water

Article Density of Seasonal in the Mountainous Environment of Five Slovak Centers

Michal Mikloš 1,*, Jaroslav Skvarenina 1,*, Martin Janˇco 2 and Jana Skvareninova 3 1 Department of Natural Environment, Faculty of Forestry, Technical University in Zvolen, Ul. T.G. Masaryka 24, 960 53 Zvolen, Slovakia 2 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04 Bratislava, Slovakia; [email protected] 3 Faculty of Ecology and Environmental Sciences, Technical University in Zvolen, Ul. T.G. Masaryka 24, 960 53 Zvolen, Slovakia; [email protected] * Correspondence: [email protected] (M.M.); [email protected] (J.S.); Tel.: +421-455-206-209 (J.S.)

 Received: 17 August 2020; Accepted: 15 December 2020; Published: 18 December 2020 

Abstract: Climate change affects snowpack properties indirectly through the greater need for artificial snow production for ski centers. The seasonal snowpacks at five ski centers in Central Slovakia were examined over the course of three winter seasons to identify and compare the seasonal development and inter-seasonal and spatial variability of depth average snow density of ski snow and uncompacted natural snow. The spatial variability in the ski piste snow density was analyzed in relation to the snow depth and snow lances at the Košútka ski center using GIS. A special snow tube for high-density snowpack sampling was developed (named the MM snow tube) and tested against the commonly used VS-43 snow tube. Measurements showed that the MM snow tube was constructed appropriately and had comparable precision. Significant differences in mean snow density were identified for the studied snow types. The similar rates of increase for the densities of the ski piste snow and uncompacted natural snow suggested that the key density differences stem from the artificial (machine-made) versus natural snow versus processes after and not densification due to machines and skiers, which was relevant only for ski piste snow. The ski piste snow density increased on slope with decreasing snow depth (18 kg/m3 per each 10 cm), while snow depth decreased 2 cm per each meter from the center of snow lances. Mean three seasons maximal measured density of ski piste snow was 917 58 kg/m3 the density of ice. This study increases the ± understanding of the snowpack development processes in a manipulated mountainous environment through examinations of temporal and spatial variability in snow densities and an investigation into the development of natural and ski piste snow densities over the winter season.

Keywords: snow density; snow tube; technology; artificial snow; ski slope; piste; VS-43; snow depth; snow lances; water balance

1. Introduction A seasonal snow cover that is deposited and melts annually is a major component of regional and global hydrologic balances due to its effects on energy and moisture budgets [1,2]. To calculate snowmelt, a major source of water from mountainous areas in temperate zones [3], the development of snow water equivalent (SWE) over the winter season shall be monitored [4]. The SWE is possible to identify from the extracted snow core directly by a calibrated scale or indirectly by calculation from the snow depth and density (weight) measurements [5]. However, both methods are time consuming due to snow core extraction and weighing. Mathematical models of snow density development over the winter season and/or models of relationship between snow depth and density could potentially

Water 2020, 12, 3563; doi:10.3390/w12123563 www.mdpi.com/journal/water Water 2020, 12, 3563 2 of 18 save lot of time and effort by allowing SWE calculations to be made on the basis of snow depth measurements and estimated snow density only [6,7]. Such models have not yet been developed for a ski piste snowpack; thus, doing so is a goal of this study. For this purpose, a series of snow density measurements must be performed via snow core extraction and weight measurements. To extract a gravimetric snow core from a snowpack, a snow tube is used [8]. The snow tube was first popularized by Church [5,9] and is still utilized by snow surveyors in forested, remote, or hilly watersheds [10]. Manual measurements utilizing a snow tube frequently underestimate depth-average snow density and the SWE of a snowpack due to sampling difficulties associated with the high density of ground ice [11]. It is impossible to extract an ice sample or sample through an ice layer when a conventional snow tube is used. Keller et al. [12], when dealing with impact of ski-slope grooming on the snowpack and soil properties, mention that after mid-December, the snow on the ski slope they were investigating was too hard for manual snow-density measurements to be obtained with a snow tube designed for uncompacted natural snow. Therefore, Rixen et al. [13] sampled such snow with a motor-driven SIPRE corer [14] to compare the physical properties of artificial and natural snow; however, this approach is not practical due to construction and operation costs. In addition, motor-driven devices for snow core extraction are much more complicated to construct and operate than snow tubes. However, snow tubes suitable for a groomed ski piste snowpack or a natural snowpack of high density have not yet been developed (an aim of the present paper). Another approach is to use a PICO coring auger [15] designed for ice sampling for the manual extraction of snow samples from a high-density snowpack [16]. The snow density of a ski piste snowpack is essential for the assessment of the environmental impacts of ski piste management [17], for the calculation of the SWE and water balance [18], for defining the snow type [19], and mainly for a quality assessment of the ski piste snowpack for winter sports [20]. Snow metamorphoses, depending on the meteorological conditions, the physical properties of the overlying snow, time on the ground, and mechanical disturbances, can change the snowpack’s density [21]. Compared to natural snow cover, the snow on the ski is increased mechanically via snow grooming machines and artificial snow [22]. Federolf et al. [23] observed that groomed ski slopes covered by natural snow have densities ranging from 330 to 660 kg/m3, while Rixen et al. [24] identified a similar density range for freshly-produced artificial snow. A whole season’s worth of systematic measurements of the depth-average density of a groomed ski piste snowpack with artificial snow added has not yet been published (another aim of the present paper). Ongoing and future changes in forest composition and climatic conditions have and will modify the seasonal distribution of both precipitation and runoff in the pilot region [25,26]. As a consequence, the operability of Central Slovakian ski slopes up until 1000 m a.s.l. is highly dependent on snow production, as shown in our previous study [27]. Winter precipitation and water availability during the season is decreasing, in general [28,29]. Therefore, a high volume of artificial snow is produced at the beginning of each season for the groomed ski pistes of Central Slovakia. However, the snow densities and microstructures, which are used to define snow types [19], of natural and artificial snow differ markedly, both in the case of freshly fallen/produced snow and in the case of older, metamorphic snow on the ground [30,31]. The following snow types were examined in the present article: (i) new natural snow (max. 2-day-old snowpack), (ii) new artificial snow (max. 2-day-old machine-made snowpack), (iii) uncompacted natural snow, and iv) ski piste snow. The main goal of this study was to identify models of temporal and spatial development of ski piste snow density that could allow density estimation to be made on the basis of the term in winter season and / or snow depth measurements. The spatial development of ski piste snow density was analyzed only in one ski center at the end of the winter season; thus, this model can be generalized only for the late snow ablation period. To reach the main goal and fill gaps in the research on the groomed and snowed ski piste snowpack described above, the following sub-objectives were set: Water 2020, 12, 3563 3 of 18

