Reasons for shortening snow cover duration in the Western Sudetes in light of global climate change

This article discusses the reasons for shortening snow cover duration in the Western Sudetes, considering local changes in: air temperature; amount and type of precipitation; sunshine duration and atmospheric circulation leading to changes in the number of days with snow cover and its depth; and its start and end dates. All factors were linked to the exposure and relief of the study area. The analysis was made for the winter seasons (Nov–Apr) 1961/1962–2020/2021. It was found that the primary reasons for the shortening of snow cover duration in the Western Sudetes are: a multi‐year increase in air temperature and sunshine duration; changes in precipitation patterns—a decrease in the proportion of solid precipitation, changes in atmospheric circulation—including an increase in anticyclonic circulation types with sunny weather, especially in April (snow cover disappears in most of the elevation profile of the Sudetes); and less cyclonic weather types. The above factors synergistically affect the lower snow depth, and fewer days with solid precipitation, which promotes its faster spring ablation. In the subsequent 30 years (climatological norms), there is a successive shortening in its duration. On the snow cover start dates, there are no clear trends in the direction and rate of change. On end dates, negative trends are observed, in most cases statistically significant. The rate of change for the end dates of snow cover is about twice as high as the start dates. The rate of decline in snow cover is higher at stations at similar altitudes with northern macro‐exposure than southern. The results correspond with other studies from Europe and the world on the earlier disappearance of snow cover. They confirm the successive global warming and shortening snow cover duration, especially evident in the last few decades.


| INTRODUCTION
Rising global air temperatures in the 20th and 21st centuries have reduced the cryosphere (IPCC, 2013(IPCC, , 2021)).Snow cover (further SC) has been successively decreasing in both the lowlands and mountains (Durand et al., 2009;IPCC, 2013IPCC, , 2021;;Marty, 2008;Park et al., 2012;Pederson et al., 2013;Valt & Cianfarra, 2010;Xu et al., 2015).However, between 1970 and2010, its rate of disappearance increased by 7% in March and 11% in April relative to the corresponding months in the pre-1970 period (Brown & Robinson, 2011).Observed trends in the reduction of SC extent in temperate latitudes are due to, among other things, changes in the thermal seasons, including the shortening of winter and the lengthening of the growing season (Czarnecki & Miętus, 2017;Menzel & Fabian, 1999;Tomczyk & Szyga-Pluta, 2019).There is also evidence that changes in atmospheric circulation around 1980, involving the North Atlantic Oscillation (NAO), contributed to a reduction in SC Eurasia in March (Brown & Robinson, 2011).Changes in NAO index values largely explain changes in dates of snow disappearance, the number of days with SC, and its depth in Poland as well (Bednorz, 2002;Czarnecka, 2011;Falarz, 2007;Tomczyk et al., 2021), whose contribution to SC in Europe is decreasing in an easterly direction (Bednorz, 2004;Hori & Yasunari, 2003;L opez-Moreno et al., 2011;Szwed et al., 2017).Recent research results indicate a progressive negative trend in snow conditions in Poland (Falarz & Bednorz, 2021;Tomczyk et al., 2021).By the end of the 21st century, SC in the Northern Hemisphere is projected to decrease further by 7% to 25%, depending on climate scenarios (IPCC, 2013(IPCC, , 2021)).Similar changes are also expected in the mountains of Europe (Beniston, 2012;Schmucki et al., 2015).
The results of studies on SC persistence in the Northern Hemisphere indicate that changes in the dates of spring SC disappearance are an important indicator of climate change in that area (Choi et al., 2010;Stone et al., 2002).There has been a reduction in the duration and persistence of SC, particularly at higher latitudes due to earlier spring melt and, in some cases, later autumn SC onset (Chen et al., 2015;Derksen & Brown, 2012;Hammond et al., 2018a;Hori et al., 2017).A shortening of SC duration due to earlier spring SC than later onset has been found in the Swiss Alps (Klein et al., 2016).
The proportion of solid to liquid precipitation depends on the thermal structure of the troposphere between the ground and cloud base (Bocchieri, 1980;Bourgouin, 2000;Thériault et al., 2010), including air temperature inversions.In general, higher air temperatures lead to a decrease in snowfall but the rate and geographic distribution of these changes are nonlinear and depend on ambient temperature and prevailing climatic conditions (Bintanja, 2018;Davis et al., 1999;Knowles et al., 2006;Krasting et al., 2013;Ye, 2008).In very cold conditions, an increase in air temperature does not cause a clear shift in precipitation phases since the temperature at high absolute altitudes remains below 0 C either way.Although snowfall is not the most important indicator of regional climate change due to its slower signal compared to air temperature (Krasting et al., 2013), many studies use indices based on precipitation type (solid, liquid) to monitor and detect responses to current climate change (Dai, 2008;Deng et al., 2017;Huntington et al., 2004;Ke et al., 2009;Łupikasza & Cielecka-Nowak, 2020).
Previously, the significant influence of orographic exposure/screening and macro-exposure of slopes on the snowiness and thermal severity of winters (Urban et al. 2018b), as well as changes in the persistence index (Urban et al., 2019) of SC of the Western Sudetes, was shown.Attention was paid to the decreasing trends in the index of thermal severity and snowiness of winters in addition to an increase in the frequency of mild and low-snow winters (Urban et al. 2018b(Urban et al. , 2019)).This article, which is a continuation of the authors' publication (Urban et al. 2018b(Urban et al. , 2019)), characterizes the other parameters and indicators of SC (including depth, number of days with threshold values, dates of onset and disappearance) that are relevant to its duration, along with their trends of change.The multi-year changes in air temperature, sunshine duration, and atmospheric circulation, as well as the mentioned SC parameters, were also evaluated.
