Ski Resort Snow Surface Roughness

1. Introduction

The snowpack surface is the interface between the atmosphere and the earth when the ground is snow-covered [1,2,3]. As such, this interface dictates the energy balance of the snowpack [4,5], in particular the latent heat flux and the sensible heat flux [6,7]. Although the snow surface is often considered static for modeling [8], the nature of a snowpack surface can vary substantially over the winter [9,10,11]. This includes the aerodynamic roughness length, or $z_0$, which is a metric to quantify the roughness of the snowpack surface. Snow surface roughness often increases during melt [10,12,13], such as with the development of sun cups [14] (Figure 1), that can be enhanced by the presence of dust (Figure 1) [9,15]. At ski areas, grooming does the opposite and provides a smoother snow surface (Figure 1) [16]. We asked the following questions: 1) how does the snow surface roughness vary at a ski area? and 2) what are the implications of the spatial variation on snowpack sublimation modeling?

2. Study Site

In Spain, most areas with continuous seasonal snow cover lie above treeline [17,18]. Snow dominates the Spanish alpine environment (Figure 2a) [19], especially in the Sierra Nevada (Figure 2b) [20]. Snow is an important resource in the Spanish Sierra Nevada [21] for ski tourism [22], water resources [23], and for sustaining endemic fauna and flora [24,25], which make this area a biodiversity hotspot [26]. However, assessing the amount of snowfall is difficult [27]. Sublimation and melt-evaporation [28] reduces the water storage and further increases uncertainty [29]. To evaluate the uncertainty of sublimation, we collected data near the city of Granada (Figure 2a), in the northwestern Sierra Nevada (Figure 2b). Specifically, data were collected to the west of the top of the Telecabina Al-Andalus (Andalucian Gondola) (Figure 2c). This area, know as Borreguiles, is at an elevation 2,700 metres. Data were collected on 19 April 2024.

3. Methods

3.1. Surface Mapping

We measured both the grooomed snow surface, or piste [30], and the ungroomed (or natural) snow surface, also known as off-piste [31] at two spatial resolutions ( 0.2 mm and 1 cm) to estimate snow roughness (Figure 1). For the groomed surface, measurements included both the compacted tracks left by the grooming machine and the flatter sections between these tracks (Figure 1). The ungroomed snow surface included natural snow with small undulations, sun cups, and dust at the surface (Figure 1 and and Table 1). Roughness boards were used as a two-dimensional representation of fine details in the snowpack (Figure 3) while iPad surface scanning was used for a more coarse three-dimensional surface geometry of the snow surface and Table 2. The latter was used for sublimation modeling.

3.1.1. Roughness Boards

A 60-cm wide snow board inserted into the snow so that the surface was fully contrasted by the board (Figure 3a). A photograph was taken of the board using a Samsung Galaxy A53 (SM-A536U1, 16MP 4624x3468 pixels, ISO50, 24 mm) [32]. Each image was clipped horizontally to the black-red edge of the board (Figure 3b). The green band was converted to a matrix of digital numbers (DNs). A DN threshold of 100 was used to identify the snow surface, i.e., board (low DN) versus snow (high DN) (Figure 3c). Once the snow surface was converted into ASCII data, it was detrended to remove any slope bias from the angle of the surface and/or camera (Figure 3d). The full method is detailed in Fassnacht et al. [33]. The raw images are in JPEG format [34].

The roughness boards were inserted parallel (Figure 3a) and perpendicular to the grooming tracks (Table 1). The surface from the roughness board perpendicular to the grooming tracks represented between groomed tracks. Some areas of the natural snow had some small undulations, while others showed sun cups (Figure 1).

3.1.2. iPad Surface Scans

The snow surface was scanned with an iPad Pro [35] using the 3-D Scanner App [36] (Figure 4). While the specific scanning mechanism is proprietary, it appears to be structure-from-motion with lidar from distance. An 0.8 m x 1.6 m rectangular area was clipped for the dust-covered natural, sun-cupped natural (left in Figure 4), within the groomer tracks, and between the groomer tracks (right in Figure 4). Each area was detrended in X and Y [33], and the point cloud was interpolated to a 1-cm resolution using kriging with the Golden SURFER program [37]. The procedure is detailed in Neville et al. [12]. The raw, unclipped scan is an ASCII file with coordinates (X, Y, Z) and colour (R, G, B) [34].

3.2. Roughness Evaluation

We used a variety of metrics to assess snow surface roughness [33]. These included 1) the Random Roughness (RR), which is the standard deviation of the detrended surface, 2) the Scale Break (SB) and fractal Dimension (D) from variogram analysis, and 3) the geometric-based aerodynamic roughness length ($z_0$). Variograms were computed at logarithmic distances for the various snow boards and surfaces. The scale break was estimated from the change in slope and D was computed from the slope of the best fit function up to SB [38]. The geometric $z_0$ value was computed using the Lettau [39] method with the watershed-identification code of Neville et al. [12].

3.3. Sublimation Estimation

One-minute meteorological data was collected for four hours (10:19 to 14:32) at the field site [40]. These data were used with the calculated geometric-based $z_0$ values to compute the bulk-transfer sublimation [41]. Concurrently, evapo-sublimation pans [42] were deployed in the groomed and ungroomed areas to provide field measurements of sublimation-evaporation and melt [28]. These field data are not presented in this current analysis; the focus is evaluating the impact of snow surface geometry on sublimation modeling.