A. Snow tube construction:

Water 2020, 12, x FOR PEER REVIEW 3 of 18 - Design and construct a snow tube suitable for depth-average snow density measurements of a groomed ski piste snowpack with artificial snow added. - Identify the precision of the designed snow tube on ski piste and off-piste sites through comparison- Identify of thesnow precision density of measurements the designed with snow commonly tube on ski used piste VS-43 and snow off-piste tube. sites through comparison of snow density measurements with commonly used VS-43 snow tube. B. Density of snow at five ski centers: B. Density of snow at five ski centers: - Identify and compare the mean, minimal, and maximal densities of ski piste snowpack with uncompacted- Identify andnatural compare snowpack the mean, on minimal,a seasonal and and maximal monthly densities scale and of ski do piste the snowpacksame for withnew artificialuncompacted snow and new natural natural snowpack snow measur on a seasonaled at the and beginning monthly of scale the and winter do theseason. same for new - Identifyartificial and compare snow and the new seasonal natural and snow inter-seas measuredonal at course the beginning densities of and the wintervariabilities season. in the densities- Identify of ski and piste compare and the uncompacted seasonal and inter-seasonalnatural snow courseand describe densities andthem variabilities with linear in mathematicalthe densities models of skiif applicable piste and to uncompacted identify slope natural of increase snow over and the describe season. them with linear mathematical models if applicable to identify slope of increase over the season. C. Snow density versus snow depth relationship on the example of Košútka ski center: C. Snow density versus snow depth relationship on the example of Košútka ski center: - Identify the spatial distribution of the snow depth and the spatial variability of the snow density in- theIdentify ski piste the area spatial and analyze distribution the correlatio of the snowns between depth and these the two spatial variables variability and the of thepositions snow of fixeddensity snow-making in the ski lances piste areaat the and end analyze of the winter the correlations season. between these two variables and the positions of fixed snow-making lances at the end of the winter season. 2. Materials and Methods 2. Materials and Methods 2.1. Study Sites 2.1. Study Sites The study was conducted at five ski centers located in Central Slovakia (Figure 1). The elevation of theThe ski study slopes was varied conducted from 510 at fiveto 1402 ski centersm a.s.l., located while all in Centralstudy sites Slovakia at the (Figureski centers1). The were elevation located ofat theelevations ski slopes lower varied than from 1000 510 m to a.s.l. 1402 (Figure m a.s.l., 1) while. According all study to sites the atgeomorph the ski centersological were classification located at elevations[32,33], alllower the ski than centers 1000 mare a.s.l. located (Figure in 1the). AccordingInner Western to the Carpathian geomorphological sub-province. classification According [ 32,33 to], allSlovakia’s the ski centers climate are classifications located in the [34], Inner the Western higher Carpathian ski resorts sub-province. (Krahule and According Donovaly) to Slovakia’sbelong to climatesubregion classifications C1 (moderately [34], cool), the higherwhile the ski lower resorts resorts (Krahule (Košútka and and Donovaly) Jasenská) belong are included to subregion in the C1climate (moderately subregions cool), M7 while (moderately the lower warm, resorts very (Koš humid,útka and highlands) Jasenská )and are includedM6 (moderately in the climatewarm, subregionshumid, highlands), M7 (moderately respectively. warm, Based very on humid, the annual highlands) temperature and M6 amplitudes, (moderately the warm,lower research humid, highlands),plots belong respectively. to the transitional Based on maritime the annual climate temperature to moderately amplitudes, continental the lower climate, research while, plots belongfor the tohigher the transitional ski resorts, maritimethe temperature climate amplitude to moderately decrea continentalses and the climate, oceanity while, of the for climate the higher increases ski resorts, [35]. theFurther temperature detailed amplitudecharacteristics decreases of the and resorts’ the oceanity climatic ofand the natural climate conditions increases [35are]. given Further in detailedTable 1, characteristicswhich has been of processed the resorts’ according climatic to and the natural Climate conditions Atlas of Slovakia are given [36] in and Table Hrvol’1, which et al. has [37]. been As processedwe can see according from the to Table the Climate 1, the Atlasnumber of Slovakia of days [36with] and snow Hrvol’ cover et al.and [37 the]. As average we can seesnow from depth the Tableincrease1, the with number increasing of days altitude with snow[38–40]. cover The and potential the average natural snow vegetation depth increase is described with increasingin terms of altitudeSkvarenina [38– et40 al.]. The[41]. potential natural vegetation is described in terms of Skvarenina et al. [41].

FigureFigure 1.1. Ski centers’ elevations and locations in Central SlovakiaSlovakia andand CentralCentral Europe.Europe.

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Table 1. The basic environmental characteristics of five ski centers in Central Slovakia at which the snow density was examined, according to the Climate Atlas of Slovakia [36] where data from 1961 to 2010 were processed.

Jasenská Košútka Králiky Krahule Donovaly Altitude 590 615 855 990 945 (m a. s. l.) N 49.00976 N 48.55909 N 48.73626 N 48.72824 N 48.87313 GPS ◦ ◦ ◦ ◦ ◦ E 19.00959◦ E 19.53484◦ E 19.01706◦ E 18.94727◦ E 19.22425◦ Vepor Kremnica Kremnica Staré Hory Geomorphological units Vel’ká Fatra Mountains Mountains Mountains Mountains Aspect N NW NE SW N Average annual air 6.9 6.7 5.2 4.8 4.5 temperature (◦C) Average winter air 2.8 3.1 3.9 4.1 4.4 temperature (◦C) − − − − − Average annual 850 755 1080 1025 1180 precipitation total (mm) Average winter 160 130 240 220 250 precipitation total (mm) Average number of day 55 48 70 68 87 with snow cover ( 10 cm) ≥ Average number of day 35 27 45 47 66 with snow cover ( 20 cm) ≥ Average number of day 9 6 10 12 27 with snow cover ( 50 cm) ≥ Average snow cover depth 40 37 53 56 65 (cm) Climatic sub region M7 M6 C1 C1 C1 Watercourse/ Drainage Beliansky Tajovský Krahulský Slanec/Hron Korytnica/Váh basin potok/Váh potok/Hron potok/Hron 3th 6th Potential natural 4th beech 5th fir–beech 5th fir–beech oak–beech spruce-beech-fir vegetation stage stage stage stage stage

2.2. Snow Tube Snow tubes are used to extract gravimetric samples of snow (snow cores) in order to measure the depth-averaged snow density and SWE [8]. The snow tube used on the groomed ski pistes with high-density snow was developed (Table2, see Figure2b in Section 3.1) and named the MM snow tube due to the highly used man-made (artificial) snow on the groomed ski slopes and the initials of its designer (first author of this article). To extract the snow core with the designed tube, it was necessary to use a heavy hammer (approx. 3.5 kg). Before removing the tube from the snowpack for weighing, the snow core had to be pressed inside to increase sample adhesiveness. To make it easier to pull it from the snowpack and taking into consideration the possible use of a hanging weight, a stainless-steel hose clamp with hanging rope was placed on the top of the tube. After weighing, the snow core was pushed out of the tube with an aluminum rod with a penny washer (M8 30 mm) on one side. × Table 2. Main characteristics of the snow tubes used in this study.

Weight (Cap) Sampling Snow Tube Cap Material Length (mm) Inner Ø (mm) (kg) Time (min.) * Stainless MM + 800 4.18 (0.76) 40 4 2 Steel ± VS-43 + Aluminum 600 1.25 (0.17) 84 15 5 ± * Average sampling time of the 30 paired measurements (mean standard deviation). ± Water 2020, 12, x FOR PEER REVIEW 6 of 18

snow lances were used to analyze the relationship between the snow depth and density [16]. The mean snow density and depth were calculated on concentric circles of radius R = 5, 7.5, 10... 30 m around each of the 17 snow lances. The maximum radius of 30 m was equal to the maximum distance that water/ice particles emitted from the used snow lances in Košútka ski centre could travel without wind support. This distance depends on the type and technology of used machines.

3. Results

3.1. Snow Tube A 800 mm-long snow tube with a 50-mm outside diameter and 5-mm-thick walls that began tapering 336 mm from the cutting end was constructed (Figure 2a). The wall thickness of the sharpened cutting end was 1.5 mm. The weight of the tube without its cap was 4.2 kg, while the 100 mm of the tube used for construction weighed 0.6 kg. An essential part of the tube was its removable cap. EN 1.4310 (X10CrNi18-8) stainless steel was selected as the construction material due to its

Waterhardness2020, 12 and, 3563 corrosion resistance. The measurement scale was engraved on the outside wall of5 of the 18 tube that was used to measure the snow depth or identify how deep the tube had penetrated.

FigureFigure 2.2. ((a)) Assembly ofof the MM snow tube, which consistedconsisted ofof aa tube and cup (dimensions inin mm); ((bb)) CommonlyCommonly usedused VS-43VS-43 snowsnow tubetube inin comparisoncomparison withwith the the designed designed tube. tube.

