Extreme wind speed prediction in mountainous area with mixed wind climates

In addition to common synoptic wind system, the mountainous terrain forms a local thermally driven wind system, which makes the mountain wind system have strong terrain dependence. Therefore, in order to estimate the reliable design wind speeds for structural safety, the samples for extreme wind speeds for certain return periods at mountainous areas can only come from field measurements at construction site. However, wind speeds measuring duration is usually short in real practice. This work proposes a novel method for calculating extreme wind speeds in mountainous areas by using short-term field measurement data and long-term nearby meteorological observatory data. Extreme wind speeds in mountainous area are affected by mixed climates composed by local-scale wind and large-scale synoptic wind. The local winds can be recorded at construction site with short observatory time, while the extreme wind speeds samples from synoptic wind climate from nearby meteorological station with long observatory time is extracted for data augmentation. The bridge construction site at Hengduan Mountains in southwestern China is taken as an example in this study. A 10-month dataset of field measurement wind speeds is recorded at this location. This study firstly provides a new method to extract wind speed time series of windstorms. Based on the different windstorm features, the local and synoptic winds are separated. Next, the synoptic wind speeds from nearby meteorological stations are converted and combined with local winds to derive the extreme wind speeds probability distribution function. The calculation results shows that the extreme wind speed in the short return period is controlled by the local wind system, and the long-period extreme wind speed is determined by the synoptic wind system in the mountain area. The descending slope of the synoptic wind speed exceeding probability exceeds the local wind by about 20%. If the influence of mixed climate is not considered, and the wind speed samples are not divided by category, the decline slope will be 7% lower.


