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--> --> -->Outdoor venues are located on sloping surfaces with significant surface elevation change, which forces changes in the pressure field and, hence, in the wind direction and speed. The flow over hills shows different behavior depending on the Froud number of the flow (Stull, 1988). At a low Froud number of <1, air would rather flow around a hill than over it. At a Froud number of 1, large-amplitude lee waves or mountain waves are formed due to natural resonance. When near-neutral air with a large Froud number flows over a hill, the flow accelerates to the hilltop, reaches its maximum velocity above the hilltop, and then decelerates behind the hill. If the hill is steep enough in the leeward direction, flow separation occurs. Regardless of flow separation, a wake region develops behind the hill with a marked velocity deficit extending for many hill heights leeward (Jackson and Hunt, 1975; Kaimal and Finnigan, 1994).
During the diurnal cycle in mountainous regions, the differential heating over sloping surfaces generates thermally induced flow, such as up- and downslope flows (Whiteman, 1990). Radiative cooling of the mountain surface at nighttime cools the air adjacent to surfaces, resulting in cold downslope wind. After sunrise, solar heating warms the air near valley walls, causing warm upslope wind. Wind within a valley blows more or less parallel to the valley axis for a variety of wind directions, which is referred to as wind channeling. (Whiteman and Doran, 1993) discussed conceptual models for four different physical mechanisms to account for the relationship between the above-valley winds and the winds within the valley; namely, thermally driven channeling, downward momentum transport, forced channeling, and pressure-driven channeling. The wind climatology of a given valley is often the result of varying contributions of these four mechanisms.
A wind gust is defined as a short-duration wind-speed maximum (Suomi et al., 2014). Severe wind gusts might cause a safety risk in skiing, and ski jumping and landing in outdoor venues. Peak gusts represent the high extremes in a turbulent wind field. Previous studies have dealt with wind gusts in the surface layer and examined the gust factor in terms of the roughness length (Paulsen and Schroeder, 2005). However, the impact of upstream terrain variation on gust factors has not been fully explored. (Miller et al., 2015) examined the impact of upstream terrain variation on gust factors, but they focused on the roughness change of upstream terrain rather than the upstream surface elevation change over complex terrain. In this study, we examine the impact of upstream surface elevation change on the gust factor using surface wind observation data.
The objectives of this study are to examine surface wind features and mechanisms, and investigate the gust factor along the sloping surface in the outdoor venues in Pyeongchang, during February and March.
2.1. Site description and data
The study sites are the Yongpyong Alpine Center(Yo) and Alpensia Ski Jumping Center (Al) located in Pyeongchang. Table 1 summarizes the locations and names of the automatic weather stations (AWSs) at each site, and Fig. 1a shows the topography of the Pyeongchang region, including the two study sites. High mountains are located to the north and south of the study sites. The mountains are approximately 1400 m high. Figures 1b and c show the detailed topography of the two study sites, respectively. The topographical maps were made using 30-m resolution terrain data from the Shuttle Radar Topographic Mission (SRTM; Reuter et al., 2007). The Yo site is located on the northwest-facing slope; the upper two stations are located on the ridge and the lower two stations are located within the valley with low sidewalls. The mean slope angle of the ski slope is ～23°. The surface elevation difference between the lowest and highest stations is ～440 m. The wind at Y1 station (1414 m) represents synoptic wind at the ridge level in the Pyeongchang region. The western sidewall at station Y4 is parallel to a northeast-southwest axis, while the eastern sidewall is parallel to a northwest-southeast axis. The slope angle of the western sidewall is ～ 20° and the half-hill height of the western sidewall is ～ 130 m. During the study period, the ski slope was covered with snow; however, the surrounding areas are covered with trees, and therefore significant solar heating occurs on the sloping surface during daytime.
Figure1. Topographic map (m) of the study sites: (a) large domain including both sites; (b) Yongpyong alpine center; (c) Alpensia ski jump center. The grey line indicates the ridge axis considered in the calculation of the Froud number.The Al site is located on the northeast-facing slope and the ridge is parallel to a northwest-southeast axis. The surface elevation difference between the lowest and highest stations is 73 m; the slope is very steep and the slope angle is ～ 25°. The half-width of the hill is ～ 100 m. The surface at the ski jumping center was covered with snow and the surrounding area is covered by trees. Station A1 is located on the ridge; the other three stations are located on the steep sloping surface.
The data used in this analysis are 1-min wind speed and direction, gust wind speed and direction, and air temperature and pressure in February and March from 2014 to 2016.