ToThe assess paired precision t-test showed and reliability no significant of the MM difference tube on ( thep-value groomed = 0.23) ski between piste, 30 pairedthe samples measurements collected wereby the performed MM tube inand January the commonly 2017 at Kr usedáliky. VS-43 A snow snow tubetube that (Figure is popular 3). The in average Europe difference and Russia between named thethe VS-43observations was used in forpairs comparison was 22.2 ± (Table 18.1 2kg/m³,)[ 42]. while The assembly the MM oftube the underestimated VS-43 snow tube the with snow its originaldensity mechanicalcompared to scales the VS-43 is illustrated tube by in about Figure 2.1 A1 ± in 3.9%, Appendix on average.A. The VS-43The VS-43 snow snow tube wastube destroyed (Figure 2b) during has a thedesign 30 paired that is measurements, similar to that because of the MM the aluminum tube, but, did when not it stand was upused to theon hammering.a ski slope, the The following precision ofdisadvantages the new snow were tube noted: was assessed(i) long sampling on uncompacted time, (ii) it natural had difficulty snow, as penetrating well. In this thecase, snowpack, 30 paired (iii) measurementsit was hard to wereremove taken from at Donovalythe snowpack in March (the 2017.sampler usually stuck in the snowpack due to the bigger diameter of the cutting end compared to the diameter of the tube), and (iv) inadequate 2.3. Snow Density construction (after a few samples, the sampler was deformed by the hammering). The tendency of the MMDepth snow average tube to density underestimate of the four the following snow densit snowy was types detected were identified for natural at snow the five as well, ski centres and it (Jasenskunderestimatedá, Košú tka,the density Králiky, by Krahule,about 6.9 Donovaly)± 2.9% (Figure across 3). In three the case winter of uncompacted seasons from natural 2014 /snow,15 to 2016the paired/17: (i) t-test new detected artificial a snow difference (max. between two-day-old the samples machine-made taken by the snow), two snow (ii) new tubes. natural Therefore, snow (max.the MM two-day-old tube is not snowpack),recommended (iii) for ski use piste mainly snowwhen (groomed the snowpack snow with is artificialshallow and snow has added), a low anddensity (iv) uncompacted(new natural snow),natural possibly snow on due off-piste to low sites. sample The weights densities (small of all tube four diameter), types of snow which were are identifieddifficult to via detect series precisely of five in measurements. the field with a If hanging natural weight. snow occurred on the off-piste site, then the measurements of the ski piste and natural snowpacks were always paired. Measurements began with the first occurrence of natural snow for the season and carried on over the course of irregular time intervals, which were 17 days long, on average. The density measurements for the ski piste and natural snowpacks were identified on the horizontal transect that intersected groomed ski piste and adjacent off-piste sites with uncompacted natural snow. A series of five measurements were made at groomed ski piste and off-piste sites that were paired according to site properties, such as elevation, slope, aspect, curvature of relief, and obscuration. The densities of uncompacted and new natural snow were sampled with the VS-43 snow tube, while new artificial snow and ski piste snow were sampled with the MM snow tube. The samples were compared via paired or unpaired Student’s t-tests at an alpha level of 0.05 and n 1 degrees of freedom. In each case, the proper test was chosen according to the assumptions required − for the samples. Both tests assumed that the variables were normally distributed, the observations were sampled independently, and the variables were from two related groups or matched pairs; the unpaired t-test assumed that the variables were from two independent groups with the same variance. The type of t-test used is identified when the results of a case are discussed. Mean values mentioned in results are accompanied with the standard deviation and number of samples (N/n) used for calculation. The total number of measured samples (N) or number of mean values (n) can be found. Water 2020, 12, 3563 6 of 18

2.4. Snow Density Versus Snow Depth At the end of the winter season on 15 March 2015, when the natural snow on the adjacent off-piste sites has melted away, the snow depth and density of the ski piste snowpack were measured along the whole ski piste at Košútka to analyze the correlations between the snow density and depth variables and the distance from the snow lances. The snow depth was measured at 96 sampling points, while the snow density was measured at 72 of these points. To analyze the spatial distribution of the snow and spatial variability of the snow density, the snow depth, and density raster layers were interpolated from the point measurements in ArcGIS 10.3.1. The raster layers, which consist of matrices of cells organized into rows and columns, where each cell contains a value representing information, such as snow depth or density, as in this paper, were created to provide pictures of these real-world phenomena. The interpolation spline technique was used to create raster layers with 1 1 m cell sizes. The spline × technique was chosen, because it guarantees that the resulting surface will pass through the data points exactly, making it ideal for generating gently varying surfaces, such as snowpack surfaces or elevation. The correlations between the snow depth and density raster layers were computed with the Band Collection Statistics tool in ArcGIS 10.3.1. Concentric circles around snow lances were used to analyze the relationship between the snow depth and density [16]. The mean snow density and depth were calculated on concentric circles of radius R = 5, 7.5, 10 ... 30 m around each of the 17 snow lances. The maximum radius of 30 m was equal to the maximum distance that water/ice particles emitted from the used snow lances in Košútka ski centre could travel without wind support. This distance depends on the type and technology of used snowmaking machines.

3. Results

3.1. Snow Tube A 800 mm-long snow tube with a 50-mm outside diameter and 5-mm-thick walls that began tapering 336 mm from the cutting end was constructed (Figure2a). The wall thickness of the sharpened cutting end was 1.5 mm. The weight of the tube without its cap was 4.2 kg, while the 100 mm of the tube used for construction weighed 0.6 kg. An essential part of the tube was its removable cap. EN 1.4310 (X10CrNi18-8) stainless steel was selected as the construction material due to its hardness and corrosion resistance. The measurement scale was engraved on the outside wall of the tube that was used to measure the snow depth or identify how deep the tube had penetrated. The paired t-test showed no significant difference (p-value = 0.23) between the samples collected by the MM tube and the commonly used VS-43 snow tube (Figure3). The average di fference between the observations in pairs was 22.2 18.1 kg/m3, while the MM tube underestimated the snow density ± compared to the VS-43 tube by about 2.1 3.9%, on average. The VS-43 snow tube (Figure2b) has ± a design that is similar to that of the MM tube, but, when it was used on a ski slope, the following disadvantages were noted: (i) long sampling time, (ii) it had difficulty penetrating the snowpack, (iii) it was hard to remove from the snowpack (the sampler usually stuck in the snowpack due to the bigger diameter of the cutting end compared to the diameter of the tube), and (iv) inadequate construction (after a few samples, the sampler was deformed by the hammering). The tendency of the MM snow tube to underestimate the snow density was detected for natural snow as well, and it underestimated the density by about 6.9 2.9% (Figure3). In the case of uncompacted natural ± snow, the paired t-test detected a difference between the samples taken by the two snow tubes. Therefore, the MM tube is not recommended for use mainly when the snowpack is shallow and has a low density (new natural snow), possibly due to low sample weights (small tube diameter), which are difficult to detect precisely in the field with a hanging weight. Water 2020, 12, 3563 7 of 18 Water 2020, 12, x FOR PEER REVIEW 7 of 18

