The average values of the coefficient of snow cover durability (V) in the Karkonosze Mountains and the Izera Mountains range from ca. 46–47% in the lowest localisations (Jelenia Góra, Hejnice) to ca. 81–82% in the upper ridges of the mountains (Śnieżka, Szrenica) (Fig. 1). Equally high average values of V are characteristic for stations with southern macro-exposure located in the altitude zone of 750–900 m a.s.l., e.g. Jakuszyce, Bedřichov, Desná–Souš (Fig. 2). The calculated average values of V relate to its average values in Poland, where they range from 40% in the west to 60% in the south-east and to over 70% in the highest reaches (Falarz 2013). In the Polish Sudetes and their foreland, the average V decreases within the range of 40–50 to 80% (Urban 2015).
The big denivelation of over 1250 m (from the station Jelenia Góra, located in a valley, to the highest peak Śnieżka) and the great variety of the topography of the area, as well as the exposure of the station cause the noticeable spatial variety of V value. This variety results from many factors, as in the case of snowiness and severity index of winters (Urban et al. 2018), including altitude and orographic deformation of the flow field of air masses that shape precipitation and air temperature. In consequence of this deformation, there emerges the distinct contrast between the snowiness in the river catchment of the Elbe (S, SW and W macro-exposures) compared with the Odra river catchment (NE and N macro-exposures). The areas with SW and W exposures are characterised by the longer period of retention and bigger depth of snow cover. This result corresponds with the previous study on the thermal and precipitation variety of the Karkonosze Mountains (Sobik et al. 2014) or of the Karkonosze and the Izera Mountains (Urban et al. 2018). This contrast stands out especially in the altitude range of 500–900 m a.s.l. (Fig. 2). In the upper ridges, the differences are becoming less distinguishable due to the snow blowing alternately from one to the other side of the range.
These were Sobik et al. (2014), as well as Urban et al. (2018), who pointed out to the fact that in the Karkonosze Mountains the essential differences in precipitation at similar altitudes exist not in the east–west direction, but between the southern of northern sides of the mountains. Also, they emphasised the increase in winter precipitation in the upper river catchment of the Kamienna and in the western part of the Polish Karkonosze. This should be accounted for by the weaker descending air currents with the southern circulation. The latter in turn results from the fact that a relatively low Main Ridge of the Karkonosze, located in the west of Szrenica, and not much lower, parallel to the Karkonosze High Ridge of the Izera Mountains hinder descending foehn currents (Kwiatkowski 1985). Similarly, as Falarz (2002) proved, foehn effect plays a significant role in shaping the Polish Tatra Mountains’ nival conditions and their diversification, as well as the component of the meridional atmospheric circulation contributes to these conditions to a greater extent than its zonal counterpart.
The above-described and graphically presented (Figs. 1 and 2) patterns for various periods at the analysed stations confirm the results obtained for the multiannual period of 1981–2010 at the selected stations (chapter 2 features the methodical justification). The average values of V (that illustrate climactic patterns) for the stations from the period 1981–2010 are almost identical to the ones from the periods in Table 1. The results are similar for extreme values (Fig. 3).
The temporal and spatial variability of the coefficient of snow cover durability and its trends of changes
Based on the multiannual mean values of the coefficient of snow cover durability (V) and its standard deviation, winter seasons with moderate V (Vavg-δ < V < Vavg+δ; where: δ – standard deviation) dominated at all analysed stations. In addition, the character of winter seasons defined by V has changed since the turn of the 1980s and 1990s. Namely, everywhere, apart from Śnieżka Mountain, the increase in frequency of seasons with small V (V ≤ Vavg-δ) and the decrease in frequency of seasons with high V (V ≥ Vavg+δ) were noted. Seasons with low V values in the Karkonosze and the Izera Mountains consist of the following periods: 1988/1989–1990/1991, 1997/1998, 2006/2007, 2013/2014 and 2015/2016 (Table 2). The seasons 1989/1990 (for stations located above 650 m a.s.l.), 2006/2007 and 2013/2014 (for stations located below 650 m a.s.l.) were marked by extremely low V, whereas winter seasons with high V values (with stable/continuous snow cover) occurred at most of the stations in the 1960s and 1986/1987, 1995/1996 and 2005/2006. Among those seasons with the highest V (100% at as many as seven stations), the period 2005/2006 stood out. High values of V were noted for season 1995/1996, but primarily at stations located below 700 m a.s.l (Table 2). Incidentally, seasons with high V only in the upper (1974/1975, 1981/1982, 1991/1992) or lower part of the altitude profile (1986/1987, 2003/2004) occurred. These results were similar to the ones presented in the earlier article by Urban et al. (2018). Since the end of the 1980s, the thermal structure in the Western Sudetes changed. Namely, gentle winters occurred more frequently than the severe ones. This pattern coincides with the ones that were obtained for Europe (Twardosz and Kossowska-Cezak 2016). The increase of warm winters occurrence was also observed in, among other regions, the Swiss Alps (Scherrer et al. 2004; Marty 2008) or in the USA (Mayes Boustead et al. 2015).
