Physical mechanisms of European winter snow cover variability and its relationship to the NAO

Transcription

1 Clim Dyn DOI 0.007/s Physical mechanisms of European winter snow cover variability and its relationship to the NAO Yoojin Kim Kwang-Yul Kim Baek-Min Kim Received: 9 January 0 / Accepted: April 0 Ó Springer-Verlag 0 Abstract Annual snow cover in the Northern Hemisphere has decreased in the past two decades, an effect associated with global warming. The regional scale changes of snow cover during winter, however, vary significantly from one region to another. In the present study, snow cover variability over Europe and its connection to other atmospheric variables was investigated using Cyclostationary Empirical Orthogonal Function (CSEOF) analysis. The evolution of atmospheric variables related to each CSEOF mode of snow cover variability was derived via regression analysis in CSEOF space. CSEOF analysis clearly shows that the North Atlantic Oscillation (NAO) is related to European snow cover, particularly in January and February. A negative NAO phase tends to result in a snow cover increases, whereas a positive NAO phase results in snow cover decreases. The temporal changes in the connection between the NAO and European snow cover are explained by time-dependent NAO-related temperature anomalies. If the NAO phase is negative, the temperature is lower in Europe and snow cover increases; by contrast, when the NAO phase is positive, the temperature is higher and snow cover decreases. Temperature and snow cover variations in Europe are associated with the thermal advection by anomalous wind by NAO. CSEOF analysis also shows an abrupt increase of snow cover in December and January and a decrease in February and March since Y. Kim K.-Y. Kim (&) School of Earth and Environmental Sciences, Seoul National University, Gwanangno, Gwanak-gu, Seoul 5-747, Republic of Korea kwang56@snu.ac.kr B.-M. Kim Korea Polar Research Institute, Gaetbeol-ro, Yeonsu-gu, Incheon , Republic of Korea the year 000, approximately. This abrupt change is associated with sub-seasonal variations of atmospheric circulation in the study region. Keywords Snow cover Europe climate NAO CSEOF Winter climate Introduction Averaged annual snow cover in the Northern Hemisphere appears to be gradually decreasing as a result of global warming (Déry and Brown 007; Brown and Mote 009). This negative trend is statistically robust, but the variability of snow cover shows diverse seasonal and regional patterns. A decrease in snow-covered areas is conspicuous in mountainous regions during summer and spring. Snowcovered areas during autumn and winter, however, appear not to have significantly declined; they have even slightly increased (Déry and Brown 007; Robinson and Frei 000). In the midst of global warming, the winter of saw severe snowfalls and extreme cold temperatures in the central United States, northwestern Europe and East Asia (Seager et al. 00; Cohen et al. 00). The local impact of snow cover on atmospheric temperatures has been discussed in the context of the cooling effects that snow cover exerts: positive feedback between snow cover and solar radiation due to the increased albedo, the absorption of latent heat by snow melting and sublimation, and the low thermal conductivity of the snowpack (Cohen and Entekhabi 999; Gong et al. 00, 007; Déry and Brown 007; Groisman et al. 994a, b; Clark et al. 999; Clark and Serreze 000). These local cooling effects, in turn, have been suggested to play a significant role in global-scale climate dynamics (Barnett et al. 988, 989).

