## 3 Results
### Development and Evaluation of Wind Speed Models  
The primary step in calculating the basic wind speed is to select an appropriate probability distribution model. We have chosen four common distribution models often used in extreme value theory and risk analysis, namely the Gumbel model (Type I extreme value), the Weibull model (in its two-parameter form), the GEV model, and the Gamma model. These four models are compared. Figure 10 illustrates the fit between the probability histogram of maximum wind speed and the probability density functions of the four models, as well as the fit between the cumulative distribution functions of the four models and the wind speed samples. Figure 10: The comparison of fitting situations among the four models. (**a**) Probability density function (PDF). (**b**) Cumulative distribution function (CDF). Figure 9: Seasonal trends in wind speed at 10 m height. From Figure 10a, it can be observed that the Gamma distribution matches the observed data best in the mid-range wind speed region, but its fit is poor in the high wind speed region. The Weibull distribution performs well in the mid-to-low wind speed range but exhibits slight deviations in the high wind speed tail. Both the Gumbel and GEV distributions fit closely throughout the entire wind speed range, particularly matching the actual data well in the tail. Figure 10b demonstrates that, apart from minor differences in the front and middle parts for the Weibull distribution, the estimates of non-extreme wind speed values from the other three distributions are close. In the extreme event probability section, the GEV and Gamma distributions closely resemble the sample CDF, possibly due to their flexibility and capability to model extreme values. Apart from the visual results, it is also necessary to consider the evaluation metrics of the four distributions to assess the optimal model among them. Table 5 provides the evaluation values of the four models under four testing methods. Based on the results, the Gumbel model fits best according to the AIC and BIC tests, with the lowest AIC and BIC values. Apart from the standard Weibull model, the other three distributions have very similar indicators, all of which are lower than those of the Weibull model. In the results for the negative log-likelihood (NLL), the best fit is the Gamma model (159.686), closely followed by the GEV model (160.038). In the K-S test, the GEV distribution fits best with the smallest D statistic (0.063) among all distributions, indicating that the sample distribution is very close to the reference distribution, and with the highest \(p\)-value (0.869), suggesting no significant difference between the sample data and the assumed distribution. Considering the flexibility of the GEV model and its theoretical foundation in extreme value theory, we choose the GEV distribution (generalized extreme value distribution) as the optimal model for the steady state. In most studies, when using the GEV model, the location, scale, and shape parameters (\(\mu\), \(\sigma\), and \(\xi\)) are considered constants, not changing over time or with other variables, i.e., a stationary GEV model, if the probability distribution of extreme events does not change over time, and the risks in the past, present, and future is the same. However, in the trend analysis in the previous section, we found that the wind speed shows significant changes on monthly, quarterly, and annual scales. Therefore, we adopted a non-stationary GEV model, if the probability distribution of the maximum wind speed changes over time, allowing the location, scale, and shape parameters to change over time. The parameters were modeled as functions dependent on time, with the expectation that the model can more flexibly adapt to environmental or climate changes. In the research conducted by previous scholars, it was discovered that allowing the shape parameter to vary could lead to computational problems [47].