Introduction
Accurately estimating the extreme wind speeds with different recurrence periods is the first step for structure windresistant design, especially for flexible structures, such as long-span bridge and super-tall building. For example, the long-span bridge must sustain the aerodynamic stability (Simiu and Yeo 2019) in strong winds, and the tall building should provide sufficient habitability through mitigating wind-induced vibration (Kwok et al. 2009;Cui and Caracoglia 2020). In engineering practice, the structure must be designed to ensure the structural resistance larger than the wind loads, which is determined by local wind climate and normally prescribed in design code (ASCE 2016).
For the past decades, there are three the most widely used extreme wind speeds estimation methods based on extreme theory including annual maxima extreme method (Gumbel 2004), the peak-over-threshold (Simiu and Heckert 1996), and the method of independent storm (Cook 1982;Harris 1999). A lot of researches have gradually improved the extreme wind speed prediction of extreme theory, which will be reviewed in details following. At present, these methods are widely used at various places to provide extreme wind speed prediction with historical meteorological records (Palutikof et al. 1999).
Ideally, the extreme wind speeds should be calculated for the location at construction site. However, normally there is almost no long-term weather observation data at the exact construction site. In engineering practice, the regional extreme wind speed is calculated by the nearest weather observation station or refereed coded value in structural design standards (ASCE 2016) to serve as extreme wind speeds for the constructed structure. The above approach implies an assumption: The wind environment will remain constantly on the large spatial scale. This assumption is almost satisfied in flatland and plateau, because the strong wind events occur on the above two plain areas are generally macro-scale or meso-scale, such as typhoons and monsoons.
However, this assumption in mountainous areas is no longer valid, because the deep valley area separated by high mounts, and the wind climate in one valley cannot represent others. From the viewpoint of meteorology, the mountain wind system basically includes local mountain wind systems and synoptic wind systems (Li et al. 2014;Wagner 1938). Local mountainous wind systems form over valley terrain (Zardi and Whiteman 2013). Synoptic wind systems are normally referred as macro-scale wind phenomena (Jackson et al. 2013). The mountain topography only affects a local region. In addition, existing researches of mountainous wind system including field measurement (Whiteman 1990;Mingjin et al. 2019;Zhang et al. 2020a), numerical simulation (Maurizi et al. 1998;Kim et al. 2000;Bitsuamlak et al. 2004;Cao et al. 2012) and wind tunnel test (Li et al. 2017(Li et al. , 2010 also proves that the speed of local wind systems vary from place to place, depending on many factors including terrain characteristics, ground cover, soil moisture, altitude and etc. Therefore, in mountainous areas, it is not accurate to use the extreme wind speed from the nearby weather station on the proposed structure in the other valley. On the other hand, the large scale synoptic wind system simultaneously affect the whole mountain area. In order to establish the relationship between weather station and construction site, several approaches has been developed, including wind tunnel methods (Li et al. 2010), numerical simulation (Bitsuamlak et al. 2004;Kim et al. 2000) and long-term synchronized field measurement (Huang et al. 2019;Beine et al. 2001). However, to calculate the extreme wind speed at a specific construction site in mountainous area, the local wind system information must be considered, but above mentioned methods cannot provide sufficiently accurate extreme wind speed estimation. Boundary layer wind tunnel test is unable to reproduce a thermally driven wind system (Zhang et al. 2020b;Tse et al. 2020). Numerical simulation, which consumes a lot of computing power, is impractical to perform many times to generate sufficient large sample required by extreme value analysis (Abd-Elaal et al. 2018;Ren et al. 2018). Field measurement is a feasible solution (Jing et al. 2020), but sufficient long-term synchronized observation between proposed structure site and weather station will delay the construction schedule, which is economically unacceptable. Therefore, it is necessary to develop economical and feasible method to estimate the extreme method based on synchronized short-term ( 1 year) in mountainous area.
To improve the accuracy of statistical predictions based on short time wind observation, several researches use the information provided by another highly correlated data with a much longer observation time (Wang 2001;Gaidai et al. 2019). Due to the special features of the mountain wind system, the records of different observatories are only highly correlated for synoptic wind systems. The local mountain wind systems are normally confined in associate small region enclosed by nearby terrain formation, thus, the records of local mountain wind from different places are irrelevant.
In summery, the extreme wind events in mountainous areas should be considered as mixture climate including large scale synoptic winds and micro-scale local mountain wind systems (Gomes and Vickery 1978;Cook et al. 2003;Cook 2004). In order to identify different wind systems from unlabeled wind speed data, several methods have been proposed including feature-based (De Gaetano et al. 2014), history-based (Lombardo et al. 2009) and databased (Cui et al. 2021;Chen and Lombardo 2020). However, those methods are seldom applied in mountainous area. In this study, feature-based method is used to classify local mountain wind systems and synoptic wind systems. For the wind observation records, a short-term field measurement from self-installed equipment has been acquired to provide the information of local mountain wind systems and long-term observation data from nearby public weather station is employed to provide synoptic wind systems data.
An improved method of wind storms identification in mountainous areas is proposed in this paper, which can applied for both short-term measurement with high recording frequency and long-term measurement with low recording frequency. Then, different extreme value distribution models are employed to fit the identified two wind systems. Finally, the extreme wind speed is calculated for different recurrence periods by extreme value theory with mixture wind climate. A flow chart of research work is shown in Fig. 1.

Theoretical background
For structural design, safety considerations must be balanced against the additional cost of over design. Accurate estimation of the occurrence of extreme wind speeds is an important factor in achieving the correct balance. Typically, for most users of wind data, estimates of the 50-year return period extreme wind speed are required, based on 10 20 (and often fewer) available years of observations. For this situation, the data are generally fitted to a theoretical distribution in order to calculate the quartiles. In this section, several extreme wind speed statistic theory are described, including annual extreme method, method of independent storm and upcrossing method. Fisher and Tippett (1928) showed that if a sample of n cases is chosen from a parent distribution, and the maximum of each sample is selected, then the distribution of the maximum approaches one of three limiting forms as the size of the samples increases. Gumbel (2004) argued that, in the case of floods, each year of record constitutes a sample with 365 cases and that the annual extreme flood is the maximum value of the sample. Thus, the Fisher Tippett distributions could be fitted to the set of annual maxima. This is the basis of all classical extreme value theory. The aim is to define the form of the limiting distribution and estimate the parameters, so that quartile value X T can be calculated.

Gumbel with annual extremes
Fish-Tippett Type I distribution (also known as Gumbel distribution) has the cumulative distribution function: where b is the location parameter and a is the scale parameter.
Gumbel distribution is most widely used in wind-resistance code around world (ASCE 2016). Equation (1) calculates the probability that the wind speed does not exceed U in one year. Extreme wind speed of a certain return period R means annual exceed probability of this wind speed equals to 1 R þ 1 .
The great advantage of using the GEV distribution [Eq.
(2)] with annual maximum is that few decisions are required during the calculation of the distribution parameters and quartiles. However, it requires a sufficient long wind observation time to provide enough extreme value samples. where b is the location parameter, a is the scale parameter and c is the shape parameter.

