The study area covers the coastal waters east of Taizhou City, Zhejiang Province, which has a water depth of approximately 12 m. A wave station (121°41.400’E, 28°17.600’N) is located at the northern part of Niushan Island ( Figure 1 ). The wave station is adjacent to the East China Sea in the east and is surrounded by open waters from north to south (clockwise) and is approximately 5 km away from the coastline in the west.

Wave observations were made at the station from September 1, 2016 to December 31, 2018. Based on the observations, 14 typhoon-induced large wave processes were identified. The initiation and termination times of each typhoon wave process were determined based on the height of the highest one-tenth wave (H _1/10) that was larger than 0.80 m, from an engineering impact perspective. The wave processes included occasional data with a wave height smaller than this value, which were included in subsequent analyses. Table 1 shows the identified wave processes, durations, and intensity classifications. Figure 2 shows the tracks of the typhoons. The data of typhoon tracks were download from https://tcdata.typhoon.org.cn (Ying et al., 2014; Lu et al., 2021).

An acoustic wave and current profiler (AWAC-600K, Nortek) equipped with an acoustic surface tracking feature and the accuracy less than 1% of the measured value was used to measure wave heights and synchronous stratified measurements of flow velocity and direction. Observations sessions were made every hour at a sampling frequency of 2 Hz, with each session lasting about 18 min. Storm software accompanying the instrument was used to calculate wave parameters, such as weight heights, periods, and directions as well as frequency spectrum data. This instrument is widely used and provides reliable data processing results (Pedersen and Nylund, 2004).

Storm software performs zero-crossing statistical analyses of wave height records to calculate various parameters for the corresponding periods, including the significant wave height H_1/3 , height of highest one-tenth wave H_1/10 , maximum wave height H_max , mean wave height H_mean , significant wave period T_1/3 , wave period T_1/10 corresponding to H_1/10 , maximum wave period T_max , and mean zero-crossing period T_z . The software uses the acoustic surface tracking and horizontal velocity U and V (SUV) method as the first choice to calculate wave directions (Pedersen et al., 2005). It uses the fast Fourier transform method to calculate frequency spectra and yields smooth frequency spectra with 64 degrees of freedom, which are truncated at a high frequency of 1 Hz. The resolution is 0.01 Hz. Other parameters can be calculated by the spectrum, such as the significant wave height H_m0 , mean wave period T₀₁ , and spectral peak period T_p . We calculated other spectral parameters based on the frequency spectra output from the software, such as the zeroth-order moment m ₀, spectral peak value S(f_p ), mean wave period T₀₂ , and spectral width ϵ (Holthuijsen, 2007).

Table 2 shows the ranges of wave parameters during typhoon wave processes, demonstrating the substantial variation in wave height. H_1/3 varied in the range of 0.66–5.35 m, with a mean of 1.74 m. According to their magnitudes, the waves were classified as smooth, slight, moderate, rough, and very rough. Among the observed typhoon wave processes, the maximum wave height of Maria (No. 201808) was markedly larger than those of other typhoon wave processes. During this process, the maximum H_1/3 was 5.35 m, maximum H_1/10 was 6.97 m, maximum H_max was 8.20 m, and the maximum mean period of the maximum wave height was long, with a maximum T_z of 10.7 s. The maximum H_1/10 occurred at 04:00 on 11 July 2018. At this moment, H _max was 8.20 m, the water depth was 13.0 m, T_z was 10.7 s, and the wave direction was SE. It is already a catastrophic wave (Tao et al., 2018).

We analyzed wave parameters (mean and extreme values) for six typhoon wave processes in the Zhoushan Islands in the northern ZCA (Yang et al., 2017), two typhoon wave processes with the largest impact in the Hangzhou Bay as observed at two stations (Yang et al., 2021), one typhoon wave process with the largest impact occurring in the Sanmen Bay in the central ZCA (Zhou et al., 2023), and one typhoon wave process occurring in the Dongji Islands during the observation period of this study (Huan, 2023) ( Figure 1 ; Table 3 ). The mean significant wave height of the typhoon wave processes observed in this study was markedly larger than those in the Zhoushan Islands (Yang et al., 2017) and Sanmen Bay (Zhou et al., 2023), and the mean wave period was longer. These findings reflect the fact that the water area observed in this study is directly adjacent to the East China Sea and deep-water waves can propagate to this area without obstruction. The difference between them is also related to the different number of typhoons counted during different statistical periods. The maximum wave height and the maximum wave period in the study area were similar to those in the Dongji Islands (Huan, 2023) and markedly larger than those in the Hangzhou Bay and Sanmen Bay. The larger maximum wave parameters in both the study area and the Dongji Islands (Huan, 2023) can be explained by typhoon tracks: the typhoons impacting these two water areas made landfall directly on the Zhejiang coast and had great intensity at landfall. They are also related to the location of the stations: the two stations for these water areas are surrounded by open sea waters in the N, E, and S directions, while the stations in the Zhoushan Islands and Hangzhou Bay are located in relatively closed waters.

