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Climate Dynamics

, Volume 47, Issue 7–8, pp 2085–2104 | Cite as

A stable snow–atmosphere coupled mode

  • Liang Zhao
  • Yuxiang Zhu
  • Haiwen Liu
  • Zhongfang Liu
  • Yanju Liu
  • Xiuping Li
  • Zhou Chen
Article

Abstract

Snow is both an important lower boundary forcing of the atmosphere and a response to atmospheric forcing in the extratropics. It is still unclear whether a stable snow–atmosphere coupled mode exists in the extratropics, like the ENSO in the tropics. Using Sliding Correlation analysis over Any Window, the present study quantitatively evaluates the stability of coupling relationships between the major modes of winter snow over the Northern Hemisphere and the winter atmospheric Arctic Oscillation (AO), the Antarctic Oscillation (AAO) and the Siberian High over the period 1872–2010, and discusses their possible relationships for different seasons. Results show that the first mode of the winter snow cover fraction and the winter AO together constitute a stable snow–atmosphere coupled mode, the SNAO. The coupled mode is stronger during recent decades than before. The snow anomaly over Europe is one key factor of the SNAO mode due to the high stability there, and the polar vortex anomaly in the atmosphere is its other key factor. The continuity of signals in the SNAO between autumn and winter is weaker than that between winter and spring. The second winter snow mode is generally stably correlated with the winter AAO and was more stable before the 1970s. The AAO signal with boreal snow has a strong continuity in seasonal transition. Generally, through these coupled modes, snow and atmosphere can interact in the same season or between different seasons: autumn snow can influence the winter atmosphere; the winter atmosphere can influence spring snow.

Keywords

SNOW Arctic oscillation Antarctic oscillation Siberia high EOF analysis Sliding correlation Snow–atmosphere coupling 

1 Introduction

The atmosphere lacks the mechanisms to generate predictable variations beyond synoptic time scales (Lorenz 1963), so for climate prediction, it is very important to study patterns of variation in atmospheric forcings. El Niño as an atmospheric forcing has become an important factor in prediction because it has somewhat predictable variation, on seasonal and interannual time scales, that significantly influences the atmosphere (Kim et al. 2012). Snow over land is another important lower boundary forcing source and another form of water that directly and persistently influences the atmosphere and soil even on interannual time scales (e.g. Allen and Zender 2011a; Dutra et al. 2011). Thus, snow has also been investigated during recent decades as another potential source of predictability (e.g. Gong et al. 2002; Wu et al. 2011). Recently, some studies found that the levels of simulation and predictability of some fundamental climate modes or factors [e.g. the Arctic Oscillation (AO), the Siberian High (SH)] are even higher when snow and its effects are taken into account (e.g. Allen and Zender 2011b; Cohen and Jones 2011). Therefore, snow may have a predictive value for seasonal forecasting (Cohen and Saito 2003; Zuo et al. 2011; Brun et al. 2013a, b).

The El Niño/La Niña mode in the tropical ocean corresponds to the Southern Oscillation (SO) in the tropical atmosphere (together called ENSO). Whether a typical mode of extratropical snow corresponding to an annular mode in the extratropical atmosphere also exists remains unclear. If there is a typical snow variation mode over the Northern Hemisphere persistently coupled with an atmospheric annular mode, the snow mode and corresponding atmospheric mode should be regarded as a single entity, like ENSO, rather than be considered separately in climate prediction. The snow–atmosphere coupled mode likely has higher predictive value than snow or atmosphere alone.

The AO and the Antarctic Oscillation (AAO) are annular modes that are the dominant modes of atmospheric winter climate variability in the extratropics over the Northern Hemisphere (NH) and Southern Hemisphere, respectively (Thompson and Wallace 2000a, b; Cohen et al. 2014). In recent years, the AAO has been considered to exert a potential influence on climate over the NH (e.g. Nan and Li 2003; Wu et al. 2014; Zheng et al. 2014). The SH dominates the Asian climate in the cold season and significantly influences climate over the other NH extratropical and even tropical regions (Cohen et al. 2001; Gong and Ho 2002; Panagiotopoulos et al. 2005). These atmospheric modes or factors account for a certain proportion of climate variability and some of them have been used as predictability sources (Lin and Wu 2011). They are all likely related to the underlying snow cover and its diabatic heating. However, the dominant mode of variability of NH snow remains unclear, and its relationship with hemispheric–scale atmospheric modes has not been studied. Therefore, the present study attempts to find a potential relationship between extratropical snow modes and the atmosphere (e.g. the AO, the AAO, and the SH). We need to carefully consider the role of snow in relation to the atmosphere because a snow–atmosphere (e.g. AO) relationship in certain spatial and temporal domains may be neither consistent (Peings et al. 2013) nor strong (Xu and Dirmeyer 2011, 2013). Therefore, in the present study, we use a new method to test and quantify the stability of the relationship between snow and the atmosphere.

Another important problem is whether a relationship exists between atmospheric or snow modes in winter and snow or atmospheric modes in leading (September–October–November; SON) and lagging (March–April–May; MAM) seasons. Cohen and Entekhabi (1999) showed a statistically significant correlation between fall Eurasian snow cover and the winter AO. Similarly Bamzai (2002) and Saito et al. (2004) showed a statistically significant correlation between the winter AO and spring Eurasian snow cover in recent decades. However, the leading forcing and lagging response of NH snow has not been regarded as an important hemispheric-scale temporal–spatial mode to study.

The present study aims to identify whether a stable coupling between extratropical snow modes and the atmosphere (the AO, the AAO, and the SH) exists in winter and to detect the relationship between the coupled mode and leading (autumn) and lagging (spring) snow and atmospheric anomalies in the past 139 years.