2 Y. Kim et al. For example, autumn and early winter snow cover conditions on the Eurasian continent strongly influence subsequent winter climates in the Northern Hemisphere by triggering the Arctic Oscillation (Saito et al. 00; Gong et al. 00, 004, 007; Cohen et al. 00). It should be cautioned, however, that operational centers have not yet realized the predictability gain from this remote impact. As a dominant winter climate pattern over the Atlantic Ocean and Europe, the North Atlantic Oscillation (NAO) is known to influence snow cover: a negative NAO index is associated with an expansion of snow cover in Europe and vice versa (Henderson and Leathers 00; Clark et al. 999). The unusually heavy snowfall in Europe during the 009/00 winter appeared to be triggered by a negative phase of the NAO and, to a much lesser extent, a positive phase of the El Niño Southern Oscillation (Seager et al. 00). Most studies on the NAO connection with snow cover variability assume that the impact of NAO is persistent throughout the winter. This connection may not necessarily be invariant throughout the winter. Previous research has focused on snow cover variability over Europe at the regional level (Falarz 004; Laternser and Schneebeli 00; Brown and Petkova 007). Some studies focused on the interannual variation of snow cover and its cause (Henderson and Leathers 00; Clark et al. 999). Apparently, sub-seasonal and sub-monthly evolution of snow cover needs to be understood more clearly. Also, little attention has been given to snow cover variability on decadal and longer time scales. In the present study, Cyclostationary EOF (CSEOF) analysis is conducted to extract individual modes of snow cover variability in Europe with distinct physical mechanisms and time scales. To explain the physical mechanism associated with each mode of snow cover variability, atmospheric conditions over Europe are examined simultaneously. The influence of the NAO is also investigated in association with the snow cover variability in Europe on sub-seasonal as well as interannual time scales. The present study extends the previous work on the NAO connection with the snow cover variability in Europe by providing a detailed physical explanation on how the altered background physical conditions by the NAO affect the snow cover. Data used in this study are described in Sect., with CSEOF analysis as the main tool for analyzing temporal evolution of variability. The multiple regression technique in CSEOF space, which is used to find physically consistent evolution of atmospheric variables with the CSEOF modes of snow cover variability, is also explained in Sect.. The seasonal cycle of snow cover and the characteristics of the corresponding atmospheric variability are shown in Sect.. The second mode of snow cover, together with the related atmospheric mechanism, is explained in Sect. 4, in conjunction with its connection to the NAO. Finally, the third mode of snow cover variability, related to the longterm variation is described in Sect. 5. Discussions and concluding remarks are presented in Sect. 6. Data and methods The primary data used in the present study are measures of snow cover over Europe as derived from weekly National Oceanic and Atmospheric Administration (NOAA) snow cover charts. The data were produced from manual interpretations of visible satellite imagery as described in (Robinson et al. 99). Next, the resulting data were digitized on an array on a polar stereographic projection in the Northern Hemisphere with the cell size ranging from 6,000 to 4,000 km. Each cell returns the value of if at least 50 % of it is covered with snow; otherwise, the cell is assumed to be snow free ( 0 ). The accuracy of the snow cover data diminishes in areas with persistent cloud cover and over the Tibetan plateau, where snow cover often resembles cloud cover. Although the accuracy is somewhat insufficient in certain regions, continental-scale snow cover patterns are reliable for conducting climate-related studies (Brown 000). The dataset represents the longest and most consistent continental-scale observations of snow cover, spanning 7 years (97/ /00). Although snowfall and snow water equivalent are better quantities in describing the amount of snow, they have limited availability in time and space. The physical target area analyzed in the current study is located between 0 W to60 E and 0 N to80 N, with a time span of sixteen weeks (from December to March) each year. Sixteen weeks of data are extracted from December to March for each year. The first day of the weekly snow cover data employed in this study varies each year and shifts by as much as 7 days. The staggering of the first day, however, exerts little impact on the result of the analysis since the evolution of snow cover is slow. Therefore, no interpolation was attempted to align the first week in the present study. Other atmospheric variables are obtained from the NCEP/NCAR reanalysis dataset (Kalnay et al. 996) for the same period of time (97/ /00). The weekly averaged geopotential height, zonal and meridional winds, and air temperatures from 90 W to90 E and from 0 N to85 N are used to study the physical mechanisms of snow cover variations. The snow cover data are decomposed into individual modes via CSEOF analysis (Kim et al. 996; Kim and North 997; Na et al. 00) to investigate the physical mechanisms of snow cover variability. In CSEOF analysis, space time variables, Vr; ð tþ, are decomposed as follows:

