Statistical characteristics of the spatial distribution of wind and snowfall in the Beijing–Tianjin–Hebei Region

In the current design specification of building structure, the basic wind pressure and basic snow pressure are two independent values, and it is impossible to acquire both of these values when snow and wind occur at the same time. Taking parameters such as snowfall intensity, snowfall amount, wind speed, and wind direction as indicators, the value of the combined distribution of wind and snowfall in the Beijing–Tianjin–Hebei region of China was extracted. A joint distribution map of the daily average snowfall among the top-ten largest consecutive snowfall events and the daily average wind scale from the first day of snowfall to the fifth day after the snowfall were obtained. The study found that after a heavy snowfall in the Zhangjiakou area, the accumulated wind power was large and, although the wind speed was favorable for the occurrence of snowdrifts, the snowfall was light. After a heavy snowfall in the Shijiazhuang area, the accumulated wind power was small, and the probability of snowdrift formation was low. In the eastern regions of Cangzhou, Beijing, Tianjin, Tangshan, and Qinhuangdao, the accumulated wind force was relatively large after a heavy snowfall, and the probability of windblown snow was relatively high.

In view of the serious disasters caused by snowdrift formation, it is essential to study the mechanisms involved in the formation of snowdrifts. The basic parameters of snowdrift research are the probability and simultaneous occurrence of snowfall intensity, wind scale during or after the snowfall, and wind direction. In the current design specification 7 , the basic wind pressure and basic snow pressure are two independent values; however, it is not possible to acquire both of these values when snow and wind occur at the same time.
At present, the movement mechanism promoting snowdrift formation is still not entirely clear. The main research methods for such investigations include theoretical analysis, field observations, wind tunnel tests, numerical simulations, and others, with each method having its own advantages and disadvantages. In 1976, Kind made a detailed theoretical derivation and analysis concerning the saltation process of snow particles 8 , and he then detailed the critical conditions concerning the drift of particles via theoretical analysis in 1990 9 . In 2002, Tsuchiya et al. proposed a relationship between the accumulation thickness of snow particles and the acceleration of wind speed based on wind and snow data, which was measured on high and low roofs in Hokkaido, Japan 10 .
Doorschot et al. previously performed field measurements to calculate the threshold friction velocity for snow saltation and mass fluxes during snowdrift formation 11 , and Lü et al. conducted a series of experiments in wind tunnel to investigate the motion of natural snow (fresh snow and old snow), which was collected outdoors without altering the surface structure 12 . To simulate the dynamic process of snowfall area boundary, Fu Zhu et al. proposed an adaptive-mesh method using radial basis function (RBF) interpolation, which realized the change of the phase boundary in both two-dimensional and three-dimensional snowdrift formation 13 . Liu et al. undertook three sets of experiments to investigate the influence of wind on snowdrift accumulation around a building model and to explore its influence on two separate building models 14 . Schön et al. proposed an efficient method for generating estimations of the changes in snow heights during blowing snow events 15 .
Weiwei Zhang and Guanghui Zhang studied the formation mechanism of snowdrifts and concluded that it was largely related to severe cold weather and heavy snowfall, as well as the topography and landform of the study area, concluding that the occurrence of snowdrifts has a distinct regional character 16 . He Wu et al. studied the formation mechanism and spatial distribution characteristics of snowdrift disasters on highways 17 . Jian Liu et al. assessed the causes and main types of snowdrift situations on the roads in Xinjiang, including windward snow type, leeward snow type, snowdrifts in horizontal curves, and road cut snow type 18 . Gao et al. studied snowdrift disasters along the Jinghe-Yining railway and the control methods employed. The main control methods included setting up anti-snowdrift corridors, placing air deflectors and side guiders, and the placement of snow fencing 19 .
Generally, snowdrift formation is a joint probability event of wind and snow variables, with the two primary variables being snowfall intensity and wind strength. Only when heavy snowfall and strong winds appear together will snowdrifts be formed 20 . The above conclusion is based on the assumption that snowdrift formation will occur when there is enough snow in a certain place and the wind is strong enough during or after the snowfall event. During the snowfall event, snowdrift formation might occur if the wind blows hard enough. After a heavy snowfall, snowdrift formation might also occur before the snow surface melts and crystallizes. Therefore, it is an important basis for the assessment of snowdrift events to extract the probability of the joint distribution of snowfall and wind in a specific region from the meteorological data and to conclude the probability of the occurrence of the two parameters at the same time. Based on this, this current study assessed the joint distribution of wind and snowfall and obtained the occurrence regularity of snowdrift events in the Beijing-Tianjin-Hebei region of China using the meteorological data available from the China Meteorological Administration.