Two main types of tropical cyclones impacted the study area during the observation period: those making landfall and those turning northeast without making landfall. The first type can be divided into two sub-types: those landing on the southern side and those landing on the northern side of the station. Table 4 shows the classification of the tracks of the 14 tropical cyclones observed in this study.

The typhoon wave processes with the largest wave heights for three types of cyclones, Ampil (No. 201810), Maria (No. 201808), and Talim (No. 201718), were analyzed based on their maximum H_1/10 .

Ampil (No. 201810), a severe tropical storm, made landfall in Hangzhou Bay north of the study area with the intensity of a severe tropical storm. H_1/10 and T_z of this wave process exhibited clear decaying trends. The maximum H_1/10 was 4.02 m at 01:00 on 22 July 2018, while the maximum T_z occurred three hours later at 04:00 on 22 July 2018 ( Figure 3A ). T_p also exhibited an overall decreasing trend, fluctuating sharply before reaching a maximum of 12.2 s and remaining at approximately 11.0 s when the wave height exceeded 1.0 m. The wave direction did not show significant variation over time and was typically E and ESE. Rumiba (No. 201818), another cyclone making landfall in the northern part of the study area, was also dominated by waves in the E and ESE directions.

Maria (No. 201808), a super typhoon, made landfall in Fujian Province south of the study area with the intensity of a severe typhoon. H _1/10 of the wave process varied between 1.0 and 2.0 m in the early stage, increased to 6.0 m on 10 July 2018, and reached a maximum of 6.97 m at 4:00 on 11 July 2018 ( Figure 3B ). T _p and T _z showed similar trends, showing an initial increase and subsequent decrease. Throughout the rough-wave stage on 10 July 2018, the two parameters exceeded 10.0 s, with a maximum of 17.7 s. The wave direction varied over time and was generally ESE and SE.

Talim (No. 201718), a super typhoon, moved through the East China Sea east of the study area with the intensity of a super typhoon. H _1/10 of the wave process exhibited a clear trend characterized by an initial increase followed by a decrease. The maximum H _1/10 was 5.18 m, and occurred at 17:00 on 15 September 2017 ( Figure 3C ). T _z also exhibited an initial increase followed by a decrease; however, the extent of change was smaller compared with that for wave height. T _p increased abruptly during the early stage and then decreased gradually. T _p was sustained at approximately 4.0 s when H _1/10 was smaller than 1.5 m and above 10 s, reaching a maximum of 14.7 s. The wave direction changed from NE to E.

The wave direction of each cyclone process was related to its track. The cyclones making landfall in the northern side of the study area were dominated by waves in the E and ESE directions. The cyclones making landfall in the southern side of the study area generated waves in the E and ESE directions as well as in the NE, ENE, and SE directions. For example, Super Typhoon Megi (No. 201617) was dominated by waves in the SE direction, while the wave directions of Meranti (No. 201614) and Mangkhut (No. 201822) varied from NE clockwise to ESE. The wave direction of Yagi (No. 201814), whose track was closest to the study area, varied from ENE to E and finally to ESE. The cyclones passing through the East China Sea were dominated by waves in the E and ESE directions. Waves also occurred in the NE, ENE, and SE directions. Overall, the wave direction exhibited complex trends. For example, the wave direction of Malakas (No. 201616) varied from SE counterclockwise to ENE and the wave direction of Prapiroon (No. 201807) varied from SE and ESE to E and ESE. These waves varied in a direction opposite to that of Talim (No. 201718).

