cannot quantify this effect, these cross correlation methods are very resilient to spurious correlations from noise, as long as there is still a clear maximum identifiable.
Density measurements of the firn at Summit Station are available from R. J. Arthern et al., Journal of Geophysical Research (Earth Surface) 118, 1257 (2013) down to 100m, and show the ice density approaching a constant value. Gow et al., Journal of Geophysical Research 102, NO. C12 (1997) put the firn/ice boundary at 75-77m based on measurements from the GISP2 borehole. This is well above the 200m depth where our measurements start.
While the Winter et al. result is much closer than 1% to ours, the difference in other measurements is around this value. Eisen et al., Journal of Glaciology, 52, 177 (2006) for example show a discrepancy at percent level between n inferred from in situ and laboratory measurements and discuss results from other measurements, arguing that these are consistent with ~1% variation. They also assume 1% as the a priori uncertainty on n.
The way the uncertainty on n affects the neutrino direction reconstruction is as follows: The direction of the neutrino can be constrained to a contour in the shape of an ellipse, with the semi major axis a given by the uncertainty on the polarization. The semi minor axis b of the ellipse is given by the uncertainty on the viewing angle (i.e. the angle between the neutrino direction and the direction the radio signal is emitted in). The area of this ellipse is given by A=pi*a*b, so it is proportional to the viewing angle resolution. For the uncertainties of 0.4° from n and 0.5° from the viewing angle reconstruction method, this would increase the uncertainty on the viewing angle to sigma=sqrt(0.5°^2 + 0.4°^2)=0.64°, a 28% increase to the size of the uncertainty contour on the sky. It is also worth noting that for a large subset of neutrino events (those resulting in a hadronic shower only), the viewing angle reconstruction is a lot more precise (see Figure 4 in Plaisier et al. Eur.Phys.J.C 83 (2023) 5, 443), making the uncertainty on n more relevant. We will add a more thorough explanation on this in the next draft.
Taking the RMS of the conductivity around a running mean is not the same as taking the derivative, and we do not claim so. The motivation behind using it is that, if there are multiple changes of conductivity within a short distance to each other, each would produce a radio echo, which would interfere with the others, resulting in a larger echo. We therefore chose RMS as a measure of the variability of the conductivity profile over a distance roughly equivalent to one wavelength of the radio signal.
Minor comments:
Fig1 and 5: We made these lines thicker to try and make the graph more readable for people with color blindness. Cryosphere seems to have rather strict guidelines on this, so maybe the editor can weigh in here?
Fig1: A good indication that the noise becomes dominant is that the integrated power approaches a constant, since the radio echo is expected to keep falling off. This does not necessarily mean that there can be no echos strong enough to be detectable over the noise after that, but peaks due to noise become more likely.
L45: As this is mostly about systematic uncertainties, it should be “accurate”. We were a bit sloppy here.
L60-64: We answered this in the text above.
L115: The end of this sentence was supposed to refer to the citations. We can rephrase it.
L124: We messed up a citation here. It is fixed.
L130-136: We answered this in the text above.
L147: We do not know why this happens, but there are some plausible reasons: It could be interpreted as a change in the index of refraction. It is also possible (and in our opinion more likely) that the depth of these layers at the measurement site differ from those at the GISP2 borehole, due to the distance from it. This is difficult to quantify, which is why we did not use these measurements for the index of refraction measurements.
L176: It is referring to the uncertainty on n. Unfortunately, this got messed up when we added the paragraph about birefringence during the editor review. Thank you for pointing this out, we will fix it.
L184: It is referring to the measurement of radio echos from ice layers, not the measurement of n itself. We will rephrase this to make it clear.
Fig 4: The same as Fig1 and 5. Maybe the editor can weigh in on if making these lines solid still keeps it readable enough for colorblindness?
Citation: https://doi.org/10.5194/egusphere-2023-745-AC2
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AC2: 'Reply on RC2', Christoph Welling, 17 Oct 2023
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