Materials
In this section, the meteorological data used in this study is introduced. It consisted of the "Daily Data Sets of Climate Data for China International Surface Exchange Station (V3.0)". This data was developed by the China Meteorological Administration in accordance with the "basic data set of monthly report data files (A0/A1/A) after data correction of China's national ground stations in 1951-2010", which is filed from the ground basic meteorological data construction project. After effective quality control, the availability rate of the meteorological factor data was generally more than 99%, and the accuracy rate was nearly 100%. This data included eight major items, including the daily air pressure values, air temperature, precipitation, evaporation, relative humidity, wind speed and direction, sunshine time, and 0 cm ground temperature. The data has been acquired daily from 824 basic meteorological stations located in China since January 1951.
In this study, precipitation, wind speed, and wind direction data were selected from the above data sets. In the precipitation data, there were ten columns of valid data, including station number, latitude, longitude, height of sea drawing in the observation field, year, month, day, accumulated precipitation from 20:00 of the previous day to 08:00, accumulated precipitation from 08:00 to 20:00, and accumulated precipitation from 20:00 of the previous day to 20:00. In the wind data, there were 12 columns of valid data, and these included the station number, latitude, longitude, height of sea drawing in the observation field, year, month, day, average wind speed, maximum wind speed, the direction of maximum wind speed, extreme wind speed, and the direction of the extreme wind speed.
Maximum wind speed refers to the average maximum wind speed over 10 min during a given period. Extreme wind speed refers to the maximum instantaneous wind speed within a given period. 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. However, when the self-recording instrument was not equipped at the observation station, the daily average wind speed was the average of three wind speed values observed at 08:00, 14:00, and 20:00. 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.
In the data sets, as there was no distinction between rainfall and snowfall, the precipitation over the whole winter period was used to represent snowfall for studying the statistical characteristics of snow and wind. In www.nature.com/scientificreports/ winter, the precipitation is mostly in the form of snowfalls in the Beijing-Tianjin-Hebei Region. The winter months are January, February, November, and December. After importing the above data into a database, the effective data from 26 observation stations in the Beijing-Tianjin-Hebei region was selected for this analysis. The location and number of the 26 stations are shown in Fig. 1. The selected time period was from 1968 to 2016 and included a total of 5893 days. During this period, due to force majeure, there was a lack of observation data for a portion of the time. However, the number of missing days at some sites was very small. The biggest lost count was 58 at station 54618. For this situation, the missing data was inferred based on the mean of the data measured before and after the gap.

Results
Wind scale distribution in winter. In this section, a method of generating the accumulative wind scale distribution map is proposed, and then, the characteristics of this map and the maximum wind direction for some stations are introduced in the Beijing-Tianjin-Hebei region 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 is "Wind Scale" 21 . The specific classification method is shown in Table 1 21 . According to this method, the appearance frequency of different daily wind scales at 26 stations in the Beijing-Tianjin-Hebei  Table 2.
If we define wind scale 1 and 2 as small wind scale, wind scale 3, 4 and 5 as moderate wind scale, and scale 6, 7 and 8 as high wind scale, it can be seen in Table 2 that high wind scales frequently appeared at station 54623 of Tianjin city as well as station 53399 and 54405 of Hebei Province. As shown in Table 1, the wind speed at the different grades of wind scale was approximately equal to an arithmetic progression. For the convenience of making calculations, we multiplied the different wind scales and their corresponding appearance frequency for every station, and then carry on 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 54525 in Tianjin city as an example, its valid data days were 5877. According to the valid data, its nominal accumulative wind grade was 0 × 38 + 1 × 2021 + 2 × 2436 + 3 × 1000 + 4 × 302 + 5 × 71 + 6 × 9 = 11,510, and its average wind scale was about 1.95848. Due to the absence of data over 16 days, the weighted cumulative wind scale calculated in this study was 11,510 + 1.95848 × 16 = 11,541.33568. After this calculation, the final distribution map representing the weighted accumulative wind scale was generated, as shown in Fig. 2.
As is shown in Fig. 2, in the Beijing-Tianjin-Hebei region, the weighted accumulative wind scale was larger in Tianjin, Beijing, and Zhangjiakou, while the other areas had a smaller accumulative wind scale. That is to say, Because of the obstruction provided by the Taihang and Yanshan mountains, the wind from the north of the Inner Mongolia autonomous region can only move into the connection gap between these two major mountains and Zhangjiakou city, which causes strong winds throughout the year in Zhangjiakou city. At the same time, this wind blows along the main wind direction to Beijing city and gradually weakens. The wind from the sea passes through the gap between the Bohai Sea and Tianjin city and then enters the Beijing-Tianjin-Hebei region, which causes strong winds to occur in Tianjin city. This wind also blows along the main wind direction to Beijing city and gradually weakens. Due to the above two events, the wind scale in Beijing is relatively larger compared with the surrounding areas. Additionally, the wind scale of coastal areas (Qinhuangdao City, Tangshan City, and Cangzhou City) are larger than that of other inland areas, which means that the wind from the sea has an evident influence on the coastal areas.