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2.2. Analysis method
The flow over the hill shows a different behavior depending on the Froud number, which is defined as (Kaimal and Finnigan, 1994) \begin{equation} F=\dfrac{U}{NL} , \ \ (1)\end{equation} where U is the wind speed, N is the Brunt-V?is?l? frequency, and L is the half-width of the hill at the half-hill height.To calculate N of the flow, we used the potential temperature difference between two stations with a height difference: \begin{equation} N=\dfrac{g}{\overline{\theta}}\dfrac{\Delta\bar{\theta}}{\Delta z} ,\ \ (2) \end{equation} where \(\bar\theta\) is potential temperature and g is gravitational acceleration and z is the height above the ground.
For the upper-level station, we selected a station which is at the ridge level and close to the lowest level station at each site. The two stations used were stations Y2 and Y4 for the Yo site and A1 and A4 for the Al site. For U, we used the wind speed at Y2 and A1 for the Yo and Al sites, respectively. To analyze the mean wind direction and speed, we used the 10-min averaged wind speed and direction with a 1-h interval.
The 1-min wind gust was obtained as the maximum 1-s wind speed during 1 min. The gust factor (GF) is defined as the ratio between the peak wind gust of a specific duration to the mean wind speed for a period of time. To analyze the GF, we used the 10-min maximum and mean wind speed. The 10-min maximum wind speed was obtained as the maximum 1-s wind during 10 min. The GF is defined as \begin{equation} {\rm GF}=\dfrac{u_{1{\rm s}}}{\overline{u}} , \ \ (3)\end{equation} where \(\overline{u}\) is the 10-min mean wind speed and u1 s is the maximum 1-s wind speed.
3.1. Climatological and meteorological characteristics
The study sites experience cold and dry winters. Based on the data measured at the Daegwallyeong surface synoptic station (Korea Meteorological Administration), which is located approximately 5 km northeast of the Yo study site, the study period is slightly warmer and drier in March compared to the 10-yr period from 2007 to 2016 (Table 2). Figure 2 shows the wind rose at eight stations for the Yo and Al sites during February and March. Both stations Y1 and Y2 are located at the ridge level. The wind is dominated by westerlies at both stations, representing a synoptic wind pattern. On the other hand, the wind at stations Y3 and Y4, which are located within the valley, blows more or less parallel to the valley axis; however, the wind directions at the two stations are opposite to each other, which is examined in section 3.3. (Whiteman and Doran, 1993) suggested four mechanisms of wind channeling. When downward momentum transport is the dominant mechanism, the valley wind directions are similar to the above-valley geostrophic wind directions, with a slight turning (～25°). The wind direction at station Y3 is northwesterly with slight turning from wind direction at station Y2, which is because the ridge to the south blocks the southerly wind at Y3. Hence, a significant wind speed reduction at station Y3 is also shown compared with the wind speed at station Y2.
Figure2. Wind rose at station (a) Y1, (b) Y2, (c) Y3, (d) Y4, (e) A1, (f) A2, (g) A3 and (h) A4, during February and March.Figure 2e represents wind at the ridge level at the Al site, which is southwesterly. Northeasterly winds are dominant at the other three stations, which are located leeward. The wind speed reduction at the three stations is significant, although the surface elevation difference is only 17 m between stations A1 and A2. The flow shows various wind directions at station A2, but the wind speed is very weak, except for the northeasterly wind. Figure 3a shows the distribution of the wind direction at station A1 when the wind speed at A2 is larger than 3 m s-1. Strong wind at A2 occurs when the wind at the ridge level is northeasterly or easterly. The wind rotates clockwise from station A1 to station A4. Under westerly conditions at the ridge level, the minimum wind speed is observed at station A3 among the four stations (figure not shown). Compared with the two stations on the sloping surface, the wind rose at station A4 shows a significant contribution of weak westerly wind. Figure 3b displays the hourly distribution of the westerly wind at A4. Most westerly wind at station A4 occurs during nighttime, implying that the westerly wind is thermally induced downslope flow.
Figure3. (a) Frequency distribution of the wind direction at A1 when the wind speed at A2 is larger than 3 m s-1. (b) Hourly frequency distribution of westerly wind at A4.2
3.2. Diurnal variation of surface wind
The diurnal pattern of the vector wind field was composited at four stations at each study site (Fig. 4). The stations at the Yo site are located on the northwest-facing slope, and hence the southwesterly and southeasterly winds are downslope flow while the northwesterly wind is upslope flow. At the two stations at the ridge level, the flow is southwesterly at night and westerly during the daytime because northerly upslope flow cancels out the southerly component of synoptic wind during daytime. The flow at station Y3 is northwesterly without a change of the wind direction; however, a significant increase in the wind speed is observed during daytime. Such wind direction and speed changes are due to the fact that the northwesterly wind at station Y3 is channeled flow parallel to the valley axis; it is enhanced by northwesterly upslope flow during the daytime and reduced by southeasterly downslope flow at night (Kuwagata and Kondo, 1989). On the other hand, the wind at station Y4 is southeasterly and shows a weaker diurnal variation compared with that at other stations. Station Y4 is on the leeward side of the western sidewall for northwesterly wind, and during daytime strong ambient northwesterly wind at upper levels leads to a reverse southeasterly flow near the surface, which is downslope flow; however, thermal forcing leads to upslope flow (northwesterly), which cancels out the southeasterly flow. We examine the mechanism of the surface wind in the next section.