Figure 3. Comparison of 30 paired measurements of the snow densities of ski piste and uncompacted natural snow measured byby designeddesigned MMMM snowsnow tubetube versusversus thethe VS-43VS-43 snowsnow tube.tube. 3.2. Snow Density 3.2. Snow Density The mean densities of the types of snow were calculated for three seasons with data from the five The mean densities of the types of snow were calculated for three seasons with data from the ski centres. These densities indicated that the mean density of new artificial snow was 2.3 times higher five ski centres. These densities indicated that the mean density of new artificial snow was 2.3 times than the mean density of new natural snow (409.6 66.2 kg/m3 versus 175.3 71.6 kg/m3;N = 209 higher than the mean density of new natural snow (409.6± ± 66.2 kg/m³ versus 175.3± ± 71.6 kg/m³; N = versus 199 samples) and that the mean density of ski piste snow was 2.5 times higher than the density 209 versus 199 samples) and that the mean density of ski piste snow was 2.5 times higher than the of uncompacted natural snow on the off-piste sites (595.9 101.0 kg/m3 versus 238.5 95.3 kg/m3; density of uncompacted natural snow on the off-piste sites± (595.9 ± 101.0 kg/m³ versus± 238.5 ± 95.3 N = 722 versus 400 samples; Figure4). The following is a list of snow types according to their mean kg/m³; N = 722 versus 400 samples; Figure 4). The following is a list of snow types according to their densities (in descending order): ski piste snow (mixture of natural and artificial snow), new artificial mean densities (in descending order): ski piste snow (mixture of natural and artificial snow), new snow (max. two-day-old machine-made snow), uncompacted natural snow, and new natural snow. artificial snow (max. two-day-old machine-made snow), uncompacted natural snow, and new The data over the three seasons showed significant differences (unpaired t-test: p < 0.5) across all four natural snow. The data over the three seasons showed significant differences (unpaired t-test: p < 0.5) studied snow types. The ski piste snow had greater seasonal variability than the uncompacted natural across all four studied snow types. The ski piste snow had greater seasonal variability than the snow (Figure4). Mean di fference between the maximal and minimal density (except for outliers; uncompacted natural snow (Figure 4). Mean difference between the maximal and minimal density Figure4b) identified in each of five ski centers over the three winter seasons for the types of snow were (except for outliers; Figure 4b) identified in each of five ski centers over the three winter seasons for as follows: (i) 420 87 kg/m3 for ski piste snow, (ii) 328 80 kg/m3 for uncompacted natural snow, the types of snow± were as follows: (i) 420 ± 87 kg/m³ ±for ski piste snow, (ii) 328 ± 80 kg/m³ for (iii) 273 66 kg/m3 for new artificial snow, and (iv) 211 59 kg/m3 for new natural snow. A paired uncompacted± natural snow, (iii) 273 ± 66 kg/m³ for new± artificial snow, and (iv) 211 ± 59 kg/m³ for comparison of the mean differences between the maximal and minimal densities of snow (excluding new natural snow. A paired comparison of the mean differences between the maximal and minimal outliers) at the ski centers showed no significant difference (paired t-test: p > 0.5) between ski piste and densities of snow (excluding outliers) at the ski centers showed no significant difference (paired t- uncompacted natural snow (comparable differences, not maximal and minimal values) but showed a test: p ˃ 0.5) between ski piste and uncompacted natural snow (comparable differences, not maximal significant difference (paired t-test: p < 0.5) between new artificial and new natural snow. Outliers were and minimal values) but showed a significant difference (paired t-test: p < 0.5) between new artificial identified mainly for ski piste snow at all five ski centers. The mean density of the ski piste snowpack and new natural snow. Outliers were identified mainly for ski piste snow at all five ski centers. The calculated from the peak outliers identified at the ski centers was 917 58 kg/m3 (n = 5; peak outlier is mean density of the ski piste snowpack calculated from the peak outlie± rs identified at the ski centers highest measured value displyed in Figure4a), which is the density of ice. The peak outliers of ski was 917 ± 58 kg/m³ (n = 5; peak outlier is highest measured value displyed in Figure 4a), which is the piste snow were not significantly different (paired t-test: p > 0.5) from the density of ice. density of ice. The peak outliers of ski piste snow were not significantly different (paired t-test: p ˃ The highest three seasons mean density of new artificial snow (435.8 55.7 kg/m3,N = 34 samples) 0.5) from the density of ice. ± and ski piste snow (621.1 111.3 kg/m3,N = 139 samples) were identified at a low-elevation ski center, The highest three seasons± mean density of new artificial snow (435.8 ± 55.7 kg/m³, N = 34 namely, Košútka (Figure4). The lowest and highest three seasons mean densities of new natural snow samples) and ski piste snow (621.1 ± 111.3 kg/m³, N = 139 samples) were identified at a low-elevation were identified at high-elevation ski centers, namely, Krahule (134.6 37.4 kg/m3;N = 30 samples) ski center, namely, Košútka (Figure 4). The lowest and highest three seasons± mean densities of new and Donovaly (210.4 68.2 kg/m3,N = 49 samples), respectively. The mean density of uncompacted natural snow were identified± at high-elevation ski centers, namely, Krahule (134.6 ± 37.4 kg/m³; N = natural snow was lowest at Košútka (181.1 88.9 kg/m3,N = 38 samples) and highest at Donovaly 30 samples) and Donovaly (210.4 ± 68.2 kg/m³,± N = 49 samples), respectively. The mean density of (270.0 96.6 kg/m3,N = 103 samples). uncompacted± natural snow was lowest at Košútka (181.1 ± 88.9 kg/m³, N = 38 samples) and highest The mean density of ski piste snow in December calculated from all measured data was at Donovaly (270.0 ± 96.6 kg/m³, N = 103 samples). 538.9 135.2 kg/m3, while its increase per month was 13.2 kg/m3 (Figure5). The mean monthly ± density of ski piste snow had a tendency to increase over the whole winter season, except at the end of the season in April, when the mean monthly density was equal to the mean density in March. The mean density of uncompacted natural snow in December was 190.8 116.5 kg/m3, while its ± increase per month was 28.2 kg/m3. The mean monthly density of uncompacted natural snow had a tendency to increase over the whole season from December to April, except for the month of March. The mean monthly densities of ski piste snow and uncompacted natural snow were significantly

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different (paired t-test: p < 0.5). The average seasonal difference between the mean monthly densities different (paired t-test: p < 0.5). The average seasonal difference between the mean monthly densities of ski piste snow and uncompacted natural snow (displayed in Figure5) was 324.6 46.0 kg/m3. of ski piste snow and uncompacted natural snow (displayed in Figure 5) was 324.6 46.0± kg/m3. The low standard deviation of this difference the mean monthly densities of both types± of snow showed The low standard deviation of this difference the mean monthly densities of both types of snow showed comparable increases. The highest difference in the mean monthly densities of ski piste snow and comparable increases. The highest(a) difference in the mean monthly densities( ofb) ski piste snow and uncompacted natural snow was found in March (372 kg/m3), which also had the highest maximal uncompacted natural snow was found in March (372 kg/m3), which also had the highest maximal (980Figure kg/m3 )4. and (a) Comparison mean (635 of kg the/m data3) densities for three seasons of ski piste with regard snowpack to the (Figure snow density5). The of new mean natural monthly (980 kg/m3) and mean (635 kg/m3) densities of ski piste snowpack (Figure 5). The mean monthly densitysnow of uncompacted(NN), new artificial natural snow snow (NA), exceeded uncompacted the mean natural monthly snow density(NS), and of ski ski piste piste snow snow (SP) in Januaryfor the five ski centers. The lowest number of measured samples (N = 30) was in the case of NA in Kraíliky and April only by about 60 and 35 kg/m3, respectively. In contrast, the minimal mean monthly density and NN in Krahule. Description of boxplot: cross = mean, horizontal line in the box = median, box = of ski piste snow never dropped below the mean monthly density of uncompacted natural snow. 50% of values, box with whiskers = 99% of values, points = outliers. (b) Boxplots of the minimal, maximal, and mean density identified in each of five ski centers (excluding outliers) over the three winter seasons for four snow types (n = 5).