The aim of the study was to explain the reasons for the shortening of SC duration in the Western Sudetes in the context of global warming, considering local changes in: air temperature, amount and type of precipitation, sunshine duration, and atmospheric circulation leading to changes in the number of days with SC and its depth, dates of the start and end of SC.All the factors were linked to the exposure and relief of the study area, which significantly modifies the climate on a local scale.The following research hypotheses were made: • a long-term increase in air temperature, changes in precipitation and its type (a decrease in the proportion of solid precipitation), an increase in sunshine duration, and changes in atmospheric circulationmodified on the orographic barrier formed by the Sudetes, cause a decrease in the depth and duration of SC, • the shortening of the duration of SC is more influenced by changes in its end dates than in its start dates, • the macro-exposure of slopes is an important factor in differentiating snow conditions.

| SOURCE DATA, STUDY AREA, AND METHODS
The study used as much available, reliable material as possible starting from 1961.The primary time range analysed was 1961/1962-2020/2021.In some cases, the study period was shorter.A similar approach using data series of different lengths has been used in studies of SC in Austria (Hantel et al., 2000), in the mountains of Bulgaria (Brown & Petkova, 2007) or in the Karkonosze and Izera Mountains in Poland and the Czech Republic (Sobik et al., 2014;Urban et al. 2018bUrban et al. , 2019)).Huang et al. (1996) found that in the case of mean values, the length of time taken to determine it, between 10 and 30 years, is of little importance.On the other hand, multi-year averages of data from several stations located at a similar altitude provide reliable information about conditions in a given altitude zone (Marty, 2008).Measurement data came from 17 meteorological stations, including 8 stations of the Institute of Meteorology and Water Management-National Research Institute (Polish acronym IMGW-PIB) and 8 stations of the Czech Hydrological and Meteorological Institute (CHMI) and 1 station-the Meteorological Observatory of the University of Wrocław (UWr) on Szrenica (Figure 1, Table 1).
The choice of the Western Sudetes for the present study was due to the fact that this area is the highest part of the Polish-Czech Sudetes, where the snow cover remains the longest and has the highest altitude.Due to its almost perpendicular location in relation to the prevailing wind directions from the south-west and west during the winter season and the greatest altitude differences (>1200 m) in the whole massif, between the summit and summit areas and the foot of the mountains, foehn effects are most spectacular here.In addition, the Western Sudetes are the area, throughout the whole of the Sudeten Mountains, most frequently visited by tourists, characterized by the best-developed infrastructure for downhill skiing (e.g., Pec pod Sněžkou-Čern a hora,   1961-2020 1961-2020 1961-2020 1961-2020 1966-2020 Harrachov-Čertov a hora, Špindleru ˚v Mlýn, Szrenica or Wysoka Kopa in the Karkonosze Mountains) as well as from the well-known European centre for cross-country skiing (the area of Jakuszyce in the Jizera Mountains).Moreover, as mentioned in the introduction, the paper is a continuation of previous publications on snow cover from this area (Urban et al. 2018b(Urban et al. , 2019)).For the aforementioned reasons, the results obtained from the present work can be a starting point for comparisons and analogous studies in other mountain areas of Europe.
Since some stations have a short, incomplete climatological data series, the trends of changes in the analysed parameters may not be statistically significant.However, the dominance of negative over positive trends in SC characteristics around the world is consistent with increasing global air temperature (Hansen et al., 2010) and documented short-term trends can have serious implications for the study area, including, for example, lower annual water supply to the ground (Hammond et al., 2018b).This paper analysed a multi-year series of SC measurements in the Western Sudetes over a whole year, understood as the period from August 1 of the year 'X' to July 31 of the year 'X + 1 0 .This was done because of the possibility of SC on the ground in the highest parts of the Western Sudetes ( Śnieżka 1603 m a.s.l., Szrenica 1331 m a.s.l.) even in the summer months.This assumption applied to the dates of the start and end of SC.For the other parameters and indicators of SC, as well as air temperature and precipitation type, and for some locations also sunshine duration, the analysis was carried out for each station and each winter/cool season, which was taken as the November-April period (Table 2).
An analogous approach has been successfully used in earlier publications (Falarz, 2000(Falarz, -2001;;Klein et al., 2016;Peng et al., 2013;Urban, 2015Urban, , 2016;;Urban et al. 2018bUrban et al. , 2019)).Most studies examining changes in snow conditions in relation to global warming focus on the months of climatological winter (DJF) and often ignore changes occurring in autumn and spring (Klein et al., 2016).Therefore, a season-wide analysis seems warranted.
A day with solid precipitation was defined as a calendar day on which at least one of the following types of precipitation containing a solid phase occurred: snow, snow and rain, snow pellets, small hail, snow grains, ice needles, and hail.In turn, a day with precipitation was defined as a day on which the daily precipitation measured from 06:00 UTC of a given day to 06:00 UTC of the following day is at least 0.1 mm (Nied źwied ź et al., 2003, Lipina et al., 2014).
