Statistical characteristics of the spatial distribution of wind and snow in the Xinjiang Uygur Autonomous Region

At present, the wind and snow loads are calculated independently when determining the design specifications for building structures. Yet, when snow drifting occurs, the basic wind and snow pressures exist almost simultaneously. Therefore, building specifications based on the independent calculations of the wind and snow loads cannot be used effectively in areas that are severely impacted by snow drifting. Some parts of the Xinjiang Uygur Autonomous Region of China have suffered particularly severe snow drifting natural disasters. In this paper, we offer an analysis of the statistical characteristics of the spatial distribution of wind and snow in this region. In particular, we extract the values of the combined distribution of the wind and snowfall in the Xinjiang Uygur Autonomous Region of China by using parameters such as snowfall intensity, snowfall amount, wind speed, and wind direction as indicators that show the snow drifting disasters. This study found that, after heavy snowfall events, the accumulative wind scale is high and the accumulative snowfall is large in the Altay, the Bortala Mongol Autonomous, and the Tacheng Prefectures of northern Xinjiang, and the Kizilsu Kirghiz Autonomous Prefecture of western Xinjiang. It has an important practical significance for the design of building structures and the treatment of snow drifting disasters.

1 3 deep drifts of snow which may close roads or simply block traffic. In severe cases, it can result in the structural damage to buildings, the collapse of roofs and houses, and other problems which disrupt the daily lives of the inhabitants, as well as industrial and agricultural production. For example, the biggest snowstorm on record occurred in Liaoning Province of China in March 2007. For the most part of Liaoning, it halted traffic; it forced airports and expressways to close, and stopped several of the trains-and this caused huge economic losses to the Liaoning Province Li et al. (2007). Since January 10 of 2008, southern China suffered a heavy snow and sleet natural disaster which was the worst in 50 years. More than 20 of China's provinces were affected. The snow and ice storms cut off travel by road and rail, and cost 151.65 billion yuan in direct economic losses Chen and Fan (2009). In January 2010, the Altay district, the Tacheng district and other places nearby in the Xinjiang Uygur Autonomous Region suffered a once-in-60-year blizzard disaster that closed off the main access roads of Tacheng city, and caused direct economic losses of 650 million Yuan. The snowfall intensity, duration, and amount of rainfall (or snowfall) for this event have rarely been seen in modern Chinese history Liu et al. (2010).
In consequence, snow drifting disasters have a serious impact on the inhabitants of colder regions. Aiming at this problem, many scholars have studied the formation and prevention of snow drifting disasters. Su (2017) has studied the causes of snow drifting disaster, and the factors that influence it. More particularly, Su has analyzed the load status of the snow particles and proposed the design parameters of a retaining wall. Ying (2007) has studied the technology of the prevention and cure of a snow drifting disaster on highways.
Having studied the causes of snow drifting disasters on the highways in the Xinjiang Uygur Autonomous Region, Liu et al. (2008) have summarized the main types of snow deposition on the region's highways, including windward snow cover, leeward snow cover, curve flow snow, cutting snow, and high embankment snow types. Wang (2009) implemented the numerical simulation of snow disasters to sum up the drifting snow disaster prevention technology of the railway. He pointed out that, in general, three conditions are required for the formation of a drifting snow disaster: the source of sufficient snow, the wind which can sweep the snow grains, and the landform which can help to decrease the accumulation of snow grains. Zhou et al. (2014) investigated the effects of wind duration, wind velocity, and roof span on the redistribution of snow on roof surfaces. And the characteristics of erosion/deposition range and the location of maximum quantities of erosion/deposition under independent effects of wind duration, wind velocity, and roof span were also studied. Zuo et al. (2019) conducted field observations of blowing snow and snow accumulation in a grassland area typical of northern China. The results showed that snow-drift cover was thicker in areas with taller grass and greater vegetation coverage. Flaga and Flaga (2019) compared and analyzed the snow load for three different roofs of sport facilities by wind tunnel test, which is very helpful for the prevention of snow drifting disasters.