The mean density of ski piste snow in December calculated from all measured data was 538.9 ± 135.2 kg/m³, while its increase per month was 13.2 kg/m³ (Figure 5). The mean monthly density of ski piste snow had a tendency to increase over the whole winter season, except at the end of the season in April, when the mean monthly density was equal to the mean density in March. The mean density of uncompacted natural snow in December was 190.8 ± 116.5 kg/m³, while its increase per month was 28.2 kg/m³. The mean monthly density of uncompacted natural snow had a tendency to increase over the whole season from December to April, except for the month of March. The mean monthly densities of ski piste snow and uncompacted natural snow were significantly different (paired t-test: p < 0.5). The average seasonal difference between the mean monthly densities of ski piste snow and uncompacted natural snow (displayed in Figure 5) was 324.6 ± 46.0 kg/m³. The low standard deviation of this difference the mean monthly densities of both types of snow showed comparable increases.Figure The 4. ( ahighest) Comparison difference of the in data the for mean three mont seasonshly with densities regard toof theski snowpiste densitysnow and of new uncompacted natural naturalsnow snow (NN), was new found artificial in March snow (NA), (372 uncompactedkg/m³), which natural also snowhad the (NS), highest and ski maximal piste snow (980 (SP) kg/m³) for the and meanfive (635 ski centers.kg/m³) Thedensities lowest numberof ski of piste measured snowpack samples (N(Figure= 30) was5). inThe the casemean of NAmonthly in Kraíliky density and of uncompactedNN in Krahule. natural Description snow exceeded of boxplot: the cross mean= mean, mont horizontalhly density line of in ski the boxpiste= median,snow in box January= 50% and NN in Krahule. Description of boxplot: cross = mean, horizontal line in the box = median, box = 50% Aprilof only values, by boxabout with 60 whiskers and 35 kg/m³,= 99% ofrespectively. values, points In= contrast,outliers. (theb) Boxplots minimal of mean the minimal, monthly maximal, density and of 50%of values, of values, box with box whiskerswith whiskers= 99% = of 99% values, of values, points =pointsoutliers. = outliers. (b) Boxplots (b) Boxplots of the minimal, of the minimal, maximal, April onlyand meanby about density 60 identifiedand 35 kg/m³, in each respectively. of five ski centers In contrast, (excluding the outliers) minimal over mean the threemonthly winter density seasons of ski maximal,andpiste mean snow and density never mean identified droppeddensity inidentified eachbelow of fivethe in each skimean centers of monthlyfive (excluding ski centers density outliers) (excluding of unco over outliers) thempacted three over winter natural the seasons three snow. ski pistefor snow four snownever types dropped (n = 5). below the mean monthly density of uncompacted natural snow. winterfor four seasons snow types for four (n = snow5). types (n = 5). SP: b = 13.21; r = 0.60 / NS: b = 28.20; r = 0.92 1000 SP: b = 13.21; r = 0.60 / NS: b = 28.20; r = 0.92 1000 The mean density of ski 800piste snow in December calculated from all measured data was 538.9 ± 800 (40) (224) (208) (162) (78) 135.2 kg/m³, while its increase600 per month(40) was 13.2(224) kg/m³(208) (Figure 5).(162) The mean(78) monthly density of ski 600 (13) piste snow had a tendency to400 increase over the whol(192)e winter(128) season,(25) except at the end of the season 400 (73) (128) (25) (13) in April, when the mean monthly200 density(73) was equal(192) to the mean density in March. The mean density

Density (kg/m³) 200 of uncompacted natural snowDensity (kg/m³) in0 December was 190.8 ± 116.5 kg/m³, while its increase per month was 0 XII. I. II. III. IV. 28.2 kg/m³. The mean monthly densityXII. of uncompacte I.d II. natural III.snow had IV. a tendency to increase over SP 538.9 576.8 594.8 634.6 575.2 the whole season from DecemberSP 538.9 to April, 576.8 except 594.8for the 634.6month of 575.2 March. The mean monthly NS 190.8 245.3 273.4 262.5 325.5 densities of ski piste snow andNS uncompacted190.8 245.3 natural 273.4 snow were 262.5 significantly 325.5 different (paired t-test: p < 0.5).Figure The average 5. IncreasesIncreases seasonal in in the the mean meandifference monthly monthly between density density the of of ski skimean piste piste monthly snow snow (SP) (SP) densities and and uncompacted uncompacted of ski piste natural natural snow snow and Figure 5. IncreasesIncreases in in the the mean mean monthly monthly density density of of ski ski piste piste snow snow (SP) (SP) and and uncompacted uncompacted natural natural snow uncompacted(NS) over natural the winter snow season (displayed (mean ± min/max). minin /max).Figure The The 5) means meanswas from324.6 from three three± 46.0 seasons seasons kg/m³. calculated The low from standard all data (NS) over the winter season (mean ± min/max).min± /max). The The means means from from three three seasons seasons calculated from all data deviationmeasured of this atdifference the fivefive ski the centers mean ± are monthly displayed.displayed. dens b =ities slslopeope of of ofboth regression types ofline, snow r = correlationcorrelation showed comparable coefficient, coefficient, measured at the fivefive ski centers are displayed.displayed. b = slslopeope of of regression line, r = correlationcorrelation coefficient, coefficient, increases.(x) = The thethe totalhighest total number number difference of of samples. samples. in the mean monthly densities of ski piste snow and uncompacted (x) = thethe total total number number of of samples. samples. natural snow was found in March (372 kg/m³), which also had the highest maximal (980 kg/m³) and The densities of the ski piste snow and uncompacted natural snow showed an increasing seasonal meanThe (635 densities kg/m³) of densities the ski piste of snowski piste and uncompactedsnowpack (Figure natural 5). snow The showed mean anmonthly increasing density seasonal of trend and inter-seasonal variability in all three winter seasons across all five ski centers, except for uncompactedtrend and inter-seasonal natural snow variability exceeded in the all threemean wintermonthly seasons density across of ski all piste five skisnow centers, in January except and for Aprilseasonsseasons only with withby shortagesabout shortages 60 and of of natural35 natural kg/m³, snow snowrespectively. (Figure (Figure6 ).In6). Thecontrast, The slopes slopes the of minimal of the the regression regression mean monthly models models indensity Figurein Figure of6 6 skiindicateindicate piste snow no no significant significantnever dropped di differenceff erencebelow between the between mean ski monthly ski piste piste snow density snow and andof uncompacted unco uncompactedmpacted naturalnatural natural snowsnow. snow when when comparedcompared with with the the paired pairedt-testt-test (p (

Figure 5. Increases in the mean monthly density of ski piste snow (SP) and uncompacted natural snow (NS) over the winter season (mean ± min/max). The means from three seasons calculated from all data measured at the five ski centers are displayed. b = slope of regression line, r = correlation coefficient, (x) = the total number of samples. Water 2020, 12, 3563 9 of 18 average, the increase in the density of uncompacted natural snow over the season was 2.3 1.3 kg/m3 ± per day, on average. The similar rates of increase for the densities of the two snow types suggest that the key density differences stem from the artificial (machine-made) versus natural snow versus processes after and not densification due to snow grooming machines and skiers, which was relevant only for ski piste snow. The difference (paired t-test: p < 0.5) between the linear models for the ski piste snow and natural snow was in the starting density. At the beginning of the winter season, the density of the ski piste snow was 434.5 63.9 kg/m3, while the density of the uncompacted natural snow ± was 169.5 63.9 kg/m3, on average (mean values for three seasons calculated from the means of first ± surveys of the seasons; n = 15). Consistent relationships between time and mean density are illustrated by the trend lines and supported by the correlation coefficients, which are high in most of the seasons, although the correlation coefficients may not be reliable measures given the few data points (Figure6). The correlation between these variables was reduced by the large outlier values, mainly in case of the ski piste snow. The outliers, for the ski piste snow were identified in the following surveys: 27 January 2015 (Králiky); 18 January 2015 (Krahule); and 21 December 2017 (Donovaly). When the density of the ski piste snow increased to outliers in these surveys, the density of natural snow did not follow same pattern. Therefore, such exceptional growth in the ski piste snow density should be connected with management activities regarding the ski piste snowpack (snowmaking, grooming, and so on). The identification of occurrences or durations of these snowpacks was not the aim of the present paper; however, in most of the paired measurements, the measurements for natural snow were missing approximately from the middle of February until the end of the winter season (Figure6). The reason for these missing values was the absence of natural snow. Therefore, the density of ski piste snow increased for a longer period and reached higher mean seasonal values compared to the density of natural snow, which melted earlier.