2 Data and methods

2.1 Data and indices

The monthly 20th Century Reanalysis V2 (20CR) data for snow cover fraction (SCF), mean sea level pressure (MSLP), geopotential height and horizontal wind from 1871 to 2010 (available from the web site http://www.esrl.noaa.gov/psd/) are used in this study because of their comprehensive spatial and temporal coverage. The 20CR reanalysis is based on the assimilation of surface pressure observations only and its boundary conditions are the observed sea–surface temperature and sea–ice distributions (Compo et al. 2011). The quality of 20CR in the extratropical NH throughout the twentieth century is generally high and similar to that of current 3-day operational NWP forecasts. It has been shown to represent the long-term variability of the NH atmospheric circulation and snow cover over the entire twentieth century (Compo et al. 2011; Ouzeau et al. 2011; Brun et al. 2013a, b; Fischer et al. 2013; Peings et al. 2013). The resolution of the dataset is roughly 1.9° and the entire NH land surface corresponds to 3442 grid points. The average SCF over the entire NH land surface (hereafter SCFN) can be obtained. To eliminate the impact of the poleward convergence of longitude, a weighting by the square root of the cosine of the corresponding latitude is applied to each grid point (Hannachi et al. 2007) to obtain SCFN. The monthly geopotential height and horizontal wind data from 1948 to 2010 from the US National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis (Kalnay et al. 1996) are also used.

Atmospheric circulation modes and systems investigated in this study include the AO, AAO, and SH, and they are denoted by standardized indices, here referred to as I AO, I AAO, and I SH, respectively. We adopt the I AO defined by Li and Wang (2003) (http://ljp.lasg.ac.cn/dct/page/65607), the I AAO defined by Nan and Li (2003) (http://ljp.lasg.ac.cn/dct/page/65609), and the I SH defined by Zhu et al. (2007) for the 1871–2010 period. Therein, I SH is defined as the standardized MSLP derived from 20CR averaged over the 40°N–60°N, 80°E–120°E region. All seasonal indices and variables in the present study are calculated by averaging over autumn (SON for 1871–2009), winter (December in the previous year and January–February (DJF) in the year for 1872–2010) and spring (MAM for 1872–2010). Their lengths are all 139 years. Seasons in the present study all refer to the NH seasons and snow refers to the NH snow.

2.2 Correlation stability analysis

We perform a Sliding Correlation analysis over Any Window (AWSC) within a time period to test the stability of the relationship between two time series and quantify the stability based on the results of the AWSC. Here, the time period is from 1872 to 2010. The sliding windows are from 11 to 129 years (to ensure sufficient degrees of freedom and time periods for a sliding window), and the samples are from all possible time periods inside a given sliding window. When the sliding window is 11 (12, …, 129) years, the total number of all possible time periods is 129 (128, …, 11), with the start year ranging from 1872, 1873, …, to 2000 (1999, …, 1881), respectively. Hence, 129 (128, …, 11) correlation coefficients are obtained. Consequently, we can get a two-dimensional sliding-correlation field with 8340 (=N) correlation coefficients (the x and y axes indicate the start years and sliding windows, respectively). Finally, after significance tests of correlation coefficients according to the size of sliding windows, the percentage of stability (PS), defined as the percentage of the number of significant correlations relative to the total number (N), can be derived as an index to measure the degree of stability of correlation between the two series.

3 Relationship between NH snow and its modes and atmospheric circulation patterns in winter

3.1 Stability of the relationship between entire NH snow and atmospheric circulation patterns

First, we identify the possible relationships between the total NH snow cover and the major atmospheric circulation patterns in winter (DJF). Figure 1 shows the time series and 11-year smoothed time series of winter SCFN and the AO and SH indices for the period 1872–2010. We calculate the correlation coefficients between winter SCFN and the AO, AAO, and SH indices and between these indices (Table 1). The SCFN is significantly correlated with the I AO (r = −0.39, p < 0.001) and the I SH (r = 0.26, p < 0.01) and insignificantly with the I AAO. The correlation between I AO and I SH is also significant (r = −0.29, p < 0.001). In Fig. 1, the evolution of both the negative I AO (—I AO is shown for ease of comparison) and I SH is generally consistent with that of the SCFN. That is to say, when positive AO and negative SH occur, the average snow cover over the entire NH tends to decrease. Although the correlations between SCFN and I AO and I SH are good over the total period 1872–2010, the correlation analysis for a given time period does not indicate whether their relationships are good for any other time periods within 1872–2010. For example, in Fig. 1 the correlation relationship between SCFN and I AO for 1901–1928 is very weak and is even positive with r = 0.03, and the correlation relationship between SCFN and I SH for 1940–1956 is very weak and is even negative, r = −0.14. The correlation analysis for a given time period cannot show the stability of the correlation between the two series. Therefore, the stability of the correlations must be explored.
Fig. 1

Unsmoothed (thin solid lines) winter SCFN, standardized −I AO (here multiplied by −1 for comparison) and I SH and their 11-year smoothed (thick solid lines) time series for the period 1872–2010

Table 1

Correlation coefficients between winter SCFN and atmospheric circulation pattern indices for 1872–2010

 

I AO

I AAO

I SH

SCFN

−0.39***

−0.13

0.26**

I AO

 

0.05

−0.29***

I AAO

  

−0.22**

** and ***: 99 and 99.9 % confidence levels, respectively

Note that for simplicity, we use AO, SH and AAO below in place of I AO, I SH and I AAO, respectively. We perform two AWSCs within the 139 years to test and quantify the stability of the relationship between SCFN and AO and between SCFN and SH, as shown in Fig. 2a, b, respectively. The PS is actually the percentage of the colored area within the trapezium. For SCFN and AO (Fig. 2a), PS = 70.6 %, meaning that the majority of correlations under the different sliding windows are significant, and suggesting that the correlation between them is generally stable. For SCFN and SH (Fig. 2b), however, PS = 47.3 %, meaning that more than half of the sliding correlations are insignificant, and suggesting that the correlation between them is not very stable. Moreover, we find that the correlation between the SCFN and AO is stronger during the second half (after the 1930s) of the 139-year period than during the first half (before the 1930s), possibly because the data is of a higher quality in the second half. Peings et al. (2013) also found that the consistent Eurasian snow–AO teleconnection emerged after the 1970s. In contrast, the correlation between SCFN and the SH is stronger during the first half than during the second half of the period. This suggests that the stable (unstable) relationship between SCFN and AO (SH) during the recent decades can (cannot) help explain the variation of the AO (SH).
Fig. 2

Correlations on any sliding window (from 11 to 129 years) within the period 1872–2010 a between winter SCFN and I AO and b between winter SCFN and I SH. The significant correlations at the 95 % confidence level are colored and insignificant correlations are contoured

