1 Introduction

In recent years, extreme coastal disasters have occurred frequently, and typhoon waves have caused significant economic losses to coastal areas which also reflected the importance of accurately and scientifically simulating the wind field. As a result, scholars from all over the world have gradually deepened their research on the characteristics of typhoon wind fields and typhoon waves.

In the typhoon wave simulation, for the research status of pressure difference and wind field, the typhoon wind field is the basis of the input conditions for wave simulation, and is also the key to ensure the accuracy of typhoon numerical simulation. Chen et al. (2009) analyzed the historical process of typhoon pressure field and typhoon wind field research, and put forward suggestions for in-depth research on the coupled model of atmosphere and ocean. Zhao et al. (2010) established a double nested typhoon wave SWAN numerical simulation model based on QSCAT/NCEP mixed wind data and Myers empirical model wind field. Chen et al. (2011) introduced the environmental radius parameter into the Fujita equation for improvement, and obtained the distribution of pressure in the typhoon region. Fang and Lin (2013) summarized the method for determining the key parameters in parametric wind fields, analyzed and discussed the progress of wind field simulation all over the word, and put forward suggestions for strengthening interdisciplinary comprehensive integration research and data observation. Kuang et al. (2015) compared the plane distribution of the Taiwan Strait wind field based on three kinds of sea surface wind field data, and found that the distribution and variation characteristics of the three wind fields are basically the same, but there are errors in each wind field under different conditions. Pei et al. (2021) improved the Kepert analysis model by introducing a turbulent diffusion model and a drag model, and simulated three typhoon cases.

For the research status of typhoon waves, Jun et al. (2015) calibrated the optimal typhoon path data and adjusted it according to the gust and bottom friction in the study area. It was found that the extreme surge is caused by the combination of strong winds on the front and right side of the typhoon track. Chen et al. (2019a) used a three-dimensional wave-current coupled hydrodynamic model to evaluate the impact of typhoon "Hato" on the response and wave-current interaction (WCI) of the Pearl River Estuary, and the results showed that due to the WCI effect, the largest storm surge in the study area was increased by 20–30%. Sheng et al. (2019) simulated typhoon waves in shallow water around Zhoushan Islands based on the WAVEWATCH III model (WW3), and evaluated the performance of the input/dissipation source term in the WW3 model using measured data. By combining the parametric Holland model and high-resolution wind data in a 0.125˚ grid, the simulated significant wave height results are higher than the observations. LE et al. (2019) used a storm surge-wave coupling model to study the impact of typhoon "JEBI", and the combination of storm surge and huge waves in the simulation results can explain the serious loss in Hyogo City, Japan. Wang et al. (2020) introduced the parameters related to the maximum wind speed and the forward moving speed of the typhoon, and the parameters related to the asymmetric typhoon structure into the Holland vortex model to optimize the model. At the same time, the WAVEWATCH III (WW3) model was combined with the optimized Holland vortex model, and finally verified. The results show that the simulation has high accuracy. Taking typhoon "Hato" as an example, Li et al. (2020) used the coupled ADCIRC-SWAN model to study the storm surge and waves caused by the typhoon, and the results showed that the waves have a non-negligible impact on the storm surge simulation. Sun et al. (2014) used a coupled system that avoided sea-air-wave interaction to simulate the South China Sea, and the results showed that the performance of the fully coupled air-wave model was generally better than that of the uncoupled model. According to the data provided by ERA5 and NCEP, Niu et al. (2021) analyzed the characteristics of waves and currents generated by typhoon "Mitaq" and found that the changes of significant wave height and average wave period affected by typhoon were related to their waveforms, and the sea level in the waters near the coast changes regularly with the distance of typhoon.