Generally, only when heavy snowfall and strong winds appear together will snowdrifts be formed. Snowdrift formation is a joint probability event of wind and snow variables, with the two primary variables being snowfall intensity and wind strength Zha et al. (2012). Therefore, the temporal and spatial distribution of wind and snow should be analyzed before we study the snow drifting disasters. In the Load Code for the Design of Building Structure of China, the wind and snow loads are calculated separately. So, the calculated load based on this load standard cannot be used to design safe architectural structures for those areas that are severely affected by snow drifting disasters China Academy of Building Research (2012). Aiming at this problem, Hong et al. (2021) proposed an updating of the probabilistic models used for calibrating the wind load, snow load, and companion load factors for the National Building Code of Canada (NBCC). In this model, different load combinations are considered and the reliability analysis is also carried out. They propounded Specific recommendations on the load and companion load factors for a future edition of NBCC. Winstral et al. (2013) developed a new, computationally efficient algorithm for distributing the complex and heterogeneous effects of wind on snow distributions, which can simulate the wind-affected accumulations of snow. Wang and Rosowsky (2013) presents an approach to statistically characterize the joint wind-snow hazard for use in performance-based design. The results of this approach can be used to construct the joint wind-snow hazard level contours corresponding to different annual exceedance probabilities. Yu et al. (2021) analyzed the temporal and spatial distribution of wind and snow in the Xinjiang Uygur Autonomous Region by using the Daily Data Sets of Climate Data for China International Surface Exchange Station (V3.0) and obtained the probability of occurrence of snow drifting disaster and the disaster grade. However, the disaster in the region of the Xinjiang Uygur Autonomous Region, suffering severe snow drifting disaster in China, is not analyzed. Therefore, in this paper, the authors studied the joint distribution of wind and snow in the Xinjiang Uygur Autonomous Region by using a mass of historical meteorological data, and summarized the distribution rules of wind and snow in Xinjiang, thereby providing a guide for the prevention and control of future snow drifting disasters in the Xinjiang Uygur Autonomous Region which, in turn, provides significant guidance on the construction and maintenance of the transportation infrastructure in the region.

Meteorological data
The meteorological data used in this study is the "Daily Data Sets of Climate Data for China International Surface Exchange Station (V3.0)". It includes eight major items, including the daily air pressure values, air temperature, precipitation, evaporation, relative humidity, wind, sunshine time, and 0 cm ground temperature. Beginning in January 1951, the data were acquired daily from 824 basic meteorological stations located in China. After effective quality control, the availability rate of the meteorological factor data was, in general, more than 99%, and the accuracy rate was nearly 100%.
In this study, the precipitation and wind data were selected from the above data sets. In the precipitation data, the accumulated precipitation from 20:00 of the previous day to 20:00 was used. In the wind data, the average wind speed, the maximum wind speed, and the direction of maximum wind speed were used. Under normal circumstances, the daily average wind speed was obtained by calculating the average of four values observed at 02:00, 08:00, 14:00, and 20:00 Beijing Time. However, when the observation station was not equipped at with a self-recording instrument, the daily average wind speed is the average of the three wind speed values observed at 08:00, 14:00, and 20:00 Beijing Time. Maximum wind speed refers to the average maximum wind speed over 10 minutes during a given period. The wind direction was expressed relative to 16 azimuths. The representation directions were N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, and NNW. The absence of wind was also recorded.
As there was no distinction between rainfall and snowfall in the data sets, the precipitation over the whole winter period was used to represent snowfall in our analysis of the statistical characteristics of snow and wind. The winter period is defined as the months of January, February, March, November, and December. After importing the above data into a database, the effective data from 64 observation stations in the Xinjiang Uygur 1 3 Autonomous Region were selected for this analysis. The location and number of the 64 stations are shown in Fig. 1. The selected period was from 1968 to 2016 and included a total of 7412 days. There was a lack of observation data for a portion of this time due to force majeure. However, the number of missing days at some sites was very small. Station 51704 had no data for 25 days, which comprised the greatest number of days with no data among all the stations. For this situation, the missing data were inferred based on the mean of the data measured before and after the gap.