3 Physical mechanisms of European winter snow cover Vr; ð tþ ¼ X n B n ðr; tþt n ðtþ; ðþ where B n ðr; tþ are CSEOF loading vectors (CSLV) and T n ðtþ are corresponding PC time series. Each CSLV shows a distinct physical evolution modulated by the corresponding PC time series, which is different from EOF spatial patterns (loading vectors). CSLVs repeat with a nested period d: B n ðr; tþ ¼ B n ðr; t þ dþ: ðþ For the snow cover data, each year consists of sixteen weeks of winter (i.e., d = 6 weeks). Similarly, d = 6 weeks (or, = days) for all the variables analyzed in this study. A multiple regression analysis is conducted in CSEOF space to derive the physically consistent relationships between snow cover and other physical variables. Once all physical variables are decomposed into CSEOF modes: Pr; ð tþ ¼ X n C n ðr; tþp n ðtþ; ðþ (a) snow mean (b) snow std where the resulting PC time series, P n ðtþ; are used for regression analysis. The PC time series of a predictor variable (e.g., air temperature) are regressed on a time series of target (i.e., snow cover): T n ðþ¼ t XM m P mðþþeðtþ; t m¼ ð4þ where m are the regression coefficients, and eðtþ is regression error. The first 0 PC time series of predictor variables are used throughout the study (M = 0). Next, using the regression coefficients, m, regressed CSLVs of the predictor variable, R n ðr; tþ, are obtained as in Eq. (5): R n ðr; tþ ¼ XM m C mðr; tþ; ð5þ m¼ where C m ðr; tþ are the CSLVs of the predictor variable. As a result of regression analysis in CSEOF space (Eqs. (4) and (5)), the predictor variable can be rewritten as: Pr; ð tþ ¼ X n R n ðr; tþt n ðþ: t ð6þ Aside from small regression error, Eq. (6) can be rewritten with the aid of Eqs. (4) and (5) as Pðr; tþ ¼ X n ¼ X k ¼ X k X k X l k C k ðr; tþ X l C k ðr; tþp l ðþ t X n l P l ðþ t k l X C k ðr; tþp l ðtþd kl ¼ X l k C k ðr; tþp k ðtþ; ð7þ where the last line is obtained by utilizing the orthonormality of the regression coefficients: X k l ¼ d kl : ð8þ n (c) snow climatology Dec Jan Feb Mar week Fig. Winter (December March) climatology of the European snow cover: a mean snow cover, b standard deviation from the winter mean, and c domain averaged climatology. Thick black lines designate 0. and 0.9 contours in a snow cover denotes the decimal areal fraction in each grid box ranging from 0 to in a

4 Y. Kim et al PC time series of CSEOF mode Year Fig. The first CSEOF mode of snow cover: PC time series and CSLV, B ðr; tþ. This mode represents the seasonal cycle. The CSLV denotes the spatial patterns for the sixteen weeks from December The regressed patterns, R n ðr; tþ, of the predictor variables depict how the physical variables evolve in tandem with snow cover and help explain how snow cover and atmospheric circulation affect each other. through March, and the PC time series describes the amplitude of the seasonal cycle from December 97 through March 00. Thick black lines designate values of 0. and 0.9 The seasonal cycle of snow cover The means and standard deviations of European snow cover are depicted in Fig. a, b: the depicted distribution