Overall, H _1/10 and T _z of the typhoon wave processes exhibited trends characterized by an increase followed by a decrease. In addition, a large wave height was accompanied by a large mean wave period. The intensity and track of a typhoon had a remarkable impact on wave height. Typhoons with a larger intensity and track closer to the study area generated larger wave height in the study area. Typhoon Maria (No. 201808), which had a track close to the station in the study area and passed it as a sever typhoon, generated a much larger wave height compared with those of other typhoons. Severe Tropical Storm Yagi (No. 201814) made landfall closest to the station; however, it had smaller maximum wave height (6.63 m) and maximum mean period (6.7 s) compared with those of Maria (No. 201808) ( Figure 2 ). Overall, most cyclones were dominated by waves in the E and ESE directions.

A statistical analysis of the typhoon wave processes in the study area showed that the wave spectra contained a single peak or two peaks ( Figure 6 ), but single-peak spectra were dominant, with an occurrence frequency of 92.33%. The spectral peak values of the typhoon waves varied considerably. The maximum spectral peak value occurred during the Maria (No. 201808) typhoon wave process, i.e., 29.25 m²/Hz ( Table 5 ), when the typhoon hit the area with the intensity of a severe typhoon and moved in the NE direction at a distance of approximately 380 km from the center of the typhoon to the observation station. Single-peak typhoon waves contained similar spectral peak frequencies (with a mean of approximately 0.10 Hz) and the spectral peak value was bigger than that of the double-peak spectra ( Tables 5 , 6 ). Double-peak typhoon waves contained relatively concentrated low- and high-frequency spectral peak frequencies that were concentrated at approximately 0.10 and 0.22 Hz, respectively ( Table 6 ).

Cyclones with a stronger intensity generated a lower spectral peak frequency in the study area due to the long-period swells generated by the cyclone propagating to the study area. Low-intensity tropical cyclones, such as Ampil (No. 201810), Yagi (No. 201814), and Rumiba (No. 201818) with the intensity of tropical storms, generated a minimum spectral peak frequency of 0.08–0.1 Hz in the study area. Cyclones with the intensity of a typhoon, severe typhoon, or super typhoon generated a minimum spectral peak frequency of 0.06–0.08 Hz in the study area ( Table 5 ).

The spectrum peak frequency variation of typhoon wave process is relatively complex, and there is no obvious single factor to represent it. During the impact of Severe Tropical Storm Ampil (No.201810), the larger wave spectrum was located at approximately 0.08 Hz, the spectral peak frequency varied considerably (between 0.08 and 0.19 Hz), and the spectrum peak value reached 12.03 m²/Hz when the distance between the center of the typhoon and study area reached the smallest value of approximately 230 km ( Figure 7A ). During the impact of Super Typhoon Maria (No. 201808), the wave spectrum in the study area was large in the frequency range of 0.06–0.13 Hz, and it reached a maximum of 29.2 m²/Hz at a frequency of 0.06 Hz ( Figure 7B ). In addition, the spectral peak frequencies of Meranti (No. 201614), Yagi (No. 201814), Soulik (No. 201819), Mangkhut (No. 201822), Trami (No. 201824), and Kong-rey (No. 201825) varied considerably. During the impact of Super Typhoon Talim (No. 201718), the wave spectrum was large at frequencies of approximately 0.08 Hz. Due to the long persistence of Talim (No. 201718) in the East China Sea, the spectral peak frequency varied insignificantly during the rough-wave stage ( Figure 7C ). During the impact of Malakas (No. 201616), Megi (No. 201617), Chaba (No. 201618), Prapiroon (No. 201807), Maria (No. 201808), Ampil (No. 201810), and Rumiba (No. 201818), the spectral peak frequency did not vary significantly.

We also distinguished between wind seas and swells using the methods proposed by Portilla et al. (2009), who defined a coefficient as the ratio λ of the measured wave spectrum S ( f p ) and the P-M spectrum S P M ( f p ) at the spectral peak, which can be written as follows,

where S_PM (f_p ) has the following basic form,

in which g is gravitational acceleration. The wave is a wind sea if λ > 1 and a swell otherwise. Figure 8 shows the variation in λ during all the typhoon wave processes. The wave processes induced by the 14 typhoon waves were dominated by swells at an occurrence ratio of 94.54%. For double-peak wave spectra, the low-frequency components corresponded to swells, while the high-frequency spectral peaks mostly corresponded to wind seas.