For the research on typhoon waves in the Taiwan Strait and its adjacent waters, Liu and Huang ( 2020) applied a coupled tidal-wave model along the coast of Taiwan for simulating storm surges during typhoon events. The validated model is then used to explore the influence of waves on storm surge and typhoon track, wind stress and atmospheric pressure on the height of storm surge along the coast of Taiwan. Tian and Zhang (2021) compared the measured data with simulated data for typhoons “Nasat” (T1709) and “Maria” (T1808). It is found that the hybrid model has a good approximation to the actual wind speed value. Ou et al. (2002) used the SWAN model to compare the simulated results of wave height and period during four representative typhoons with the measured data from field wave stations on the east and west coasts. It is found that most typhoon waves can be reasonably simulated in the eastern coastal waters. However, because the mountainous area in the central part of the island partially destroyed the cyclone structure that the typhoon passed through, the difference in the simulation results in the western coastal waters increased. Chen et al. (2019b) evaluated the performance of SWH modeling of typhoons off the coast of northeastern Taiwan using different wind fields and a fully coupled tide-surge-wave model.

For the selection of parameters in the numerical model, Ying et al. (2017) constructed a wave numerical model in the East China Sea through the SWAN model, and analyzed the friction parameterization scheme, wave breaking parameters, wind energy input, white crown dissipation, wave-wave nonlinear interaction and other factors. Kim and Lee (2018) established a typhoon wave forecasting system to provide precise parameters through SWAN and WAVEWATCH III. Zhou et al. (2016) simulated the wave field distribution and evolution characteristics of the three typhoons in the Northwest Pacific in 2015 through the WAVEWATCH III model. They concluded that the size of the wind and waves not only depended on the typhoon intensity, but also was affected by the sea area. For the study of the typhoon's travel path, Chen (2018) based on the SWAN model, simulated and analyzed the wind speed changes in the Taiwan Strait and its surrounding waters when the typhoon passes through the northern, central and southern paths of the Taiwan Strait. Wang et al. (2019) obtained the drag coefficient of Pingtan Island from nine typhoon processes, and used weather research and forecast models to obtain wind parameters, and explored the influence of the drag coefficient on typhoons by simulating the typhoon field. The results show that the model has good accuracy. Pei et al. (2021) improved the Kepert analytical model by introducing the turbulent diffusion coefficient model that varies along the height and the drag coefficient model affected by the velocity, and analyzed the ability of different models to simulate the wind field characteristics of the typhoon surface. Yang et al. (2021) coupled the land cover and terrain into the typhoon wind field model in the mesoscale meteorological model WRF. Yang et al. (2017) analyzed he measurement data of two stations in the coastal waters of the northeast of Zhoushan Island, and found that underwater topography plays a major role in the change of wave direction, and typhoons with different paths have a significant impact on the spectral patterns of the stations. In recent years, most of the researches on typhoons in Fujian Province of China has stayed in the typhoon waves simulation under the influence of the wind fields. The research on the typhoon track is mainly about the reduction effect of the typhoon after it passing through Taiwan Island, but there are few studies on the reasons for the weakening of the typhoon wind field caused by the terrain. For example, Chen and Li (2018) established the "Molave" wind field model and found that the influence of terrain and building friction was not considered, which would lead to the deviation of the wind speed after the typhoon landed. It is of certain significance to analyze the influence of terrain factors on the formation of wind field in the Taiwan Strait and the optimization of the existing wind field equation.

In order to study the effect of topography on typhoon wind fields, this paper introduces terrain factors into the Holland typhoon equation. Based on the optimized equation, the third-generation numerical model (SWAN) is used to simulated the wave field in the Taiwan Strait and its surrounding waters. The simulation results were compared with the measured data to verify the accuracy of the typhoon wind field simulation and analyze the optimization effect.

2 Description of wind field and wave models

2.1 Wind model

CCMP (Cross Calibrated Multi-Platform) sea surface wind field is the assimilation data of global surface wind field launched by NASA in 2009. I t adopts the enhanced variational assimilation analysis combining relevant data collected on many oceans through passive microwave and remote sensing platforms of scatterometer. The CCMP wind field with high precision and high spatial and temporal resolution can meet the needs of oceanic and atmospheric research (Chong and Pan 2012). In this paper, this wind field is selected as the background wind field in the driven wind field of the SWAN model (Zhang et al. 2011; Egraham 1959). The data comes from ESE (NASA Earth Science Enterprise) with a temporal resolution of 6 h and a spatial resolution of 0.25° × 0.25°. In addition, ranges are from July 1927 to December 2020 for time, 78.375–78.375°N for space, and from 180°W to 180°E for longitude.