5 Physical mechanisms of European winter snow cover (a) (b) (c) (d) Fig. CSLVs of,000 hpa temperature ( C) and 850 hpa wind vector (m s - ) regressed on the seasonal cycle of snow cover and averaged for each month: a December, b January, c February, and d March. Thick red lines designate the -5 and 5 C contours denotes the snow fraction in each grid box. The mean in Fig. a and the standard deviation in Fig. b of the European winter snow cover indicate the primary origin of the variability of snow cover. As expected, the standard deviation from the winter mean (Fig. b) is large in regions of transient snow cover because of seasonal fluctuations of snow cover in winter. This region is also called the active region, as will be explained in more detail below. The climatology of snow cover, averaged over Europe, is plotted in Fig. c. Snow cover increases until mid-winter, with the maximum cover occurring in the first week of February, and then decreases until the end of March. Figure shows the first CSEOF mode of European snow cover, which explains approximately 90 % of the total variance. The PC time series of the first mode (top panel) and the CSLV during the sixteen weeks from December to March are presented in Fig.. This mode denotes the seasonal cycle. The CSLV depicts slowly varying snow cover throughout the winter. The corresponding PC time series exhibits inter-annual and decadal variations of the seasonal cycle; the amplitude of the seasonal cycle fluctuates by approximately 5 % on inter-annual time scales. The seasonal cycle appears to be fairly stable, with amplitude fluctuations of approximately 5 % of the mean only. Much of the area north of 50 N is nearly 00 % covered with snow throughout the winter season. Areas covered with 0 90 % snow show noticeable variation in snow cover during the winter. Partial snow cover is found from the southwest of Russia to the Mediterranean Sea. The spatial average of the CSLV over Europe domain, as expected, exhibits a similar trend to that in Fig. c, with a general increase in snow cover until the first week of February and a decrease afterward. Multiple regression analysis is conducted to examine the variation of atmospheric variables in association with the first CSEOF (the seasonal cycle) of snow cover. The regressed patterns of low-level temperature and wind added to the respective winter mean fields are averaged for each month to depict their monthly evolution (Fig. ). Temperatures at,000 hpa range from about -5to5 C in Europe. The continental region becomes gradually colder toward the east because of the continental effect. At the eastern side of the Atlantic Ocean, temperatures are higher than the western part because the low-level southwesterly winds carry

6 Y. Kim et al. PC time series of CSEOF mode Year December (-4) January (5-8) February (9-) March (-6) Fig. 4 The second CSEOF mode, B ðr; tþ, and the corresponding PC time series of the snow cover anomalies in Europe. Shown here are the monthly averaged patterns warm air toward the eastern part of the Atlantic. The prevailing southwesterly wind is strongest in mid-winter because of the strong meridional pressure gradient and the land ocean pressure contrast arising from differential cooling of land and ocean. Temperatures decrease from December to January and then increase in February and March. The temperature patterns should be interpreted as a necessary but not sufficient condition for the formation of snow cover. The intra-seasonal variations of temperature and wind are small throughout the winter season. The evolution of the snow-covered region in Fig. is strongly affected by the temperature distribution shown in Fig.. The transient region, where snow cover is between 0. and 0.9, lies between approximately -5 and 5 C (thick red lines in Fig. ). The snow cover area between 0. and 0.9 in winter is defined as the transition or active region; snow cover in this area is sensitive to temperature changes (Clark et al. 999; Brown and Mote 009). This suggests that the primary condition for the formation of snow cover is temperatures under the threshold value of

7 Physical mechanisms of European winter snow cover (a) (b) (c) Fig. 5 Regressed atmospheric fields to the second CSEOF mode of snow cover variability. Shown here are the patterns averaged for January March, which is the period of increased snow cover over the transition region: anomalies of a,000 hpa temperature ( C), b 850 hpa geopotential height (shaded; m) and wind vectors (arrows; ms - ), and c 850 hpa thermal advection (0-6 Cs - ) approximately 5 C. The transition region moves primarily in the meridional direction according to sub-seasonal variations in temperature. The southeastern region of the Black Sea is covered with more snow than other regions of the same temperature due to sea-effect snow (Kindap 00). 4 Snow cover variation and its relationship to the NAO The second mode shown in Fig. 4 explains 5 % of the total variance after omitting the seasonal cycle (the first CSEOF). When the PC is positive, snow cover over Europe diminishes in December and then increases over Europe, centered at approximately 50 N until the end of March. Note that the CSLV depicted in Fig. 4 shows that the snow cover anomaly is primarily located in the region bounded by -5 and 5 C isotherms in the transition snow cover region (Figs., ). Thus, the second mode indicates, when the PC is positive, slightly less snow cover in much of Europe in December and relatively large snow cover increases from January to March over Europe. According to the PC time series and the CSLV, the range of snow cover variation is approximately (-0.4, ) for the second CSEOF mode. Multiple regression analysis is conducted on the second mode of snow cover as described in (4) and (5) above. The January March average pattern of the resulting regressed,000 hpa air temperature is given in Fig. 5a and those of the 850 hpa geopotential height and wind are given in Fig. 5b. The regressed temperature shows that colder temperatures in Europe are associated with increased snow cover in the transition region. The strongest snow cover increase in the second mode occurs in February; the,000 hpa air temperatures at this time are decreased by approximately 5 C in Europe, according to the average amplitude of the PC time series. The distribution of the temperature anomaly, in turn, seems to be related to wind anomaly patterns, which are shown in Fig. 5b with the geopotential height anomaly field at 850 hpa; these are also the January-March average patterns. In the mid-latitudes (approximately 50 N), westerlies are dominant during winter (see Fig. ), whereas relative easterlies develop from January through March (Fig. 5b). The magnitude of the wind anomalies is only about /5 of the magnitude of the mean winds in winter. Thus, the primary direction of winds does not change, while the magnitude is weakened in association with the second mode with positive amplitude. This implies that advection from the warm ocean decreases when the PC time series is positive, resulting in an increase in snow cover. To examine the anomalous thermal advection more closely, it is divided into three terms as in Wang et al. (00) aside from other sources of heating: ot 0 ot ¼ u 0 ot ot ot ot ot ot v0 u v u0 v0 ox oy ox oy ox oy ; ð9þ where the first two terms on the right-hand side represent the advection of mean temperature by anomalous wind, the next two terms the advection of anomalous temperature by mean wind, and the last two terms the nonlinear eddy term. The sum of the three advection terms, averaged from January to March, is shown in Fig. 5c. The advection of mean temperature by anomalous zonal wind is the largest