3.2 Stability of the relationships between NH major snow modes and atmospheric circulation patterns in winter

The above analysis is based on the snow averaged over the entire NH. In order to obtain the possible spatial modes of snow that are coupled with the major atmospheric circulation patterns, an empirical orthogonal function (EOF) analysis of winter SCF over the NH land surface is performed. To eliminate the influence of the poleward convergence of longitude, a weighting by the square root of the cosine of the corresponding latitude is applied to each grid point of SCF over the NH (Hannachi et al. 2007), before EOF analysis. Figures 3a, and 4a, b show the first two EOF modes of winter SCF over the NH. For comparison, Figs. 3c, d and 4c show the correlation maps between AO, SH, and AAO and SCF over each grid point of the NH land surface, respectively. Over Greenland, SCF is always 100 % in all winters, so eigenvectors and correlation coefficients could not be obtained. The first EOF (EOF1) explains 13.3 % of the total variance. We found that EOF1 (Fig. 3a) is the most similar to the SCF–AO correlation map (Fig. 3c), the second most similar to the negative SCF–SH correlation map (Fig. 3d), but very different from the SCF–AAO correlation map (Fig. 4c). Figure 3a, c, and d all show similar “ − + − + − ” distributions; i.e., three negative centers over Europe, northern China and Mongolia, and eastern North America, and two positive centers over western and northern Asia and western North America. Note that although there is a significant inverse correlation between AO and SCFN, the relationship between AO and snow does not always exist in each region, even at the same latitude. This is also the case for the SH. Table 2 shows correlations between the atmospheric circulation indices and the first and second principal components (PC1 and PC2) for 1872–2010. The absolute value of the PC1–AO correlation is the highest (r = 0.56, p < 0.0001), PC1–SH is the second highest (r = −0.38, p < 0.001), and PC1–AAO is the lowest and insignificant. Figure 3b shows that the evolution of PC1 and AO is indeed similar. Overall, according to the similarity of the spatial distributions and correlation of the time series, the EOF1 mode is most likely related to AO and is likely related to SH.
Fig. 3

a The EOF1 of NH winter SCF anomalies during the period 1872–2010 and b corresponding PC1 and I AO time series (thin) and their 11-year smoothed means (thick), maps of correlation coefficients, c between winter I AO and SCF field and d between winter −I SH and SCF field (here multiplied by −1 so that the pattern is easy to compare with the EOF1 and AO–SCF correlation map), PS (units: %) maps for e AO–SCF and f SH–SCF correlation in each grid point over the NH land surface for 1872–2010 (the variable sliding windows from 11 to 129 years). The deepest and the second deepest shadings in c and d are significant at 95 and 90 % confidence level, respectively

Fig. 4

Same as Fig. 3, but a for EOF2, b for PC2 and I AAO series, c correlation map between I AAO and SCF field and d PS (units: %) map for the AAO–SCF correlation

Table 2

Correlation coefficients between atmospheric circulation indices and PC1 and PC2 for 1872–2010

 

I AO

I AAO

I SH

PC1

0.56***

0.09

−0.38***

PC2

−0.25**

0.24**

−0.11

** and ***: 99 and 99.9 % confidence levels, respectively

However, these analysis results cannot reflect the stability of the relationships within the 139 years and thus cannot clearly illustrate whether they are coupled with each other. Therefore, the stability of the relationships between the EOF1 mode and AO and SH is analyzed using the AWSC method. First, we test the stability of the SCF–AO and SCF–SH correlations at each grid point over the NH land surface for 1872–2010 (with sliding windows from 11 to 129 years) and obtain a PS for each grid point. Then, we plot the PS maps (Fig. 3e–f). If PS ≥ 50 % is the criterion for a stable correlation, stable SCF–AO correlations exist mainly over Europe, western Asia, and western and eastern North America (Fig. 3e), similar to the distributions of extremes of EOF1 and the SCF–AO correlations. In comparison with Fig. 3c, it is noteworthy that the extent of the stable correlation regions is smaller than that of the significant correlation regions, which implies that significant correlations are not always stable; e.g. in East Asia. In contrast, the major stable correlations between SCF and SH (Fig. 3f) appear in East Asia with regions of relatively minor stable correlation at the border between Europe and Asia and in northwestern North America. Obviously, the distribution of stable SCF–SH correlations is different from that of EOF1 extremes.

We also test stability of correlation between the AO and PC1 and between the SH and PC1, using the AWSC method, as shown in Fig. 5a, b. For AO–PC1 (Fig. 5a), PS = 92.8 %, so the AO–PC1 correlation is very stable over the 139 years and the stability is much higher than that of AO–SCFN (PS = 70.6 %), which suggests that the first mode of NH snow is more closely coupled with the AO than the averaged snow (i.e., SCFN) For SH–PC1 (Fig. 5b), PS = 83.4 %, which is also much higher than for SH–SCFN (PS = 47.3 %), suggesting that the EOF1 mode may also be stably connected with the SH, to some extent. Nevertheless, when the sliding window is shorter than 40 years, there are large areas of insignificant correlation in Fig. 5b, suggesting that the SH–PC1 correlation is relatively stable only over long time periods (>40 years). Furthermore, we find that the correlation between AO and PC1 is stronger after the 1920s, especially after the 1960s, than before the 1920s. This suggests that the close relationship between the AO and NH snow EOF1 during recent decades can help explain the close relationship between the AO and SCFN and illuminate the variation of AO during recent decades. For windows shorter than 30 years, the strong and consistent correlation between AO and PC1 since the 1970s suggests that the teleconnection between the snow EOF1 mode and AO likely contributes to the consistent relationship between Eurasian snow and the AO since the 1970s found by Peings et al. (2013).
Fig. 5

