# Full-Scale Measurements of Wind Characteristics on a High- Rise Building during Typhoon Sarika
## 3 Wind Characteristics of Typhoon Sarika
### Typhoon Stationarity Test  
A runs test is adopted to process the 36.7 h wind-field data of Typhoon Sarika collected at 23:00 on 17 October 2016, and the total wind-field samples are 220 within 10 min as presented in Figure 6. First, samples of the measured fluctuating wind speed are divided into \(N\) intervals to calculate the root mean square (RMS) \(\sigma_{i}^{2}\) and the average value \(\sigma_{0}^{2}\) of these RMS. Then the RMS of each interval is compared with its average value alternatively, and when the RMS of the \(i\)th interval is greater than the average value, the section is marked as \"+\", otherwise, it is marked as \"-\". These marks are then arranged successively according to the order of each interval, and the total number of rounds is recorded as \(r\) in the condition that each change of marks is defined as one round. Significance level \(\alpha\) is 0.05, and if the number of recorded rounds is within the probability interval (\(\alpha/2\), \(1-\alpha/2\)), then the assumption under significance level \(\alpha\) is accepted. Normal distribution can be used to determine the acceptance domain of the stationarity test, and the acceptance domain is the excepted number of rounds \(\pm\)1.96 \(\times\) the standard deviation of round number. If the number of rounds is within this acceptance domain, then the sample is stationary, otherwise it is non-stationary. When the interval number \(N_{1}\) (marked as +) or the interval number \(N_{2}\) (marked as \(-\)) is greater than 15, it can be considered that the sample size is large, thus the acceptance and negation domains of the test can be determined by the normal distribution table as follows:  
\[\mu=\frac{2N_{1}N_{2}}{N}+1 \tag{4}\]  
\[\sigma=\sqrt{\frac{2N_{1}N_{2}(2N_{1}N_{2}-N)}{N^{2}(N-1)}} \tag{5}\]  
\[Z=\frac{r-\mu}{\sigma} \tag{6}\]  
where \(N_{1}\) is the number of intervals marked as \"+\", and \(N_{2}\) is the number of intervals marked as \"\(-\)\"; \(N\) is the equal subinterval, and \(N=N_{1}+N_{2}\); \(r\) is the total number of rounds. When the significance level \(\alpha\) is 0.05 and \(|Z|\leq 1.96\) in the runs test, then the sample is stationary. The non-stationarity samples of Typhoon Sarika are investigated at different time scales; thus, the 10-min fluctuating wind speed are segmented with 30 s, 20 s, 10 s and 3 s as time steps in sequence, and the stationarity test results of 220 samples within 10 min during Typhoon Sarika are obtained. More details are shown in Table 1.  
Figure 6: 10-min mean wind speed and direction during Typhoon Sarika. (**a**) 10-min mean wind speed (**b**) 10-min mean wind direction.  
Table 1 shows that 113 samples with 3 s as a time step in 113 samples conform to the runs test with a significance level of \(\alpha\) = 0.05. The non-stationary samples with a time step of 3 s account for 51.36% of the total samples, which is significantly greater than 21.82%, 13.64%, and 10.00% of the samples with 10 s, 20 s, and 30 s as time steps in sequence, indicating that the shorter the time steps, the stricter the stationarity test, and the more obvious the non-stationarity samples of Typhoon Sarika. Therefore, the non-stationary samples are eliminated based on the test results of samples with 3 s as a time step, and the wind characteristics of 113 stationary samples during Typhoon Sarika are investigated.