In this paper, Typhoons Doksuri (2023) and Nesat (2017) were selected for model validation due to their significant impacts. Typhoon Doksuri made landfall along the Fujian Province coast on July 28, 2023, with maximum winds at landfall reaching 50 m/s, classifying it as a strong typhoon. It also recorded a minimum central pressure of 945 hPa. Typhoon Nesat made its initial landfall on the eastern coast of Taiwan Province on July 29, 2017, followed by a subsequent landfall on the Fujian coast on July 30, with maximum winds of 33 m/s at landfall and a minimum central pressure of 975 hPa. The trajectories of these two typhoons are shown in Figure 1 , offering a visual representation of their paths and the areas impacted by their landfalls.

The buoys shown in Figure 1 are situated in the East and South China Seas, near the Chinese mainland, and include buoys #1, #2, #3, #4, #5, HX1, and HX2. The wave and wind speed observational data are obtained from the large buoy observational data of the Fujian Provincial Marine Forecasting Station. The buoy is 10m high, with a diameter of 10m, and data is recorded at 10-minute intervals. Detailed information about these buoys, including their longitude, latitude, and water depth, is shown in Table 1 .

In this paper, the third-generation numerical ocean wave model, SWAN 41.45, is employed for the study. This model represents an advanced numerical simulation method, grounded in ocean dynamics and wave theory, that describes and simulates wave motions in the ocean using mathematical equations and physical principles. The SWAN model is solved numerically by using computer technology to simulate various physical properties of waves, such as wave heights, periods, directions, and wave spectra.

The SWAN model represents random waves by means of a two-dimensional kinetic spectral density, and when the driving element includes tidal conditions, the interaction between waves and currents leads to a conservation of the kinetic spectral density but not the wave energy spectral density, the kinetic spectral density and the wave energy spectral density are calculated as:

Where N denotes the kinetic spectral density, E denotes the energy spectral density, and σ and θ denote the relative frequency and wave direction, respectively. Expanding the control equation to the spherical and right-angle coordinate systems, the control equation is calculated as:

Where σ is the relative frequency of the wave, θ is the wave direction perpendicular to the crest line in the spectral component, C x , C y are the wave propagation speeds in the X and Y directions in the direct coordinate system, C λ , C φ are the wave propagation speeds in the λ and φ directions in the spherical coordinate system, C σ , C θ are the wave propagation speeds in the σ and θ directions. the first term on the left hand side of the equation is the change rate of momentum spectral density N with time t in different coordinate systems. the 2nd and 3rd terms are the rates of change of momentum spectral density N propagating in spatial positions in different coordinate systems. the 4th term is the frequency shift, refraction and shallowing change of N in frequency space σ caused by changes in the flow field and water depth. The 5th term is the propagation of N in the direction θ of the spectral distribution. S on the right side of the equation is the spectral density source and sink terms, including energy dissipation terms such as wind field input, wave-wave nonlinear interactions, and bottom friction dissipation, the equation is calculated as:

Where S i n denotes the wind input term, S d s , b denotes the bottom friction effect, S n l 4 denotes the fourth-order wave interaction, S d s , b r denotes the wave breaking due to the change in depth, S d s , w denotes the white crown dissipation effect, and S n l 3 denotes the third-order wave interaction.

The computational domain of the model encompasses the entire coast of Fujian, extending from 116°E to 128°E in longitude and from 18°N to 28°N in latitude. It employs an unstructured grid, comprising a total of 44,274 grids and 86,213 nodes. The bathymetric data were sourced from the ETOPO2022 global topographic dataset, featuring a resolution of 15 arc seconds. Shoreline data were derived from the GSHHS dataset.

The SWAN model incorporates several source terms, including the wind input method, wave breaking term, bottom friction term, whitecapping dissipation, and interactions involving three and four waves. After multiple attempts, the optimal parameter settings are shown in Table 3 .

To assess the accuracy of both synthetic and reanalyzed wind fields, this study utilizes observational data and simulation results for Typhoon Doksuri, covering the period from July 24 to July 30, 2023, for comparative analysis. This study employed two reanalysis datasets, ERA5 and CCMP, which were integrated with the Holland typhoon model to generate four distinct wind field datasets: ERA5, CCMP, ERA5+Holland, and CCMP+Holland.

Figure 1 illustrates that buoys #1, #2, and HX2 are positioned nearer to the typhoon's center, in contrast to the other buoys which are located further away. In Figures 6A–G , the wind speed measurements derived from both the ERA5 and ERA5+Holland datasets exhibit considerable overlap, similarly to those from the CCMP and CCMP+Holland datasets. This overlap indicates that there are no significant differences between the synthetic and reanalyzed wind fields for buoys situated farther from the typhoon's center. Moreover, this study conducts a detailed analysis of error metrics for the four datasets. The analysis concerning buoys #1 and #2 is shown in Tables 5 and 6 , while the analysis for HX2 is shown in Table 7 .

A comparison of wave height simulations using the SWAN model integrated with the synthetic wind field (Holland+ERA5) against actual measurements from various buoy locations during Typhoon Doksuri is shown in Figure 7 . Error indicators are shown in Table 8. The simulations show close alignment with the measured wave heights, especially at the extremes, which highlights the model's high accuracy. The correlation coefficients, as shown in Table 7 , range from 0.80 to 0.93, confirming a strong correlation between the predictions of the SWAN model and the observed data. Despite the general proximity of simulated results to the measured values across most buoys, the root mean square errors (RMSE) for buoy #2 and buoy HX2 are notably higher, recorded at 0.69 and 0.80 respectively. This increased error is likely due to the direct passage of Typhoon Doksuri's center over these buoys, exacerbating discrepancies under extreme weather conditions. Capturing such dynamic changes in wave heights accurately poses a significant challenge for any model, particularly when complex, nonlinear dynamic processes are involved.