8 Y. Kim et al. (a) (b) T mode (c) U mode Longitude Longitude Snow mode Longitude 6 Dec Jan Feb Mar Month Fig. 6 Longitude-time plots of a zonal wind (m s - ) anomalies at 850 hpa, b temperature ( C) anomalies at,000 hpa, and c snow cover anomalies for the second mode in mid-latitude Europe. Shown (a) (b) Fig. 7 Anomalies of a,000 hpa temperature ( C), and b 850 hpa geopotential height (m) and wind vectors (m s - ) regressed on the negative (multiplied by -) NAO index. They represent the atmospheric conditions for the negative phase of the NAO here are the averages in the latitude band of N for temperature and zonal wind, and in the band of N for snow cover contribution to the thermal advection. This indicates that advection of warm air from the Atlantic Ocean is an important source of temperature variability in Europe. During the positive phase of the second CSEOF mode, temperature advection over the western and the northern Europe is negative (Fig. 5c) and is consistent with the temperature anomalies (Fig. 5a). It appears that geopotential height anomalies are connected to temperature anomalies, particularly on the western side of Europe. This implies that temperature anomalies associated with the second mode may exert some influence on the direction and magnitude of wind anomalies over western Europe. These connections among zonal wind anomalies, temperature anomalies and snow cover anomalies are clearly depicted in Fig. 6, which shows the longitude-time plot of anomalies between N for each variable. Along the mid-latitude area of Europe, positive snow cover anomalies are related to negative zonal wind anomalies and negative temperature anomalies, whereas negative snow cover anomalies are related to positive zonal wind anomalies and positive temperature anomalies. The patterns of atmospheric variables regressed on the NAO index, as in conventional methods, are shown in Fig. 7. The negative phase of the NAO is associated with cooling in Europe and warming in Greenland and with higher pressure at high latitudes (e.g., north of 50 N) over the Atlantic Ocean and lower pressure at low latitudes (e.g., south of 50 N). These patterns closely resemble the regressed patterns on the second mode of snow cover in