Precipitation measurements in mountain conditions are subject to errors, especially during strong winds and snowfall (Green & Helliwell, 1972;Pollock et al., 2018;Wolff et al., 2015).The largest measurement errors are found in the summit-surface zone, especially on Śnieżka.It is estimated that on an annual basis, actual precipitation is greater than measured precipitation anywhere from 24% in the foothills of the mountains up to 50% in the summit zone of the Karkonosze (Kwiatkowski, 1982), and errors for the winter months can be even greater.In addition, the measured precipitation totals at Śnieżka for the period Nov-Apr (548 mm from 1961 to 2020, see Table 5) are so understated that they result in a fictitious decrease in precipitation totals in the higher parts of the Karkonosze with increasing altitude.Hence, the precipitation totals from Śnieżka or Szrenica in this paper should be treated with caution, as measured values, and not as actual values.However, information on the number of days with precipitation and the type of precipitation should be considered reliable at these locations.
To determine changes in atmospheric circulation, atmospheric circulation macrotypes were used according to the classification of Hess andBrezowsky (1952, 1977).The time series of data for each macrotype (German: Katalog der Grosswetterlagen) was compiled from a calendar updated by Werner and Gerstengarbe (2010) and data from the website of the German meteorological service-Deutscher Wetterdienst (www.dwd.de).This calendar has been successfully used, among other things, to assess multi-year changes in annual air temperature in the highest range of the Sudeten Mountains-Karkonosze (Migała et al., 2016), changes in the occurrence of SC (Szyga-Pluta, 2022) or determination of late spring frosts in Poland (Ustrnul et al., 2014), as well as frost and frost-free periods in central Europe (Tomczyk et al., 2015).The GWL developed for Central Europe (Germany) works well in a much larger region, covering all of Europe (Khokhlov & Umanska, 2018).
The article also uses available multi-year series of sunshine duration totals.They express the general conditions of radiation in the atmosphere and affect various processes in SC, such as its metamorphosis and ablation process (Baker et al., 1999;Fukami et al., 1985;Järvinen & Leppäranta, 2011).At most stations, sunshine duration series is composed of data obtained from a Campbell-Stokes heliograph and electronic sensors.In the Czech Republic, these are electronic sensors of the SD type from Meteoservis (since 2004/2005-Desn a-Souš and 2012/2013-Hejnice).While in Poland, they are CSD sensors from Kipp & Zonen (since 2014).Only the Śnieżka and Szrenica stations have the entire series of sunshine duration totals from the heliograph.However, only from Śnieżka is it complete for the entire 60-year period analysed.Therefore, the sunshine duration totals from Śnieżka in this paper are crucial for the analyses of this element.Nevertheless, the analysis of sunshine duration trends on the basis of the combined series of heliograph and electronic sensor data is possible and the differences are small and do not break the homogeneity of the series (Bartoszek et al., 2020;Falarz et al., 2021).The results of a study on the homogeneity of the series of sunshine duration data from a heliograph and an SD sensor in the Czech Republic indicate that data from automatic measurements generally indicate smaller totals compared to data obtained from a heliograph.However, the differences in the indications of the two types of instruments are smallest in the winter months and the general nature of the fluctuations in long-term and annual sunshine duration totals remain more or less the same (Valík et al., 2019).
The trends of changes in the analysed parameters of SC, air temperature, total and type of precipitation, sunshine duration and atmospheric circulation were also determined.As in previous studies on SC in the Sudetes (Urban et al. 2018b(Urban et al. , 2019) ) or in Poland (Tomczyk et al., 2021), the statistical significance of the trends was checked using Student's t-test.The longest 60-year measurement data series were used to analyse the direction and rate of change of individual meteorological elements.Trends from shorter periods, where are shown in the text, are only additional information.They are not analysed or compared due to the fact that they are determined for different periods.

| Atmospheric circulation
The intensity of SC formation and ablation processes depends on the general atmospheric circulation and local Foehn phenomena.The influence of circulation on snow cover on the scale of the Western Sudetes (local) is related, among other things, to the effect of foehn winds.This, in turn, is dependent on the pattern of baric centres over Europe, causing air to flow over Poland from a south-westerly/southern direction, perpendicular to the course (WSW-ENE) of the main axis of the Sudetes.The foehn, as a warm, dry, and gusty descending wind, contributes to the faster disappearance of snow cover on the leeward side of the mountains (Figure 2).
The frequency distribution of circulation types, according to Hess and Brezowsky, in the winter season and in April, indicates the dominance of the following several types, that is: western, cyclonic (Wz), ridge over Central Europe (BM), furrow over Western Europe (TRW), and furrow over Central Europe (TRM).BM, TRW, and TRM were the dominant types in April-the month of intense SC disappearance in the Sudetes (Figure 3).
Based on the 1961-2020 multi-year period, in terms of the impact on SC, it is important to note the distribution of trends of each circulation type in both periods and which ones are statistically significant.In the winter season, statistically significant increasing trends occurred in the TRM, BM, and NWa (North-Western, anticyclonic) types.There was an increase of 1%, 0.8%, and 0.7%Ádecade −1 , respectively.In contrast, there was a significant negative in the types HNFz (high and North Sea- Fennoscandia, cyclonic) and TM (low over central Europe).There was a decrease of 0.5% and 0.4%Ádecade −1 , respectively (Figure 4).On the other hand, in April, statistically significant trends at the 0.05 level were noted only in the NWa (+0.9%Ádecade −1 ) and TM (−1.4%Á decade −1 ) types.Thus, there was an increase in anticyclonic weather associated with the NWa type and a marked decrease in cyclonic weather accompanying the TM type (Figure 4).This distribution of trends favours the spring ablation of SC.

