The steps of the improved typhoon simulation method are summarized as follows.

### Generation of simulated typhoon key parameters with Latin hypercube sampling method

#### Obtaining Independent Historical Parameters with the Cholesky Decomposition Method

Key typhoon parameters including central pressure difference ∆*p*_{0}travel speed *vs*direction of travel *θ*the minimum of the nearest distance *D*_{min} and the radius at maximum winds *r*_{m} obtained from historical typhoon wind data are expressed by a vector {*X*}, as following:

$$ { x}^{T} = left{ {lnleft( {Delta p_{0} } right) , lnleft( {r_{max} } right) , c , theta , d_{min} } right} $$

(1)

Then matrix [*S*] and [*R*] can be calculated according to the equations. (2) and (3). They represent respectively the correlation matrix and the covariance matrix of the key parameters of the typhoon, then the upper triangular matrix [*T*] can be obtained from [*R*] by Cholesky decomposition as shown in Equation. (4).

$$ left[ {S – lambda_{k} E} right]left{ {varphi_{k} } right} = 0{kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} k = 1 ldots 5 $$

(2)

$$ left[ R right] = Eleft{ {left[ {x_{i} – Eleft( {x_{i} } right)} right]{kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} left[ {x_{j} – Eleft( {x_{j} } right)} right]} right}{kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} {kern 1pt} left( {i,j = 1 ldots 5} right ) $$

(3)

$$ left[ R right] = left[ T right]left[ T right]^{^{first}} $$

(4)

The independent historical key parameter vector {Z} can be calculated from the lower triangular matrix [T]^{−1} (the inverse of the upper triangular matrix [T]) and the typhoon key parameter vector {*X*}, as shown in the equation. (5).

$$ left{ z right} = left[ T right]^{ – 1} left{ x right} $$

(5)

#### Generation of independent parameters simulated with the Latin hypercube sampling method

In vector {z}, the typhoon-independent key parameters represented by each data column correspond to vector {x}. The central pressure difference ∆*p*_{0} and t the radius at maximum winds *r*_{m} can be fitted by a log-normal distribution, and the translational speed *vs*direction of travel *θ* and the minimum of the nearest distance *D*_{min} can be fitted by normal distribution. Based on the theory of the Latin hypercube sampling method, each probability function curve corresponding to the typhoon key parameters is divided into n equal intervals (*not* is the typhoon simulation numbers) and *not* random values for *not* equal intervals can be generated^{14}. Then the vector (left{ {z^{prime}} right}) for the simulated independent parameter can be generated with an inverse transformation of all probability functions for the historical independent parameters.

#### Generation of simulated typhoon key parameters

In order to obtain the key parameter vector of the simulated typhoon (left{ {x^{prime}} right})the upper triangular matrix [*T*] can be multiplied by the above vector (left{ {z^{prime}} right})expressed as follows:

$$ left{ {x^{prime}} right} = left[ T right]left{ {z^{prime}} right} $$

(6)

Unlike the Monte Carlo simulation method^{seven}By using the Latin hypercube sampling method, correlations between key typhoon parameters can be satisfactorily maintained when generating simulated typhoon key parameters.

### Generation of typhoons with the typhoon model

In order to obtain an initial position of the typhoon, we bring the key parameters of the simulated typhoon into the typhoon wind field model. Next, it is assumed that the typhoon is moving in a straight line and the speed of movement *vs* is always maintained until it disappears. The model proposed by Vickery and Twisdale^{ten} was used to calculate the central differential pressure ∆*p*_{0}and the central differential pressure ∆*p*_{0} remains unchanged. This study adopts the empirical typhoon model proposed by Ishihara et al.^{15}which is described in detail in Huang et al.^{16}but I will not dwell on it here.

### Perform extreme wind speed analysis

This article uses the extreme wind speed theory of the typhoon^{17} to calculate the extreme wind speed of the typhoon.

Assuming the probability that the wind speed of a typhoon is less than a specific wind speed *v* is *F*_{v}if the maximum score of a typhoon is *you*the probability that the *you* in *not* typhoons is less than *v* is recorded as

$$ Fleft( {left. {U

(seven)

To calculate the probability that *you* v in *τ*years, eq. (7) can be transformed into:

$$ Fleft( {U

(8)

It is generally considered that*p*( *not*, *τ* ) satisfies the Poisson distribution, and Eq. (8) is transformed into:

$$ Fleft( {U

(9)

where λ is the annual incidence of typhoons within a radius of 250 km around the research site. Whether *τ* = 1, Eq. (9) becomes:

$$ Fleft( {U

(ten)

It expresses the probability that *you* v in a year.

Record the maximum wind speed of m typhoons obtained by simulation from small to large as*v*_{1}, *v*_{2},… *v*_{m}. So the probability of *you*v_{I} is

$$ F_{{v_{i} }} = frac{i}{m + 1};;;;left( {i = 1, cdots ,m} right) $$

(11)

Combine Eq. (10) to obtain the probability of *you*v_{I} in a year

$$ Fleft( {U

(12)

Extreme wind speeds in typhoons are usually fitted to one of the generalized extreme value distributions. The type I (Gumbel) extreme value distribution is used in this study and can be written as:

$$ F(v) = exp left[ { – exp left( { – alpha left( {v – mu } right)} right)} right] $$

(13)

where*v*is the maximum annual wind speed;*α*and*µ*represent dispersion and mode respectively, which can be calculated by Eq. (12).