9 Physical mechanisms of European winter snow cover Correlation Coeff (a) T000 of NAO vs. snow nd mode Dec Jan Feb Mar Correlation Coeff (b) H850 of NAO vs. snow nd mode Dec Jan Feb Mar Fig. 8 Pattern correlation coefficients between a,000 hpa temperature anomalies, and b 850 hpa geopotential height anomalies of the second CSEOF mode of snow cover and the NAO patterns Fig. 5, suggesting that the increased snow cover in Europe from January through March shown in Fig. 4 is related to the negative phase of the NAO. Correlations between the NAO patterns in Fig. 7 and the temperature and the geopotential height anomalies of the second mode are calculated in Fig. 8. The weekly patterns of temperature and geopotential height anomalies for the second mode were compared with the NAO-regressed patterns in Fig. 7. There are significant negative correlations between the NAO patterns and those of the second mode; the spatial patterns of the second mode are similar to the negative NAO patterns from the fourth through the twelfth week (January February). The association between the NAO and European snow cover can also be established via regression analysis in CSEOF space of snow cover with the NAO index as the target time series. The spatial patterns of the regressed snow cover are similar to those of the second mode in Fig. 4, except for the opposite signs (figure not shown). This indicates that the snow cover variability for the second CSEOF mode is negatively correlated with NAO climate patterns. In fact, the correlation between the monthly averaged PC time series of the second mode and the NAO index is -0.5 for January and February. 5 Abrupt shift in snow cover variability in the late 990s The third mode of snow cover explains *9 % of the total variance, apart from the seasonal cycle. The CSLV and the PC time series of the third mode are shown in Fig. 9. Snow cover is anomalously positive during December and January, and negative in March when this mode is positive in amplitude. This implies that snow cover expands in early to mid-winter and retreats in early spring. According to the PC time series and the CSLV, the maximum snow cover change is about ± in the third mode. The PC time series shows a positive phase shift of the third mode after 000. Compared with the years before 000, recent snow cover in December and January tends to be more extensive; it decreases slightly in February and March. The corresponding PC time series exhibits a linear trend of 57 year -, which is significant at a 95 % level but is not conspicuous in the midst of stronger natural variability. The phase shift reflects the snow cover difference between the 000s and the 970s although this mode alone does not explain the observed difference fully. It can be inferred from Fig. 9 and confirmed from snow cover observations that the snow cover has decreased in the mean sense in

10 Y. Kim et al PC time series of CSEOF mode Year December (-4) January (5-8) February (9-) March (-6) Fig. 9 The third CSEOF mode, B ðr; tþ, and the corresponding PC time series of the snow cover anomalies in Europe. Shown here are the monthly averaged patterns. This mode includes an abrupt transition of snow cover in 000 February and March and has increased in December and January particularly in eastern Europe. As seen in the previous analysis, low-level temperatures, geopotential height, and wind vectors are regressed on the third mode of snow cover. During the period of snow cover expansion (5th 8th weeks), temperature anomalies, geopotential height and wind anomalies are shown in Fig. 0a, c. Positive anomalies of snow cover are related to decreased temperatures and zonal winds in the European region. The resulting temperature, geopotential height and wind anomaly patterns are quite different from those of the second mode. The degree of cooling is weaker than that of the second mode over Europe, whereas the warming over the Barents Sea and the northern part of Scandinavia is stronger than that of the second mode. The geopotential height over the northern Atlantic Ocean shows weaker meridional gradients than the second mode and is tilted in a northeast-southwest direction. During the period of snow cover retreat (th 6th weeks), regressed maps of temperature, geopotential height and wind anomalies show similar patterns over Europe, with the sign

11 Physical mechanisms of European winter snow cover (a) (b) (c) (d) (e) (f) Fig. 0 Atmospheric fields regressed to the third CSEOF mode: anomalies of a, b,000 hpa temperature ( C); c, d 850 hpa geopotential height (shaded; m) and wind vectors (arrow; ms - ); e, f 850 hpa thermal advection (0-6 Cs - ) averaged over 5th 8th reversed from that of the expansion period (Fig. 0b, d). Figure 0e, f illustrate the sum of all the thermal advection terms in Eq. (9) during the periods of positive and negative snow cover anomalies, respectively. As can be seen, temperature anomaly patterns are reasonably similar to those of thermal advection over Europe. As in the second mode, advection of mean temperature by anomalous wind contributes most significantly to the temperature change and the resulting snow cover variation in Europe. Physical relationships among the key atmospheric variables for the third mode are illustrated in Fig.. Similar to the second mode, increased snow cover is related to weaker zonal wind and colder temperatures, and decreased snow cover is related to stronger zonal winds and warmer temperatures. The sign reversal during winter is clear; the positive phase of the third mode is associated weeks of winter (left column) and th 6th weeks (right column). Left column is consistent with the period of increased snow cover and right column the period of decreased snow cover with more snow from December to January and less snow in February and March. 6 Discussion and concluding remarks The physical relationships between snow cover in the European region and key atmospheric variables during winter are investigated via CSEOF analysis. The first three modes of snow cover variability are analyzed in the current study. The first mode represents the seasonal cycle and explains approximately 90 % of snow cover variability. In the European region, snow cover extends from southern Russia to Spain. By the end of January, Europe is fully covered with snow north of 50 N. The seasonal cycle of snow cover is sensitive to low-level temperatures, the