| Air temperature
The mean seasonal values of air temperature for successive decades and climatological norms gradually increased in almost all analysed Sudeten stations from 1961 to 2020 (Table 3).Similarly, the changes in the mean values of selected air temperature parameters during the winter seasons (Nov-Apr) in the Western Sudetes show an increasing trend.In contrast, the number of days with a given temperature parameter below 0 C is decreasing.For example, at stations with a full 60-year data series, mean seasonal air temperature (T avg ) increases at a rate of about 0.4 CÁdecade −1 and number of days with mean daily air temperature <0 C (NDT avg<0 C ) decreases by about 4-6 daysÁdecade −1 (Figure 5, Table 4).These trends are statistically significant usually at the 0.01 level.The stations representing the full 60 measurement seasons are noted (except for Świerad ow Zdr oj) to have a higher rate of increase in minimum air temperature than in maximum air temperature (Table 4).
The relationship between seasonal T avg and selected SC parameters (MMSC, mean maximum depth of snow cover; NDSC, number of days with snow cover ≥1 cm, etc.) was investigated, taking into account the absolute  1.
Seasonal number of days with solid precipitation (NDRS), *statistically significant at the level of 0.05.
(d) the strongest correlation (r = 0.7-0.9) in the middle and lower parts of the slopes, mainly with macro-exposure 'N', which is related to the more frequent foehn effects that reduce SC (Table 5).

| Precipitation
The high precipitation of the winter season is typical for most of the area of the Czech Western Sudetes and especially its extreme western ridge-the Jizera Mountains, and on the Polish side, it occurs in the Jakuszyce region (Table 6).The station in Jakuszyce shows a large positive precipitation anomaly and, especially in the cold half of the year, is influenced by the accumulation of air on the Czech side, from the southern sector (Sobik et al., 2014).Analysed changes in precipitation parameters in the Western Sudetes in the winter seasons 1961/1962-2020/2021 usually indicate slightly negative (not statistically significant) trends in precipitation totals.In turn, the seasonal NDR lacks clear trends in the direction and rate of change (Table 6).Hence, the observed changes in precipitation totals and NDR of the winter season should not be significant for changes in SC parameters.
The situation is different when looking at changes in the type and proportion of precipitation, which affect the formation and duration of SC.There is a decreasing trend in the number of days with continuous precipitation (NDRS) in almost all the studied locations.In several of them, it is statistically significant at the 0.05 level and amounts to about 3-5 daysÁdecade −1 .Their exemplary course in selected stations is illustrated below (Figure 6).NDRS increases with the absolute altitude of the station.There is a decreasing trend in the proportion of days with solid precipitation to the total number of days with precipitation in the analysed seasons.This trend, depending on the location, is in the range of 1%-4%Ádecade −1 .It is statistically significant in most of the stations with the longest measurement series (Table 7).

| Sunshine duration
Apart from precipitation and air temperature, an important element influencing SC is the intensity of solar radiation, the basic component of which is sunshine duration.F I G U R E 7 Relationship of selected seasonal snow cover characteristics with altitude (MMSC, mean maximum depth of snow cover; MSC.maximum depth of snow cover; MSDSC, mean seasonal depth of snow cover; SDSC, the sum of depth snow cover; NDSC, number of days with snow cover ≥1 cm; NDSC20, number of days with snow cover ≥20 cm), along with equations of simple regressions.The station Śnieżka (1603 m a.s.l.), as an uncovered, isolated peak, was included in both macro-exposures.[Colour figure can be viewed at wileyonlinelibrary.com]Sunshine duration on Śnieżka in the winter seasons shows an increasing, statistically significant, trend.In the individual months of the season, only April is characterized by the largest increase (about 12 hÁdecade −1 ) of this meteorological element.Similar patterns are observed at the other stations (Table 8).In April, there is intensive ablation of SC and most stations in the Sudetes experience its disappearance.

| Snow cover
Seasonal values of SC parameters related to its altitude (MSC, MMSC, MSDSC, and SDSC) and number of days (NDSC, NDSC20) increase with altitude.Their increase also depends on the macro-escape of the slopes.On northfacing slopes, it is greater than on south-facing slopes.Stations located on northern slopes are also characterized by a higher coefficient of determination (0.94-0.98) between absolute altitude and the value of a given SC parameter than those on southern slopes (0.75-0.87) (Figure 7).
The spatial distribution of SC characteristics was visualized on the basis of MMSC and MSDSC and by NDSC (Figure 6).The MMSC in the Western Sudetes ranges from about 12 to 16 cm in the lowest locations (Jelenia G ora, Hejnice) to about 86-95 cm in the summit-surface zone ( Śnieżka, Szrenica).High MMSCs (65-75 cm) are characteristic of stations with southern macro-exposure located in the 750-900 m altitude zone in the Jizera Mountains, for example, Jakuszyce, Desn a-Souš.The greatest contrast between stations located at similar altitudes (e.g., Harrachov and Szklarska Poręba, Vysoké nad Jizerou and Przesieka, Horní Maršov and Karpacz_2), but with opposite macro-exposures, is in the 500-900 m zone (Figure 8).Evidently, one can clearly see higher (on the order of 25%-50%) altitudes and the number of days with SC at stations with southern macro-exposure than at stations at analogous altitudes with northern macro-exposure.The strong variation of SC parameters in the area is the result of many factors, including the altitude of the stations above sea level, denivelations, diversity of relief and, above all, the macro-exposure of the slopes and the orographic deformation of the air mass flow field shaping precipitation and air temperature (more strongly in the N-S than E-W direction).