Same as Fig. 2, but a between I AO and PC1 and b between I SH and PC1

The second EOF (EOF2) explains 11.4 % of the total variance. Comparing the EOF2 (Fig. 4a) and the correlation maps (Fig. 3c and d and Fig. 4c), we found that EOF2 is the most similar to the SCF–AAO correlation map (Fig. 4c), but very different from the SCF–AO and SCF–SH correlation maps (Fig. 3c, d). Both Fig. 4a, c shows a similar zonal distribution in Eurasia and meridional distribution in North America. Figure 4b shows the time series of PC2 and AAO. Both are similar, particularly before the 1970s. For the period 1872–2010, r = 0.24 (p < 0.01), as shown in Table 2; for 1872–1975, r = 0.38 (p < 0.001); however, for 1976–2010, r = −0.36 (p = 0.04), which suggests a possible multidecadal transition of the AAO–PC2 relationship in the mid-1970s. Thus, it is important to identify further the stability of the possible teleconnection between the AAO and NH snow and the relationship between AAO and the EOF2 mode. Figure 4d gives the spatial distribution of the PS of correlations of SCF–AAO and Fig. 6a, b shows the stability analysis of the AAO–PC2 and AO–PC2 correlations, respectively, using the AWSC method. In Fig. 4d, if PS ≥ 50 % is the criterion for a stable correlation, the extent of SCF–AAO stable correlation is very small, but relatively large PS (e.g. PS > 30 %) is found over small areas of mid-eastern Asia and North America. Nevertheless, the distribution of large PS is basically consistent with those of the extremes of EOF2 and the SCF–AAO correlations. Moreover, stability analysis of AAO–PC2 correlation shows PS = 60.7 % (Fig. 6a), much larger than the PS of AAO–SCFN (12.9 %) (not shown), denoting a stable correlation relationship overall, although in fact the stable correlation mainly exists for sliding windows >50 years with pre-1970s start years. Therefore, based on the similarity of the spatial distributions and stability of correlation, the EOF2 mode is likely related to the AAO, especially before the 1970s.
Fig. 6

Same as Fig. 2, but a between I AAO and PC2 and b between I AO and PC2

However, regarding the AO and the EOF2 mode, although the AO–PC2 correlation is significant (r = −0.25), the PS of AO–PC2 correlation is only 36.3 % (Fig. 6b), much less than for AO–SCFN (70.6 %) (Fig. 2a), denoting an unstable correlation between AO and PC2. Furthermore, the spatial distribution of SCF–AO correlation (Fig. 3c) is obviously different from that of EOF2 (Fig. 4a).

Therefore, the correlation stability analysis suggests that the EOF1 mode of NH winter snow is the most stably correlated with AO, and second-most stably correlated with SH, and not correlated with AAO; the EOF2 mode is generally stably correlated with AAO especially for sliding windows >50 years and unstably correlated with AO and insignificantly correlated with SH.

Figure 7 shows maps of the variance of NH winter SCF and percentage of variance contributed by winter SCF regressed onto PC1 and PC2 in the real (total) winter SCF variance. The large variance shown in Fig. 7a over mid-latitude regions and most of Europe indicates large interannual variability in NH winter SCF. However, the SCF interannual variation in these regions is not uniform and is associated with different modes with certain specific foci. The large variability in Europe and Mongolia and North China corresponding to extremes in the EOF1 mode of Fig. 3a explains >30 % of the overall variance (Fig. 7b), but in contrast there is little explained variance in other regions, even in some regions with large overall variance (e.g. Middle Asia). There is >30 % explained variance in Fig. 7c within a strip of mid-latitude Asia and western America corresponding to extremes in the EOF2 mode of Fig. 4a. These results suggest that the EOF1 or EOF2 modes may explain >30 % of the interannual variance of winter SCF in some key regions with large interannual variability, but that they may not influence the other regions with small interannual variability.
Fig. 7

Maps of a variance of NH winter SCF and percentage of variance of regressed winter SCF onto the b PC1 and c PC2 in real SCF variance during the period 1872–2010

3.3 Identification of the relationship between NH major snow modes and atmospheric circulation patterns in winter

The above analysis statistically supports the hypothesis that the first leading mode of NH winter snow is most likely coupled with the AO in the NH and the second mode may be related to the AAO in the Southern Hemisphere. Xu and Dirmeyer (2013) have found that signals of strong snow–atmosphere coupling can propagate vertically into the troposphere (at least up to 500 hPa). Therefore, it is important to investigate further the relationships with the atmospheric circulation field by testing whether the NH winter circulation fields correlated with AO, SH, and AAO support the snow EOF1 or EOF2 modes. Figure 8 shows the correlations (colors) between the AO, SH, and AAO and 500-hPa geopotential height (Z500, hereafter) fields and vector resultants (arrows) of correlation between the indices and 500-hPa zonal (U500, hereafter) and meridional (V500, hereafter) wind. In order to ensure data independence, two datasets of geopotential height are used here: 20CR for 1872–2010 and NCEP/NCAR reanalysis for 1948–2010. It is found that the correlation distributions (Fig. 8a, b) over land between AO and Z500 for both datasets are very similar to the EOF1 (Fig. 3a), supporting the coupling between the AO and snow EOF1 mode. During strong positive AO winters, a strong polar vortex over the Arctic region (implied by the significant negative AO–Z500 correlation) extends southwards to form a pathway from Eurasia to northern Africa and the Atlantic as shown by the negative correlation distribution, where vector resultants (arrows) of correlation between AO and U500 and V500 generally show cyclonic shearing in favor of more snow. That is to say, snow and atmospheric circulation fields coherently match each other to support the consistent relationship between the EOF1 in the entire NH winter snow and the winter AO. However, note that the correlations between both the autumn (Peings et al. 2013) and winter (as shown in Fig. 3e of the present paper) snow in Siberia and the winter AO over the past 120 years are moderately variable. Therefore, we may combine the first snow mode and the AO to give the SNAO mode. Figure 3a, e together then represent its spatial pattern in terms of snow cover, and Fig. 8a, b represents its atmospheric pattern. PC1 and I AO denote the time coefficients of the SNAO mode in the snow and atmosphere, respectively. The SNAO mode has a key factor in snow (i.e., snow anomaly especially over Europe where there is high PS of snow–AO correlation and large explained variance of the EOF1 mode) and a crucial factor in the atmosphere (i.e., polar vortex anomaly), as does the sea surface temperature anomaly in Niño regions and trade wind anomaly in the ENSO mode.
Fig. 8