To explore the impact of reanalyzing both synthetic and reanalyzed datasets of wind fields on wind speed measurements, this study utilizes four distinct wind field datasets: ERA5, CCMP, ERA5+Holland, and CCMP+Holland for comparative analysis against the empirical wind speed data recorded during Typhoon Doksuri.

The error metrics for buoy #1, derived from each wind field dataset, are shown in Table 5 . The metrics for buoy #2 are shown in Table 6 , and those for buoy HX2 are shown in Table 7 . These tables indicate that ERA5 generally exhibits lower root mean square error (RMSE) and mean absolute error (MAE) compared to CCMP. However, as shown in Table 9 , CCMP outperforms ERA5 in simulating the maximum wind speeds of typhoons. This observation is consistent with findings from Li et al. (2021), who evaluated different wind field datasets in the East China Sea and noted that despite ERA5's lower error rates, it tends to underperform in capturing the very high wind speeds associated with typhoons.

Further analysis reveals that the incorporation of the synthetic wind field significantly reduces the root mean square error (RMSE) for both the ERA5 and CCMP datasets, as evidenced by the data shown in Tables 5 – 7 . This reduction indicates that the synthetic wind field effectively enhances the accuracy of wind data, compensating for ERA5's limitations in capturing the extreme wind speeds of typhoons. Consequently, the ERA5+Holland synthetic wind field has been selected as the primary driving field for this study. This approach serves as a benchmark for future typhoon wave forecasting and wind field dataset selection in Fujian waters and provides valuable guidance for selecting wind fields in other maritime regions.

In this study, the BP neural network and random forest algorithm were employed to enhance the accuracy of wave predictions by the SWAN model, resulting in the development of two hybrid models: SWAN-BP and SWAN-Tree. These machine learning-enhanced models significantly improved the precision of the numerical wave model predictions, demonstrating their efficacy in refining wave forecasting techniques.

During the optimization phase, the SWAN-BP model required 58 seconds to complete, whereas the SWAN-Tree model only needed 8 seconds, demonstrating a significant advantage in computational efficiency for the SWAN-Tree model. Furthermore, as shown in Figures 8A and 9A , the performance metrics from the training set indicate that the SWAN-BP model achieved an RMSE of 0.20 and an MAE of 0.15. In comparison, the SWAN-Tree model recorded a lower RMSE of 0.16 and an MAE of 0.12, suggesting that the SWAN-Tree model not only operates more efficiently but also provides slightly better accuracy during the training phase.

Although the SWAN-Tree model demonstrates superior computational efficiency and training performance, the SWAN-BP model exhibits better performance on the test set, indicating greater robustness in generalizing to unseen data. Notably, the SWAN-BP model more accurately simulated the maximum wave height, achieving a value of 3.9 meters, as presented in Figure 8B , which is closer to the actual measured maximum wave height of 4.0 meters. In contrast, the SWAN-Tree model predicted a maximum wave height of 3.4 meters, as shown in Figure 9B . This disparity underscores the SWAN-BP model's enhanced accuracy, particularly in predicting extreme wave heights, highlighting its utility in scenarios requiring precise forecasts of severe marine conditions.

In simulating Typhoon Doksuri using the SWAN model, the RMSE recorded at buoy #5 was initially 0.45. Upon applying the SWAN-BP and SWAN-Tree models to optimize the simulation, the RMSE was reduced to 0.30 and 0.34, respectively. This improvement translates to a 33% enhancement in the accuracy of wave height predictions with the SWAN-BP model and a 24% improvement with the SWAN-Tree model. The specific error metrics for each model are detailed in Table 10 , illustrating the effectiveness of these optimizations in refining the accuracy of wave height predictions during typhoon conditions.

For Typhoon Nesat (2017), the pre-existing SWAN-BP and SWAN-Tree models, initially developed and refined using data from Typhoon Doksuri (2023), were applied to retrospectively analyze wave heights, as shown in Figure 10 . This application of the models to different typhoon allows for an assessment of their generalizability and effectiveness across varied meteorological conditions. This approach helps evaluate whether the models maintain their predictive accuracy when faced with different typhoon characteristics and conditions.

According to Table 11 , utilizing the SWAN-BP model for wave height prediction results in a 0.14 reduction in RMSE compared to the standard SWAN-only model, marking a 23% enhancement in predictive accuracy. Similarly, the SWAN-Tree model also demonstrates improved performance, achieving a 0.13 decrease in RMSE, which corresponds to a 21% improvement in accuracy relative to the SWAN-only model. These results confirm that although these machine learning models were initially trained using data from Typhoon Doksuri, they are still effectively applicable to predicting wave heights for other typhoons, such as Nesat. This highlights the adaptability and robustness of the models across different typhoon scenarios.

Integrating machine learning techniques with traditional numerical models significantly enhances the prediction of extreme wave heights and their fluctuations, also bolsters the models' generalization capabilities across various typhoon. This methodology demonstrates the substantial potential of machine learning in elevating the accuracy of numerical ocean wave models. By combining conventional physical modeling with advanced machine learning strategies, wave height predictions can be effectively optimized. This approach addresses inherent biases in numerical models that might otherwise compromise the accuracy of using direct meteorological ocean data as input for forecasting wave heights. This synergy between machine learning and physical modeling is a promising avenue for refining predictive models in oceanography.