In the Western Sudetes in the 1961/1962-2020/2021 seasons, declining, in most cases statistically significant, trends are found in SC parameters regarding its height as well as the number of days.For example, NDSC is decreasing from about 1 to 8 daysÁdecade −1 .The same is true of MSC.The rate of decline of MSC is faster than that of MMSC.Changes in the mean dates of onset and disappearance are different.Namely, in the onset dates there are no clear trends in the direction and rate of change.In the end dates, negative trends are observed, in most cases statistically significant.In addition, the rate of change of the end dates is higher than that of the start dates of SC (Table 12).It can be noted that the lowest-lying stations are less likely to show significant negative trends in height or in the number of days with SC than those lying higher up (Table 9).This is due to the greater interannual variability of SC (Marty et al., 2017).In the summit zone ( Śnieżka), where winters are the snowiest and most severe, as a result of snow blowing from one side of the mountains to the other, changes in most of the analysed SC parameters are also smaller (Table 9).
The observed changes in the height and duration of SC are mainly due to the transition from solid to liquid precipitation and more frequent and more intense melting with positive air temperature trends of the winter season.
T A B L E 1 0 Mean dates of the start (StartSC) and end (EndSC) of the snow cover and its mean potential (PT) and actual (RT) duration.Trends in the analysed SC parameters of the Western Sudetes reflect the ongoing global warming.

| Snow cover duration
The observed increase in air temperature in the lower and middle troposphere over Poland (Urban et al., 2021) confirmed by measurements from ground stations in the Western Sudetes (Migała et al., 2016) with a simultaneous increase in sunshine duration (Urban, Migała, & Pawliczek, 2018) and changes in the frequency of circulation types with warm marine air masses affect various indicators of SC and its occurrence.An analysis of the mean dates of the start and end of SC in the Western Sudetes shows that it appears earliest in the highest parts of the mountains (early October) and progresses down the slopes (mid-November) and disappears earliest in the lower parts of the slopes (early April) and progresses up the slopes and toward the tops of the mountains (late May).On average, the potential duration (PT) ranges of SC from 140 to 150 days in the lower part of the profile to more than 220-230 days in the summit-surface zone.However, the actual duration (RT) is much shorter than the potential one.At stations with the longest SC (high above sea level and with southern macro-exposure) it is about 80% of PT.At the stations with the lowest altitude and northern macro-exposure RT is about 45%-50% of PT (Table 10).
When considering changes in the duration of SC in successive 30-year periods (climatological norms), a successive shortening of PT and RT of SC is observed.The mean PT of duration in the current 1991-2020 norm, relative to the 1961-1990 norm, has shortened from 7 to 16 days (Table 11, Figure 9).
Analysis of the direction and rate of change in the mean dates of the start and end of SC indicates no clear trends in the direction and rate of change in start dates; PotenƟal Ɵme 1961-1990 1971-2000 1981-2010 1991-2020 the trends of change in end dates are downward and statistically significant at most stations.The rate of change and correlation coefficients in the end dates tend to be about two-times greater than those in the start dates; hence, changes in the end dates of SC have a greater impact on changes in its duration.Differences in the rate of disappearance of SC appear to be greater at stations with northern macro-exposure than southern, located at similar absolute altitudes (e.g., Przesieka-Harrachov. Świerad ow Zdr oj-Horní Maršov).In addition, variation in stations at similar altitudes located in the same macroexposure, for example, Jelenia G ora-Hejnice, becomes apparent (Table 12).The reason for this is that the Jelenia G ora station is decidedly more susceptible to strong foehn effects, where the denivelation between the Main Ridge of the Karkonosze Mountains and the bottom of the Jeleniog orska Basin, where Jelenia G ora is located reaches 1200 m.In contrast, the Hejnice station, located in the Jizera Mountains, where there are no or very weak foehn effects, is thus extremely rarely exposed to them.

| DISCUSSION
The statistically significant increase in the frequency of anticyclonic, with a simultaneous decrease in cyclonic, weather types in the Western Sudetes found in this study refers to analogous patterns in the multiannual period 1991-2020 relative to the multiannual period 1961-1990 in the Czech Republic (Br azdil et al., 2022).Snowfall, the amount of SC, and its duration significantly depend on air pressure as an indicator of the synoptic situation.They are negatively correlated with air pressure (Gaji c-Čapka, 2011).Similar results were obtained on the alpine plateau in Switzerland for lower elevations of up to 1000-1500 m above sea level (Rebetez, 1996).This conclusion can be applied to the Western Sudetes, where, in the cold half of the year, on the leeward side of the mountains (the northern macro-exposure), there is an increased frequency of foehn situations, which favours a faster disappearance of SC.Their frequency reaches 40% (Kwiatkowski & Hołdys, 1985).
The variability of precipitation occurring in Central Europe is explained primarily by its dependence on atmospheric circulation, which determines the occurrence of continental or oceanic weather trends and shapes global and regional climate (Degirmendži c et al., 2004;Mły nski et al., 2018;Tomczyk et al., 2021;Twardosz et al., 2011).The relationship between air temperature and atmospheric circulation is strongest in the DJF, when more than half of the warming was due to changes in circulation (Cahynov a & Huth, 2009), which promotes SC ablation (Tomczyk et al., 2021).
