Typhoon waves are most damaging ocean disasters and always cause considerable damage to coastal engineering, ship navigation and marine engineering applications. Study on the influences of wind fields on evolution of the typhoon wave are important for accurate modelling typhoon waves and providing supports for ocean and coastal disaster prevention and mitigation.

Several studies on numerical simulations of typhoon waves by using different wind data have been conducted (Zhang et al., 2011; Liang et al., 2016, 2019; Zhou et al., 2016; Shao et al., 2018; Wang et al., 2018; Mo et al., 2019). Zhang et al. (2011) simulated the wave process in the Bohai Sea by using the simulating waves nearshore model (SWAN), in which the wind data from the cross-calibrated multi-platform (CCMP) was used as the driving wind field. Liang et al. (2016) investigated the wave climate of the Bohai Sea, Yellow Sea, and East China Sea for the period from 1990 to 2011 by using the SWAN wave model, and the wind parameters were obtained from the weather research and forecasting (WRF) model. Wang et al. (2018) investigated the extreme wave climate variability in the South China Sea (SCS) by using the WAVEWATCH III, and the wind data was using the objective reanalysis wind dataset from the WRF model. Li et al. (2018) utilized ERA-interim reanalysis wind data from the European Centre for Medium-Range Weather Forecasts (ECMWF) to simulate the waves and surges over the northwest Pacific region for a 35-year period. Liang et al. (2019) studied the characteristics of global waves simulated by using SWAN model driven by the ERA-Interim wind database from 1979 to 2017. Zhou et al. (2016) simulated typhoon waves by using the WAVEWATCH III model driven by the National Centers for Environmental Prediction (NCEP) Final Analysis (FNL) wind field during the occurrence of typhoons Chan-hom (1509), Linfa (1510) and Nangka (1511) in 2015. To improve the accuracy of typhoon waves, the combined wind fields based on reanalysis wind data and theoretical wind model, such as Holland wind model (Holland, 1980), have also been used for driving wave models. Shao et al. (2018) simulated 29 tropical cyclones (TCs) in the South China Sea (SCS) and East China Sea (ECS) by using the SWAN wave model driven by ERA-Interim wind data, Holland theoretical model and blended model wind data, and the results showed that the blended wind model demonstrated better performance than that of both the ERA-interim and the Holland model. Compared to the progress of numerical simulations of typhoon waves caused by a single typhoon, the simulations of typhoon waves in a unique weather background involving multiple typhoons have still not been well investigated. The evolution of the typhoon waves generated by multiple typhoons are more complex and difficult to predict than those generated by a single typhoon, and it is crucial to study the influences of wind fields on typhoon waves caused by multiple simultaneous typhoons.

The present study intended to perform a numerical study of the typhoon waves in offshore China under the influence of three typhoons where the wind fields for driving waves were derived respectively from the ERA-interim, climate forecast systerm version 2 (CFSv2) and CCMP datasets. The remaining paper is organized as follows. Section 2 presents the principle of the wave model, modelling data and model setup used in the study. Section 3 presents the validation results pertaining to the occurrence of three typhoons in offshore China in 2015 against altimetry and buoy data. In addition, the investigation concerning the improvement of the wind field, and the comparison of the accuracy of the wave field simulation before and after wind field correction is discussed. The conclusions are presented in Section 4.

The Pearson correlation coefficient, mean deviation (Bias) and root mean square error (RMSE) were used for data deviation analysis. The parameters of the evaluation used for verification included the significant wave height obtained from buoy observation and the significant wave height and wind speed obtained from Jason-2 observation. Here, $ {X}_{\mathrm{S}\mathrm{L}} $ represents the calculated results and $ {X}_{\mathrm{M}\mathrm{E}\mathrm{A}} $ denotes the buoy altimetry or satellite data. The relevant expressions are as follows:

The simulated wave height at different buoys during the three typhoons were compared with the observed data, and the results are shown in Fig. 3 and Table 1. It can be seen that the correlation coefficients of the simulation results of two buoys driven by the three wind fields in the East China Sea are as much as 0.966, and the correlation coefficient of Buoy 1# in the Yellow Sea is also larger than 0.8. This means that the typhoon waves during the three typhoons driven by the ERA-Interim, CFSv2 and CCMP wind fields, could be simulated well overall. The calculated wave height at Buoy 4# at the South China Sea is close to that observed, but the correlation coefficient is relatively low compared with those at other buoys. This may be due to that Buoy 4# is very close to the shallow coast and the water depth around it is relatively shallow, and errors always get larger when getting closer to the coast. These lead to the correlation coefficient of the Buoy 4# in the South China Sea being lower than the correlation coefficients for buoys in the Yellow Sea and East China Sea. Generally, for a small wave height, the simulated wave heights driven by CCMP wind field are closer to the measured values, and the simulated wave heights driven by ERA-Interim and CFSv2 wind fields are smaller. For a large wave height, the simulated wave heights driven by CFSv2 wind field demonstrates the best performance, while the simulated wave heights driven by CCMP ERA-Interim and CCMP wind fields are smaller. According to the interaction between wind and waves, large winds usually generate large waves. It can be inferred that the wind speeds near the typhoon centre in the study area, pertaining to the ERA-Interim and CCMP wind fields, are smaller than the actual values. The CCMP wind field is more reasonable when the wind speed is low.