The correlations (colours) between (top) I AO, (middle) −I SH (here multiplied by −1 for comparison) and (bottom) I AAO and Z500 and vector resultants (arrows) of correlation between the indices and U500 and V500 (a positive correlation for zonal or meridional wind is denoted by an eastward or poleward arrow, respectively; equatorward and poleward arrows are white and black, respectively; for clarity one value is taken every three grids in zonal wind and every two grids in meridional wind, respectively). 20CR Z500 for 1872–2010 and NCEP/NCAR Z500 for 1948–2010 are used in the left and right panels, respectively. The deepest and the second deepest shadings are significant at 95 and 90 % confidence level, respectively

In addition, we find that the snow–AO relationship does not always depend on latitude. For example, the correlation (Fig. 3c) and its stability analysis between winter AO and the NH winter SCF (Fig. 3e) and the EOF1 of the NH winter SCF (Fig. 3a) all show that the relationship between the winter AO and winter snow is not uniform over the Eurasian continent at the same latitude. Therefore, snow over the Eurasian continent should not be regarded as a homogeneous whole when studying its variation. Consequently, the SNAO mode is not a zonal mode.

Figure 8c, d shows the maps of correlation between −SH and Z500 and vector resultants of the correlation between −SH and U500 and V500 (the correlations are reversed in sign for comparison). Both maps of the correlation between −SH and Z500 over land are also similar to the EOF1 except over northern Africa and a part of northern North America, while the vector resultants of the SH–wind correlations also generally support a distribution of snow anomalies similar to the EOF1. Furthermore, the more obvious negative correlation belt over western North America, seen particularly in Fig. 8d more than in Fig. 8a, suggests that the pathway is likely associated with the SH during the last 60 years. The result supports the role of the SH for western North America, as highlighted by Cohen and Saito (2003). Note that according to Fig. 3f, the impact of the SH on the majority of western North America is not very stable.

We find that the AAO–Z500 correlation maps (Fig. 8e, f) and the EOF2 (Fig. 4a) are roughly consistent over land, and the vector resultant fields of the AAO–wind correlations also tend to support a distribution of snow anomalies similar to EOF2. Although the physical mechanism for the possible influence of AAO on NH climate is not yet clear, we found that results from some studies probably support the result. For example, Wu et al. (2009) found that the EOF1 mode of winter air temperature variation over China is significantly correlated with the AO and the EOF2 mode is significantly correlated with the AAO. Wu et al. (2014) recently argued that the strong AAO has a potential influence on East Asian winter precipitation (less precipitation) through a South Atlantic–Pacific dipole (SAPD) sea surface temperature anomaly. The SAPD can influence the variability of the inter-tropical convergence zone (ITCZ) in the Pacific, and the ITCZ induces an atmospheric teleconnection pattern over the NH mid-latitudes associated with less precipitation (rainfall and snow) in most regions of China and western North America.

Overall, the correlations between AO, SH, and AAO and the NH winter height field generally support the foregoing statistical relationships. The EOF1 mode of NH winter snow and the winter AO may be regarded as another water (snow)–air coupled mode, the SNAO, which implies that its variability is likely more helpful for climate research and prediction than that of snow or the AO itself.

4 Relationships between winter and leading (SON) and lagging (MAM) atmospheric and snow modes

4.1 Autumn NH snow cover modes and their relationships with autumn atmospheric modes

It is clearly important to study the relationships between leading and lagging snow cover modes and winter atmospheric modes, and those between leading and lagging atmospheric modes and winter snow cover modes over the past 100 years. There is also the question of whether a snow cover mode coupled with AO or SH or AAO in autumn can be identified. Figure 9a–d shows the first four EOF modes of NH autumn SCF anomalies during the period 1872–2010. For comparison, Fig. 9e–g shows the correlation maps between AO, −SH, and AAO and SCF over each grid point of the NH land surface, respectively, during the same period. Table 3 shows the correlation coefficients for all possible pairs of the first four PCs in autumn and spring and the first two PCs in winter and AO, SH, and AAO indices in the three seasons.
Fig. 9

ad The first four EOF modes of NH autumn SCF anomalies during the period 1872–2010. Correlation maps between autumn e AO, f −SH and g AAO and autumn SCF over each grid point of NH land surface, respectively, during the same period

Table 3

Correlation coefficients between the first four PCs in autumn and spring and the first two PCs in winter and I AO, I SH and I AAO in the three seasons for each other for 1872–2010

Red and black values are significant and insignificant correlations, respectively. 0.17, 0.22 and 0.28 denote threshold values at the 95, 99 and 99.9 % confidence levels. The span of autumn series is from 1871 to 2009, and the spans of winter and spring are from 1872 to 2010

The autumn AO is better correlated with autumn PC3 (r = −0.36, p < 0.001) than with the other autumn PCs. The autumn −EOF3 (Fig. 9c) somewhat resembles the correlation map between autumn AO and SCF (Fig. 9e) and the winter EOF1 (Fig. 3a), and the correlation between autumn PC3 and winter PC1 is significant (r = −0.23, p < 0.01). This suggests that there could be a coupling between the snow EOF3 and the AO in autumn similar to the winter SNAO mode, but with a weaker coupling relationship.

The correlation between autumn SH and autumn PC1 is the only significant (r = −0.18, p = 0.04) correlation between autumn SH and the four autumn PCs. The autumn EOF1 (Fig. 9a) is similar to the correlation map between −SH and NH SCF in autumn (Fig. 9f). Therefore, the autumn SH is most closely related to the autumn snow EOF1 mode.

The autumn AAO is not significantly correlated with any of the four autumn PCs (Table 3), and the correlation map between autumn AAO and SCF (Fig. 9g) is not similar to any of the four EOFs in autumn (Fig. 9a–d). Therefore, the autumn AAO is not closely related to NH autumn snow variation. However, note that the autumn AAO has a close relationship with winter and even spring AAO (r = 0.46, 0.30, p < 0.001).