12 Y. Kim et al. (a) U mode (b) T mode (c) Snow mode Dec Jan Feb Mar Longitude Longitude Longitude Month Fig. Longitude-time plots of a zonal wind (m s - ) anomalies at 850 hpa, b temperature ( C) anomalies at,000 hpa, and c snow cover anomalies for the third mode in mid-latitude Europe. Shown distribution of which closely follows latitude and continentality. The transition region, where snow cover varies from 0 to 90 % in winter, approximately matches the region with temperatures between -5 and 5 C in Europe. This area slowly changes from December to March, and the seasonal cycle of snow cover is reasonably consistent with this change. The second mode represents deviations from snow cover climatology and explains 5 % of the total variance apart from the seasonal cycle. The second mode shows strong fluctuations of snow cover in the northern part of central Europe, where the standard deviation from snow cover climatology is large. Specifically, a positive phase of this mode shows snow cover decreasing in December and increasing from January to March. The variation of snow cover associated with the second mode is strongly linked to temperature anomalies following the variation of mean temperature advection by anomalous wind from the warm Atlantic Ocean in the lower troposphere. Negative zonal wind anomalies are associated with lower temperatures and increasing snow cover, whereas positive zonal wind anomalies are associated with higher temperatures and decreasing snow cover. If the average temperature in Europe falls by approximately C, snow cover expands by up to 0. (0 %). The NAO, a dominant low-frequency climate pattern in Europe, is closely linked to snow cover variability for the second mode, particularly from mid- to late winter. The here are the averages in the latitude band of N for temperature and zonal wind and in the band of N for snow cover NAO negative phase is related to snow cover increases from January to February; in contrast, the NAO positive phase is related to snow cover decreases from January to February. However, early winter snow cover is not significantly influenced by the NAO pattern. The link between the NAO and snow cover change may be explained by lowlevel temperature changes in the European region modulated by the NAO index. Low temperatures at the low level, modulated by the NAO, appear to be responsible for increased snow cover in the transition region in Europe. The correlation between the NAO and temperature is relatively weak in early winter and early spring (December and March). Reason for the decreased correlation in early winter and early spring is not clear; further test confirms that the decreased correlation is not associated with the NAO phase transition. The third mode explains 9 % of the total snow cover variability, apart from the seasonal cycle. Although the explained variance is limited, this mode provides interesting results: the transition from a negative phase to a positive phase after 000. The third mode indicates that during the 000s, snow cover increased in December and January and decreased in February and March. Terzago et al. (00) used satellite data to show that snow days have shifted in the Italian Alps, and their result is consistent with the third mode in the present study. The sub-seasonal variations of the key atmospheric variables, is responsible for snow cover variations in the third mode; as in the second mode, temperature change

13 Physical mechanisms of European winter snow cover due to the advection of heat by anomalous wind is the key ingredient for the snow cover variation. In closing, a trend in European winter snow cover is not well defined, as already mentioned in Sect.. However, the third mode of snow cover variability appears to exhibit a gradual increase in amplitude. The corresponding spatial patterns, however, shows decreased snow cover in Europe in late winter and early spring, but increased snow cover in early and mid-winter. Although global warming is clearly present in the Northern Hemisphere, the local manifestation of warming in European winters is significantly different from global warming, and the resulting snow cover variability. In addition, increased temperatures are not guaranteed to be above the threshold required for melting snow cover in winter. 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