Wind scale distribution in winter
In the field of meteorological forecasting, the wind scale of a certain day is divided into 18 classes according to the average wind speed. The basis of the classification in China is the "Wind Scale" National Meteorological Centre (2012). The specific classification method is shown in Table 1, National Meteorological Centre (2012). According to this method, the appearance frequency of different daily wind scales at 64 stations in the Xinjiang Uygur Autonomous Region was extracted over the periods of 1st, 2nd, 3rd, 11th, and 12th months from 1968 to 2016. The specific results are shown in Table 4 of Section Appendixes.
From Table 4, we know that strong winds appeared frequently at stations 51059, 52112, 51060, 51053, 51232, 51477, 51495, and 52313. As shown in Table 1, the wind speed at the different grades of wind scale was approximately equal to a mathematical progression. For the convenience of making calculations, we multiplied the different wind scales and their corresponding appearance frequency for every station and then carried the accumulation. Based on this method, the accumulative wind scale distribution map can be obtained if the contemporaneous data from the nearby regional sites are added during the calculation process. Taking station 52112 as an example, the total number of days with valid data was 7412. According to the valid data, the nominal accumulative wind grade was 0 × 193 + 1 × 1591 + 2 × 3189 + 3 × 1362 + 4 × 640 + 5 × 263 + 6 × 120 + 7 × 45 + 8× 6 + 9 × 1 = 17022 , and its average wind scale was about 2.29717. Due to the absence of data for 2 days, the weighted cumulative wind scale calculated in this study was 17022 + 2.29717 × 2 = 17026.5943 . After this calculation, the final distribution map representing the weighted accumulative wind scale was generated, as shown in Fig. 2.
It can be seen from Fig. 2 that the weighted accumulated wind scale is large in the northwest of Altay, the east and west of Hami, and at the junction of Urumqi and Turpan. However, it is relatively small in other regions. The Altay region is known as one of the nine strong wind regions in Xinjiang, and it is a typical terrain named "a valley between two mountains", which is composed of the Altay and Saur Mountains, and the Irtysh River Valley. For this reason, the weighted accumulated wind scale in this region is large. The junction of Urumqi and Turpan lies between the middle and the southern Tianshan Mountains. This place is called the Daban Town wind region and is also well known as one of the nine strong wind regions in Xinjiang. It's the key airflow channel between north and south Xinjiang. The development and construction conditions regarding wind energy in this area are the best among the nine strong wind regions. The special terrain in the Hami area is called the "four mountains lock three basins," where cold air activity is frequent. So, the wind scale is high in this area. Meanwhile, the authors extracted the maximum wind direction data for all the stations in Xinjiang during this period and drew the wind rose maps of the stations with high wind scales (including 51053, 51059, 51060, 51232, 51477, 51495, 52112, and 52313). They are shown in Fig. 3. The results show that the east wind prevails in the northwest of Altay. The southeast and west winds prevail at the junction of Urumqi and Turpan and in the southwest corner of Tacheng city. The north wind prevails in the west of Hami city, while the west and east winds prevail in the east.

Basic wind speed in winter
In China's design specifications for buildings that deal with wind load, the reoccurrence period of wind load for general structures is set at 50 years. Therefore, it is important to calculate the reoccurrence period of wind and snow accurately. Consequently, the annual maximum wind speed in winter during the 49-year period was extracted. For historical reasons, this data for the years 1968, 1969, and 1970 for all the stations in this region are missing. In addition, the data for station 54618 in the year 1971 and for station 54606 for the years 1971 and 1972 are also absent.
Based on the above available data, the basic wind speed in the reoccurrence period of 50 and 100 years was calculated using a Gumbel curve with an extreme type I distribution. The calculation steps are as follows.
First, the average maximum wind speed v i and its root variance i within a specified period of each station were calculated. The calculation formula v i for station number i is shown in Eq. 1, where n is the year from 1971 to 2016 for most stations. The formula i for station number i is shown in Eq. 2. v ij is the maximum wind speed for station number i in the winter of the year j, and n is the year from 1971 to 2016 for most stations.
