Editor’s comment:

Both reviewers recommended a large number of edits to the manuscript, and raised a few major points requiring more significant revisions. The authors made almost all of the recommended major revisions, and all of the minor revisions, but the revised paper is still very difficult to read because of non-standard use of English expressions, and because the analysis in the methods section (section 3.x) is not well motivated. I would recommend a thorough re-write of the paper with careful attention to how the reader is to understand the choices the authors made in their analysis, and detailed editing. Some of my own comments on the revised manuscript are below.


Section 1. Reviewer 1 asked for more information on the glaciological setting, and the authors said that they would provide it. This is not apparent in the revised manuscript.

Section 2.2:
Both reviewers questioned the choice of station BE for the temperature and precip records, and the authors gave them a plot and a rationale for the choice in their response to the reviews. This information needs to be conveyed in some way in this section of the paper.


Section 2.3:
This section needs to be carefully checked for English grammar and word choice. It is at present difficult to interpret, and leaves considerable room for misinterpretation by readers.

The FFT/IFFT procedure appears to be important in dating the cores, but the description of the algorithm does not explain how the analysis was performed. A more detailed technical discussion, including range of frequencies chosen, is needed here.

Section 2.4:
It is not clear how the GPR results relate to the other analysis performed here. It does not appear that the authors make much use of these data, and I suggest removing this section from the paper to save space.

3.1.1 and 3.1.2
These sections also needs rewriting for clarity. The authors use the term “direct relation” and “inverse relation” to mean (I think) “positive correlation” and “negative correlation.” They also use a very complex sentence structure without many clues to the reader as to the significance of different parts of their analysis. More motivation and more standard use of English idiom would help here.

When presenting statistical significance values, the authors should make clear how many independent variables they believe they have. Is every measurement statistically independent from every other?

3.2.1.
Reviewer 2 suggested that using the d_excess_meteo to date the core should result in strong correlations between d_excess_meteo and d_excess_core, so the correlation between the two should not be surprising. The authors claimed that this resulted from a misstatement in the original manuscript, but the revised MS appears to make the same claim. If I am misreading this, the text needs to be clarified to prevent this misunderstanding.

3.2.2
It is not clear from the discussion what the 2-year pattern is. The sentence that should explain it has two clauses, and it is difficult to understand which of the two expresses the nature of the signal.

This section gives a fairly confusing analysis of the data. Are the authors using three different D18-O-vs-temperature functions for three different seasons? What are these functions? Are they from the accumulation –sampling analysis? If they’re derived from the core, how do we know that they express something significant about the climate? It seems that by allowing themselves to select three different D18-O-vs-temperature relationships for two different sets of years, the authors have too many degrees of freedom in interpreting their data. With this many adjustable parameters they are bound to find correlations among the results. Am I just misreading this section? Again, the analysis needs more motivation.


The justification for using BE should be presented in the data section, rather than here.

Section 4.1:

P. 13 Line 26: “mean δ18O and δD values show a decreasing tendency with increasing height from sea level” : what does “tendency” mean here. Correlation?

Dear Dr. Fernandoy,

Thank you for your revisions in response to my previous comments. I would like to request some more changes to the manuscript before I send it back to the reviewers.
First, I would like you to see my previous comments about the use of "direct relationship" and "inverse relationship." These terms are not clear-- I think you mean positive linear correlation and negative linear correlation, but I'm not entirely sure. This comes up often in the paper, and is consistently confusing.

Second, please provide the number of degrees of freedom when you provide a P value for a statistical correlation. The P values you state are consistently small (with two or three exceptions) even though the correlations are weak, but I am not sure the number of degrees of freedom necessarily justifies the interpretation that the correlations are unlikely to have come about by random chance. If two low-frequency-content signals are compared, they may show a strong linear correlation simply because the low-frequency signals have similar periods. In these cases, assuming that the number of degrees of freedom is equal to the number of data points is incorrect, and results in spuriously small P values.

Third, and perhaps most important: Please provide motivation to the statistical correlations examined in sections 2 and 3. You frequently describe analyses you have performed without explaining what they were intended to accomplish, which makes the discussion in section 4 very difficult to relate to the analysis performed in section 3.

A few more editorial comments are attached below. Thanks for your attention to this.

P3 ~30 – the glaciological background should go in its own section.
P6 26: You need to specify that this is now the reanalysis data you are talking about (e.g. “For every precipitation event registered in the (NCEP?) data”)

P9, top- Need to specify whether the “precipitation samples” are modeled or are actual samples from a different study.

P9 line 20: Need to evaluate the significance of the correlation between dexcess meteo and dexcess core in light of the fact that dexcess meteo was use to date the core. What is the probability that one time series, stretched to match another, shows a 75% correlation with the series it is stretched to match? How many degrees of freedom are involved?