Method of independent storm
The principal drawback to the classical Gumbel method is that only one value is selected per epoch (e.g. one year). This greatly reduces the extreme data samples available for analysis, such that the underlying datasets must be long. This method is not suggested to be employed with fewer than 10 years. To increase the number of cases for analysis, method of independent storms (MIS) had been developed (Cook 1982;Harris 1999). MIS increases the number of extreme available for analysis, whilst ensuring their independence by separating the parent time series of wind speeds into independent storms and then selecting the highest value from each storm. The storms is separated by a lull (period of wind speeds below a selected low threshold). Cook (1982) found a typical storm frequency rate to be around 100 events/ year. After pre-processing, the extreme wind speed sample is fitted to the Gumbel distribution. Harris (1999) introduced two improvements to the MIS. This method modified the plotting position used by Cook (1982) to avoid systematic errors and fitted the distribution is given. The extreme wind speed exceed probability could be calculated by Poisson process [Eq. (3)] where i is the number of occurrences, r is the rate of independent events per unit time, T is the epoch and Pðu UÞ is the Cumulative Distribution Function of gumbel distribution fitted by independent storms wind speed sample. When T equals to 1, Eq. (3) is used to calculated annual extreme wind speed exceed probability.

Upcrossing method
When the available wind speed data is further reduced, only a few years or less, the data utilization of MIS is also not enough. In this case, Gomes and Vickery (1977) suggested a method to estimate extreme wind speeds from the parameters of the parent distribution. This method is based on continue wind speed data from the site of interest. The average number of upcrossings of u per unit time (crossings with positive slope) can be obtained using Rice's formula (Rice 1944).
in which U þ ðuÞ is the crossing rate and f u; _ u ðu; _ uÞ is the joint probability distribution of the mean wind speed and the rate of change of the wind speed. Assuming that u and _ u are independent and uncorrelated, and further assuming that _ u is a stationary Gaussian process with zero mean, Eq. (4) could be rewritten as: Equation (5) yields an expression for the excepted number of crossing per unit time for a threshold. Assuming these crossings to be rare and independent events, the probability of exceed can be modeled using a Poisson approximation:

Mixed climate theory
The technique for mixed wind climate extreme wind speed calculation required a separate extreme-value analysis of the values stemming from each significant wind-producing mechanism, followed by synthesis of the individual mechanisms into a composite extreme-value distribution. Gomes and Vickery (1978) carried out the different causative mechanisms extreme wind speed analysis for Australia and America. Consider two wind independent mechanisms A and B, giving sets of wind speeds U A and U B , respectively, from each. The cumulative probability P T ðu\UÞ of the maximum value u from either mechanism in an epoch T is less than some value U could be calculated by where u A ; u B is the wind speed from mechanism A or B. Equation (7) could only be used if T is long enough that each mechanism events are sufficiently frequent to occur in every epoch.

The measurement equipment and recorded data
The construction site of Murong Bridge in China is employed as the research object. This section describes the topography and location of Murong Bridge, the installation of the wind recording system and the general description of wind speed data from field measurement and weather observation station.

Description of the bridge site
The study area of this work is in southwestern China, which is located on the Xianshui River in Yajiang County, Ganzi Prefecture, Sichuan Province specifically. It is in the middle of the Hengduan Mountain Range, which is in the southeastern of the Tibetan Plateau. Figure 2 shows the location of the study area in the view of macro-scale. The bridge site located at the Hengduan Mountains of southwestern China is a typical narrowed V-shaped deepcut canyon and the depth of the canyon is about 500-1500 meters. Altitude around the bridge site is 3900-4800 meters. Moreover, the lower reaches of the river are meandering and topography near the bridge varies dramatically. The terrain at the bridge site is shown as Fig. 3.