The maximum wind direction from all stations in the region was extracted from the study period, and this data was used to draw wind direction rose diagrams representing the maximum wind scale. The wind direction rose diagrams for some stations are shown in Fig. 3. As is shown in Fig. 3, it can be seen that a northwest wind prevails in Zhangjiakou city and Tianjin city in the winter, while east and west winds prevail in Tangshan city Basic wind speed in winter. In this section, a method of calculating the basic wind speed is introduced, and then, the basic wind speed distribution map is generated and analyzed in the Beijing-Tianjin-Hebei region in winter. In the design specification of wind load on buildings, the reoccurrence period of wind load for general structures in China is set as 50 years. Therefore, it is important to calculate the reoccurrence period of wind and snow accurately. As a consequence, the annual maximum wind speed in winter during the 49-year period was extracted. For historical reasons, this data in the years 1968, 1969, and 1970 for all of the stations in this region are missing. In addition, the data in the year 1971 for station 54618 and for the years 1971 and 1972 for station 54606 are also absent. Based on the above available data, using a Gumbel curve with an extreme type I distribution, the basic wind speed in the reoccurrence period of 50 and 100 years was calculated. The calculation steps are as follows.
First, the average maximum wind speed v i and its root variance σ i within a specified period of each station were calculated. The calculation formula v i for station number i is shown in Eq. (1). The formula σ 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  www.nature.com/scientificreports/ 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 ϕ 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 3.
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 4 Based on the results presented in Table 4, a distribution map of the basic wind speed in winter at the 50-year reoccurrence period in the Beijing-Tianjin-Hebei region was generated, as shown in Fig. 4. This analysis Snowfall distribution in winter. In this section, a method of generating the accumulative snowfall distribution map is proposed, and then, the characteristics of this map are introduced in the Beijing-Tianjin-Hebei region in winter. In winter, precipitation is usually represented as snowfall. There is strict regulation about snowfall grade standard in meteorology. Snowfall is the depth of an equal amount of water, which is turned from 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" 22 , snowfall is divided into seven grades: sporadic light snow, light snow, moderate snow, heavy snow, blizzard, storm snow, and super-big blizzard 22 . If the snowfall is much bigger than 10 mm, the grade super-big blizzard can be sub-divided into two levels: big blizzard and super-big blizzard. www.nature.com/scientificreports/ The defined snowfall occurring at each grade within 24 h is shown in Table 5. As the occurrence of sporadic light snow was very small, the sporadic light snow and light snow data were merged. Subsequently, the times of the different snowfall grades at the 26 stations in the Beijing-Tianjin-Hebei region within 1, 2, 11, and 12 months from 1968 to 2016 were extracted. The results are shown in Table 6.
As can be seen in Table 6, the times of high snowfall at stations 53399, 53593, 54308, 54311, 54401, 54405, and 54423 in Hebei were relatively less compared to 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 54525 in Tianjin, the weighted cumulative snowfall grade was 214 × 1 + 52 × 2 + 41 × 4 + 15 × 8 + 4 × 12 + 1 × 16 = 666. Based on this method, the weighted accumulative snowfall grade for all of the stations in the Beijing-Tianjin-Hebei region and nearby was calculated, and the distribution map of the weighted cumulative snowfall grade in the Beijing-Tianjin-Hebei region was generated, as shown in Fig. 5.
As can be seen in Fig. 5, the snowfall in the Beijing-Tianjin-Hebei region could be divided into three zones. The heavy snowfall area included Shijiazhuang, Xingtai, and Handan. The moderate snowfall area included Hengshui, Cangzhou, Baoding, Tianjin, Beijing, Langfang, Tangshan, and Qinhuangdao. The light snowfall www.nature.com/scientificreports/ area included Zhangjiakou and Chengde. Based on these observations, the snowfall was roughly in line with the occurrence of heavy snowfall in the southern region, moderate snowfall in the central region, and light snowfall in the northern region. Additionally, the boundary between the heavy snowfall area and moderate snowfall area could be defined as the connection between the northern part of Shijiazhuang City and the central part of Hengshui City, indicating that the boundary between the different snowfall areas was not strictly based on latitude.
The boundary between the moderate snowfall area and light snowfall area could be defined as the connection between Baoding city, the northwest part of Beijing City, and the south part of Chengde City.