The wind field calculation grid adopts a rectangular distribution, and the grid points are arranged as 131 × 131. Its spatial resolution is 6' × 6', distributed in the area of 17.625–30.625°N, 115.625–128.625°E. In the process of setting the SWAN model, white wave dissipation, wave breaking, bottom friction, nonlinear interactions and other physical processes are considered. Every calculation takes 6 h.

2.2 Wave model

In the SWAN model, the random wave is represented by a two-dimensional dynamic spectral density, that is, \(N\left(\sigma ,\theta \right)=E\left(\sigma ,\theta \right)/\sigma\), where \(N\left(\sigma ,\theta \right)\) is the dynamic spectral density, and \(E\left(\sigma ,\theta \right)\) is the energy spectral density. In the spherical coordinate system, the energy balance equation can be expressed as:

$$\frac{\partial }{\partial t}N+\frac{\partial }{\partial x}{C}_{x}N+\frac{\partial }{\partial y}{C}_{y}N+\frac{\partial }{\partial \sigma }{C}_{\sigma }N+\frac{\partial }{\partial \theta }{C}_{\theta }N=\frac{S}{\sigma }$$
(1)

On the left, the first term refers to the change rate of the action density over time, the second and third ones to the propagation of the action density over geometric space, the fourth represents the frequency shift due to flow and changing depth, and the fifth represents the effect of refraction and shallowing due to flow and changing water depth. S on the right side of the equation represents the energy source-sink, including wind energy input, white-hat dissipation, bottom friction, dissipation due to shallowing, three-wave interaction and four-wave interaction.

In the action balance equation, the headwind scheme determines the state. Therefore, a fully implicit finite difference scheme is adopted in SWAN model using a much larger time step than the explicit one in shallow water, so as to realize higher calculation accuracy (Chen et al. 2009).

3 Study objects and areas

The bathymetry data used in this study comes from ETOPO1 of NOAA (National Oceanic and Atmospheric Administration of the United States), and the topographic data is processed by the interpolation method. The scale range of this calculation was 18–30°N, 116–128°E, and the spatial resolution was 1' × 1'. Water depth distribution is shown in Fig. 1, which indicates that higher seabed topography gradually from inner to outer sea and deeper seabed as longitude and latitude rise. The maximum water depth reaches 7500 m, and the minimum water depth is less than 100 m.

Fig. 1
figure 1

Bathymetric map

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Typhoon Fung-wong (see Fig. 2a for its path) was formed southeast of Ryukyu on July 25, 2008 and moved northwest. It crossed Taiwan Island and then landed in Fujian province of China, weakening and dissipating as it moved northwest into Jiangxi Province, China. Fung-wong, a typhoon with a northwest track, is one of the rare typhoons that still made landfall in Fujian province after passing through Taiwan, bringing significant impact to the southeast coast of China.

Fig. 2
figure 2

Track chart of typhoon

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Typhoon Jangmi (see Fig. 2b for its path) was formed in the western North Pacific on 24 September 2008. Since the formation of the cyclone, it has moved west-northwestward. It crossed the northern part of Taiwan that night and moved southwest briefly and rapidly weakened into a severe tropical storm due to the topography of Taiwan. Typhoon Jangmi also passed the island, but unlike Fung-wong, it did not pass Taiwan but moved north of the island toward Japan.

Figure 2 shows the path map of typhoon Fung-wong and typhoon Jangmi. The thick solid line represents the coastline, and the thin solid line represents the water depth isoline (unit: m). The circle marks the location of typhoon center at different times. The above two typhoons pass through Taiwan island and are greatly affected by land topography, which are very typical for the study of this topic. Therefore, the above two typhoons are selected for numerical simulation calculation.