The variability of the coefficient of snow cover durability in the analysed winter seasons expressed by the coefficient of variability (Vz) allows for the comparison of V variability in temporal series as well as between the stations. The smallest values of Vz (around 10–15%) occur in the upper parts of the Karkonosze and the Izera Mountains. This means that the snow cover there is more stable and is subject to smaller fluctuations, whereas the biggest values of Vz (around 35%) occur at the stations that are located at the lowest altitudes (Table 2). Generally, the variability of the coefficient of snow cover durability is inversely proportional to altitude. This result is consistent with the previously gained conclusions for the coefficient of the variability of parameters of snow cover in the Polish Tatra Mountains (Leśniak 1973; Falarz 2000–2001) or in the Polish Sudetes (Urban 2015, 2016).
Nonetheless, in the wide slope zone 600–700 m, the variability of coefficient V varies significantly. This is especially noticeable in the zone 600–700 m (Harrachov, Vysoké nad Jizerou), where the stations with macro-exposure S are characterised by the variability of V (16–18%), which is distinctly smaller than that of the stations with macro-exposure N (Szklarska Poręba, Przesieka) (ca. 30%). Therefore, at similar altitudes, snow cover at the stations with southern macro-exposure is subject to smaller fluctuations than at the stations with northern macro-exposure (Table 2).
The spatial and temporal variabilities of V are well illustrated by its line at stations Harrachov and Przesieka, which are located on the opposite sides of the main ridge of the Karkonosze and at similar altitudes. The significantly smaller amplitude of V changes characterises slopes with southern macro-exposure (Harrachov) than those with southern macro-exposure (Przesieka). Moreover, in Harrachov, the lowest values of V incidentally drop below 50%, while in Przesieka, profound drops occur relatively frequently, often reaching even the values below 30%. The occurrence of low V values has been observed since the beginning of 1990s, whereas on slope S, the coefficient of snow cover reaches the value 90% or above much more frequently than on slopes N. As a result, the multiannual difference in V value between Harrachov and Przesieka equals ca. 20% points (Fig. 4). The correlation the value of V between Harrachov and Przesieka is positive and strong. The correlation coefficient R calculated between Harrachov and Przesieka for 1961/1962–2011/2012 winter seasons was 0.6.
Contrary to common expectations, the maximum values of the coefficient of snow cover are noted not only at the stations that are located at the highest altitudes but also on the slopes, Pogórze or intermontane valleys. Possibly in a given season, the stations located at lower altitudes can have higher coefficient V than those located at considerably higher altitudes. Such situation took place between Jelenia Góra (342 m a.s.l.) and Szrenica (1331 m a.s.l.) stations in winter seasons 1986/1987, 1995/1996 or Harrachov (675 m a.s.l.) as well as Szrenica/Śnieżka in several seasons in the 1960s: 1978/1979, 1986/1987 and 1999/2000 (Table 2). This result is consistent with the earlier results of Leśniak (1981), who demonstrated analogous patterns in the river basin of the upper Wisła. The author explains this fact by the renewal of snow cover at higher altitudes during spring recurrent cold spells. This sometimes significantly prolongs the potential time of snow cover retention, while the actual time of this retention is only slightly longer. At the stations located at lower altitudes, the thermal conditions during recurrent cold spells in spring are far less likely to facilitate propitious conditions for forming snow cover again. Similarly, in autumn, in the upper parts of the mountains, snow cover appears quite early (September–October), prolonging the potential time of snow cover retention. Also, Urban (2015) obtained analogous results for the Polish Sudetes and their foreland.