Cumulative snowfall and wind scale in relation to the top ten maximum snowfall events in winter. In this section, a method of generating the cumulative snowfall and wind scale distribution map in relation to the top ten maximum snowfall events in winter is proposed, and then, the characteristics of this map are introduced and analyzed in the Beijing-Tianjin-Hebei region. As the occurrence of snowdrift formation requires heavy snowfall and strong winds to appear at the same time, the top-ten biggest snowfalls at all of the stations in the Beijing-Tianjin-Hebei region from the year 1965 to 2016 were first extracted, and the values of www.nature.com/scientificreports/ wind scale for each day in this period, from the first day of snowing to 5 days after the day the snow had stopped, was then extracted. Ultimately, the above snowfalls and wind scales were summed by station prior to the statistical analysis. Based on this method, the accumulative amount of snowfall, total snow days, average daily snowfall, accumulative wind scale, total wind days, and average daily wind scale were calculated for each station. Among these wind data, one day of data for stations 53399, 53593, and 54436 in Hebei were missing, and three days of data for station 54525 in Tianjin were missing. In order to account for the missing data, the weighted cumulative wind scale was obtained using the method detailed above. The processing for these stations was the same as that described in "Conclusions and discussions". To facilitate comparisons between the wind and snowfall numbers, the accumulative amount of snowfall and accumulative wind scale data were normalized. The final statistical results are presented in Table 7. Based on the normalized snowfall and normalized wind scale data, a joint distribution map of the accumulative snowfall and accumulative wind scale from the top ten maximum snowfall events at each station in the Beijing-Tianjin-Hebei region was generated (Fig. 6). It can be seen from this analysis that the wind scale and snowfall values in Tianjin, Tangshan, Cangzhou, Qinhuangdao, and Langfang were large, and each of these areas is proximal to the Bohai Sea. The wind and snowfall values were medium in Baoding and Hengshui, and the snowfall amount was larger and the wind value was smaller in Shijiazhuang. In Zhangjiakou, the wind value was large, but the snowfall amount was small. Both the wind and snowfall values in Chengde were small.

Conclusions and discussions
This study assessed the spatial distribution characteristics of wind and snowfall in the Beijing-Tianjin-Hebei 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 accumulative wind scale is larger in Tianjin, Beijing, and Zhangjiakou and smaller in the other areas of the Beijing-Tianjin-Hebei region. In the Beijing-Tianjin-Hebei region, there is a wide ventilation corridor along Zhangjiakou, Beijing, and Tianjin. The wind scale in coastal areas (Qinhuangdao, Tangshan, and Cangzhou) is larger than that in the other inland areas, which also indicates that wind coming from the sea has a certain influence on the coastal areas. . A methodology to extract the joint combination of wind scale and snowfall was proposed. The joint distribution map of the accumulative snowfall and accumulative wind scale for the top ten maximum snowfall events at each station in winter in the Beijing-Tianjin-Hebei region was generated based on these data. The wind scale and snowfall values in Tianjin, Tangshan, Cangzhou, Qinhuangdao, and Langfang are large, and these areas are proximal to the Bohai Sea. The snowfall amount is larger and the wind speed is lower in Figure 6. Joint distribution map of the accumulative snowfall and accumulative wind scale from the top ten maximum snowfall events at each station in the Beijing-Tianjin-Hebei region. The present map was done by using ArcGIS 10.0 desktop version (https ://www.esri.com/zh-cn/arcgi s/produ cts/arcgi s-pro/overv iew). www.nature.com/scientificreports/ Shijiazhuang. In Zhangjiakou, the wind speed is high, but the snowfall amount is low. Both the wind speed and snowfall amounts in Chengde are low.
The above results and conclusions have important practical significance for the design of building structures in the Beijing-Tianjin-Hebei region. When we calculate the snow and wind load for a building structure in this region, the current method is that: first, query the basic snow pressure and the basic wind pressure in this region from the Load code for the design of building structures of China 7 , second, calculate the snow and wind load marked by L snow and L windO , respectively, third, add two numbers together and get the total load of snow and wind, which is marked by L snow+windO . Actually the total load calculated by this method is bigger than the true value. That is the problem which is solved in this study. For the same building structure in this region, the snow load is still expressed by L snow , and the temp wind pressure after the biggest snowfall events should be calculated according to this study, which is marked by L windT , and then, the joint load of snow and wind can be gotten by adding the two numbers L snow and L windT together, which is marked by L snow+windT . The value of L snow+windT should be bigger than the value of L snow , and smaller than the value of L snow+windO . If the value of L snow+windT is bigger than the value of L windO , the total load of snow and wind should be the value of L snow+windT , not the value of L snow+windO . If the value of L snow+windT is smaller than the value of L windO , the total load should be the value of L windO . In this study, we just studied statistical characteristics of the spatial distribution of wind and snowfall in the Beijing-Tianjin-Hebei region of China. In the future, their spatial distributive characteristics in more areas will be surveyed and analyzed.