4 Model establishment and verification

4.1 Construction of optimized wind field based on terrain parameters

4.1.1 Typhoon gradient wind field

At present, most scholars use a variety of typhoon wind field models, and their accuracy is also different. In this paper, the Holland typhoon wind field model with high simulation accuracy is used. The expression of the typhoon gradient wind field is as follows (Zhenjin et al.2018):

$$V{\text{r}} = \sqrt {\left( {P_{n} - P_{c} } \right)\frac{B}{{\rho_{a} }}\left( {\frac{{R_{\max } }}{r}} \right)^{B} \exp \left( { - \frac{{R_{\max } }}{r}} \right)^{B} + \left( \frac{rf}{2} \right)^{2} } - \frac{rf}{2}$$
(2)

where \({P}_{c}\) is the pressure at the center of the cyclone. \({P}_{n}\) is the peripheral pressure outside the center of the typhoon. r is the distance from the grid point to the center. \({\rho }_{a}\) is the air density. \({R}_{max}\) is the maximum wind speed radius of typhoon. B is fit parameters for Holland, it adopts the empirical equation given by Hubbert et al. (1991)\(B=1.5+\left(980-{P}_{c}\right)/120\). f is the Coriolis force parameter,\(f=2\omega \mathit{sin}\varphi\),where ω is the angular velocity of the Earth's rotation. This paper adopts the empirical equation (Egraham 1959) of the maximum wind speed radius:

$$R_{{\max }} \,= \,28.52\tanh \left[ {0.0873\left( {\varphi - 28} \right)} \right] + 12.22^{*} \exp \left[ {\left( {P_{c} - 1032.2} \right)/33.86} \right] + 0.2v_{f} + 37.22$$
(3)

where φ is the latitude of the cyclone center. \({v}_{f}\) is the speed of the cyclone center.

4.1.2 Optimization for terrain parameter

After the typhoon passes through the islands or landing on land, its wind field will be reduced due to the effect of terrain factors. In this paper, the altitude of each point and topographic data of typhoon center point are brought into the wind height conversion equation as a reference. Among them, the height conversion equation of wind (Hubbert et al. 1991) is:

$$V = \mathop V\nolimits_{r} \mathop {\left( {\frac{Z}{{\mathop Z\nolimits_{c} }}} \right)}\nolimits^{\alpha }$$
(4)

where \({V}_{r}\) is the gradient wind field calculated by Holland equation. Z is related to the altitude of each point. \({Z}_{c}\) is related to the altitude of the typhoon center. α is the roughness coefficient of the ground (See in Table 1).

Table 1 Roughness classification table
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According to the characteristics of topographic and geomorphic, the effect of the terrain on the typhoon wind field is studied by changing the ground roughness coefficient. Roughness can be divided into 4 categories according to different topographic features, as shown in Table 1.

Since most of the land areas within the selected calculation range are Fujian Province and Taiwan Island, while this area can be regarded as a hilly area, the terrain roughness of all land areas is selected as the type B, α = 0.16 was substituted into the equation for calculation.

4.1.3 Construction for synthetic wind field

The background wind field and the gradient wind field calculated by the Holland equation (Eq. (4)) are superimposed by the correlation weight coefficient to construct the typhoon wind field that input into SWAN model. The expression of the resultant wind field (Yang et al. 2015) is as follows:

$${V}_{hc}=\left(1-e\right){V}_{r}{\left(\frac{Z}{{Z}_{c}}\right)}^{a}+e{V}_{ccmp}$$
(5)

where \({V}_{hc}\) is the synthetic wind field. \({V}_{r}{\left(\frac{Z}{{Z}_{c}}\right)}^{a}\) is the height conversion equation. \({V}_{ccmp}\) is CCMP background wind field. e is the weight coefficient (Jin et al. 2015). After debugging, fetch \(E={E}_{0}+0.2\), \({E}_{0}=\frac{{C}^{4}}{1+{C}^{4}}\), \(C=\frac{r}{n{R}_{max}}\),where the parameter n is 9, and the weight coefficient e is:

$$e = \left\{ \begin{gathered} E\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;r \le 3R_{\max } \hfill \\ E + \left( {1 - E} \right)*\frac{{r - 3R_{\max } }}{{R_{\max } }}\;\;\;\;\;3R_{\max } < r < 4R_{\max } \hfill \\ 1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;r \ge 4R_{\max } \hfill \\ \end{gathered} \right.$$
(6)

where Rmax is the maximum wind speed radius, and the value of the weight coefficient E is determined by the distance between each grid point and the cyclone center. For example, when the distance between the grid point and the cyclone center is greater than or equal to 4 times the maximum wind speed radius, the wind field is entirely composed of the background wind field.

Figure 3 shows the changes of wind speed contours before and after the optimization. The thick solid line represents the coastline, and the thin solid line represents the contour line of wind speed. The circular area represents the typhoon eye, and the wind speed decreases from the maximum to zero. It can be seen from the figure that the optimization effect is obvious, which can be further studied.

Fig. 3
figure 3

Contour curves of wind speed before and after optimization

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4.2 Validation for wind speed

By referring to the measured wind speed and significant wave height of Suao Port when typhoon Fung-wong and typhoon Jangmi approached, the simulation results are verified. The location of verification points are shown in Fig. 4 below.

Fig. 4
figure 4

Location of the verification point

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After optimization, the simulation results of typhoon wind field were compared with the measured data of maximum wind speed at each moment for verification. The results are shown in Fig. 5, it can be seen from the figure that the variation trend of wind speed in the simulation results of typhoons Fung-wong and Jangmi coincide with the measured data, and the error between the simulated and measured maximum wind speed is small. The absolute error of optimized maximum wind speed of typhoon Fung-wong was reduced from 1.93 to 0.42 m/s, and the relative error was reduced from 2.95 to 1.05%. The absolute error of maximum wind speed of typhoon Jangmi was reduced from 1.93 to 1.50 m/s, and the relative error is reduced from 4.22 to 3.27%. This shows that the maximum wind speed calculated by the optimized typhoon wind field is closer to the measured value, and the model accuracy is improved.

Fig. 5
figure 5

Comparsion between simulated and measured maximum wind speeds of typhoon Fung-wong and Jangmi before and after optimization

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Figure 6a, b is the comparison of the wind speed before and after optimization when typhoon Fung-wong and typhoon Jangmi made landfall. It can be seen from the figure that the optimized wind speed of both typhoons has decreased in all the time, but the weakening effect of typhoon Fung-wong is more obvious. This is because typhoon Fung-wong landed in the middle part of Taiwan, so it was greatly affected by land terrain, while typhoon Jangmi made landfall in northern Taiwan, and the land around the landfall site was less than that of typhoon Fung-wong, so the typhoon Jangmi was less affected by land terrain.

Fig. 6
figure 6

Comparison of hourly variation curves of typhoon wind speed before and after optimization

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4.3 Validation for significant wave height

Figure 7 shows the comparison between the measured and simulated values of the significant wave heights of typhoon Fung-wong and typhoon Jangmi at Suao Port, respectively. It can be seen from the figure that the simulated values before and after the optimization have the same trend as the measured values. Specifically, the optimized significant wave height of typhoon Fung-wong decreased up to 0.4 m, the absolute error was reduced from 0.37 to 0.02 m, and the relative error was reduced from 3.9 to 0.2%. The optimized significant wave height of typhoon Jangmi decreased up to 0.38 m, the absolute error is reduced from 0.78 to 0.4 m, and the relative error is reduced from 6.1% to 3.1%. The results show that the accuracy of the numerical model is improved by optimizing the wind field equation.

Fig. 7
figure 7

Comparison between calculated and measured values of significant wave height before and after the optimization

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Although the significant wave height and wind speed have the same changing trend and the peak time, there is still a certain error between the simulated and the measured values. The reasons include insufficient accuracy of water depth and terrain, lack of wave volatility, and failure to consider factors such as tide. But in general, the simulation results are consistent with the actual typhoon wind field, which ensures the rationality and feasibility of the model.