The calculated trends of V changes are negative for most of the analysed stations in the Western Sudetes (Table 3). This means that the values of V successively decreased, indicating at the same time, that the time of retention shortened in successive winters. This result is confirmed by the previous study on snow cover in Śnieżka in the period 1901–2000 (Głowicki 2005) or in the Polish Sudetes and their foreland in 1951–2007 (Urban 2015, 2016). The pace of decrease fell within the range from ca. − 0.6% points (pp)/decade in station Desná–Souš to ca. − 2.7 pp/decade in Świeradów Zdrój station or even − 3.1 pp/decade in station Horní Maršov. The average pace of the drop of coefficient V for all stations for which its trends of changes were determined was − 1.43 pp/decade (Table 3). The trend of V change is statistically significant at the p = 0.05 significance level merely for one out of eight stations which were selected for the analysis of snow conditions (Table 3). A slight decreasing trend in the characteristics of snow cover was observed in most of Polish area in the second half of the twentieth century. The changes in snow cover relate to the changes in the atmospheric circulation and especially with the increased frequency of the advection of air masses from the western sector (Falarz 2004). The more frequent occurrence of winters with a relatively low V coefficient might be related to the changes in atmospheric circulation types over the Northern Atlantic. The growth of zonal cyclonic circulation from the south-western direction in last decades of the twentieth century was proved by Migała (2005) and Migała et al. (2016). This circulation generates in Western and Mid-Europe a vast atmospheric front with increased cloudiness and brings warming and precipitation in the cold season (Urban et al. 2018).
This does not relate to the upper zone of the mountains (Śnieżka, Szrenica), where winters are more snowy and severe, and, as a result of snow blowing alternately from one to the other side of the mountain, no significant changes of snow cover durability are observed. On the contrary, a slight positive trend of the coefficient of snow cover durability is noticed there (Table 3). In certain areas, as well as in the upper zone of the Western Sudetes, an increasing trend in snow cover retention is noted (Räisänen 2008). Such phenomenon has been observed in the recent decadesin the Alps (Zemp et al. 2008) or in Norway (Andreassen et al. 2005).
A direct cause of the decrease in days with snow cover should be sought in the long-term change of air temperature and precipitation (Falarz 2004). Primary proofs of this can be the significantly increasing trends of air temperature in both Poland (Kożuchowski and Żmudzka 2001; Wibig and Głowicki 2002) and Europe (Schönwiese and Rapp 1997). This fact remains in close relation to the increase of the frequency of western circulation over Poland (Ustrnul 1998). Winter temperature increase can reduce winter precipitation share in general precipitation, the trends of which in the majority of Polish area in the years 1930–1980 were upward (Kożuchowski 1985). In consequence of all this, the durability of snow cover might reduce.
Spatial and temporal variabilities of disappearance of snow cover
Similar patterns described for the coefficient of snow cover durability also mark the distribution of snow cover disappearance with relation to the macro-exposures and altitudes of analysed stations. On average in December–March period, snow cover on the ground disappears completely from ca. 0.4 times at the stations in the upper ridges to ca. 6–7 times at the stations located at the lowest altitudes (Fig. 5; Table 4). For many years, the maximum number of cases of snow cover disappearance in these months decreases within the range from 4 to 17. The minimum can be zero (Fig. 5). Beside Śnieżka and Szrenica, the stations on the slopes with southern macro-exposure (e.g. Bedřichov, Desná-Souš, Harrachov, Vysoké nad Jizerou, Horní Maršov) are distinctly characterised by a small number of snow cover disappearance. On average, this number ranges from 1.5 to 3.0. The stations with northern macro-exposure (Przesieka, Szklarska Poręba, Karpacz_1, Karpacz_2) and localised at similar altitudes as the ones with southern macro-exposure are characterised by 2 ÷ 3 times bigger frequency of total disappearance of snow cover. The situation in the eastern part of the Karkonosze Mts looks particularly unfavourable—in the area of the stations representing middle and lower parts of the slopes, i.e. Karpacz_1, Przesieka and Karpacz_2, the average number of total disappearance in the middle of winter season equals 4 ÷ 6 (Fig. 5; Table 4). This is due to the warming impact of the foehn effect on leeward slopes (with the wind dominating in the winter from SW and S directions—perpendicular to the course of the Karkonosze), which contributes to the faster disappearance of the snow cover (Kwiatkowski 1972, 1975, 1979). The greater the height difference between the ridge and the station, the stronger the effect is. In the Eastern Karkonosze, the denivelation is approx. 200 m larger than in their western part. This phenomenon is unpropitious, because the region features many winter sports centres, including skiing ones.