Installation of the wind measuring system on Murong bridge
The site observation station had been placed on the top of the construction tower crane. It was 20 meters higher than the main beam, so wind speed accuracy is less affected by the structure. As shown in Fig. 4, the wind measuring system includes one 3 Axis Ultrasonic anemometer (WindMaster, 32Hz sampling rate, measurement range 0-50 m/s) and one propeller anemometer (RM Young 05103, measurement range 0-60 m/s). The propeller anemometers is a mechanical anemometer composed by a propeller to collect wind speed data. The ultrasonic anemometer measures 3D wind speed based on the transit time of ultrasonic acoustic signals. The data recorded contain instantaneous wind speed in longitudinal (North-South direction), lateral (East-West direction) and vertical directions.The short-term monitored wind data, which were collected from this system, used for this study covered a 10 month period from December 2019 to September 2020.

Observation of meteorological station
Besides the on-site short-term wind speeds measurement, long-term regional wind speed data with large sample of synoptic strong wind events is also needed for extreme wind speed calculation in mountainous area. The nearest meteorological observatory is DAWU station, which is located in the same canyon (Xianshui River Canyon) with Murong Bridge. The spatial relationship between Murong Bridge and DAWU station and region terrine are shown in Fig. 5. The direct distance between Murong and DAWU is about 70 km. When one synoptic wind system approaches this area, both Murong and DAWU will be affected simultaneously with short temporal delay. So the wind speed record from DAWU can be used to predict the extreme speeds from synoptic winds in Murong. Data source of DAWU station is downloaded from Global Integrated Surface Dataset (https://www.ncei.noaa.gov/access/search/datasearch/global-hourly). The station ID is 561670. It has recorded meteorological data since 1979-07-01. Data type covers wind-observation, hourly liquid-precipitation, sky condition, air temperature, sea level pressure. Total 30 years wind-observation history from 1990 to 2020 are used in this study since data before 1990 was recorded manually with less credibility.

Wind system extraction and classification
In order to calculate the extreme wind speed in mountainous area, it is necessary to classify and then extract the local wind events and synoptic wind events from original continuous wind speed records. The strong wind events extraction algorithm based on feature points is described firstly in this section. Wind event characteristics of different wind systems are analyzed later. Based on these characteristics, the wind event type classification method is proposed.

Wind events identification and extraction algorithm
There are two purposes of wind events extraction. One is creating the basic data set of wind speed extremes. The other is classifying different wind event types from original wind speed data. The wind events extraction algorithm needs to find each event sequence with the maximum wind speed above a predefined threshold from a long continuous wind speed data. Each wind event sequence must contain the whole process of wind event from the beginning to the end, in order to identify the type of each wind event. This is different from the method of independent storm, which only ensure the independence between storms but not require the whole process of storm. The whole process of wind events contains necessary information for category recognition. So a new storm extraction algorithm based on feature points is proposed. The feature point is the demarcation point in the time series where can the changes of sequence trending occurs (Deng et al. 2013;Pavan et al. 2017). It is aimed to find all peaks and valleys, termed as landmarks, from time series (Zhao and Itti 2015). It has been applied widely in the research field of the trend of the time series (Fulcher and Jones 2014;Simo-Serra et al. 2015). In a discrete wind speed time series sequence UðtÞ ¼ ðU 1 ; U 2 ; :::; U n Þ, all the wind speed points i that meet Þ [ 0 are feature points (e is a positive hyper-parameter). Feature points set is second-order difference maximum point of original sequence. The purpose of second-order difference is to avoid local non-trend maximum point interference wind event extraction algorithm.
Extraction feature points process could be described as Algorithm 1.
Here's example to explain feature points algorithm specifically by Fig. 6. Original wind speed extracted from DAWU meteorological station represents U(t). As Fig. 6 shown, U 0 ðtÞ (red star) is a set that satisfies u i [ u iÀ1 and u i [ u iþ1 . In the view of mathematical, U 0 ðtÞ is the firstorder derivative changing points set of U(t). The feature points of continued records U(t) are the peaks of wind speeds, which are the highest points of each wind events. e is used to avoid small fluctuations being misidentified as wind events feature points. Without , some small variety will be identified wrongly as feature points like green dashed circle in Fig. 6.
In the wind speed time series, each strong wind event starts with a low wind speed, and then develops to high wind speed, and finally reaches to the end with low wind speed. The above algorithm could find the wind speed peak index of each wind event, regardless of the sampling rate of the wind speed sequence. The start point and the end point of event could be iteratively searched out on both sides of feature points. The condition for stopping iterative search is wind speed is lower than the static wind speed V s for a period of time Dt.
Hyper-parameters determination decides the performance of algorithm and accuracy of extreme wind speed prediction. There are three hyper-parameters need to be chosen. The algorithm ignores feature points whose fluctuation range is less than the parameter e. Considering the characteristics of wind speed sequence in Murong area, these hyper-parameters are chosen manually: e ¼ 1 m/s; V s ¼ 2 m/s; Dt ¼ 1 hour. That means a wind event is terminated when wind speed consistently below 2m/s for more than an hour. These hyper-parameters may be only suitable for this case. It's difficult to propose a metric to optimize hyper-parameters.
In order to verify the effectiveness and robustness of the wind event extraction algorithm, Figs. 7 and 8 show the result of algorithm on datasets with different sampling rate. The wind event extraction algorithm based on feature points and iterative search has good effects on wind speed sequences of different sampling rates.

