GENERAL COMMENTS

This study first uses the National Oceanographic and Atmospheric Administration (NOAA) 20th Century Reanalysis version 3 (20CRv3), together with some other observational data sets, to investigate trends in the Eurasian autumn (September to November) snow cover in years 1836-2015. Then, the variations in the interannual correlation between Eurasian autumn snow cover and the following winter Arctic Oscillation (AO) index are studied. The study adds to previous knowledge by (i) extending its analysis further back in time than has been done thus far and (ii) by also looking in some detail at the regional characteristics of the trends and the snow cover – AO relationship. In addition to the monthly mean snow cover extent in September, October and November, the rate of advance of snow cover during October and November is also analysed.

The main findings of the study include (i) an overall decreasing trend in snow cover extent in October and November since 1836, but particularly since 1966; (ii) a tendency for anticorrelated variations in the rate of snow cover advance between October and November, which is also reflected in the trends for 1966-2015 (slower advance in October but faster in November, due to a delay in the onset of the snow season); (iii) highly variable decadal correlations between the studied snow cover indices and the winter AO; and (iv) the rates of October snow advance in western and eastern Eurasia have typically opposite correlations with the subsequent winter AO index.

One may question the meaningfulness of analysing snow cover variations back to the year 1836, when little data was available to constrain the 20CRv3 reanalysis. However, I believe that this analysis still makes sense, particularly for the interannual variations. Assimilating surface pressure observations, the reanalysis should at least qualitatively capture the snow cover variability, which is largely forced by atmospheric circulation on the interannual time scale. For the same reason, the reanalysis also likely qualitatively captures the correlation between the autumn snow cover and the winter AO even in the 19th century, even though the number of pressure observations was much smaller than today.

My main concerns about this study relate to Section 4.2. Specifically, the manuscript suffers from a too uncritical interpretation of the snow cover (SC) – AO correlations. The finding that the decadal correlation between snow cover and AO indices has varied widely with time, between sometimes negative and sometimes positive values for all the five snow cover indices studied (Figure 7), allows for two diverging scenarios:

1. There is a real connection between autumn Eurasian SC and winter AO, but this connection varies with the changing background state of the climate system (e.g., low-frequency variations in SST). The connection may be causal (autumn SC affecting winter AO), or it may reflect a common underlying factor (e.g., interannual variations in SST) that affects both the autumn SC and the winter AO.
2. The connection between autumn Eurasian SC and winter AO is a statistical artefact. When the sample size is small, as it is for 10-year correlations of detrended SC and AO indices, strong correlations sometimes occur by pure chance, occasionally reaching the threshold of statistical significance.

The manuscript does not discuss these two possibilities explicitly, but the spirit of discussion appears to favour the first explanation. However, the results in Figure 7 and Table 3 call for caution. In Table 3, the proportion of decadal correlations that reach the 10 % significance level varies from 4.2 % (SAI_NOV) to 14.1 % (SC_10). A pure chance would give 10 % on the average, but with a substantial variation around this expected number.

I explored the potential importance of chance in creating apparently significant correlations by a Monte Carlo method. I created 179-year time series of pseudo-SC and pseudo-AO indices from normally distributed random numbers with no serial correlation (thus, pure white noise). Then I calculated the 170-year time series of running 10-year correlation between the two indices, after detrending them in the same way as in the manuscript, and further counted the proportion of correlations that exceeded the threshold for 10 % statistical significance. I repeated this 100 000 times.

Within this large Monte Carlo sample, the proportion of statistically significant correlations was 14.1% or larger in 19.9 % of cases. Thus, this fraction of significant correlations could easily be explained by chance. The largest fraction of significant negative correlations (11.8 % for SC_09) turned out to be slightly more unusual, occurring in 5.9 % of the generated time series. However, the probability of getting either at least 11.8 % of negative or at least 11.8 % of positive correlations was nearly twice as large (11.6 %). Finally, the probability of getting a large fraction of significant correlations for at least one of the five SC indices is much larger than that for any specific index alone.

Thus, based on the results presented in this manuscript, one cannot reject the null hypothesis that Eurasian autumn SC has no impact on winter AO at all. This is an important result as such.

In the regional analysis, larger fractions of significant correlations are found, occasionally more than 20 % (Figure 8). The Monte Carlo tests described above indicate a chance of only 1 / 300 of getting either at least 20 % of significantly positive or at least 20 % of significantly negative correlations, provided that full 179 years of data are available (which, however, is not the case for all regions). Again, however, the probability of getting such a large fraction of significant correlations for some of the regions and some of the five SC indices is much larger than that for a single region and a single SC index. Therefore, similar statistical concerns may apply to them as for the whole-Eurasia SC indices in Figure 7 and Table 3.

Obviously, absence of evidence is not evidence of absence. Some connection between Eurasian autumn SC and winter AO may exist, even if it is not convincingly seen in the correlation analysis. However, the lack of clear statistical evidence suggest that this connection is weak, explaining at best a modest fraction of the AO variability.