P9 line ~29: What standard deviation is in question here? The amplitude of the oscillations in the cores? The difference between the cores?

P 10, Line 16-20: Where do you describe the bounds on the seasons you have defined this way (after sometimes stretching seasons to include groups of similar data?) How and where do you use these classifications?

Dear Dr. Fernandoy,

Two referees have now returned reviews of your second manuscript for TC-2016-298. Both were generally positive, and felt that the manuscript has improved since the previous version that they saw. However, both felt that further work would be required before the manuscript would become suitable for publication. I feel that as the English in the manuscript has improved, some other problems have become more obvious. I am recommending extensive revisions before we reconsider the manuscript.

Methods:
The methods are not always clearly described. In particular, in section 3.3, the Fourier transform procedure does not make sense. The IFFT is usually used to convert from the frequency domain to the space domain, not the other way around. The expression "The signal obtained from each step of the FFT decomposition" does not mean anything to me, and the statement that "By studying the progression of these variations, the frequency of the second mode showed the highest frequency where the Sdev reaches an equilibrium" needs to be rewritten, as it does not correspond to anything I understand about signal processing.

I think what is going on is that the authors looked at the FFT spectrum of the signal and decided what parts of it were meaningful, then edited out the higher-frequency, less meaningful portion and used the IFFT to produce a filtered signal containing only low-frequency information. They then matched the peaks and troughs of the two d signal to date the core. What is not clear is whether only a single rescaling value was adequate to match the the core and the meterological signal, or whether different stretching values were used to move each peak in the core inline with the meterological signal. I, and the referees, assumed the latter, based on which the correlations drawn between the core and the meterological signal are meaningless. Under this understanding, the authors' explanation that the correlation was between the composite core and the meterological records is not helpful, because the composite core would suffer the same, or nearly the same, spurious correlation with the meterological data.

If only a single stretching value was used, then the correlations between the two signals may be significant. Someone familiar with standard English terminology for Fourier analysis needs to read and revise this section carefully.

Results:
As in previous versions, the motivation for the correlations presented in section 4 were not at all easy to follow in the revised manuscript. Each time the authors compare two variables and calculate a correlation value between them, the need to explain WHY they performed this correlation, WHAT they expected to learn from the correlation, and what the statistical test indicates.

The alpha values now included in the manuscript do not generally add clarity to the results: much more helpful would be to list the number of degrees of freedom in the correlations that was used in calculating the p values.

Presenting the correlation results in line with the text generally makes the paper much harder to read. In particular, the long paragraph in 4.1.1 could be improved by presenting the s values and their significance statistics in a separate table, along with the monthly correlations.

Section 4.1.1, line 25:
This sentence:
"Thus, the time series of monthly averages shows a positive correlation between both parameters"
did not seem to follow from the other material in the paragraph, which is largely about the daily correlations (the s values).

General considerations:

The use of the terms "inverse/direct behavior" and "inverse/direct relationship" remains common in the manuscript. I recommended, and the reviewers agreed, that this expression should not be used, and that "positive/negative correlation" should be used instead.

The authors need to break the discussion section into shorter paragraphs, with a topic sentence for each to indicate what point they are trying to make, and why. The very long paragraphs used here are difficult to untangle, and the line of the argument gets lost.

Dear Dr. Fernandoy,

The manuscript has changed a lot since the last time I saw it, and most of my, and the reviewers' objections have been addressed. Thank you for your hard work on this.

I am still confused by one remaining question about the filtering of the d_excess data. In the current version of the paper, quoted below, you say that you filtered the the two d_excess signals so that they contained only the lowest frequency data. You say: "The second lowest frequency was the one with the lowest power. We therefore reconstructed the low-frequency d_excess signal by calculating the [IFFT] from the lowest two identified frequency peaks." You did the same thing with the d_excess_meteo data.

My question is whether you looked at a FFT spectrum, and identified two peaks, each including a number of frequencies, or if you only used the two lowest-frequency bins in the FFT (i.e. the 1-cycle-per-record and the two-cycle-per-record bins). If the former, you should state the cutoff frequency (or wavelength) that you applied. If the latter, something is wrong, because any two signals reconstructed from only two Fourier components are likely to have good correlation.

In either case, the number of degrees of freedom in the filtered signals cannot be larger than the number of Fourier components included in the spectrum input to the IFFT, so this is an important number to quote in the text.

Anyway, I think we're close here. Please check on this matter, and make sure the text is clear.

Thanks for reading over the paper again, and for adding a bit more detail into the Fourier analysis. The manuscript looks ready to go from here.

Best
Ben