Characteristics of two typical mountainous Wind events
According to features of mountainous wind system, strong wind events are divided into local mountain wind systems and synoptic wind systems. In order to classify, this section will analyze the characteristics of these two wind systems. A power-spectrum analysis of wind speed in Murong is plotted in Fig. 9. There appear to be two major energy peaks in the spectrum; blue peak (local wind system) occurs at a period of about 24 hours, and red peak (synoptic wind system) occurs at a period of 7-15 days, which is similar as van der Hoven's spectrum (van der Hoven Fig. 7 Wind event extraction algorithm processing high-frequency wind speed sequence (Data source: Murong Bridge field measurement; Sampling period: 10 min) Fig. 6 The example of wind event feature point detection algorithm 1957). The reason of the different peaks is that the mountainous wind systems is a different meteorological process with plain terrain. Mountainous terrain generates local temperature gradients everyday, leading to local wind system. In non-mountainous cities, the modified van der Hoven spectrum also has a one-day peak, but the cause of this peak is the urban heat island effect.
Based on the definition of mountainous wind system and the analysis of the field measured data, the characteristics of the mountainous wind system are summarized following. Local mountainous wind system occurs everyday. Since it is driven by diurnal variation of local temperature, the duration of local mountainous wind system are normally much shorter than synoptic wind events. In addition, because of complex terrain in mountainous area shown in Fig. 5, the local wind system at different locations are almost irrelevant. In contrast, the ''power'' driving synoptic wind system is much stronger than local mountainous wind system. So it will affect large region with longer duration and higher wind speed rather than being confined in a specific area. When synoptic wind system occur, the wind event could be recorded by all station nearby concurrently.

Storm type classification method
The most important differences between local mountain wind and synoptic wind are the occurring frequency and duration of the wind storm. Frequency is how often a certain type wind event occurs. The frequency information is not available before wind event identification. So, the other characteristics are used to establish a wind event type classification algorithm. For each wind speed sub-sequence extracted by wind event identification algorithm, sequence length which represents duration could be used as a classification metric. In addition, the wind speed metric needs to indicate the proportion of low wind speeds in sub-sequence. Wind direction is a key feature for wind storm classification in general, especially in the difference between typhoon and non-typhoon (Cui et al. 2021). However, mountainous deep canyon is a specific case for wind system. Local and synoptic wind systems are restricted in a specific direction by canyon topography. The wind speed frequency diagram of Murong are shown in Fig. 11, which has only two main directions at 22.5 and 210. The main wind directions are same as the trend of canyon, whatever the type of wind storm is. So the wind direction could not be used to identify local and synoptic wind.
Wind event duration and low-speed ratio are used to identify synoptic wind and local wind events. Wind event duration means how long a wind event lasts. The low-speed ratio is the ratio of low wind speed data points to the total. An assumption is applied that all mountain wind events include only two types: synoptic wind and local wind. Therefore, synoptic wind events are only defined and remaining wind events are local. Normally, synoptic wind events have greater energy source and a wider range of influence. It can be inferred that synoptic winds last longer. So synoptic wind storms should satisfy two judgments at the same time. Firstly, its duration should be longer than 24 hours. And the second judgment is that low-speed ratio accounts for less than 50%. In Murong area, synoptic wind system is defined as a wind event with more than 24 hours duration and low-speed time (wind speed is lower than 4 m/s) accounts for less than 50%. Figure 12 shows how these two judgments works in real wind speed data from Murong meteorological station.
The classification method is verified though the comparison between field measurement data at Murong and meteorological data at DAWU. The verified metric is the time overlap ratio between synoptic wind system in Murong and DAWU. As shown in Fig. 10, time overlap is the time period during when two wind events recorded by different observatory are overlapped. Because one synoptic wind system will affect Murong site and DAWU meteorological observatory simultaneously during in a certain period. From December 2019 to September 2020, 184 wind event sub-sequences are extracted from original sequence recorded by Murong construction site, including 6 synoptic wind system. In DAWU station, wind event extraction algorithm finds 1334 wind event since 1990. The maximum wind speed and duration distribution of wind events are shown in Figs. 13 and 14. Maximum wind speed is the maximum value of a wind event wind speed records. The distribution of duration shows that long-duration wind events account for a small part of all wind event, which conforms to the definition and frequency feature of synoptic wind events. According to classification metrics, synoptic wind events information and visualization from two stations recorded from December 2019 to September 2020 is shown in Table 1 and Fig. 16. The records of each synoptic wind event at different stations have a high time overlap ratio.
Field measurement always could not last for a long time, especially in real construction practice. Wind speed at Murong in October and November are not recorded in this work because of some objective reasons in construction. Wind speed measurement for less than one year might influence the results of extreme wind speed analysis. And this influence must be discussed. Local and synoptic wind system occurring frequency from 30 years DAWU meteorological station records are shown in Fig. 15. It could be clearly seen that winter wind system is infrequent compared with other seasons.