My recommendations for improving the statistical analysis in Section 4.2 are as follows:

1. Explicitly acknowledge the fact that much of the correlations and their apparent temporal variation may be due to pure chance.
2. Shorten the discussion of the details in this section.
3. Make the significance testing more rigorous. For the results in Figure 7 and Table 3, also report the statistical significance of the proportion of statistically significant correlations. Going beyond the simple Monte Carlo method described above, another choice could be tests in which the connection between SC and AO is broken by randomly scrambling the years of the AO index. For the regional analysis in Fig. 8, only show in colour those regions where the proportion of significant correlations is statistically significant and report the proportion of such regions in the figure itself or in a table.

Apart from the statistical analysis, the manuscript is in reasonable shape. However, as described in the detailed comments below, there is room for improvement in some of the figures and some pieces of the text, and a few details in the methodology. There are also some typos and peculiarities in the wording.

DETAILED COMMENTS

1. Replace “positive (negative) relationships” with “statistically significant (positive) negative decadal correlations”.
2. Summing of correlations makes no mathematical sense. For example, if both A and B are perfectly correlated with C (r = 1), the correlation of A + B with C is still 1 and not 2.
3. L23-24. A new study suggests an underlying ratio of three when internal climate variability is filtered out from the Arctic temperature time series (Zhou et al.., 2024, Nature Geoscience, doi: 10.1038/s41561-024-01441-1).
4. L37-39. A study published in 2002 gives no information of the recent decades, but rather the late 20th century.
5. at the end of November?
6. L83-84. Please name explicitly the emission scenarios that lead to a -10 % vs. -38 % decrease in SC.
7. L155-156. It would seem better to explicitly exclude the fully oceanic regions from the analysis, as well as the regions with very little land (say less than 20 %).
8. Figure 2. The dashed lines are barely visible. Darker blue or thicker lines would be preferable.
9. I did not understand this. If SC is either 0 % or 100 % in all days of the month, there is no change with time and thus SAI = 0.
10. Figure 5. The dashed line in (a) are very faint and could be made thicker. Also, there is a slight mismatch in the logic of colours between (a) and (b), since red is used for September in (a) but for October in (b)
11. There is very little land in this subregion and thus no reason to pay any attention to it. It might make better sense to totally omit such strongly ocean-dominated regions from the analysis (cf. comment 7 above).
12. Very little land in this region as well!
13. Figure 7. Please include the index acronyms (SC_09, SC_10, SC_11, SAI_OCT, SAI_NOV) directly within the figure panels, e.g. in their top-left corners.
14. Figure 8. As discussed in the General comments, it could be better to only use colours for those regions where the fraction of statistically significant decadal correlations is statistically significant at least at the 10 % level.
15. Beware of the caveats of multiple testing. The probability that a high fraction of significant correlations is found in some of many areas just by pure chance is far larger than the probability that this happens in any single region.
16. What is the correlation of SAI_OCT(west) and SAI_OCT(east)?
17. L555-559 and Figure 10. Summing of correlations makes no mathematical sense (cf. Comment 2). In contrast to correlations, covariances are additive, but only if the SAI indices are expressed in absolute (area) units rather than in normalized form. Thus, one option would be to make a plot that shows the absolute covariances of SAI_Oct(East), SAI_Oct(West) and SAI_OCT(East + West) with AO. Another option is to omit Figure 10.
18. L591-592. The interpretation would be this if Figures 11c (11d) showed the correlation between SAI_OCT in west (east) and the 850 hPa geopotential height. However, what is shown is the correlation between the SAI_OCT – AO_winter *correlation* and 850 hPa geopotential height. Modify accordingly.
19. L657-658. a trend from negative to positive correlations with winter AO?
20. L679-682. What is the correlation between SAI_NOV(west) and AO for the whole period 1836-2015? What is the corresponding correlation between SAI_NOV(east) and AO?
    
    

TYPOS ETC.

1. momentum or moisture?
2. there have been
3. either SAI index?
4. Snow cover indices from 20CRv3 and ERA5 ( ) are shown as red and blue lines
5. Caption of Table 3. Check the years. The numbers in the table suggest a sample size of exactly 170.
6. October and November?

This study uses a long snow cover data to examine the Eurasian autumn snow cover change and its relation with AO. This is an important and interesting topic because of the critical effect of snow cover on the various components of the earth system especially under the warming climate. Overall, this paper has clear structure and the results are well supported by the figures and tables. However, I think the paper lacks impressive findings. The characters of snow cover change and the snow-AO relationship have been investigated by numerous previous studies. Although author uses the long data to explore these issues, there is no new thing in comparison with other studies. Therefore, I would recommend rejecting it for publication in TC.

Major issues

This is a quite long paper. The author has put a lot of efforts into the Introduction, Data and Method parts, while the Results part seems a little hasty. Also, I cannot easily get the point from the lengthy introduction. I suggest the author to delete the text that unrelated to the main topic of your study and put some methods into the supplementary materials.