4.2 Relationships between winter and leading (SON) atmospheric and snow modes

Another important and interesting problem is whether winter atmospheric or snow modes can be influenced by leading autumn snow or atmospheric modes. The correlation maps between winter PC1, PC2, AO, −SH and −AAO and autumn NH SCF in Fig. 10 and the correlation coefficients between these winter factors and autumn atmospheric modes (see Table 3) are enlightening.
Fig. 10

Correlation maps between winter. a PC1, b PC2, c AO, d −SH and e −AAO and autumn SCF over each grid point of NH land surface, respectively, during the period 1872–2010

For the winter snow EOF1 mode, its principal component (winter PC1) is significantly correlated with autumn PC1, PC2, and PC3 (r = 0.24, −0.29, and −0.23, p < 0.01, respectively). The correlation map between winter PC1 and leading autumn SCF (Fig. 10a), which suggests a leading autumn snow spatial distribution associated with the winter EOF1 mode, is somewhat or partly similar to the autumn EOF1, −EOF2, and −EOF3 (Fig. 9a–c). However, the winter PC1 is not significantly correlated with leading autumn atmospheric modes (AO, SH, and AAO): the highest correlation is with autumn AO (r = 0.12, p = 0.17). This suggests that the winter snow EOF1 mode may have some relationship to the first three snow modes of the autumn, but that it is not very significantly influenced by leading autumn atmospheric modes (AO, SH, and AAO).

The winter PC2 is not significantly correlated with any of the four autumn PCs or the leading autumn atmospheric modes (AO, SH, and AAO) (Table 3), and the correlation map between winter PC2 and leading autumn SCF (Fig. 10b) does not resemble any of the four EOFs in autumn (Fig. 9a–d). Therefore, the winter snow EOF2 mode is not closely related to the snow or atmospheric modes in the leading (autumn) season.

The winter AO is not significantly correlated with any of the four autumn PCs or the leading autumn atmospheric modes (AO, SH, and AAO) (Table 3). The correlation map between winter AO and leading autumn SCF (Fig. 10c) shows that although the area with significant correlation is small, the correlations over the polar land region are generally positive and correlations to the south of it are generally negative, which is very similar to Fig. 10a. This indicates that in the leading autumn of a strong winter AO and PC1, there is more snow in polar regions and less snow to the south (40°N–60°N) than for a weak winter AO and PC1. This result shows some consistency with some previous studies (e.g. Cohen and Entekhabi 1999; Cohen and Jones 2011; Peings et al. 2013) that indicate a good negative-correlation relationship between autumn Eurasian snow and winter AO. However, the quasi-double-ring pattern in Fig. 10c cannot be found in the four autumn snow EOFs (Fig. 9a–d), but Fig. 10c is somewhat similar to the autumn −EOF3 (opposite-color Fig. 9c) and is similar to the autumn AO–SCF correlation map (Fig. 9e). This suggests that although the winter AO does not have a statistically significant linear relationship with any of the four autumn snow PCs and leading autumn atmospheric modes (AO, SH and AAO), it may still be related to the autumn EOF3.

For the winter SH, the correlation map between −SH and leading autumn SCF (Fig. 10d) is similar to the autumn EOF1 (Fig. 9a), and the absolute value of correlation between winter SH and autumn PC1 is higher (r = −0.27, p < 0.01) than for the other autumn PCs. This suggests that the winter SH is closely related to the leading autumn EOF1. Moreover, both of the correlations between the winter SH and autumn SH (r = 0.34, p < 0.001) and AO (r = −0.20, p < 0.05) are significant and the analysis above also indicates that autumn EOF1 is closely related to autumn SH. These results imply that the winter SH is influenced by the leading autumn snow EOF1 and atmospheric modes (SH and AO). The high correlations between winter and autumn SH and between winter SH and autumn and winter AO mean that the SH plays an important role in the interaction between snow and atmosphere from autumn to winter. The role is likely more notable than that of the AO. Therefore, although the SH and the AO in winter are coupled with the same snow EOF1 mode in winter, they likely correspond to two different modes in autumn.

For the winter AAO, the correlation with autumn PC2 is the only significant (r = −0.17, p = 0.05) correlation with any of the four autumn PCs. The correlation map between winter −AAO and NH autumn SCF (Fig. 10e) shows some similarity to the autumn snow EOF2 (Fig. 9b). This suggests that the winter AAO has some relationship with the leading autumn NH snow EOF2 mode. The analysis above also indicates that AAO has some relationship with NH snow EOF2 in boreal winter, but not in autumn. Therefore, the boreal winter AAO is related to both autumn and winter NH snow EOF2 modes, but in autumn the teleconnection relationship between the AAO and NH snow is not significant. Winter AAO is also significantly correlated with leading autumn AAO (r = 0.46, p < 0.001) and SH (r = −0.26, p < 0.01). These results suggest that when the NH snow anomaly distribution in autumn is similar to the autumn and winter EOF2 modes and the SH and AAO in autumn are anomalous, the boreal winter AAO in Southern Hemisphere should also be anomalous.

4.3 Spring NH snow cover modes and their relationships with spring atmospheric modes

Is there also a spring snow cover mode coupled with a spring atmospheric mode? Figure 11a–d shows the first four EOFs of NH spring SCF anomalies during the period 1872–2010 and Fig. 11e–g shows the correlation maps between spring −AO, SH, and −AAO and spring SCF during the same period.
Fig. 11

Same as Fig. 9, but for spring

The spring AO has a higher absolute value of correlation with spring PC3 (r = −0.36, p < 0.001) than with the other three spring PCs. The spring −EOF3 (Fig. 11c) is very similar to the winter EOF1 (Fig. 3a), suggesting it is likely a continuation of the latter. However, the correlation map between spring −AO and SCF (Fig. 11e) does not resemble any of the four spring EOFs and the area of significant correlation is small. Even so, there could be a coupling between the spring snow EOF3 and AO similar to the winter SNAO mode, but with a weaker coupling relationship.

The spring SH and spring snow PC3 and PC4 have correlation coefficients of 0.38 and 0.43, respectively. The correlation map between spring SH and SCF (Fig. 11f) is somewhat similar to spring EOF3 and EOF4 (Fig. 11c, d, respectively). This suggests that spring SH is also related to spring EOF3. Besides, spring SH is also significantly correlated with spring AO (r = −0.24, p < 0.01). Therefore, the correlations between spring EOF3 and AO and SH are consistent, similar to those between winter EOF1 and AO and SH.