Mixture climate extreme wind speed calculation
Mountainous wind system is a mixture climate system composed of local mountainous wind system and synoptic wind system. These two wind system should be analyzed separately for extreme wind speed calculation. Rely on the wind speed records from Murong field measurement and DAWU observatory, two calculation case studies are carried out to discuss the extreme wind speed in mixture mountainous wind system. The primary case focus on DAWU station, which has long-term wind speed records. The advanced case is for Murong Bridge, which is a real construction site with short-term field measurement records.

First case: calculation extreme wind speed for DAWU meteorological station
We begin by considering the mountainous extreme wind speed problem of meteorological station. In this case, the wind speed record is long enough to calculate different wind system including synoptic and local. So this case will only focus on the characteristics of mixture wind climate in mountainous areas and discuss whether this method is useful for mountainous area. DAWU is an example for this case, which has more than 30 years of wind speed records. The records from 1990 to 2020 is used to calculate the extreme wind speed. Totally, 1334 wind events are extracted by 30-year wind speeds records by using wind events identification and extraction algorithm in Sect. 4. These wind events can be divided into 202 synoptic wind events and 1132 local wind events by two judgments including wind event duration and lowspeed ratio. The maximum wind speed value of each wind event is extracted to form an extreme value sample of ''Method of independent storm''.
All distribution parameters estimation is calculated in the python program by using scipy.stats library. In order to fit the tail of distribution well, the maximum likelihood method is used in this work. The distribution parameters estimated by the maximum likelihood method are shown in Table 2. Local and synoptic extreme wind speed samples are used to fit the Gumbel [Eq. (1)] distribution. And Akaike information criterion (AIC) and Bayesian information criterion (BIC) are used to quantitative fitting performance. AIC and BIC metrics are calculated by Eq. (8)(9). where k is the parameter number of distribution, N is the number of observations. The likelihood is the sum of observations probability density function. Figures 17, 18 and 19 are used to show which distribution is more suitable for different extreme wind samples. Figures 17 and 18 shows the histogram of extreme wind speed observations and Gumbel distribution fitting curve. Figure 19 is a quantile-quantile plot of two sample fitted by Gumbel and GEV distribution. The quantitative result from AIC/BIC and visualization from Q-Q plot and histogramcurve all prove that Gumbel has a good fitting performance in this case.
According to the fitted Gumbel distribution, extreme wind speed could be calculated by Quartile. Quartile is the inverse of Cumulative distribution function (CDF), which means the extreme wind speed with specific probability. The annual probability that the maximum wind speed u of the synoptic wind system exceeds U can be expressed by Eq. (3). The mixed wind system consists of local mountainous wind system and synoptic wind system. These two wind system events are independent. So within a year, the maximum wind speed does not exceed U is equivalent t that the maximum wind speed of local mountainous wind system and synoptic wind system does not exceed U, as Eq. (7). Figure 20 shows the extreme wind speed calculation results by the above method. The slope of local(blue dash line) wind speed is lower than synoptic(red dotted-dash line), which is consistent with their shape parameters. That means the extreme wind speeds in different return periods are controlled by different types of wind events. Synoptic wind events play an important role in high return period. In this case, demarcation point is on around 300 years. The green solid line is mixed extreme wind speed curve, which is the envelope of local and synoptic. Comparing the mixed climate method and annual extreme method(thick black solid line), it can be seen that the annual extreme method is not applicable in calculating extreme wind speed in mountainous areas. This is because the annual extreme sample is mixed and could be divided into 76% Local wind and 24% Synoptic wind. Orange Points are from Chinese Code Wind-resistant Design Specification for Highway Bridges (Tongji-University 2018). The trend of Code is similar to mixed line, but the Chinese code are conservative with generalized extreme distribution fitting.
