## 2 Experimental Study
### Meteorology Variation Due to Cold Wave Event  
According to the characteristics of the diurnal temperature variation curve, the period from the time of reaching the daily maximum temperature until the following day's minimum temperature is defined as the cooling period. The formula for calculating the magnitude of temperature cooling \(\Delta T_{i}\) during each cooling period is as follows:  
\[\Delta T_{i}=T_{i\text{max}}-T_{(i+1)\text{min}} \tag{1}\]  
where \(T_{i\text{max}}\) is the maximum temperature of day \(i\); \(T_{(i+1)\text{min}}\) is the minimum temperature of day \(i+1\).  
Figure 1: The concrete box girder model.  
Based on atmospheric temperature data collected from 1 January 2017 to 30 January 2018, the magnitude of temperature cooling in the high-latitude region of northern Xinjiang was calculated using Equation (1). Subsequently, an extreme value analysis (EVA) was conducted on the temperature data to obtain the generalized extreme value (GEV) distribution. GEV distribution is a unified expression of Gumbel distribution, Frechet distribution, and Weibull distribution. The cumulative distribution function (CDF) \(H(TD,\,\mu,\,\sigma,\,k)\) is as follows [25]:  
\[H(TD,u,\sigma,k)=\exp\left[-\left(1+k\frac{TD-u}{\sigma}\right)^{-1/k}\right],1+k\frac{TD-u}{\sigma}>0 \tag{2}\]  
where \(u,\,\sigma,\,k\) represents location parameter, scale parameter, and shape parameter, respectively. \(TD\) represents the magnitude of temperature cooling (\(\Delta T_{i}\)), which was determined using Equation (1). Through fitting the temperature data, the coefficients \(u,\,\sigma,\,k\) were determined to be 7.961, 4.916, and \(-0.249\), respectively.  
The frequency histogram of temperature cooling magnitudes and its probability density function are presented in Figure 2, illustrating the annual distribution. By fitting an extreme value distribution function and employing the statistical analysis theory for extreme value analysis [26], it is predicted that a once-in-50-year cold wave event in this region would result in a temperature decrease of 26.42 \({}^{\circ}\)C. Considering January as the month with the lowest average temperature during winter, this study focuses on the week from 11 to 17 January, depicting local meteorological conditions during this period in Figure 3. As depicted in Figure 3, the average weekly temperature significantly drops to 16.04 \({}^{\circ}\)C. Notably, there are three distinct periods of significant temperature drop around 13, 15, and 16 January, which have been categorized into three stages of cooling, as shown in Table 1. Among these stages, stage II exhibits the most substantial decrease with a magnitude of \(-18.39\)\({}^{\circ}\)C, lasting for approximately 13.30 h; its recurrence period is calculated to be approximately every 49.76 days. Concurrently, solar radiation intensity reaches its peak value at 356.97 W/m\({}^{2}\) on 14 January at 13:48 during stage II of cooling, while strong winter winds prevail, with a maximum speed recorded as Level 7 (16.92 m/s) on 11 January at 14:32.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cooling Stage** & **Starting Time** & **End Time** & **Cooling Time/h** & \(T_{\text{min}}\) /\({}^{\circ}\)C** & \(T_{\text{min}}\) /\({}^{\circ}\)C** & **Cooling** & **Return** \\  & & & & & Range/\({}^{\circ}\)C & **Period/Day** \\ \hline Cooling stage I & 12/1 17.46 & 13/1 5:41 & 11.92 & \(-5.24\) & \(-21.75\) & 16.51 & 30.15 \\ Cooling stage II & 14/1 12:43 & 15/1 2:01 & 13.30 & \(-10.42\) & \(-28.81\) & 18.39 & 49.76 \\ Cooling stage III & 15/1 16:47 & 16/1 8:36 & 15.82 & \(-15.61\) & \(-30.23\) & 14.62 & 20.60 \\ \hline \hline \end{tabular} Note: \(T_{\text{max}}\) represents maximum temperature, and \(T_{\text{min}}\) represents minimum temperature.  
\end{table}
Table 1: Temperature cooling stages.  
Figure 2: Frequency histogram and fitting probability density function of temperature cooling amplitude.