3.3. Snow Density Versus Snow Depth on the Ski Piste of Košútka Ski Center The snow depth and density were measured manually on 5 March 2015, from 72 sampling points at Košútka, and a moderately strong negative linear correlation was calculated with the data (Figure7). According to this correlation, the density increased 18 kg/m3 per 10 cm of decreasing snow depth. The average deviation of this linear model was calculated as 72 kg/m3 and represents the standard ± error of estimation (RMSE with two degrees of freedom). The snow density ranged from 457 to 969 kg/m3 (Figure7), with a mean of 632 85 kg/m3 (mean standard deviation). The minimal ± ± average density was found at a maximal depth of 135 cm, while the maximal density was associated with nearly the minimal depth of snow (969 kg/m3 for 13 cm versus 640 kg/m3 for 5 cm). The Snow profile was saturated with meltwater during measurements; thus, the maximal density of the snow was higher than the density of ice. Water 2020, 12, 3563 10 of 18 Water 2020, 12, x FOR PEER REVIEW 10 of 18

Jasesnká 2014/15 SP NS Jasesnká 2015/16 SP NS Jasenská 2016/17 SP NS 800 800 800 b = 0.55; r = 0.31 ) 600 600 600

kg/m³ 400 400 400

200 200 200

Density ( b = 2.97; r = 0.96 0 0 0 16/11 28/12 8/2 22/3 16/11 28/12 8/2 21/3 16/11 28/12 8/2 22/3

Košútka 2014/15 SP NS Košútka 2015/16 SP Košútka 2016/17 SP NS 800 800 800 b = 1.90; r = 0.74 b = 4.28; r = 0.94 b = 2.88; r = 0.94 600 600 600

400 400 400

200 200 200 Density (kg/m³) 0 0 0 16/11 28/12 8/2 22/3 16/11 28/12 8/2 21/3 16/11 28/12 8/2 22/3

Králiky 2014/15 SP NS Králiky 2015/16 SP NS Králiky 2016/17 SP NS 800 800 800 b = 0.95; r = 0.54 b = 1.03; r = 0.51 b = 0.85; r = 0.27 600 600 600

400 b = 0.79; r = 0.68 400 400 200 200 200

Density (kg/m³) b = 1.46; r = 0.47 0 0 0 16/11 28/12 8/2 22/3 16/11 28/12 8/2 21/3 16/11 28/12 8/2 22/3

Krahule 2014/15 SP NS Krahule 2015/16 SP NS Krahule 2016/17 SP NS 800 800 800 b = 2.32; r = 0.68 b = 1.83; r = 0.75 600 600 600 b = 3.52; r = 0.91 400 400 400

200 200 200

Density (kg/m³) b = 3.12; r = 0.72 b = 1.13; r = 0.49 0 0 0 16/11 28/12 8/2 22/3 16/11 28/12 8/2 21/3 16/11 28/12 8/2 22/3 Donovaly 2014/15 SP NS Donovaly 2015/16 SP NS Donovaly 2016/17 SP NS 800 800 800 b = 1.18; r = 0.64 b = 2.07; r = 0.68 b = 1.04; r = 0.50 600 600 600

400 b = 3.99; r = 0.98 400 400 200 200 200 Density (kg/m³) b = 1.61; r = 0.80 0 0 0 16/11 28/12 8/2 22/3 16/11 28/12 8/2 21/3 16/11 28/12 8/2 22/3 Figure 6. The mean densities of ski piste snow (SP) and uncompacted natural snow (NS) and their increasesFigure 6. overThe threemean winter densities seasons of ski (from piste 2014 snow/15 (SP) to 2016 and/17) uncompacted at five ski centers. natural The snow mean (NS) density and their was calculatedincreases over from three at least winter five seas measurementsons (from 2014/15/samples. to The2016/17) slopes at offive the ski regression centers. The lines mean (b) indicate density thewas increase calculated in thefrom mean at least densities five measurements/samples. of the snow per day, andThe theslopes correlation of the regression coefficients lines (r) (b) indicates indicate weakthe increase (+30), moderatein the mean (+50), densities or strong of the (+ 70)snow linear per models.day, and The the snowcorrelation density co measurementsefficients (r) indicates for SP andweak NS (+30), were moderate paired. The (+50), absence or strong of measurements (+70) linear models. for NS The means snow the density absence measurements of natural snowpack for SP and on theseNS were dates. paired. The absence of measurements for NS means the absence of natural snowpack on these dates.

Water 2020, 12, x FOR PEER REVIEW 11 of 18

3.3. Snow Density Versus Snow Depth on the Ski Piste of Košútka Ski Center The snow depth and density were measured manually on 5 March 2015, from 72 sampling points at Košútka, and a moderately strong negative linear correlation was calculated with the data (Figure 7). According to this correlation, the density increased 18 kg/m³ per 10 cm of decreasing snow depth. The average deviation of this linear model was calculated as ± 72 kg/m³ and represents the standard error of estimation (RMSE with two degrees of freedom). The snow density ranged from 457 to 969 kg/m³ (Figure 7), with a mean of 632 ± 85 kg/m³ (mean ± standard deviation). The minimal average density was found at a maximal depth of 135 cm, while the maximal density was associated with nearly the minimal depth of snow (969 kg/m³ for 13 cm versus 640 kg/m³ for 5 cm). The Snow profile was saturated with meltwater during measurements; thus, the maximal density of the snow was Water 2020, 12, 3563 11 of 18 higher than the density of ice.

Interpolated (y = −1.0195x + 678.79; r = 0.60; p-value < 0.05) 1000 Measured (y = −1.7889x + 700.5; r = 0.54; p-value < 0.05) 900 800 700 600 500 Snow density (kg/m³) Snow density 400 0 20 40 60 80 100 120 140 160 180 200 Snow depth (cm)

Figure 7. Correlation between measured values on 5 March 2015, (red line) and correlation between Figure 7. Correlation between measured values on 5 March 2015, (red line) and correlation between the mean depth and density of the interpolated ski piste snowpack on the basis of 181 concentric circles the mean depth and density of the interpolated ski piste snowpack on the basis of 181 concentric around snow lances. Correlation coefficients (r) and p-values from analysis of variance (ANOVA) circles around snow lances. Correlation coefficients (r) and p-values from analysis of variance are displayed. (ANOVA) are displayed. The snow depth and snow density raster layer were interpolated from the 72 sampling points (FigureThe8) tosnow analyze depth the and spatial snow distribution density raster of these layer variables were interpolated on the ski piste. from Boththe 72 snow sampling density points and depth(Figure showed 8) to analyze similar, the but spatial reverse, distribution geometric ofpatterns these variables alongthe on the entire ski skipiste. piste, Both as snow indicated density by and the negativedepth showed correlation. similar, The but correlation reverse, geometric between patterns these two along raster the layers entire was ski lowerpiste, as than indicated that between by the thenegative 72 paired, correlation. manually The measured correlation values between (r = 0.31 thes versuse two rraster= 0.54). layers Intensive was lower snow than making that at between the ski centerthe 72 resultedpaired, manually in the occurrence measured of values snow piles (r = 0.31 with versus maximum r = 0.54). measured Intensive and snow interpolated making depths at the ski of 198center and resulted 211 cm, in respectively the occurrence (Figure of snow8). Each piles of with the 17maximum snow lances measured produced and ainterpolated di fferent volume depths ofof snow198 and during 211 cm, the respectively season; thus, (Figure the depths 8). Each of the of snowthe 17 piles snow di lancesffered produced significantly. a different According volume to the of interpolatedsnow during snow the season; depth raster thus, (Figurethe depths8), the of centers the snow of snow piles pilesdiffered were significantly. located 12.5 According4.9 m from to thethe ± closestinterpolated snow lance,snow ondepth average. raster These (Figure centers 8), the were cent situateders of snow down piles the slope,were located except for12.5 first ± 4.9 two m snow from lancesthe closest at the snow foot oflance, the slope.on average. The average These centers snow depth were andsituated snow down density the inslop thee, centers except offor the first snow two pilessnow were lances 110 at the52 cmfoot and of the 573 slope.70 kg The/m3 average, respectively. snow Strengthdepth and and snow slope density of correlation in the centers between of thethe ± ± meansnow depthpiles andwere density 110 ± 52 of thecm interpolatedand 573 ± 70 values kg/m³, on respectively. the basis of181 Strength concentric and circlesslope of around correlation snow lancesbetween was the comparable mean depth as correlationand density between of the interpolat measureded values values (Figure on the7 ).basis The of mean 181 snowconcentric depth circles and densityaround calculatedsnow lances on was such comparable circles decreased as correlation 2 cm and between 3 kg/m3 permeasured each meter values from (Figure the center 7). The of snowmean lance,snow respectively.depth and density These ratioscalculated were on identified such circle froms decreased slopes of the 2 cm linear and relationships 3 kg/m³ per betweeneach meter a series from ofthe raddi center around of snow snowmaking lance, respectively. lances (5, 7.5, These 10 ... ra30tios m) were and(i) identified snow depth from (y =slopes1.9648x of the+ 99.019; linear − rrelationships= 0.97; n = 181), between and (ii) a series depth of average raddi snowaround density snowmaking (y = 2.8164x lances+ 563.41;(5, 7.5, r10…= 1.00; 30 m)n = and181). (i) snow depth (y = −1.9648x + 99.019; r = 0.97; n = 181), and (ii) depth average snow density (y = 2.8164x + 563.41; r = 1.00; n = 181).