The last four decades  were the warmest in the history of instrumental measurements and each successive decade was warmer than the previous one (IPCC, 2021).The increase in air temperature, which determines the courses of other climate elements, including SC, was marked in all regions of the globe at different spatial scales, both horizontally and vertically (IPCC, 2021).Twardosz et al. (2021) showed, based on 210 stations in Europe, that air temperature has been increasing linearly since 1985, and that the years 1991-2020 appear to have had a T A B L E 1 2 Pearson's correlation coefficient 'r' and the direction and value of the trend for the mean seasonal (Nov-Apr) start (StartSC) and end (EndSC) dates of snow cover.greater impact on global warming than the years 1961-1990(Br azdil et al., 2022)).The faster increase in minimum air temperature than maximum air temperature shown in this study confirms this previously found regularity for the Sudetes (Głowicki, 2000(Głowicki, , 2003;;Migała et al., 2016).The relationship between SC and air temperature is greatest in areas located in the warm temperate climate zone and where there is susceptibility to temperature changes associated with, for example, the advection of different air masses, the influence of terrain morphology, exposure, etc.Such regions in temperate climates are, for example, humid areas at relatively low altitudes, where the greatest snow losses are likely to occur (Luce et al., 2014).The Sudetes are undoubtedly such an area, with altitudes in the summit zones of 1300-1500 m a.s.l, being influenced by the prevailing humid polar-marine air masses throughout the year and with frequent foehn effects in the cold season.Thus, the variation of climatic conditions in the cold season in the Western Sudetes is generally greater on the Polish (north/eastern) than on the Czech (south/eastern) side, results from the location of the site in relation to the frequency and intensity of the foehn, and is noted mainly in the mean and lower altitude levels (Bła s, 2021;Sobik et al., 2014).This fact reflects SC conditions of the area (Urban et al. 2018b(Urban et al. , 2019;;Urban & Richterov a, 2010).

Macro
The relative importance of air temperature in reducing SC is usually greatest in periods and zones with intermittent SC of relatively low absolute height, where such weather patterns occur every year (Hammond et al., 2018a;Harpold et al., 2017).In addition, the windward/leeward macro-exposures of mountain ranges also affect changes in SC parameters, trends in its duration, etc. and the extent of change is not consistent even within a single mountain ridge (Hammond et al., 2018a) and varies even over small horizontal distances (Sevruk, 1997;Wastl & Zängl, 2008).
Winter thermal conditions in Poland were and are largely determined by atmospheric circulation (Degirmendži c et al., 2004;Piotrowski & Jędruszkiewicz, 2013;Tomczyk et al., 2021;Van Loon & Rogers, 1978).Since the early 1990s, there has been a noticeable increase in the frequency of warm and very warm months, with fewer cold and very cold months, which in turn affects the length of the winter seasons and SC duration (Migała et al., 2016).The steady increase in air temperature is influenced by the changing frequency of circulation types and directions of incoming air masses throughout the year.The zonal circulation of maritime air masses from the North Atlantic has a direct influence, as illustrated by the strong relationship between thermal conditions at Śnieżka and the NAO index (Migała et al., 2016).An assessment of the spatial variability of winter temperature in Poland in the 2021-2050 period, based on CLM, HIRHAM5 and RACMO2 models with reference to measurement data from 1971 to 2000, indicates a further increase (Piotrowski & Jędruszkiewicz, 2013).
In the winter season, precipitation totals measured at similar altitudes on the Czech side of the Western Sudetes are about 25%-30% higher than on the Polish side (Sobik et al., 2014;Urban & Richterov a, 2010).This is due to the definite predominance of advection of air masses from the west and southwest with the occurring accumulation on the windward slopes, mainly on the Czech side of the Karkonosze.The Polish part is then on the leeward side, so the gravitational descent of air causes adiabatic heating and reduction of precipitation totals.
Increased precipitation over the mountains is much more effective at low air temperatures than at high temperatures and increases with the density of the incoming moist air mass (Wastl & Zängl, 2008).Thus, in the cold season, taking into account the more frequent foehn effects on the 'N' than on the 'S' side of the Karkonosze (the highest range of the Sudetes), the differences in precipitation at the same altitudes on both sides of the mountain ridge are significant in winter and are hardly noticeable in summer (Bła s, 2021;Sobik et al., 2014).
However, from 1951 to 2018, the southwestern part of Poland, where the Sudetes are also located, showed negative trends for most monthly precipitation totals of the cold half of the year (Kalbarczyk & Kalbarczyk, 2021).This fact may also have an impact on the faster disappearance of SC in this region.
In regions where winters are mild, even a slight increase in air temperature reduces the frequency of solid precipitation (snow) in favour of liquid precipitation, thereby increasing the frequency and intensity of melting episodes (Räisänen, 2008;Serquet et al., 2013).Lowerlying stations are strongly influenced by the change in both elements, particularly in spring.The above conclusions are confirmed in the present study results, which were also documented in earlier works by authors from the analysed area (Urban et al. 2018b(Urban et al. , 2019)).
An increasing and statistically significant trend in sunshine duration was found for winter and the cold half of the year, with the largest increase for April, for Śnieżka from 1901 to 2014 (Urban, Migała, & Pawliczek, 2018).In the Czech Republic, on the other hand, an increase in sunshine duration totals was also observed in the 1991-2020 multi-year period compared to 1961-1990, with statistically significant increases for annual and monthly totals for MAM and JJA (Br azdil et al., 2022).
The demonstrated multi-year increase in air temperature in the Western Sudetes (Chapter 3.2), was also reflected in changes in sunshine duration from the corresponding period.The increase in air temperature at Śnieżka, especially noticeable since the 1990s, including in the winter months, showed consistency with the global URBAN ET AL. and local trends of increasing sunshine duration (global brightening) during this period (Wild 2009;Matuszko and Węglarczyk, 2015;Migała et al., 2016;Urban, Migała, & Pawliczek, 2018).