5 Numerical results and discussion

5.1 Comparison of wind field before and after optimization

Figure 8 shows the wind speed distribution of typhoons, and the optimization effect was explored by comparing through them. It can be seen from the figure that the wind field rotates in the counterclockwise direction, and the distribution of wind speed along the direction of the typhoon center is greater than that of the left direction, this is because the study area is located in the northern hemisphere, so it is affected by the earth's rotation force, and the wind direction is to the right, causing the wind size of the typhoon path to be asymmetrical, the left side is small and the right side is large. This phenomenon corresponds to the regularity of tropical cyclone fields in the northern hemisphere.

Fig. 8
figure 8

The distribution of wind speed and vector before and after optimization when typhoon Fung-wong left Taiwan Island (2008-07-28T06:00) and when Jangmi landed on Taiwan Island (2008-09-27T18:00)

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Figure 8a, b is the distribution of wind field of typhoon Fung-wong. It can be seen from the figure that the reduction effect of the wind speed is obvious, and the wind speed is generally reduced. The area with high wind speed (> 30 m/s) in the center of the typhoon was significantly reduced, and the area with wind speed greater than 20 m/s was also significantly reduced. After optimization, the maximum wind speed is reduced from 33.2 to 29.1 m. Figure 8c, d shows the wind speed distribution of typhoon Jangmi. It can be seen from the figure that after considering topographic factors, the effect of wind speed reduction is less obvious than that of typhoon Fung-wong, and the area of high wind field changes significantly, especially in the area where the wind speed is greater than 35 m/s. The optimized maximum wind speed is reduced from 11.37 to 11.25 m.

Comprehensive analysis of the wind field optimization effect of typhoon Fung-wong and typhoon Jangmi shows that at all times, the wind speed weakened most obviously after the typhoon left Taiwan Island. This is because by the time the typhoon is ready to leave Taiwan, it has been completely affected by the land topography and various structures, so the reduction effect is the most obvious.

5.2 Comparison of significant wave height before and after optimization

The optimized typhoon wind field is brought into the SWAN model to simulate the typhoon wind and waves in the Taiwan Strait and the nearby sea area, so that the significant wave height distribution before and after optimization can be obtained. Figure 9 shows the distribution of wind speed vector and significant wave height before and after optimization. It can be seen from the figure that the significant wave height follows the law of decreasing from inside to outside of the typhoon center, and the distribution of wave height corresponds to the distribution of wind field. This is because in sea area affected by typhoons, most of the waves are wind waves, so the wind speed is positively correlated with the significant wave height. In addition, there is a wave height asymmetry in the moving direction of the typhoon center when the typhoon landed and left Taiwan. There are two reasons for this phenomenon. On the one hand, the swell propagation on the west side of Taiwan Island is hindered by the land, so the significant wave height is in the Taiwan Strait is smaller. On the other hand, the asymmetry of the wind field mentioned above also leads to the asymmetry of the wave height. The superposition of the two causes the wave height on the west side of Taiwan Island to be smaller than that on the east side.

Fig. 9
figure 9

The distribution of wind speed and significant wave height before and after optimization of typhoon fung-wong when it landed (2008-07-28T06:00) and left Taiwan (2008-09-27T18:00)

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Figure 9a, b shows the distribution of significant wave heights when typhoon Fung-wong landed on Taiwan Island. It can be seen from the figure that after optimization, the significant wave height distribution generally presents a downward trend. The area of wave height in the range of 8–10 m is reduced compared with that before optimization, and the maximum significant wave height decreases from 11.7 to 11.62 m. Figure 9c, d shows the distribution of significant wave height when typhoon leaves Taiwan Island. It can be seen from the figure that due to the asymmetric wind speed, the significant wave height in the Taiwan Strait is small, while that on the outer side of Taiwan Island is large. After optimization, the wave height between 7 and 8 m decreases to less than 7 m, and the maximum significant wave height decreases from 9.47 to 8.57 m.