Water 2020, 12, 3563 12 of 18 Water 2020, 12, x FOR PEER REVIEW 12 of 18

FigureFigure 8.8. Snow densities and depth mapping of the ski pistepiste snowpacksnowpack for 55 MarchMarch 2015,2015, afterafter thethe disappearancedisappearance of naturalnatural snowsnow fromfrom thethe ooff-pisteff-piste sites.sites. DisplayedDisplayed areare snowsnow pilepile centerscenters (points(points ofof maximummaximum snow depth depth within within a 20 a 20m mradius radius around around snow snow lances) lances) and concentric and concentric circles circles around around snow- snow-makingmaking lances lances with 5 with m spacing 5 m spacing and maximum and maximum radii of radii 30 m. of 30 m. 4. Discussion 4. Discussion 4.1. Snow Tube 4.1. Snow Tube The difference in construction of designed MM snow tube resulted in a different method for snowThe sample difference extraction. in construction While commonly of designed used MM snow snow tubes tube are resulted pushed in and a different turned through method thefor snowpacksnow sample [5], theextraction. MM snow While tube commonly is hammered. used Compared snow tubes to are most pushed of the ofand commonly turned through used snow the tubessnowpack (VS-43, [5], Standard the MM Federal, snow tube SnowHydro) is hammered. characterized Compared by to aluminum most of orthe non-opaque of commonly plastic used bodies, snow thetubes presence (VS-43,/absence Standard of slotsFederal, in the SnowHydro) tube, and serrated characterized cutting endsby aluminum with teeth or [43 non-opaque,44], the MM plastic snow tubebodies, was the made presence/absence of stainless steelof slots and in designedthe tube, an withd serrated a keen cutting cutting ends end with and noteeth slots [43,44], in the the body MM ofsnow the tube tube. was This made design of stainless reduces steel significant and designed errors resultingwith a keen from cutting the presence end and ofno slotsslots inin the body tube, whichof the increasetube. This the design snow reduces density andsignificant the presence errors ofresulting a cutter from with the teeth, presence which of underestimates slots in the tube, the snowpackwhich increase [8,45, 46the]. snow The MM density snow and tube the slightly presence underestimated of a cutter with the density teeth, which of the skiunderestimates piste and natural the snowpackssnowpack [8,45,46]. compared The to theMM VS-43 snow snow tube tube, slightly most underestimated likely due to its the sharp density and non-serratedof the ski piste cutting and end.natural According snowpacks to Bindon compared [47] to and the Beaumont VS-43 snow [45 tube], the, most sharper likely tube due allows to its the sharp cleaner and extractionnon-serrated of snowcutting samples end. According from the snowpackto Bindon and [47] reduces and Beau possiblemont overestimation[45], the sharper by uptube to allows 50%. The the serrated cleaner cuttingextraction end of of snow the VS-43 samples snow from tube the had snowpack difficulty and penetrating reduces possible through overestimation the ski piste snowpack by up to when 50%. hammered,The serrated resulting cutting inend snow of the compression VS-43 snow and tube higher had density difficulty readings. penetrating These through results coincide the ski withpiste thesnowpack findings when of Turˇcanand hammered, Loijens resulting [48], in who snow showed compression that the and average higher snow density density readings. at depth These can beresults artificially coincide increased with the during findings snow of tubeTurčan penetration and Loijens through [48], who the snowpackshowed that as thethe resultaverage of snowsnow sampledensity compression.at depth can be The artificially lower densities increased of duri theng snow snow samples tube penetration extracted by through the MM the tube snowpack were not as thethe resultresult ofof missedsnow sample ice-soil compression. plugs, as described The lower by densities Dixon et of al. the [49 snow] when samples comparing extracted three by snow the tubesMM tube used were in Canada, not the because result theof snowmissed inside ice-soil the pl examinedugs, as described tubes was by pressed Dixon before et al. removing [49] when it fromcomparing the snowpack, three snow and tubes therefore used ice-soil in Canada, plugs be werecause not the missed. snow Theinside underestimation the examined oftubes the MMwas snowpressed tube before with removing its small it cutting from the end snowpack, area (13 cm and2) istherefore in contrast ice-soil to the plugs findings were ofnot Peterson missed. andThe underestimation of the MM snow tube with its small cutting end area (13 cm2) is in contrast to the findings of Peterson and Brown [46] and Farnes et al. [50], who found that snow tubes with small

Water 2020, 12, 3563 13 of 18

Brown [46] and Farnes et al. [50], who found that snow tubes with small cutting end areas overestimate. These authors also found that snow tubes with cutting end areas >20 cm2 had the least error. The results of abovementioned studies could differ due to different snowpack characteristics during snow surveys, mainly in terms of the hardness of the snow/ice layers in the snow profile and the snow grain size, which could influence penetration and consequently the accuracy of the measurements.

4.2. Snow Density The mean minimal and mean maximal densities (excluding outliers) of uncompacted natural snow in the ski centers of Central Slovakia were 83 kg/m3 and 411 kg/m3, respectively. Mössner et al. [20] found comparable densities for seasonal natural snow, which varied from 100 kg/m3 to 500 kg/m3. Fassnacht [21] observed that prior to melt, the snow can attain a density of 300 to 500 kg/m3, depending on the time period, meteorological conditions, and depth of the snow. As the present article shows, the density of new natural snowpack, maximally two days old, can vary between 78 to 289 kg/m3. Singh [51] explained that the density of natural snow increased from 80 to 250 kg/m3 when freshly fallen to a density of 300 kg/m3 over 100 days due to equi-temperature snow metamorphism, during which the snow strength increases and compression occurs. This explanation coincides with our findings that the average density of the February snow was 263 kg/m3 when this snow cover started to form in December. López-Moreno et al. [7], who analyzed snowpack characteristics in the Spanish Pyrenees (1517–3015 m a.s.l.), discovered an increase in snow density from 300 kg/m3 in February to 455 kg/m3 in April. These values are slightly higher than the mean values identified in the present paper, which could be explained by the longer durability of old, dense snow in the higher elevations of the Pyrenees or by the wider range of snow density values at lower elevations due to the occurrence of low-density new snow on previously melted areas. The current paper found a wide range of snow densities in April, which varied from 149 to 611 kg/m3, that could be explained by new snow from the beginning of winter metamorphosing into snow from late winter. Jonas et al. [6] identified a comparable range of values at the end of the winter season for elevations below 1400 m a.s.l. (Swiss Alps). These authors also found a lower range of snow density values at higher elevations. The present paper has demonstrated a classification of four snow types according to their mean densities (in descending order): ski piste snow (snowed/groomed snowpack), new artificial snow, uncompacted natural snow, and new natural snow. The findings of Rixen et al. [13,30] confirm the higher density of ski piste snow compared to uncompacted natural snow due to the intensive production of artificial snow and compaction of snow on the ski pistes; however, new artificial and natural snow were not examined in these studies. In the present article, the mean density of March snow on the snowed/groomed ski pistes was 2.4 times higher than the mean density of uncompacted natural snow beside pistes (635 versus 263 kg/m3). Rixen et al. [24] found lower ratio in Swiss ski centers (elevation above 1500 m a.s.l.) in March (1.3 times; approximately 570 versus 430 kg/m3;[30]), because of the lower density of ski piste snow and the higher density of natural uncompacted snow beside the piste, compared to present study. This difference can be explained by the lower elevation of the Slovakian ski pistes, where artificial snow has to be produced even at higher air temperatures [27] and where the continuous natural snowpack is present for a shorter duration compared to conditions at elevations above 1000 m a.s.l. [27]. A shorter continuous duration of the snowpack means a shorter time for snow metamorphism, during which the snow density increases [52]. The mean minimal and maximal densities of snow on the snowed and groomed ski pistes of Central Slovakian were 392 and 812 kg/m3. Fauve et al. [53] and Federolf et al. [23] identified comparable minimums (400 and 430 kg/m3), while their maximums were considerably lower (600 and 660 kg/m3). The all-season high maximal density of the ski piste snowpack in the studied ski centers could have resulted from a high density of artificial snow produced at the beginning of each winter season in all studied ski centers. The mean density of new artificial snow at the ski centers was 410 kg/m3, while it ranged between 282 and 556 kg/m3, on average. Melanie and Rixen [31] found a comparable range for the density of new artificial snow (350 to 600 kg/m3). The present study shows that the mean density of new artificial snow Water 2020, 12, 3563 14 of 18 was 2.3 times higher than that of new natural snow. The higher density of artificial snow compared to natural snow results from its small grain size and subsequently higher degree of compaction [54].