The faster disappearance of SC in spring is associated with high net radiation, which, combined with the already thin SC and increasing air temperature trend, promotes earlier snowmelt (Peng et al., 2013).In addition, springtime SC, which is lingering (coarse) and visibly contaminated at the surface, is characterized by a strongly reduced albedo (He et al., 2014).As a result, the ground absorbs more solar energy and warms up, accelerating spring SC thawing.Reduced albedo and greater absorption of solar radiation is also facilitated by vegetation cover (Barlage et al., 2005).Under Sudetenland conditions, this is mostly spruce stands, which, after the ecological disaster of the 1970s and 1980s, have undergone successful restoration in recent decades (Bałazy, Ciesielski, et al., 2019;Bałazy, Zasada, et al., 2019).
Higher radiation and, at the same time, sunshine duration is also favoured by better atmospheric transparency, which is associated, among other things, with reduced water vapour content.A statistically significant decrease in water vapour content in the troposphere over Poland was observed in spring (MAM) in 1983-2010(Ojrzy nska et al., 2022)).
The results of the SC parameters examined in this study, including a reduction in its duration or decreased depth, correspond to other studies.The rate of decline of MSC in Poland is projected to double between 2071 and 2100 (Szwed et al., 2019).In the Swiss Alps, on the other hand, there has been a significant decline in the depth and duration of SC since the mid-1980s (Beniston, 1997).Similarly, decreasing trends in the duration of SC and the amount of spring snowfall have been observed in the Italian Alps at 800-1500 m a.s.l.over the period 1950-2009, with the greatest rate of decline in the 1990s (Valt & Cianfarra, 2010).An earlier spring disappearance and decline in SC depth is observed in the Alps, especially at stations at mean and low altitudes (Marty & Meister, 2012;Scherrer et al., 2004;Valt & Cianfarra, 2010), in the Pyrenees (L opez-Moreno & Vicente-Serrano, 2007;Mor an-Tejeda, Herrera, et al., 2013) or in the Himalayas (Jain et al., 2010).Analogous results were obtained in the Romanian Carpathians (Micu, 2009).Modelling results for the Alps suggest that snow at low and mean altitudes (up to about 1.500 m a.s.l.) may disappear completely by 2100 (Beniston, 2012).
Trends in the duration of SC in the Western Sudetes calculated for the 1961/1962-2020/2021 seasons are stronger than those from older periods in Poland (Falarz, 2004;Szwed et al., 2017) which is also confirmed by Tomczyk et al. (2021).The results of measurements from ground stations and remote sensing in areas at lower absolute altitudes or with higher mean air temperatures are characterized by the largest decreasing trends in SC characteristics (Vaughan et al., 2013).Such areas include the Western Sudetes.This confirms previous observations in this regard from other areas of Europe (Klein et al., 2016;Nikolova et al., 2013;Serquet et al., 2011).In addition to the influence of higher winter and spring air temperatures, both processes in Europe, including in its mountainous areas, also depend on largescale changes in atmospheric circulation, such as the North Atlantic Oscillation (Bednorz, 2011;Beniston et al., 2018;Buisan et al., 2015;Skaugen et al., 2012).
As long as the duration of SC is strongly related to air temperature, the amount of snow, which translates into snow depth, depends on the amount of precipitation in the form of snow.This explains the different rates of change in the height and duration of SC, which is particularly evident at higher latitudes and, among other things, has been shown for northern Eurasia (Bulygina et al., 2009) and has also been confirmed in the Western Sudetes.
Different methods of observing the timing of SC in recent decades show different rates and directions of change in different parts of the world (Stewart, 2009;McCabe & Wolock, 2010;Kunkel et al., 2016;Saavedra et al., 2018).Studies indicate that in the Northern Hemisphere, rising air temperatures (resulting in warmer winters and a reduction in the proportion of precipitation in the form of snow) over the past few decades have contributed to a significant spring reduction in SC extent and earlier snow melt, leading to shorter SC duration (Brown & Robinson, 2011;Derksen & Brown, 2012;Peng et al., 2013;Rupp et al., 2013).This was particularly pronounced after 1970 in the temperate latitudes of the Northern Hemisphere (McCabe & Wolock, 2010), including the Western Sudetes.Analyses of NOAA satellite data from 1972 to 2007 have shown that the duration of continuous SC in the Northern Hemisphere has decreased by 5.3 daysÁdecade −1 , and this is primarily due to the increasingly earlier timing of snow melt (Choi et al., 2010).SC duration also showed a statistically significant decline in the central Andes between 2000 and 2014 (Saavedra et al., 2018).Spring snow melt occurred earlier, while the onset of SC did not change markedly (Choi et al., 2010).The established trends in the duration of SC in the Western Sudetes are thus consistent with trends throughout the Northern Hemisphere.
In this study, significant decreasing trends in SC duration were found at most of the analysed stations, confirming previous results obtained in this regard for Poland (Falarz, 2004(Falarz, , 2008;;Szwed et al., 2017).In addition, the earlier spring snow melt causes a successive deterioration of the water balance in the area and its broader foreland which also results in an increased frequency of droughts during the growing season (Urban et al., 2022).The reduction in the duration and depth of SC in the study area shown in this article is one of the most important negative effects of warm winters in the Western Sudetes (Urban et al. 2018b(Urban et al. , 2019)).

