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?