Second, the assurance rate P (according to the recurrence period T ) was obtained. The calculation formula for P is shown in Eq. 3. The value of T was set to 50 and 100 years.
Based on the assurance rate P, the assurance coefficient can be further obtained according to the reference table presenting the assurance coefficient of the Gumbel curve with an extreme type I distribution, which is shown in Table 2. Finally, formula 4 was adopted to calculate the basic wind speed at each station during the different reoccurrence periods. The calculated results are shown in Table 5 of Section Appendixes.
Due to historical reasons, only partial annual data are available for some stations, but the amount of time is over 12 years for most stations. This data can reflect the realities and be used in the above calculation. Based on the results presented in Table 5, a distribution map of the basic wind speed in winter at the 50-year reoccurrence period in the Xinjiang Uygur Autonomous Region was generated, as shown in Fig. 4. This analysis indicated that the wind speed was high in the west of the Changji Hui Autonomous Prefecture, the west of Turfan, the west of the Bayingolin Mongol Autonomous Prefecture, Hami, Tacheng, and the Bortala Mongol Autonomous Prefecture. The wind speed was low in Aksu, Khotan, Kashgar, and the east of the Bayingolin Mongol Autonomous Prefecture. Consequently, these results can be referred to the code of building structure design in these regions.  1 3

Snowfall distribution in winter
In winter, precipitation is usually represented by snowfall. China has a strict regulation about the snowfall grade standard. Snowfall is the depth of an equal amount of water that originated as snow. Like rainfall, snowfall refers to the amount of snow that falls within a certain period, and this is generally measured over 24 h. According to the standard Short-Range Weather Forecast National Meteorological Centre (2017), snowfall is divided into seven grades: sporadic light snow, light snow, moderate snow, heavy snow, blizzard, storm snow, and super-big blizzard National Meteorological Centre (2017). If the snowfall is much more than 10 mm, the grade super-big blizzard can be sub-divided into two levels: big blizzard and super-big blizzard. The defined snowfall occurring at each grade within 24 h is shown in Table 3.
As the occurrence of sporadic light snow is very small, the sporadic light snow and light snow data can be merged. Subsequently, the times of the different snowfall grades at the 64 stations in the Xinjiang Uygur Autonomous Region within 1st, 2nd, 3rd, 11th, and 12th months from 1968 to 2016 were extracted. The results are shown in Table 6 of Section Appendixes.
As can be seen in Table 6, the times of high snowfall grade at stations 51433, 51133, and 51431 in the west of the Xinjiang Uygur Autonomous Region are relatively more than that of the other stations. According to the snowfall amount at each snowfall grade over 24 h, the grades were standardized: light snow, 1; moderate snow, 2; heavy snow, 4; blizzard, 8; storm snow, 12; and super-big blizzard, 16. As an example, at station 51431, the defined weighted cumulative snowfall grade was 918 × 1 + 331 × 2 + 223 × 4 + 78 × 8 + 16 × 12 + 1 × 16 = 3304 . Based on this method, the weighted accumulative snowfall grade for all of the stations in this region, as well as those nearby, was calculated, and the distribution map of the weighted cumulative snowfall grade in the Xinjiang Uygur Autonomous Region was generated, as shown in Fig. 5.
According to Fig. 5, we know that the snowfall areas of the Xinjiang Uygur Autonomous Region are mainly in the north, and the heaviest snowfalls are in the Yili Kazak Autonomous and the northwestern Tacheng Prefectures. The snowfall is medium in Altay, the Changji Hui Autonomous Prefecture, Shihezi City, Urumqi, and the Tacheng Prefectures except for the northwest. Snowfall in other areas is very slight.

