## 2 Model and Data Description
### Empirical Parametric Typhoon Models  
The Holland Typhoon Model is an empirical parametric model developed by [PERSON] [12]. Building on [PERSON]'s exponential pressure distribution model, [PERSON] introduced the \"B parameter\" and based the model on the gradient wind field to simulate the wind speed and pressure distribution within a typhoon. The equations for pressure and wind fields in the [PERSON] model are as follows [12]:  
\[p(r)=p_{c}+(p_{n}-p_{c})(-\frac{R_{max}}{r})^{B} \tag{1}\]  
\[V_{g}(r)=\sqrt{(p_{n}-p_{c})\frac{B}{p_{a}}(\frac{R_{max}}{r})^{B}exp(-\frac{ R_{max}}{r})^{B}+(\frac{rf}{2})^{2}}-\frac{rf}{2} \tag{2}\]  
In these equations, \(p_{c}\) (hPa) represents the central pressure of the typhoon, and \(p_{n}\) (hPa) is the ambient pressure outside the typhoon, set to 1013.15 hPa in this study. \(R_{max}\) (m) is the radius of maximum wind speed, \(\rho_{a}\) (kg/m\({}^{3}\)) denotes air density (set to 1.205 kg/m\({}^{3}\)), and \(f\) (rad/s) is the Coriolis parameter.  
\(R_{max}\) and \(B\) are two key parameters in the Holland model, determining the distribution of the wind field. In this study, the parameters \(R_{max}\) and \(B\) are determined using formulas derived from [PERSON]'s work [34]. The formula for \(R_{max}\) is based on a fitting analysis conducted for the Northwest Pacific, while the parameter \(B\) is referenced from [PERSON] et al.'s statistical results [35] and [PERSON] et al.'s comparative analysis across different sea regions [36]. The specific formulas are as follows [34]:  
\[R_{max}=69.52 exp\ (-0.0136V_{max}) \tag{3}\]  
\[B=\left\{\begin{matrix}0.606+0.0177V_{max}+0.0094\Phi\quad V_{max}\leq 40(m/s) \\ 1.314+0.00895(V_{max}-40)+0.0094\Phi\quad V_{max}>40(m/s)\end{matrix}\right. \tag{4}\]  
\(V_{max}\) (m/s) represents the maximum wind speed, and \(\Phi\) (rad) denotes the latitude.  
The formula for the translation wind field is as follows [13]:  
\[V_{s}=\left\{\begin{matrix}V_{sm}\frac{r}{R_{max+r}}\ (0<r\leq R_{max})\\ V_{sm}\frac{R_{max}}{R_{max+r}}\ (r>R_{max})\end{matrix}\right. \tag{5}\]  
In this equation, \(V_{sm}\) (m/s) represents the translational velocity of the typhoon center.  
Figure 1: Workflow Diagram for WRF Model Simulation.  
The Jelesnianski typhoon model is derived by superimposing a circularly symmetric typhoon wind field with the typhoon translation wind field. The Jelesnianski model exists in two versions: Jelesnianski-1 and Jelesnianski-2 [13; 37]. The primary distinction between these two versions lies in the method of constructing the wind profile. In this study, the Jelesnianski-2 version was utilized. The Jelesnianski-2 model is a wind field model that employs a single function to describe the wind profile of a typhoon, which helps to avoid the discontinuity issues near the maximum wind speed that are present in some other models. The circularly symmetric wind field is described as follows [13]:  
\[\begin{split}\overset{\rightarrow}{V}_{r}=V_{max}\frac{2(r/R_{ max})}{1+(r/R_{max})^{2}}(A^{*}\overset{\rightarrow}{i}+B^{*}\overset{ \rightarrow}{j})\\ A^{*}=-\frac{y\cos\theta+xsin\theta}{r}\\ B^{*}=\frac{x\cos\theta-ysin\theta}{r}\\ r=\sqrt{x^{2}+y^{2}}\end{split} \tag{6}\]  
In this equation, \(\theta\) (\({}^{\circ}\)) represents the inflow angle, set to 30\({}^{\circ}\) in this study; \(r\) (m) is the distance from the calculation point to the center of the typhoon; \(\overset{\rightarrow}{i}\) and \(\overset{\rightarrow}{j}\) are the unit vectors in the x and y directions, respectively.  
The formula for calculating the translation wind field is consistent with the one used in the Holland model.