the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Spatial and temporal changes in autumn Eurasian snow cover and its relationship with the Arctic Oscillation
Abstract. Previous studies have demonstrated that variations in the seasonal expansion of Eurasian snow cover (SC) can influence the following winter Arctic Oscillation (AO) and, consequently, affect midlatitude weather. We examine changes in the extent and rate of autumn Eurasian SC advance and the temporal variability of the magnitude and sign of the SCAO relationship. Novel aspects are (i) the use of the latest version of the 20^{th} Century Reanalysis (20CR), allowing analysis back to 1836; (ii) adjusting the reanalysis SC through comparison with observations; and (iii) investigating spatial variation in the frequency of significant SCAO relationships across Eurasia.
Over the past 50 years the snow advance indices (SAI) demonstrate a slowing and accelerating of snow advance in October and November (p < 0.01), respectively, corresponding to a greater contemporaneous decrease in SC extent in October than November and thus a postponement of SC onset. The most temporally robust spatial SCAO relationship is a longitudinal dipole such that positive (negative) relationships between October SAI and the AO are more frequent in western (eastern) Eurasia. As the sum of the two regional correlations closely matches the correlation for Eurasia as a whole, an especially strong October SAIAO relationship occurs when the sign of the relationship in one of these regions is reversed from climatology. Future work will aim to determine the exact linkages behind this new finding in the context of contemporaneous changes in regional atmospheric circulation and snow cover and the many additional factors observed to influence the SCAO relationship.
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RC1: 'Comment on egusphere20241892', Anonymous Referee #1, 14 Jul 2024
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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 18362015. 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 19662015 (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:
 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., lowfrequency 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.
 The connection between autumn Eurasian SC and winter AO is a statistical artefact. When the sample size is small, as it is for 10year 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 179year time series of pseudoSC and pseudoAO indices from normally distributed random numbers with no serial correlation (thus, pure white noise). Then I calculated the 170year time series of running 10year 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 wholeEurasia 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:
 Explicitly acknowledge the fact that much of the correlations and their apparent temporal variation may be due to pure chance.
 Shorten the discussion of the details in this section.
 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
 Replace “positive (negative) relationships” with “statistically significant (positive) negative decadal correlations”.
 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.
 L2324. 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/s41561024014411).
 L3739. A study published in 2002 gives no information of the recent decades, but rather the late 20th century.
 at the end of November?
 L8384. Please name explicitly the emission scenarios that lead to a 10 % vs. 38 % decrease in SC.
 L155156. 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 %).
 Figure 2. The dashed lines are barely visible. Darker blue or thicker lines would be preferable.
 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.
 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)
 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 oceandominated regions from the analysis (cf. comment 7 above).
 Very little land in this region as well!
 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 topleft corners.
 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.
 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.
 What is the correlation of SAI_OCT(west) and SAI_OCT(east)?
 L555559 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.
 L591592. 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.
 L657658. a trend from negative to positive correlations with winter AO?
 L679682. What is the correlation between SAI_NOV(west) and AO for the whole period 18362015? What is the corresponding correlation between SAI_NOV(east) and AO?
TYPOS ETC.
 momentum or moisture?
 there have been
 either SAI index?
 Snow cover indices from 20CRv3 and ERA5 ( ) are shown as red and blue lines
 Caption of Table 3. Check the years. The numbers in the table suggest a sample size of exactly 170.
 October and November?
Citation: https://doi.org/10.5194/egusphere20241892RC1
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