## 3 Results and Discussion
### Sensitivity Analysis  
#### 3.4.1 Selection of Simulated Circular Data  
Following the screening of historical typhoon samples impacting the target location via the simulated circular domain method, it is essential to extract and fit key parameters from the dataset. This process involves selective data inclusion from both inside and outside the simulated circular domain, requiring explicit consideration of their respective influences. While previous analyses utilized entire typhoon trajectory data, this section focuses exclusively on data within the simulated circular domain for comparative validation.  
Furthermore, reduced sample sizes facilitated improved parametric distribution fitting for key typhoon parameters. Notably, parameters previously requiring empirical distributions (central pressure deficit and movement direction) achieved optimal representations through lognormal (lognormal) and bimodal von Mises (bimodalVM) distributions.  
Table 6 presents extreme wind speed predictions for Guangzhou across various return periods via empirical, Weibull, and Gumbel distributions (with simulated circle-only data), and the corresponding Kolmogorov-Smirnov (KS) test results are summarized in Table 7.  
For Guangzhou, only the Gumbel distribution demonstrated statistical validation, confirming its superior applicability in this region. When exclusively considering simulated circle data, Gumbel-based return period wind speeds presented systematically lower estimates than did the full-trajectory results did, whereas the empirical and Weibull distributions yielded higher predictions.  
The improvement in the statistical fitting of the central pressure deficit (\(\Delta p\)) and movement direction (\(\theta\)) when only the simulated circle data are used can be attributed to two main factors. First, restricting the dataset to typhoon records within the simulation circle reduces sample heterogeneity. The retained samples are more directly relevant to the target location, excluding typhoon records from earlier or later stages of storm development,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Return Period (Year)** & **10** & **30** & **50** & **100** & **200** \\ \hline Weibull (m/s) & 18.44 & 21.87 & 23.24 & 24.94 & 26.51 \\ Gumbel (m/s) & 17.03 & 20.98 & 22.78 & 25.21 & 27.62 \\ Empirical(m/s) & 18.25 & 22.30 & 23.94 & 25.05 & 29.76 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Predicted average wind speeds as a function of the return period for Guangzhou (with simulated circle-only data).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Probability** & **\(p\) Value** & **Test Statistic** & **Critical Value (\%)** & **Critical Value (\%)** \\ \hline Weibull & \(\sim\)0 & 0.1002 & & \\ [PERSON] & 0.0665 & 0.0424 & 0.0444 & 0.0532 \\ \hline \hline \end{tabular}
\end{table}
Table 7: KS test results of extreme value distributions for Guangzhou (with simulated circle-only data).  
which often exhibit different characteristics. This reduction in data variability improves the internal consistency of the dataset and facilitates more reliable parameter fitting. Second, the restricted dataset naturally constrains the range of \(\Delta p\) and \(\theta\), as it excludes observations from distant segments of the typhoon trajectory. By focusing only on typhoons actively affecting the target area, extreme or atypical parameter values are filtered out, which helps improve the fit of standard probability distributions, such as lognormal and bimodal von Mises distributions. In summary, localized data filtering not only reduces heterogeneity but also limits parameter variability, collectively improving the statistical representation of key typhoon parameters. This result highlights that selective spatial data inclusion can be an effective strategy for enhancing parameter distribution fitting in typhoon hazard modeling.