Accumulative snowfall and wind scale for the top ten maximum snowfall days in winter
As most snowdrift disasters occur after a heavy snowfall, the authors extracted the wind scales of 6 days (including the day of the snowfall) after the top ten maximum snowfall days in winter in the Xinjiang Uygur Autonomous Region by using the above data, and then the wind grades on these 60 days are classified. The numbers of occurrences of different wind scales at all stations during these 60 days are shown in Table 7 of Section Appendixes. In this data of 60 days at all stations, 1 day's data at stations 51431 and 51470 and 2 days' data at stations 51433 and 51704 are missing. To analyze the wind power during these 60 days, the authors multiplied the different wind scales and their corresponding appearance frequency for each station and then calculated the accumulation. Based on this method, the cumulative wind scale distribution map can be obtained if the contemporaneous data from the nearby regional sites are added during the calculation process. The distribution map is shown in Fig. 6. For the missing data at different stations, we used the average value on the other days. From Fig. 6, we can know that the wind is very strong in northern Altay, western Hami city, western Urumqi, and at the junction of the Bortala Mongol Autonomous and Tacheng Prefectures after heavy snowfalls. The wind in eastern Hami city and the northern Kizilsukirgiz Autonomous Prefecture is weaker than the above areas. While in the other areas, the wind is weakest.
The above is the analysis of the cumulative wind scale for 6 days (including the day of snowfall) after the top ten maximum snowfall days in winter at all stations in the Xinjiang  Uygur Autonomous Region, without considering the total snowfall on the top ten maximum snowfall days. Therefore, the authors analyzed the joint distribution of the total snowfall on the top ten maximum snowfall days and the accumulated wind scale on 6 days (including the day of the snowfall) after the top ten maximum snowfall days. First, the authors calculated the total snowfall for the top ten maximum snowfall days and then calculated the cumulative wind scale for 6 days (including the day of snowfall) after the top ten maximum snowfall days. In order to compare the joint distribution of the total snowfall and the accumulated wind scale, these data are normalized according to Formulas 5 and 6. After these calculations, the total snowfall, the accumulated wind scale, average wind scale, normalized total snowfall, and normalized accumulated wind scale are shown in Table 8 of Section Appendixes.
Finally, the authors display the normalized total snowfall and accumulated wind scale on the map of the Xinjiang Uygur Autonomous Region, which is shown in Fig. 7. From Fig. 7, we can draw four conclusions.
(1) After heavy snowfalls, the wind is very strong in the northwestern Altay, the northwestern Tacheng Prefecture, and Urumqi city. So, the snowdrift disasters that occur in these areas are very serious.
(2) After a heavy snowfall, the wind is not very strong in the Kizilsu Kirghiz Autonomous Prefecture, the Bortala Mongol Autonomous Prefecture, and northeastern Altay. So, the snowdrift disasters in these areas are not serious. (3) After a snowfall, the wind is very strong, but it does not snow very much in Hami city. So, it has potential to become an area with serious snowdrift disasters. (4) After snowfalls, the wind is very weak, and the snowfall is less than it is in other areas. So, the probability of the occurrence of snowdrift disasters is much lower than in the other areas.

Cumulative snowfall and wind scale in relation to the top ten maximum snowfall events in winter
In Sect. 5, the authors analyzed the cumulative wind scale for the top ten maximum snowfall days at all stations in the Xinjiang Uygur Autonomous Region, without considering the total snowfall of the top ten maximum snowfall events in winter. Therefore, the authors extracted the wind scales of the days on which the top ten maximum snowfall events happened, and the wind scales of the 5 days after these snowfall events in winter in the Xinjiang Uygur Autonomous Region by using the above data. In this data on the different days at all stations, 1 day's data at stations 51431, 51470, 51431, 51346, and 51704, and 2 days' data at stations 51433 is missing. For the missing data at different stations, we used the average value of the rest days. To compare the joint distribution of the total snowfall and the accumulated wind scale, these data are also normalized according to Formulas 1 and 2. After these processes, the average wind scale, maximum wind scale, normalized total snowfall, and normalized accumulated wind scale are shown in Table 9 of Section Appendixes. (5) Based on the above-normalized snowfall and wind scale data, a joint distribution map of the accumulative snowfall and wind scales at each station in the Xinjiang Uygur Autonomous Region was generated (Fig. 8). It can be seen from this map that, after the top ten heavy snowfall events, the accumulative wind scale is high and the cumulative snowfall is large in the Altay Prefecture, the Bortala Mongol Autonomous Prefecture, the Tacheng Prefecture of the northern Xinjiang, and the Kizilsu Kirghiz Autonomous Prefecture of the western Xinjiang. However, in regard to the Altay Prefecture, the accumulative wind scale is higher in its northwestern quadrant than its southeastern counterpart. The cumulative wind scale is high, but the accumulative snowfall is small in the Hami Prefecture. In other areas, both are small.