In combination with the analysis presented in Table 1, the absolute values of the Bias and RMSE of Buoy 2# are determined to be less than 0.2 m, which represents the best performance. The Bias and RMSE of Buoy 4# are small. Buoy 3# presents remarkably satisfactory trends, with the maximum absolute values of Bias and RMSE being 0.796 m and 1.038 m, owing to the large wave height. The overall simulation results for Buoy 1# can be considered moderate, as determined by the characteristics of the original wind field.

To further verify the model, the altimetry and sea surface wind speed obtained from Jason-2 as it passed through the simulated sea during the occurrence of typhoon waves were adopted. The data accuracy is high owing to the high orbit accuracy of GDR (geographical data record) and the waveform being re-corrected. The satellite trajectory points were divided into three categories: those pertaining to the Yellow Sea (31°–39°N, 119°–127°E), the East China Sea (23°–31.18°N, 117.18°–131°E) and the South China Sea (4°–23°N, 105°–119°E). The detailed verification results are shown in Fig. 4.

The significant wave height products observed by Jason-2 include those pertaining to the Ku-band and C-band. In the product specification of OSTM/Jason-2 in 2011, Ku-band observations are better than C-band. Therefore, the study used Ku band data with a data accuracy of 0.001 m (Wang et al., 2016). The comparison results of Jason-2 presented in Table 2 show that the correlation coefficients of the simulated wave height and wind speed between the satellite observations are relatively big under the three wind fields. The correlation coefficients of the wave height and wind speed reach up to 0.969 and 0.971. Even at the South China Sea, the correlation coefficients are larger than 0.7. Overall, the trend of the wave height is similar to that of the wind speed, and this is also consistent with that obtained by Zhou et al. (2016). The results show that the RMSEs of the wave height in the Yellow Sea and South China Sea are smaller than 1 m. The maximum wave height in the East China Sea is as much as 12 m, and the RMSE of the wave height is larger. This is mainly attribute to the deviation of simulated wind speed in the East China Sea. Moreover, the track of typhoon Chan-hom (1509) is close to the coast in the East China Sea and the waves are deeply influenced by the complicated coastal topography and shorelines, and the measurement errors of satellite data are also bigger than those in the open ocean zones, which may also cause the relative large simulation deviation in the East China Sea. However, the trend of the wave heights in the East China Sea fit quite well with the observed results and those obtained by Zhou et al. (2016). The wind field comparison results indicate that the CCMP wind field fits the satellite observation better, followed by the fitting of the CFSv2 wind field. The CFSv2 wind field data is slightly larger, and the CCMP wind field and CFSv2 wind field are closer to the satellite data than the ERA-Interim wind field is.

To study the typhoon waves corresponding to three typhoons accurately, it is necessary to verify the accuracy of the description of the typhoon centres. The maximum average wind speed near the centre of the three typhoons (the maximum average wind speed pertaining to the three wind fields at the corresponding time) and the best track values (http:www.tcdata.typhoon.org.cn) (2014) were compared, and the results are shown in Fig. 5.

It can be seen from Fig. 5 that the values of the maximum wind speed pertaining to the CFSv2 wind field, for which the correlation coefficients are larger than 0.85, is the most close to the best track values, whereas the wind speeds pertaining to the ERA-Interim and CCMP wind fields are notably smaller in comparison.

To accurately simulate the waves during three typhoons, the CCMP wind field, which demonstrated the best performance in terms of the wave height and wind speed in the simulation of typhoon waves in three typhoons that occurred in 2015, was selected as the background wind field, and it was blended with the Holland theoretical wind model (1980) to overcome the shortcomings of CCMP, these shortcomings include the wind speed near the typhoon centre being small and the deviation of the typhoon centre. The Holland model (Holland, 1980) is a theoretical wind field model based on the exponential distribution of the atmospheric pressure field defined by Schloemer (1954) and a peak parameter B, and it can be expressed as follows:

where $ {U}_{\mathrm{g}} $ represents the gradient wind speed at radius ${{ r}} $, $ f $ is the Coriolis force parameter, $ {P}_{{\rm{n}}} $ is the atmospheric pressure around the typhoon, $ {P}_{{\rm{c}}} $ is the atmospheric pressure at the typhoon centre, $ {R}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ is the maximum wind speed radius and B is the parameter defined by Hubbert et al. (1991).