Although the spring AAO is not significantly correlated with any of the four spring snow PCs (the absolute value of the correlation with PC2 is highest, r = −0.12, p < 0.17), the correlation map between spring −AAO and SCF (Fig. 11g) is similar to the spring EOF2 (Fig. 11b) and winter −EOF2 (opposite-color Fig. 4a). Therefore, the spring AAO is likely related to the spring EOF2, but the relationship is weaker than that between winter AAO and EOF2.

4.4 Relationships between winter and lagging (MAM) atmospheric and snow modes

Another important and interesting problem is whether winter atmospheric or snow modes could influence lagging spring snow cover modes. Figure 12 gives correlation maps between winter PC1, PC2, −AO, SH, and −AAO and spring NH SCF. We find that the extents of significant correlation between winter factors and spring snow in Fig. 12 are not only much larger than those between winter factors and autumn snow in Fig. 10 but also larger than those between spring factors and spring snow in Fig. 11e–g, suggesting that the snow–atmosphere relationship between winter and spring is stronger than that between autumn and winter, and spring snow can be influenced more by the preceding winter factors than by those of the concurrent spring.
Fig. 12

Same as Fig. 10, but between winter and spring

The winter PC1 is more highly correlated with spring PC3 (r = −0.42, p < 0.001) than with the other spring PCs, and is not significantly correlated with the spring AO, SH, and AAO. Both winter −EOF1 (opposite-color Fig. 3a) and the correlation map between winter PC1 and spring SCF (Fig. 12a) are very similar to the spring EOF3 (Fig. 11c). Therefore, the winter snow EOF1 mode is very likely related to the lagging spring snow EOF3 mode.

The winter PC2 is only significantly correlated with spring PC3 (r = 0.31, p < 0.001) and has no significant correlation with the other spring PCs or the AO, SH, and AAO (the correlations with spring PC1 and AAO are −0.16 and 0.16, respectively, p < 0.07). The correlation with spring PC3 is weaker than that between winter PC1 and spring PC3 (r = −0.42, p < 0.001) and winter AO and spring PC3 (r = −0.51, p < 0.001), suggesting that the spring EOF3 mode could be related to the winter EOF2 mode but is more likely related to the winter EOF1 and AO. Moreover, the correlation map between winter PC2 and spring SCF (Fig. 12b) does not resemble the spring EOF3 (Fig. 11c), but is similar to the spring EOF2 (Fig. 11b) and winter −EOF2 (opposite-color Fig. 4a). Therefore, the correlation analysis and the similarity analysis disagree; we are inclined to give more weight to the result of the similarity analysis.

For winter atmospheric modes, the correlation between winter AO and spring PC3 has a higher absolute value (r = −0.51, p < 0.001) than the correlations with the other three spring PCs, and even higher than that of the correlation between spring AO and PC3 (r = −0.36, p < 0.001). The correlation map between winter −AO and lagging spring SCF (Fig. 12c) resembles the spring EOF3 (Fig. 11c) and the correlation map between winter PC1 and spring SCF (Fig. 12a). The strong relationship between winter AO and spring snow is consistent with Saito et al. (2004), although they considered that the relationship appeared after the 1980s. Winter AO may also influence spring SH (r = −0.18, p < 0.05).

The correlation between winter SH and spring PC3 is also the highest (r = 0.40, p < 0.001) of the correlations with the four spring PCs, and also higher than the correlation between spring SH and PC3 (r = 0.38, p < 0.001). The correlation map between winter SH and lagging spring SCF (Fig. 12d) also resembles the spring EOF3 (Fig. 11c). This suggests that the spring EOF3 mode is likely influenced by both leading winter AO and SH and is likely a continuation of the winter SNAO mode. Winter SH may also influence the spring SH (r = 0.31, p < 0.001).

For winter AAO, the correlation with spring PC2 is the only significant (r = −0.24, p < 0.01) correlation with any of the four spring PCs. The correlation map between winter −AAO and lagging spring SCF (Fig. 12e) resembles the spring EOF2 (Fig. 11b) and the correlation map between spring −AAO and spring SCF (Fig. 11g). This suggests that in both winter and spring, the AAO is closely related to the NH snow EOF2 mode. There are also significant correlations between winter AAO and autumn and spring AAO (r = 0.46, 0.47, p < 0.001), and even between autumn and spring AAO (r = 0.30, p < 0.001), which implies that the AAO signal from the Southern Hemisphere has a strong persistence in the NH.

Overall, based on statistical significance and the similarity of correlation maps, for interactions between snow and atmosphere in the same season, winter interactions are strongest (maximum r = 0.56) and steadiest (maximum PS = 92.8 %) and there is one coupled mode (the SNAO mode) linking the AO, SH and snow EOF1 and another coupled mode linking the AAO and snow EOF2. Spring interactions are second strongest and there is a coupled mode linking the AO, SH and snow EOF3 and another coupled mode between the AAO and snow EOF2, both of which are likely the successors of winter coupled modes. In autumn, the interactions are complicated, and there can be two coupled modes both related to the winter SNAO mode: the mode between AO and snow EOF3 and the other mode between SH and snow EOF1. These two modes are independent of each other. The autumn AAO is not correlated with any of the first four autumn snow EOFs.

For snow–atmosphere interactions in different seasons, previous studies linking autumn snow and the winter AO have used indices of areal extent and are limited to the month of October (e.g. Cohen et al. 2001; Allen and Zender 2011a; Cohen and Jones 2011; Peings et al. 2013). In contrast, the present study uses the PCs of snow cover and is not limited to October. Our analysis shows that the snow–atmosphere interactions between two different seasons have the following features: the winter AO is not related to the first four PCs of snow cover or the indices of the atmospheric modes in the leading autumn, but is related to lagging spring snow EOF3 and SH; the winter SH is not only related to leading autumn snow EOF1 and atmospheric modes (SH and AO), but also to lagging spring snow EOF3; the winter AAO is related to leading autumn, winter and lagging spring snow EOF2; the winter snow EOF1 is not related to leading autumn and lagging spring atmospheric modes, but is related to the leading autumn first three snow modes and lagging spring snow EOF3; the winter snow EOF2 is generally not related to the leading autumn and lagging spring first four snow modes and atmospheric modes, but is somewhat related to lagging spring snow EOF2 and AAO. No clear evidence has been found in this study for the first two modes of snow cover influencing the atmospheric circulation from winter to spring, which is consistent with Saito et al. (2004).