Figure 10a, b shows the significant wave height distribution of typhoon Jangmi when it landed on Taiwan Island. It can be seen from the figure that the optimized significant wave height distribution presents a general downward trend. After optimization, the wave height range of 7–9 m has a certain degree of reduction, and the maximum significant wave height decreases from 11.37 to 11.25 m. Figure 10c, d shows the distribution of significant wave height when typhoon left Taiwan Island. The figure shows the asymmetry of the significant wave height in the moving direction of the typhoon center was more significant and showed a downward trend. After optimization, the significant wave height maximum decreased from 9.7 to 9.25 m.

Fig. 10
figure 10

The distribution of wind speed and significant wave height before and after optimization of typhoon Jiangmi when it landed (2008-09-28 T16:00) and left Taiwan (2008-09-29 T00:000)

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It should be noted that the wind speed and significant wave height reduction effect of typhoon Jangmi is less obvious than that of typhoon Fung-wong (Fig. 8), because their paths are different. For typhoon Jangmi, it only passed a small part of the land in northern Taiwan, while typhoon Fung-wong passed right in the middle of Taiwan. Therefore, Fung-wong is much more affected by the land topography than Jangmi. The reduction effect of the significant wave height is similar (Figs. 9 and 10), but the reduction effect of the wave height when the typhoon left the land is more obvious than that when the typhoon landed on the land. This is because when the typhoon leaves the land, it has been completely affected by the land terrain, which leads to a more obvious reduction effect.

6 Conclusions

In this study, the wind field models of typhoon Fung-wong (200808) and typhoon Jangmi (200815) are established through the typhoon background wind field equation and the gradient wind field equation that optimized by adding terrain parameters, and then the numerical model of the typhoon wave is established through the wind field model, the simulation results are verified and compared with the measured data, and the effect of the optimization and simulation results are discussed. The main conclusions are as follows:

  1. 1.

    By comparing the simulation results with the observed data, it is found that the simulated wind speeds and significant wave heights of the typhoon Fung-wong and typhoon Jangmi are in good agreement with the observation data. However, there are still some errors between them, which may be caused by inaccurate bathymetric data and terrain, lack of wave volatility, and failure to consider factors such as tide.

  2. 2.

    After the optimization, the absolute error of maximum wind speed of typhoon Fung-wong was reduced from 1.93 to 0.42 m/s, and the relative error was reduced from 2.95% to 1.05%. The absolute error of maximum wind speed of typhoon Jangmi was reduced from 1.93 to 1.50 m/s, and the relative error is reduced from 4.22% to 3.27%. The relative error of the peak value of the significant wave height has been reduced. The error for typhoon Fung-wong was reduced from 3.9% to 0.2%. The error for typhoon Jangmi was reduced to 3.1%. Obviously, the simulation accuracy of the model has been improved.

  3. 3.

    The significant wave heights of the two typhoons are positively correlated with the distribution of the typhoon wind field, which is because the waves are mainly generated by wind. The distribution of the wind speed vector in the wind field rotates counterclockwise. The simulated wind speeds are consistent with the characteristics of the wind field in the northern hemisphere. Due to the influence of the earth rotation bias force and the change of atmospheric pressure in the typhoon area, the wind speed and significant wave height are small from left to right and large from the center to the outside.

  4. 4.

    The significant wave height in the Taiwan Strait is lower than that of the outside of Taiwan Island, there are two reasons for this phenomenon. One is that the wind speed after passing through Taiwan Island has decreased. The other is the asymmetry of wind field leads to the asymmetry of wave height, so the wave height of the inside of Taiwan Island is lower than that of the outside.

In this study, the calculation area is small when optimizing the wind field equation, and only the influence of altitude on the typhoon wind field was considered (Chen 2022), and the same friction index was used for all terrains. Therefore, in the future, a larger calculation area can be used to grid the terrain, and different friction indicators of different terrains can be imported into the grid to optimize the typhoon wind field in more detail, thereby further improving the accuracy of the model.