Figure4. Mean diurnal variation of the wind at the (a) Yo site and (b) Al site.The flow at station A1 is southwesterly throughout the day, with little diurnal variation. Station A1 is located on the ridge top, and hence the influence of slope flow on the wind is not shown. On the other hand, at the other stations, the flow is northeasterly throughout the day, with larger wind speeds during daytime. The northeasterly wind at three stations is upslope flow. Such a wind pattern could be explained with recirculation on the leeward side and thermal forcing. In the recirculation zone, upper- and lower-level flows show opposite wind directions (Poggi and Katul, 2007; Berg et al., 2011). And during daytime, thermal forcing enhances the wind speed of the upslope flow.
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3.3. Mechanism for the surface wind
To examine the mechanism of surface wind with an opposite direction, we focused on wind at two stations at each site. Stations Y3 and Y4 were selected at the Yo site and stations A1 and A4 were selected at the Al site. First, we examined the scatter plot of the wind speed at the two stations. Station Y4 at the Yo site is located on the valley floor with both sidewalls in the east and west, while station Y3 is located on the eastern sidewall of the valley; the western side wall is lower than the surface elevation of station Y3 (Fig. 5). When neutral air flows over the hill, the windward and leeward flows show a significantly different behavior. Therefore, we divided the data into two groups based on the wind direction at station Y2 at the ridge level: easterly and westerly.Figures 6a and b show scatterplots of the wind speed at stations Y3 and Y4 for the easterly and westerly groups, respectively. The different relationships between the wind speeds at two stations are shown for the easterly and westerly groups (Table 3). The wind speed at Y3 for the westerly group shows a broad distribution extending to 10 m s-1, while most of the winds at Y3 for the easterly group have low wind speeds of <2 m s-1. The different range of wind speed at Y3 is due to the fact that station Y3 is located in the leeward region with a velocity deficit in the easterly case, while it is located in the windward region in the westerly case (Fig. 5); hence, the wind at Y3 represents upper-level wind in the westerly case.
Figure5. East-west cross section of topography crossing station (a) Y3 and (b) Y4 at the Yo site. The open circle indicates the location of the station.
Figure6. Scatterplot of the wind speed between stations (a) Y3 and Y4 for easterly wind, (b) Y3 and Y4 for westerly wind, (c) A1 and A4 for easterly wind, and (d) A1 and A4 for westerly wind.The correlation of the wind speeds between stations Y3 and Y4 is higher for westerly (0.76) than for easterly (0.49) winds (Table 3). Figure 7 shows the joint frequency distribution of wind direction at the two stations. Most of winds at station Y4 are southeasterly, which are accompanied by northwesterly winds at station Y3. The wind directions at stations Y3 and Y4 are opposite, with a 180° difference for the westerly group (Fig. 7a). This indicates that the good correlation of the wind speed between the two stations (Y3 and Y4) for the westerly group is not due to downward momentum transport. One possible cause for the good correlation of wind speed in the westerly group is the development of recirculation flow in the leeward region. Strong upper-level wind might lead to strong recirculation near the surface in the leeward direction, leading to significant correlation between upper- and lower-level winds. On the other hand, in the easterly case, stations Y3 and Y4 are both located leeward (Fig. 5), and hence winds at both stations represent lower-level wind in the wake regions, leading to low correlation of wind speed between the two stations.
Figure7. Joint frequency distribution of the wind direction at (a) Y3 and Y4 and (b) A1 and A4 for February and March 2014-16.Figures 6c and d show scatterplots of the wind speed at stations A1 and A4 for the easterly and westerly cases at the Al site. For the easterly case, the two stations show similar wind speeds, while the wind speed at station A4 is much lower than that at station A1 in the westerly case. The wind speed correlation between the two stations is larger for easterly wind than for westerly wind (Table 3). This can be explained by the different flow behavior over the hill in the windward and leeward regions. A higher correlation of the wind speeds between upper and lower levels is expected in the windward region compared with the leeward region. Station A1 is located on the ridge, and hence wind at A1 represents upper-level wind. Therefore, the correlation of wind speed between the two stations reflects that between the upper and lower levels. Figure 7b shows the joint frequency distribution of the wind direction at A1 and A4. When the wind at A1 is easterly, the wind at A4 is also easterly, indicating that A4 is located windward in the easterly case. On the other hand, when the wind at A1 is westerly, the dominant wind is easterly at A4, indicating recirculation flow in the leeward region. (Berg et al., 2011) reported observed features of mean wind over a steep escarpment. They showed significant wind speed reduction and reverse flow in the leeward region and a slight reduction of wind speed in the windward region.