| SUMMARY AND CONCLUSIONS
The analysis of the reasons for the shortening of SC duration in the Western Sudetes in the winter seasons 1961/1962-2020/2021, considering exposure and relief, confirms the research hypotheses put forward at the beginning of the paper and authorizes the following statements: 1.There is a clear relationship between Tavg and SC parameters (MMSC; NDSC, etc.).It is stronger in stations with northern macro-exposure than southern, while it is weakest in the summit-surface zone.The strongest correlation is in the middle and lower parts of the slopes, mainly northern, which is related to foehn effects.2. For precipitation, there are no clear trends in the direction and rate of change of NDR.However, the NDRS is decreasing (about 3-5 daysÁdecade −1 ), this trend is statistically significant at the level of 0.05.In turn, for precipitation totals, there is a tendency usually negative, in most cases not statistically significant.3. Sunshine duration shows a statistically significant upward trend both in the season and in April-the month of the disappearance of SC.The trends are from about 15 to 50 hÁdecade −1 and from about 12 to 19 h decade, in the summit zone and at the foot of the mountains, respectively.Of the individual months of the winter season, the greatest upward trend is in April.4.There was a statistically significant upward trend in the frequency of NWa, BM anticyclonic circulation types by about 1%Ádecade −1 , with a decrease in the situation with lows over Central Europe (TM).The largest upward trend (about +1.0%Ádecade −1 ) of all 30 circulation types is observed for the NWa type at the same time the largest downward trend (about −1.5%Ádecade −1 ) of the situation with the lows (TM) and occurs in April. 5.The values of the analysed SC parameters (MSDSC, SDSC, MSC, MMSC, NDSC, and NDSC20) increase with altitude, and are higher at analogous heights (m a.s.l.) on slopes with southern macro-exposure (windward in winter) than on slopes with northern macro-exposure (leeward in winter).The greatest differences in SC parameters at stations located at similar altitudes, but with opposite macro-exposures, occur in the 500-900 m altitude zone.
The above meteorological elements and factors that affect the duration of SC are described in more detail in Section 3.6.Of the most important conclusions, it should be remembered that the successive 30 years (climatological norms) have seen a successive shortening of PT and RT of SC duration.The mean PT of duration in the current 1991-2020 norm, relative to the 1961-1990 norm, has shortened from 7 to 16 days.In the mean StartSC dates, there are no clear trends in the direction and rate of change; however, there are negative trends in the EndSC dates, most of which are statistically significant.The rate of change of EndSC is approximately two times greater than that of StartSC.Hence, changes in the end dates of SC have a greater impact on changes in the duration of SC.
In addition, differences in the rate of SC disappearance appear to be greater at stations with northern macro-exposure than southern macro-exposure located at similar absolute altitudes.Differences in stations at similar altitudes located in the same macro-exposure, such as Jelenia G ora-Hejnice, are also apparent, which are due to the susceptibility (or lack thereof) of a given location to foehn effects.
In summary, the reasons for the shortening of SC duration in the Western Sudetes are: 1. Long-term increase in air temperature (warm and thus moist air promotes faster ablation of SC). 2. Long-term increase in sunshine duration-accelerates spring ablation of lingering, thinner and contaminated SC. 3. Changes in precipitation patterns-a reduction in the proportion of solid precipitation in warmer climates, in the absence of significant changes in precipitation totals, affects the SC depth and earlier spring melt.4. Changes in atmospheric circulation-including an increase in the frequency of anticyclonic circulation types with sunshine weather, especially in April (the month of the disappearance of SC in most of the altitudinal profile of the Sudetes), while reducing the share of cyclonic weather types.
All of the above synergistically have an effect on the lower SC depth, a lower number of days with solid precipitation and promote its faster spring disappearance.
The results obtained regarding the reasons for the shortening of SC duration in the Western Sudetes correspond with the results of earlier studies from Europe and the world cited in this paper.They confirm the successive global warming, especially evident in the last few decades.
Abbreviation Affiliation Frequency of circulation types the GWL classification afterHess and Brezowsky (1952, 1977), 1961-2020.[Colour figure can  be viewed at wileyonlinelibrary.com] The rate of change of individual snow cover parameters and indicators in the period Nov-Apr (unitÁdecade −1 ).
Locations of the measurement stations used in the study.Station name abbreviations as per Table 1.[Colour figure can be viewed at wileyonlinelibrary.com] T A B L E 1 Characteristics of weather stations.
Mean seasonal air temperature values ( C) in successive decades and climatological norms.The rate of change of individual air temperature indices in the period Nov-Apr ( CÁdecade −1 ).Pearson's correlation coefficient 'r', direction and trend value for the number of days with precipitation (NDR) and precipitation totals (R), and mean precipitation for the winter seasons (Nov-Apr).
T A B L E 3 height and macro-exposure of the slopes.It was found to be:(a) moderate and strong in stations with macro-exposure 'N', (b) moderate in stations with macro-exposure 'S', (c) the weakest correlation (r = 0.3) is in the summitsurface zone of the mountains, which should be combined with the influence of strong winds that cause the snow to blow away, etc.,TA B L E 4*Statistically significant at the 0.05; **Statistically significant at the 0.01 level.aSeasonsaccording to Table1.T A B L E 5 Pearson's correlation coefficients 'r' between the mean seasonal air temperature and selected SC parameters in the period Nov-Apr.*Statisticallysignificant at the level of 0.05.a Seasons according to Table T A B L E 7 Mean seasonal (Nov-Apr) number of days with precipitation (NDR), including total precipitation (R) and solid precipitation (RS).
a Seasons according to Table1.T A B L E 8 Pearson's correlation coefficient 'r' and the direction and value of the trend 'a' (hÁdecade −1 ) for seasonal (Nov-Apr) sunshine duration totals (HSD/ASD).aSeasonsaccording to Table1.