4. Results

The groomed snow was much smoother than the ungroomed snow, especially when sun cups were present (Figure 4 and Figure 5). Grooming provided relatively homogeneous grooves (Figure 5a) and the area between the tracks was essentially flat (Figure 5b). The natural surface had some undulations (Figure 5c) that were enhanced where sun cups formed (Figure 5d).

The four surfaces interpolated from the iPad scans (Figure A1) exhibited distinct spatial variability. Despite these visual differences, the roughness of the iPad scanned surfaces (Figure A1) broadly matched those from the roughness boards (Figure 5). Variograms illustrated the same roughness structure between the same features (Figure 6), although the order of magnitude of the roughness differed between methods (Figure A2).

The scale breaks (SB), or change in slope in the variograms (Figure 6), were in a similar range for the two measurement types (boards versus scans), though they did not match exactly. The fractal dimensions (D) were more similar among the surfaces (Figure 7). Similarly, RR values were almost the same between the roughness boards (Figure 7a) and the iPad scans (Figure 7b).

RR values are largest for the sun cups, and thus most organized, i.e., D was smallest for the longer scales (light green in Figure 7). For the shorter scales (dark green), D was similar with the grooming surface (up to 16 mm which was the period of the groomer teeth; (Figure 3 and Figure 5a), and for the natural and sun cups board and iPad surface. For the latter two, D of about 1.5, for a distance of 7 mm, represented the rounded snow grains. The board parallel to grooming was almost flat and the surface was more random (D was larger).

The default $z_0$ modeling value was 0.24 mm. The geometric-based $z_0$ for groomed surface was almost the same (0.35 mm) (Figure 8). The other $z_0$ values matched the pattern in RR, with low RR values (groomed flat) yielding low $z_0$ values and larger roughness surfaces, i.e., sun cups, being larger ($z_0$ of 9.5 mm). The variations in $z_0$ influenced the sublimation estimates modelled (Figure 9), illustrating an order magnitude of variation.

5. Discussion

A ski area can have a variety of snow surfaces (Figure 5 and Figure A1) that have a different roughness (Figure 6 and Figure 7). This will impact wind movement across the surface that yields varying aerodynamic roughness lengths (Figure 8). Different $z_0$ values produces a variety of sublimation estimates (Figure 9). Sublimation is an important process for the water balance in mountainous regions [43]. Sublimation and melt-evaporation [28] on ski slopes will influence snow making due to consumptive use [44,45,46]. These processes need to be implemented into models [47], especially due to reduced reliability of snow under climate change [48].

There is consistency in the roughness features across scales, i.e., between the roughness boards and the iPad scanning (Figure 6 and Figure 7). Sun cups had the largest roughness (largest magnitude in the variograms and largest RR) and were most organized (lowest D), while the groomed surface between the tracks was smoothest and most random [33]. The tracked surfaces were similar (Figure 7 and Figure A2). While we did not measure the dust on snow surface with the roughness boards, its roughness was also similar to the natural snow without the sun cups. We measured the natural snow (without sun cups) at two locations in both the north-south and west-east directions. These four variograms were essentially on top of one another, illustrating consistency among the same surface form.

The iPad scanning appears to not be able to resolve the flat snow surface (Figure 6b), especially compared to the roughness board (Figure A2). The iPad flat surface between the tracks (Figure A1b) was essentially random (D = 2.99; Figure 6b and Figure 7b). For the roughness board, there was some order (D = 1.56) at the shorter scale (up to 7 mm) (Figure 5b and Figure 7a), but this was not picked up by the iPad scanning. For the longer scale, there was the same slight order (D = 1.92 and 2.92 for the board and iPad, respectively). The interpolated iPad surface appears to have much roughness (polygons in Figure A1a), but these are all plus or minus zero and less than 5 mm.

The actual process to create the point cloud from the iPad scanning [35,36] is proprietary and more information is needed to determine the accuracy of scanning smooth snow surfaces. It is recommended that this scanning be compared to data collected from terrestrial lidar (e.g., [13]). Here, we used the 3D Scanner App [36]; other software could also be evaluated. However, for the surfaces with more roughness (natural, dust and sun cups), the iPad surfaces ( 1 cm resolutions) seemed to match the roughness boards ( 0.2 mm resolution).

The iPad scanning also produces point cloud of RGB colour returns (Figure 4). These data could be used to estimate albedo in the visible portion of the spectrum [49]. At our study area, this is relevant due to the presence of dust (Figure 1) which lowers albedo, increases snow melt [50], and changes snow roughness [9,15].

6. Conclusions

The snowpack at a ski resort can have a variety of surfaces. At the Sierra Nevada ski area, investigated here, we saw two natural surfaces with the presence of dust and sun cups, and two groomed surfaces with rills from the tracks and a flatter surface between. The sun cup surface had the most roughness, followed by the natural and dust covered surfaces. Both saw similar roughness values with the finer resolution 2-D roughness board and the coarser resolution 3-D iPad scanning. The tracked 3-D surface was similar to the board, while the flat surface was less similar among the methods. This was likely due to the iPad scanning not resolving features in the flat surface.

The differences in roughness among the surfaces was seen in the geometric-based $z_0$ values that varied by more than an order of magnitude. These were used to model sublimation, yielding large differences. These differences in surface roughness need to be considered when modelling the snowpack across ski resorts, and any snow covered area where the surface varies.