Flow separation occurs over hills with a slope angle >18° (Kaimal and Finnigan, 1994), in which the flow direction at the lowest level is opposite to that above. The slope angles of the western sidewall at station Y4 and the ski jumping surface at the Al site satisfy the flow separation condition. Figure 8 shows the frequency distribution of the Froud number at the Yo and Al sites for westerly conditions. Most of the flows have a large Froud number, supporting the presence of recirculation flow in the leeward region.
Figure8. Frequency distribution of the Froud number at the Yo and Al sites for westerly wind.2
3.4. Wind gust analysis
The GF depends on numerous factors such as roughness length, distance from upstream terrain change, stability, measurement height, and the presence of convection (Paulsen and Schroeder, 2005). During the study period, all stations (which are located in mountainous areas) had surfaces covered with snow; hence, the roughness length of each station is similar and the measurement height above the ground is the same at all stations. However, the upstream terrain change is different at each station depending on the wind direction. The difference in GF among the stations might be due to the difference in upstream terrain change, such as upslope or downslope.Table 4 displays the GF for the wind speed range of 2-6 m s-1 at the Yo and Al sites. The wind speed regime was selected to compare the GFs at different stations for similar wind conditions. Within the same wind speed regimes, the GF increases with decreasing surface elevation at each site. The GFs are 1.56 and 1.47 at the Y1 and A1 stations on the ridge at the Yo and Al sites, respectively. (Suomi et al., 2014) reported a GF of 1.3-1.4 at 10 m over flat grass fields for the wind speed range of 2-12 m s-1. The difference in GF between the two studies is due to the different topography and gust duration. The GF increases with increasing roughness length (Paulsen and Schroeder, 2005), and our study sites are located in mountainous areas, which are typically characterized by large roughness length (Arya, 2001). The GF decreases with increasing gust duration (Suomi et al., 2014). The gust duration was 3 s in (Suomi et al., 2014), while it is 1 s in our study. The GF during daytime is larger than that during nighttime, except at station Y4, which is located in the wake region. The larger GF during daytime is due to convection, which is consistent with a larger GF under unstable conditions than under stable conditions (Suomi et al., 2014). The larger GF at the Yo site might be due to its more complex topography compared to the Al site. The significant increase in GF at low elevation at each site is associated with the fact that the stations are located in the leeward wake region in the westerly case.
Figure9. GF in terms of the wind speed for the (a) easterly case and (b) westerly case at station Y4, and (c) easterly case and (d) westerly case at station A4.Figure 9 compares the GF in terms of the wind speed for easterly and westerly winds at stations Y4 and A4. The GF generally decreases with increasing wind speed because the environments with lower average wind speeds are much more conducive to free convection, introducing additional turbulence (Paulsen and Schroeder, 2005). Of note is that the GF is larger for westerly than for easterly wind, indicating a larger GF in the leeward wake region than in the windward region. The wake region is dominated by turbulence, which provides favorable conditions for a large GF. (Berg et al., 2011) reported low wind speed and high variance (σu) in the leeward region. Therefore, athletes should keep in mind the possibility of strong gusts at the leeward foot of the hill, although the mean wind is weak at the leeward foot.
To understand the mechanisms of surface winds with opposite directions, we examined scatter plots of the wind speed at two stations with opposite wind directions for westerly and easterly cases at the ridge level. Different relationships between the wind speeds at the two stations are shown for easterly and westerly cases at both the Yo and Al sites. The different relationships between the winds at the two stations for the easterly and westerly cases can be explained by the flow behavior over the hill: Under a large Froud number, the flow shows typical behavior, with recirculation on the leeward slope. A higher correlation of the wind speeds between upper and lower levels is apparent in the windward region compared with the leeward region. The slope angles of the western sidewall at station Y4 and the ski jumping surface at the Al site satisfy the flow separation condition at the leeward foot. Most of the flow at the study stations has a large Froud number (F>2), supporting the presence of leeward flow separation. The strong synoptic wind, small width of the ridge, and steep downwind ridge slope angle provide favorable conditions for flow separation at the leeward foot of the ridge of the study sites.
Within the same wind speed regimes, the GF increases with decreasing surface elevation at each site. The GF during daytime is larger than that during nighttime, except at station Y4, which is in the wake region. The significant increase in the GF at the low-elevation station at each site is due to the fact that the stations are located in the leeward region of dominant winds. The GFs at stations Y4 and A4 are larger for westerly than for easterly wind, indicating a larger GF at the leeward foot.
The wind information presented in this paper will help the venue forecasters and judges of the 2018 Winter Olympics to understand the wind features at the outdoor venues in Pyeongchang, and can be used to properly plan and prepare for the Games.