The maximum wind scale after a heavy snowfall is of great concern because it determines the intensity of the snow drifting disaster. The authors generated the joint distribution map of the accumulative snowfall and maximum wind scale from the top ten maximum snowfall events at each station in the Xinjiang Uygur Autonomous Region, which is shown in Fig. 9. From this, we can know that the maximum wind scale after a heavy snowfall is high in the northwestern Altay Prefecture, the western Bortala Mongol Autonomous Prefecture, the western Kizilsu Kirghiz Autonomous Prefecture, the eastern Ili Kazakh Autonomous Prefecture, the eastern Hami city, and the eastern Urumqi. Among the above regions, the snowfall in the Altay region, Ili Kazakh Autonomous Prefecture, and Tacheng Prefecture are very heavy. So, these three regions are the hardest hit by the snow drifting Fig. 7 Joint distribution map of the total snowfall for the top ten maximum snowfall days and the accumulative wind scale for 6 days (including the day of snowfall) after the top ten maximum snowfall days at all stations in the Xinjiang Uygur Autonomous Region disasters. The snowfall is not very heavy in the western Bortala Mongol Autonomous Prefecture, the western Kizilsu Kirghiz Autonomous Prefecture, the eastern section of Hami city, and the eastern neighborhoods in Urumqi. However, if heavy snowfall occurs, which provides plenty of snow particles, it's very easy to pose a snow drifting disaster. These are the key regions in terms of snow drifting disasters and deserve our focus. Other areas are not as peculiarly prone to this type of disaster.

Conclusions
This study assessed the spatial distribution characteristics of wind and snowfall in the Xinjiang Uygur Autonomous Region of China based on the "Daily Data Sets of Climate Data for China International Surface Exchange Station (V3.0)". The following conclusions can be drawn from this analysis.
(1) The weighted accumulated wind scale is large in the northwest of Altay, the east and west of Hami, and at the junction of Urumqi and Turpan. However, it's relatively small in other regions.
(2) The distribution map of the basic wind speed in winter at the 50-year reoccurrence period in the Xinjiang Uygur Autonomous Region was generated, which can be used in building structure design. (4) After heavy snowfall, the wind is very strong in northwestern Altay, the northwestern section of the Tacheng Prefecture, and Urumqi city. So, the snowdrift disasters are very serious if they occur in these areas. (5) After the top ten heavy snowfall events, the accumulative wind scale is high, and the accumulative snowfall is large in the Altay Prefecture, the Bortala Mongol Autonomous Prefecture, and the Tacheng Prefecture of the northern Xinjiang, and the Kizilsu Kirghiz Autonomous Prefecture of the western Xinjiang.

Discussion
The above conclusions have great practical significance for the prevention and control of snow drifting disasters in the Xinjiang Uygur Autonomous Region. However, some problems should be discussed in the future.
(1) In this paper, the top ten maximum snowfall days and snowfall events in winter are extracted, and the wind speeds in these periods are analyzed. When the time of two snowfall events is very close, and the snow of the first snow event has not merged or crust, it can also lead to severe natural disasters. While this situation is not analyzed. (2) As the precipitation value in the raw data cannot be classified as snow or rainfall, there are some mistakes when we take the precipitation pattern in the winter as snow. For example, sometimes rain falls in winter and snow falls in spring and autumn. In the future, more detailed data should be acquired, and then, all snowfall events can be extracted strictly.
(3) The wind data in this paper are daily data. Actually, more detailed instantaneous wind speed data can reveal the extent of the snow drifting disaster in 1 day, and then the conclusions in this paper will be more persuasive.