As Fig. 20 shown, the extreme wind speed curves increase almost linearly, and the slope is marked above each curve. The descending slope of the synoptic wind speed exceeding probability exceeds the local wind by about 20%. If the influence of mixed climate is not considered, and the wind speed samples are not divided by category, the decline slope will be 7% lower.  In previous case, extreme wind speed in a mountainous area with long-term wind speed records could be calculated. In this part, we will calculate the extreme wind speed of an actual mountainous construction site only with a short-term wind speed field measurement records. But this amount of field measurement data is much smaller than the requirement of extreme wind speed statistical model fitting.
For the local mountains wind system, it must be analyzed with field measurement data extracted from anemometer installed on the constructed bridge. Because of only 10 months recording time, the wind speed parent population is directly used based on uncrossing method (Gomes and Vickery 1977), which is based on Rice's formula (Rice 1944) for the uncrossing rate U þ ðuÞ of a stationary random function of time U(t). On the other hand, for synoptic wind system, only 6 samples recorded within 10 month field measurement shown in Table 1 is insufficient to calculate the extreme wind speed of 50-year or longer return period. However, because of its large scale, very synoptic wind event will be recorded by the nearby meteorological observatory. If the synoptic wind event records of the meteorological observatory could be mapped to bridge construction site, there will be sufficient synoptic wind event data available.
The parent population of local wind event is all wind speed records in Murong except six synoptic wind events. Figure 22 illustrates the empirical histogram of the parent population of wind speed from December 2019 to September 2020 and corresponding PDF obtained from the Weibull model. Good correspondence between the raw data and the model confirms that the Weibull model is adequate to model the wind speed parent distribution. The cumulative distribution function could be written as Eq. (10).
where b is the location parameter, a is the scale parameter and c is the shape parameter. Through maximum likelihood method, the Weibull distribution parameter is estimated as Table 3 shown. And Fig. 21 shows the quantile-quantile plot of wind speed observation against distribution fitting result. The Weibull distribution with a ¼ 3:229; b ¼ 0:011; c ¼ 1:189 could stand for local wind event parent sample observations.
The correlation between wind speed U and the first derivative of wind speed _ U is -0.05, which proves that U; _ U are approximately independent. So Eq. (5) could be used to calculate U þ ðuÞ. The annual exceed probability of local wind P D ðu UÞ is calculated by Eq. (6) by T ¼ 1.
Compared with local wind system, synoptic wind events is an less frequent phenomenon in mountainous wind climate. The extreme wind speed of synoptic wind events will be calculated by the method of Independent Storm too. The extreme value samples are divided into two parts, including Murong measurement data and DAWU data with wind speed mapping. Wind speed mapping is a converting formula of synoptic wind event from nearby meteorological observatory to the target site. In this study, each synoptic wind event are recorded at DAWU meteorological observatory and Murong field measurement. The topography and height of these two observations are different. In order to simplify the mapping process, this research only establishes the quadratic function relationship of the maximum wind speed in each wind event between DAWU station and Murong bridge deck.
The fitted line are shown in Fig. 23. By fitting the data in Table 1, Murong to DAWU converting function is a quadratic function with zero intercept. This fitting model shows that the maximum wind speed in synoptic wind After wind speed mapping, synoptic wind events extreme sample in Murong is ready to fit Gumbel distribution. Murong synoptic wind distribution shape is very similar with Fig. 17. The annual exceed probability of synoptic wind P S ðu UÞ is calculated by Eq. (3) by T ¼ 1.
Extreme wind speed of different type wind events and mixture climate could be calculated by Eq. (7). The calculation result is shown in Fig. 24. The mixed line is the envelope of the extreme wind speed of the local wind system and synoptic wind system. ''Commingled line'' stands for the results from MIS without sorted windspeed data, which contains few synoptic wind. So it is very closed to ''Local line''. In order to consider the synoptic wind effect on Murong, the synoptic wind speed record at DAWU is used by maximum wind speed transferring. As shown in Fig. 24, ''synoptic line'' has a larger slope compared to ''local line''. In mountainous areas, the extreme wind speeds of long and short return periods are determined by different wind systems. For short return period, local wind system is more important. On the contrary, it is the synoptic wind system that plays a dominating role for long return period. The extreme wind speed will be underestimated without sorted data and synoptic wind augmentation, especially for long return period.