The combined scheme can be defined with reference to Wang et al. (2017). First, according to the position of the typhoon centre, the radius of the circle that pertains to the most similar wind speed of the theoretical wind field and that of the CCMP wind field was determined as the reference superposition radius R. $ R_1 $ and $ R_2 $ denote the characteristic superposition radius. $ R_1 $ is determined from the inward $ L_1 $ distance and $ R_2 $ is determined from the outward $ L_2 $ distance based on R. To ensure smooth integration of the theoretical wind field and CCMP reanalysis of the wind field, $ L_1 $ and $ L_2 $ are generally defined to be between 0.05$ R $ and 0.15$ R $. The superposition formula can be defined as follows:

where $ {V}_{x} $ and $ {V}_{y} $ represent the components of the superimposed wind speed in the $ x $ and $ y $ directions, respectively. $ {V}_{Hx} $ and $ {V}_{Hy} $ represent the components of Holland wind speed in the $ x $ and $ y $ directions, respectively; and $ {V}_{\mathrm{C}\mathrm{C}\mathrm{M}\mathrm{P}x} $ and $ {V}_{\mathrm{C}\mathrm{C}\mathrm{M}\mathrm{P}y} $ represent the components of the CCMP wind speed in the $ x $ and $ y $ directions, respectively.

To adjust the wind speed to the standard 10-m elevation above the sea surface, multiplication by a correction factor K should be performed. In the present study, the K values for Chan-hom, Linfa and Nangka were determined to be 0.82, 0.78 and 0.78, respectively. The superimposed radius R was 2.3 times the maximum typhoon radius. Next, a blended wind field was used to drive the SWAN model, and the comparison between the simulated wave heights driven by the blended wind field and those driven by the CCMP is shown in Fig. 6.

From Fig. 6, it can be seen that the simulated wave height driven by the blended wind field is mostly consistent with the buoy data, and the simulated maximum wave height due to the blended wind field is more consistent with the buoy data. It can be concluded that the blended wind field overcomes a limitation of the CCMP which the wind speed near the centre of typhoon is too small, and the simulated wave driven by the blended wind is more accurate.

In conclusion, the above mentioned verification results obtained using observation data from buoys and satellites indicate that the present model is suitable for modelling waves caused by three typhoons in offshore China. It is found that the simulated wave height driven by the CCMP wind field is closer to buoy data overall, and the RMSE is smaller in this case. When the wave height is small, the simulated wave heights driven by the CCMP wind field are close to the measured data, and the simulated wave heights driven by both ERA-Interim and CFSv2 are smaller than the measured data; when the wave height is large, the simulated wave heights driven by the CFSv2 wind field agree best with the measured data, and those driven by the ERA-Interim and CCMP wind fields are smaller than the measured data. It can be concluded that the wind speed of the CCMP wind field far from the centre of typhoon is more reasonable; in addition, this observation is consistent with the results from Kuang et al. (2015). It is further noted that the maximum wind speed near the typhoon centre of the ERA-Interim and CCMP wind fields is significantly smaller than the corresponding best track value. For the wind speed near the centre of the typhoon, the blended wind field constructed by using the CCMP-superimposed Holland model is more reasonable. The simulated maximum wave height driven by the blended wind field is more reasonable.

The influences of the three types of wind fields on typhoon wave simulations were numerically investigated. The typhoon waves driven by the ERA-Interim, CFSv2 and CCMP reanalysis wind fields were simulated via SWAN considering three typhoons that occurred in offshore China in 2015. Next, the maximum wind speeds near the typhoon centres during three typhoons that occurred in 2015 were evaluated by comparing the values with the best track data. Furthermore, the simulated wave heights driven by the CCMP and CCMP/Holland blended wind fields during three typhoons that occurred in 2015 were analysed. The following conclusions could be obtained.

(1) The typhoon waves in offshore China during the three typhoons, driven by the ERA-Interim, CFSv2 and CCMP wind fields, could be simulated well overall. The simulated wave heights driven by the CCMP wind field were more accurate for small waves. The simulated wave heights driven by the CFSv2 wind fields were more accurate for large waves, and the simulated wave heights driven by the ERA-Interim and CCMP wind field were relatively smaller than the measured data. The maximum wind speeds near the typhoon centre of the three typhoons that occurred in 2015 were compared with the best track data, and it was found that the wind speeds of the ERA-Interim, CFSv2 and CCMP wind fields were relatively smaller than the corresponding best track values.

(2) Moreover, the CCMP/Holland blended wind field was noted to be superior to the CCMP wind field for the simulation of extremely large wave heights. Furthermore, the wind speed pertaining to the CCMP wind field near the centre of the typhoon was relatively small, and the position and moving track of the typhoon eye were deviated. The CCMP/Holland blended wind field could overcome these shortcomings and effectively improve the simulation accuracy of the wave field, especially for extreme waves.