In the multiannual course, for the selected pairs of the stations that are located on similar altitudes, but with opposite exposures, the significantly greater frequency of total disappearance of snow cover characterises slopes with northern macro-exposure (red continuous line in Fig. 6). However, there are seasons when total ablations occur more frequently at the stations located on the slopes with southern macro-exposure. The examples of extreme differences in this respect can be the seasons 1993/1994 and 1997/1998 (Fig. 6). In the first of them, ablations at the stations with northern macro-exposure (Przesieka, Karpacz_2) evidently outnumber the ones at the stations with southern macro-exposure (Harrachov, Horní Maršov). In the other period, the situation is the opposite. Probably, this extreme results from the domination of the opposite directions of atmospheric circulation. Namely, in the period December–March 1993/1994, the north-eastern direction of circulation occurred, according to classification by Lityński (1969), three times less frequently than in the same months in the season 1997/1998 (Pawłowska et al. 2000). NE direction is perpendicular to the course of the Sudetes massif. Thus, in the season 1993/1994 at the stations with southern macro-exposure, there appeared more frequent foehn phenomena and the adiabatic warming of descending air on the leeward side of the orographic barrier. The advancing frequency of the advection of polar and sea air masses from SW and W directions in the cold season in the Sudetes as well as their thermal and precipitation implications have already drawn attention of the researches in this field (Kwiatkowski 1972, 1975, 1979; Sobik et al. 2014; Urban et al. 2018). Although the correlation of the number of days with total disappearance of snow cover between Harrachov-Przesieka and Horní Maršov-Karpacz_2 stations is positive, it is clearly weaker than in the case of the V coefficients. The calculated correlation coefficient R for the common period 1983/1984–2010/2011 in the pairs of mentioned stations were 0.3.
The results presented in Fig. 5 and Table 4 are further specified in the graphic representation of the number of days with total disappearance of snow cover, depending on the altitude of the station with southern or northern macro-expositions. Here total disappearance of snow cover in the period December–March at the stations with northern macro-exposure significantly outnumbers (over twice) the ones at the stations with southern macro-exposure. This is especially visible at the altitude zone 500–900 m a.s.l. (Fig. 7).
Relationship between snow cover durability coefficient and total disappearance of snow cover
Analysis of the relationship between the snow cover durability coefficient V and total snow disappearance in the winter seasons 1981/1982–2010/2011 indicates that there is a negative correlation between these features. The linear correlation coefficients R in the analysed stations range from 0.0 to 0.7. In the stations with southern macro-exposure and at Śnieżka Mt., they are significant statistically at the 0.05 significance level. The correlation coefficient is clearly differentiated depending on the macro-exposure and altitude (Table 5). Namely, the stations with southern macro-exposure (eg Bedřichov, Harrachov, Horni Maršov) are characterised by the explicitly higher R values (0.7 ÷ 0.5) than stations with northern macro-exposure (eg. Przesieka, Karpacz_2, Świeradów Zdrój), where R is in the range of 0.3 ÷ 0.2. Thus, in the stations on the slopes of the Western Sudetes with southern macro-exposure, these features are usually strongly or very strongly correlated with each other, whereas in the stations with northern macro-exposure, the strength of the relationship is usually moderate or very weak. This is well illustrated by the correlations of the selected stations located at similar altitudes, but with opposite macro-exposures, i.e. Horní Maršov—Karpacz_2 and Harrachov—Przesieka (Fig. 8). In addition, the strongest correlation occurs in the middle parts of the slopes with macro-exposure S and SW. The weakest correlation (0.0 ÷ 0.1) or even lack of it is shown by the stations with the lowest locations and northern macro-exposure, i.e. Hejnice and Jelenia Góra (Table 5). This is due to differences (already mentioned in the study) in temperatures and winter precipitation in slope stations with opposite macro-exposures conditioned by the foehn effect and the altitude above sea level.