Discussion
Extreme data need to be sorted according to the different wind producing weather systems before carrying out any analyses, as suggested by Vickery (1977, 1978). Sorting is needed since the wind that is generated by the different weather systems has different characteristics and probability of occurrences (Choi and Tanurdjaja 2002). In this section, how mountainous mixed wind climate influence the extreme wind speed will be discussed. Extreme wind speed in mixed climate is a historical topic since 1970s. First interest of mixed wind climate system is thunderstorm. Lots of scholars focus on how thunderstorm control the extreme wind speed prediction value of different return periods in different places, such as Australia (Gomes and Vickery 1978), Melbourne (Holmes 2007), West Texas (Twisdale and Vickery 1992) and New York (Lombardo et al. 2009). Choi and Tanurdjaja (2002) proposed that mixed wind climate in Singapore should be divided into large-and small-scale wind systems. Most of those researches show that gathering the ensemble of all the extremes into a single set leads to underestimating the extreme peak wind speed especially for high return periods. Mountainous mixed wind system is firstly discussed in this work. This section will discuss how the mountainous wind system influence the extreme wind speed by sorting into local and synoptic wind system.
Compared with the traditional method which do not distinguish different wind systems, mountainous extreme wind speed shows a similar conclusion to other studies. Firstly, results from the DAWU station show the influence of mountainous mixed wind climate on extreme wind speed. The way of extreme wind speed calculation and distribution types of sample are totally the same. The only difference between mixed and commingled curves is that one distinguishes samples and the other is not. The results  show only a slight difference between those of the mixed and commingled curves. Non-sorted wind speed data (commingled curve) underestimates mountainous extreme wind speeds during high return periods. This slight difference is likely due to the characteristics of the local and synoptic wind systems in mountain.

Conclusion
This paper presents a novel method for mountainous extreme wind speed calculation with a focus on mountainous mixture wind system composed of local wind system and synoptic wind system. This method can be separated into three parts. First, each wind event sub-sequence are extracted by feature points and iterative searching from the wind speed raw data and classified into local wind and synoptic wind. Second, the mapping relationship on maximum wind speed of synoptic wind system between meteorological observatory and target site is established. And it is used to increase the sample size of synoptic wind events. Third, the annual wind speed exceeding probability of the local wind system and synoptic wind system are calculated by uncrossing rate and method of independent storm respectively. At last, different return period extreme wind speed could be calculated. The difficulty in calculating extreme wind speed in mountainous areas is the limited amount effective field measurement wind speed data. This method extracts synoptic wind event which is the effective information for target site extreme wind speed from surrounding meteorological observatory based on the different characteristics of mountain wind system. Therefore, the calculation of extreme wind speed in mountainous areas could be cheap and accurate. Murong bridge site is an application in this research which is located in a canyon on western China. In order to calculate the extreme wind speed in Murong, this work uses 10 months of field-measured data and 30 years of wind speed data from the DAWU weather station which is 70 km away from Murong. The calculation results prove that the extreme wind speed in the short return period is controlled by the local wind system, and synoptic wind system plays a decisive role on long return period extreme wind speed.