4.3. Snow Density versus Snow Depth High snow production at Košútka resulted in snow piles with average depths and distances from snow lances of 110 cm and 13 m down the slope, respectively. Spandre et al. [16], who examined ski piste snow from November 2015 to January 2016 near the Les 2 Alpes (Oisans Range, French Alps; elevation 1680 m a.s.l.), identified lower snow depths in the centers of snow piles at approximately half the distance from snow lances than found in this article, probably due an earlier winter season and the lower slopes of the ski piste (5◦ versus 20◦). The snow lances used in the studies were comparable, while a low mean hourly wind speed was observed during months with snow production, even at Košútka [27]. The presented article shows that snow depth decreases away from snow lances, on average. Spandre et al. [16] showed a decrease in the snow depth of piles that were approximately 7 m away from the snow lances. The current article found a moderately strong negative correlation between the snow depth and density of the ski piste snowpack on 15 March, 2015, at Košútka. No one else has published anything on this relationship yet, in contrast to studies dealing with uncompacted natural snow [55]. Numerous studies cited by Lunberg et al. [55] that analyzed data on a regional or continental scale identified a positive correlation between the depth and density of natural snow. For example, a long-term survey done in Yakutia (USSR; [56]) showed an increase in the snow density of about 180 kg/m3 per each meter of increased snow depth. The present article showed a decrease in ski piste snow density. Lopez Moreno et al. [7], who performed measurements at approximately 100 m intervals using a local scale in the Spain Pyrenees, found an inconsistent relation between snow depth and density (strong/weak and negative/positive correlations) and pointed out that snow depth alone explained as much variability in the snow density as any other variable (terrain characteristics). In any comparison with the present article, it is important to point out that the natural snowpack does not have such variability on a local scale [7], thereby bolstering the consistent relationship between snow depth and density in the case of the ski piste snowpack. The negative correlation between the snow depth and density on the ski piste could be explained by the occurrence of basal ice layers on the bottom of the snowpack, as found for Košútka by Mikloš et al. [2]. These authors found, that with lower snow depth, the higher thickness of basal ice layer or bare ice (ice instead of snow) can be expected at the end of winter when warm and frosty days alternates [2]. Thus, it could be assumed that as the depth of the snow above the basal ice layer decreases during melting, the depth average density of snowpack increases in Košútka until snow melted away and pure ice remained.

5. Conclusions Compared to the commonly used VS-43 snow tube, the designed MM snow tube has a smaller diameter, higher wall thickness, and sharpened cutting end and is resistant to damage during snow sample extraction. The MM snow tube has proved to be suitable for sampling high-density snow, such as the snow found on snowed/groomed ski pistes, due to its precision, rugged construction, and short sampling time. The MM tube is not recommended for sampling snow of low density and depth due to the small diameter of the tube and hardly detectable sample weights. Four snow types occurring in at ski centers were classified according to their mean seasonal densities and are listed in descending order: ski piste snow, new artificial snow, uncompacted natural snow, and new natural snow. While the mean seasonal densities of these four snow types differ significantly, the ranges were similar between new natural and new artificial snow and between uncompacted natural snow and ski piste snow. The lowest density recorded for freshly fallen natural snow was slightly above zero, while the density of ski piste snow can reach the density of ice or higher if it is saturated with meltwater. The density of the seasonal snow increases at a comparable rate over the season at piste and off-piste sites. Therefore, snow metamorphosis changes are major factors driving the snow density Water 2020, 12, 3563 15 of 18

Water 2020, 12, x FOR PEER REVIEW 15 of 18 increases, because densification by snow-grooming machines and skiers was relevant only for ski pistes.caused The by artificial increase insnow the snowand snow density compaction on pistes isvia less snow-grooming rapid due to the vehicles high initial and skiers. density At caused the end by artificialof the winter snow season, and snow the range compaction of the snow via snow-grooming density on the vehiclespistes is andcomparable skiers. At with the the end wide of the seasonal winter season,range. At the this range time of of the melting snow density period, on the the spatial pistes variability is comparable of the with snow the density wide seasonal on the range.piste changes At this timewith ofsnow melting depth period, and distance the spatial from variability the snow lanc of thees. snowThe snow density density on the increases piste changes as the snow with depth snow depthdecreases, and while distance the fromsnow the depth snow decreases lances. Thewith snow greater density distances increases from the asthe snow snow lances. depth The decreases, basal ice whilelayers theincrease snow depth depth average decreases density with of greater snowpack distances when fromsnow theabove snow is melting, lances. while The basal the snow ice layers piles increaseat almost depth half the average distance density of the of snow snowpack lances’ when range snow occur above on the is melting, piste unt whileil the theend snow of season piles atas almostresult of half high the artifi distancecial snow of the production. snow lances’ range occur on the piste until the end of season as result of high artificial snow production. Author Contributions: M.M. designed the MM snow tube and conducted the main data collection, analyses, Authorand writing; Contributions: M.J. helpedM.M. with designeddata collection; the MM J.S. snow (Jaroslav tube Skvarenina) and conducted and the J.S.main (Jana dataSkvareninova) collection, provided analyses, andoverall writing; guidance M.J. and helped supervised with data the collection; study. All J.S. authors (Jaroslav have Skvarenina) read and agr andeed J.S. to (Jana the Skvareninova)published version provided of the overall guidance and supervised the study. All authors have read and agreed to the published version of manuscript. the manuscript. Funding: This work was accomplished as a part of VEGAVEGA projectsprojects No.No. 11/0500/19,/0500/19, 11/0111/18/0111/18 of thethe MinistryMinistry ofof Education, Science, Research, and Sport of the Slovak Republic and the Slovak Academy of Science and thethe projectsprojects No.No. APVV-15-0425, APVV-18-0347 ofof thethe SlovakSlovak ResearchResearch and Development Agency.Agency. The authors thank thethe agenciesagencies forfor theirtheir support.support. Acknowledgments: Authors would like to extend their gratitude to Igor Mikloš for his help with the MM snow Acknowledgments: Authors would like to extend their gratitude to Igor Mikloš for his help with the MM snow tube construction and production. tube construction and production. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflicts of interest. Appendix A Appendix A

Figure A1. AssemblyAssembly of of the the VS-43 VS-43 snow snow tube tube with with orig originalinal mechanical mechanical scales scales and and shovel. shovel. Scales: Scales: 1- 1-metalmetal ruler, ruler, 2-movable 2-movable rider, rider, 3-pointer, 3-pointer, 4-suspensi 4-suspension,on, 5-hook; 5-hook; Snow Snow tube: tube: 6-handle, 6-handle, 7-cutting 7-cutting end, end, 8- 8-movablemovable ring, ring, 9-aluminum 9-aluminum tube, tube, 10-tube 10-tube cover cover (cap (cap),), 11-a shovel.shovel. Source: [[42,57].42,57]. Digital KernKern HDB10K10N scalesscales werewere usedused inin thethe presentedpresented articlearticle insteadinstead ofof mechanicalmechanical scales.scales.

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