5 Discussion and conclusions

We have studied NH snow variability modes during the last 139 years and identified the snow–atmosphere coupling modes in the NH and some relationships between them and the snow and atmosphere in leading and lagging seasons. First we have shown that in winter the NH snow EOF1 mode and the AO and the SH together form a stable snow–atmosphere coupled mode, the SNAO, and that the coupling relationship in winter is strongest, which is somewhat analogous to the ocean–atmosphere coupled mode ENSO that also usually peaks in winter. Second, in general, the continuity and transitivity of signals in the SNAO between autumn and winter are weaker than those between winter and spring, which is different from the behavior of ENSO. For example, the winter AO is not related to any of the leading autumn first four EOFs, but is obviously related to lagging spring EOF3 (r = −0.51), which supports the conclusions of Bamzai (2002). Third, the AAO signal from the Southern Hemisphere has a strong continuity and transitivity in season transition and is closely related to the boreal snow EOF2 mode. The time continuity and spatial propagation may be related to persistence of the SAPD sea surface temperature anomaly associated with the AAO. Less snow in Eurasian mid-latitudes and western North America in the snow EOF2 mode may be related to a series of changes in the AAO, SAPD, and ITCZ. This topic will be examined further in a future study.

Allen and Zender (2011b) indicate that Eurasian snow cover has helped force the observed AO trends during the recent decades. Our results demonstrate that the winter SCF first mode for the whole NH land surface has always been closely related to the AO variations over the past 139 years. The mode has an uneven spatial distribution in Eurasia and North America. The stability analysis also indicates that the winter EOF1–AO relationship (i.e., the SNAO mode) is stronger after the 1960s than before, which contributes to the increasing trend of the AO from the late 1960s to early 1990s and the following decreasing trend.

The snow–atmosphere relationships for different seasons are complicated. However, if the correlated atmospheric and snow modes of the same season are regarded as a whole like ENSO, based on the correlations between snow and atmosphere shown in Table 3 and the analysis in the present paper, the relationships between snow and atmospheric modes between different seasons can be summarized as Fig. 13. The snow–atmosphere relationship between autumn and winter is messier than that between winter and spring. We can deduce roughly from Fig. 13 that there is likely a succession relation between snow autumn EOF3, winter EOF1 and spring EOF3 (associated with the SNAO mode), and between autumn, winter and spring EOF2s (associated with the AAO). However, mechanisms for the two snow–atmosphere coupling processes are unclear. The identification of the connection between SNAO modes of different seasons and the investigation of features on different time scales are subjects for future research.
Fig. 13

Schematic diagram of changes of the seasonal relationships between atmospheric modes (AO, AAO and SH) and boreal snow cover modes, if the correlative atmospheric and snow modes in the same season are regarded as a whole. Arrows denote significant relations. Thick frames denote that there are likely snow–atmosphere coupling among the factors and associated with winter PC1 or PC2. Double-headed arrows denote significant concurrent relations in the same season. Single headed arrows with shading denote that there are one or more significant lead-lag relations between any two factors in two thick frames of two different seasons. Thick and thin solid arrows denote that confidence levels of correlations are >99 % and between 95 and 99 %, respectively. Dashed arrows denote confidence level between 90 and 95 % or a possible relationship according to foregoing analysis. Red and blue arrows denote the relationships between the factors only related to winter PC1 and PC2, respectively; green (black) arrows denote the relationships between the factors related to both (neither) winter PC1 and (nor) PC2. The correlation relationships between autumn and spring are not shown

However, if the atmospheric modes and snow modes are considered independently and all the modes considered in a season are attributed to these two types, the seasonal relationships of the covariability between snow and atmospheric modes during the period 1872–2010 can be summarized schematically as Fig. 14. In autumn, winter and spring, there are significant concurrent relations between all atmospheric and snow modes. However, the relations between the two different modes in two different seasons are not always significant. Significant relationships exist between autumn snow modes and winter atmospheric or snow modes, between winter atmospheric modes and spring atmospheric or snow modes, and between winter and spring snow modes. That is to say, autumn snow can influence winter atmosphere and snow; winter atmosphere can influence spring atmosphere and snow. It can be also seen that the continuity and transitivity of snow signals between two seasons are generally stronger than those of the atmosphere.
Fig. 14

Schematic diagram of changes of the seasonal relationships in the covariability between atmospheric modes (AO, AAO and SH) and boreal snow cover modes during the period of 1872–2010, if the atmospheric modes and snow modes are considered independently. Arrows denote significant relation. Double-headed (single headed) arrows denote significant concurrent (lagging) relation

Notes

Acknowledgement

Support for the Twentieth Century Reanalysis Project data set is provided by the U.S. Department of Energy, the Office of Science Innovative and Novel Computational Impact on Theory and Experiment (DOE INCITE) program, and the Office of Biological and Environmental Research (BER), as well as by the National Oceanic and Atmospheric Administration Climate Program Office. We thank Jianping Li for the AO and AAO index data. This research was supported by the National Basic Research Program of China (2012CB957800 and 2012CB417205), the National Natural Science Foundation of China (41305131, 41375105 and 41405146), and the China Special Fund for Meteorological Research in the Public Interest (GYHY201406001 and GYHY201406020).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Liang Zhao
    • 1
    • 2
  • Yuxiang Zhu
    • 2
  • Haiwen Liu
    • 3
  • Zhongfang Liu
    • 4
  • Yanju Liu
    • 5
  • Xiuping Li
    • 6
  • Zhou Chen
    • 7
  1. 1.61741 TroopsBeijingChina
  2. 2.CMA Training CenterChina Meteorological AdministrationBeijingChina
  3. 3.College of Atmospheric Sciences, Plateau Atmosphere and Environment Key Laboratory of Sichuan ProvinceChengdu University of Information TechnologyChengduChina
  4. 4.State Key Laboratory of Marine GeologyTongji UniversityShanghaiChina
  5. 5.National Climate CenterBeijingChina
  6. 6.Key Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau ResearchChinese Academy of SciencesBeijingChina
  7. 7.Institute of Space Science and TechnologyNanchang UniversityNanchangChina

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