Form figure 7 and table 3, I find that there is hardly any significant correlation between snow and AO. Does it imply that the Eurasian snow cover has little influence on the AO, or the snow-AO relation is a stochastic event?

How to calculate the running decadal mean and correlation in figure 5 and 7? How long is the sliding window？If you use different sliding window, will it change the existing results?

Line 160: Why reverse the sign of SAI index? It is contrary to common sense and makes readers difficult to follow. 

GENERAL REMARKS

In the manuscript "Spatial and temporal changes in autumn Eurasian snow cover and its relationship with the Arctic Oscillation" the author uses long-term reanalysis data to subdivide the correlations between autumn snow cover and winter AO sign regionally. This topic is of great importance and fits the scope of the journal.

That said, I am really torn about the quality of this manuscript. I really want to love it, but I find myself wondering about the goal and the impact. 

In general, I agree with the previously published reviews that the results are not substantially new and it is difficult for me to see the key point of the exercise. 

However, I can see many positive and useful parts in this paper. I think it would be very helpful for the community to have an updated evaluation of SD in 20CRv3, versus the older products and stations, kind of like an update of the cited Wegmann et al 2017 study with the nice bias removal procedure shown here. And then that can be looked at regionally and you can discuss about why and how 20CRv3 might be improved or not, you could go into more detail for other seasons etc. I think this would be of great value for this community. So basically everything until 4.2 I like. 

With 4.2 the science becomes unfocused and diffuse. In the end you have a huge array of mediocre findings in a very complicated form. All of this regionalisation could be, in my opinion, be performed by EOF analysis of the whole field, similar to what Han & Sun did in 2019 (see the link below). You mention and show that there are decadal changes in correlation, but offer no process that might explain that. You remain too superficial for novelty in my eyes. Your KEY result in my eyes, after filtering a lot of text and data for meaning, is the west east anti-correlation pattern between autumn SC and AO. Unfortunately, Han & Sun and Wegmann et al. looked into this already to some degree and you do not put your results in the context of those studies at any point. This is an important oversight. 

So what is the goal of this manuscript? Is it to find the most impactful regions for seasonal prediction? Is it to find an explanation for the decadal variability? Is it to evaluate snow in 20CRv3? Is it to do something different, maybe in terms of method, season and region that previous studies did? The goal and thus the evaluation if you reached this goal stays elusive. One major difference to previous studies is the use of 20CRv3, but again, you did not really show the reader how different that product is from 20CRv2c and 20CRv2.

So my recommendation is that you sharpen your manuscript (agreeing with the two other Reviews) and pinpoint towards your goal. I personally would recommend the goal to be SD evaluation rather than looking at dynamics, simply because arguing for novelty in the dynamics part seems difficult from my side of things. 

A few notes on the overall structure:

I think the discussion and conclusion sections are misused.

The discussion section in this manuscript is actually just another result section.

And the conclusion is the discussion. However, some key context is missing here.

The conclusion is missing. 

I was constantly confused by the direction of the correlation. For me more snow to negative AO should be a negative correlation. 

SPECIFIC REMARKS

L12: You point out the novelty of going back to 1836, but here you only mention the last 50 years. I am missing some coherence between the two statements.

L34: "There is often" is too imprecise. When does this dipole happen in the season, when was it strong and why and what is the direction of the gradient? Is it usually a lot of snow in the west and no snow in the east? Does the sign flip interannually? Decadally?

L45: Upward trend of what? Do you mean positive trend? 

L47: When you say "in reality", what data product do you refer to, if we assume that the CDR is "not reality"?

L57: First you mention that the Arctic air is "warmer", then you mention that the cyclones bring "Cold" Arctic air. This is confusing. 

L78: I would summerize Arctic amplification and Climate Change to anthropogenic global warming. 

L108: In this context, Wegmann et al 2021 investigated an interesting middle ground, where free running seasonal forecast models were induced with different snow regimes (https://wcd.copernicus.org/articles/2/1245/2021/). They found a small but measurable impact onto the NAO sign. 

L125: Building up on Peings and Douville, Wegmann et al 2020 looked at the link between Eurasian snow and NAO and found that the snow impact is highest during Arctic warm periods, when the Albedo impact of additional snow is strong (https://esd.copernicus.org/articles/11/509/2020/).

L290: I think it is worth mentioning in this manuscript, that the grid size of ERA5 is substantially smaller than than of 20CRv2c, so we would expect better agreement between a station and ERA5 vs a station and 20CRv2c. Also you assume here that the errors of 20CRv2c are carried over to 20CRv3. Until now in the manuscript, you did not show the reader that that is indeed the case. Maybe that would be a worthwhile information for the community to have.

L694 to end: I think your manuscript would really benefit from discussing the work of Han & Sun 2019 (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018JD028443), Wegmann et al 2020 and Wegmann et al 2021 regarding this west-east difference in snow impact. In there you will also find some initial explanations for what could be the reason for this behavior. In there you will also find some answers to your last sentence in this manuscript.