The South China Sea (SCS) is the largest semienclosed sea in the western tropical Pacific Ocean. More than 14 tropical cyclones (TCs) pass or directly influence this area annually. A consequence of the high frequency of typhoon occurrence is the high frequency of disasters related to ocean waves. Waves generated by typhoons can cause considerable damage to both marine engineering and coastal infrastructure. Therefore, the study of the spatiotemporal distribution of typhoon waves and their dynamic mechanism has important socioeconomic significance.

A moving TC causes significant changes in the characteristics of ocean waves, including significant wave height, directional wave spectra and wave propagation. However, because of a lack of observational studies in the northern SCS, the wave spectrum characteristics during the passage of typhoons in this area have not been clearly identified. Lan (1984) proposed a type of typhoon-generated wave spectrum based on empirical relations between the characteristics of the typhoon-generated waves (e.g., significant wave height and average wave period) and typhoon features (central pressure, speed of movement, and distance between the observation station and typhoon eye). The form of the presented spectrum is similar to the Joint North Sea Wave Project (JONSWAP) spectrum. In the 1990s, Chen et al. (1990) fitted a typhoon wave spectrum that was measured at the Xichong Station by applying the JONSWAP spectrum form. Previous research has concentrated mainly on the analysis of ocean wind wave models. Young (2003) found that the hurricane wave spectrum were fitted to the JONSWAP spectrum form. Chu and Cheng (2008) used the Wavewatch-III model to study the response of the SCS to Typhoon Muifa (2004). The results revealed features of the wave characteristics unique to the SCS, such as nondecaying, monsoon-generated swell throughout the typhoon period and strong topographic effects on the directional wave spectra. Zhou et al. (2008), who also used Wavewatch-III, performed numerical simulations of the sea surface directional wave spectra under typhoon wind forcing in the SCS. They found that the typhoon-generated wave field was determined mainly by the radius of the maximum wind speed and the distance from the typhoon center.

The Wave Rider buoy, which records wave spectrum data, was deployed at coordinates 21.89°N, 115.13°E; about 53 km offshore between Hong Kong Island and Dasanmen Island ( Fig. 1).

According to the time series data recorded by the Wave Rider buoy and typhoon information, we selected three typhoons for this study: Conson, Chanthu, and Megi.

Fig. 1 Paths of the three typhoons: Conson, Chanthu, and Megi Red star denotes position of the Wave Rider buoy.

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Typhoon Conson formed on July 6 and dissipated on July 12, 2010. Its greatest impact on the northern SCS was on July 15 and 16. Typhoon Chanthu formed on July 19 and dissipated on July 23. Its greatest effect on the northern SCS was on July 21 and July 22. Typhoon Megiformed on October 13 and dissipated on October 23. Its greatest effect on the northern SCS was on October 21 and October 22.

Comparing the spectra of the three typhoons, shown in Figs.2-4, reveals that the changes in the wave spectrum during the passage of each typhoon are similar. The variation and shape of the spectra associated with all three typhoons are comparable; however, it can be seen that Typhoon Megihad greater impact on the observation point than Chanthu. The maximum spectral value under the influence of Typhoon Megi was 25 m² /Hz ( Fig. 4), while the maximum during the passage of Typhoon Chanthu was 8 m² /Hz ( Fig. 3). When Typhoon Conson weakened temporarily on July 14, it had not apparently affected the observation point. However, by July 15, Typhoon Conson had strengthened again and it began to affect the northern SCS. Figure 2 shows that the spectrum follows a unimodal distribution; the peak spectral value is 28.95 m² /Hz and the peak frequency is 0.085 Hz. Wave energy is concentrated mainly in the low-frequency part of the spectrum. When the intensity of the typhoon gradually weakened on July 17 and 18, the spectral value reduced, spectral shape gradually exp and ed, and peak frequency moved to the high-frequency part of the spectrum. As sea conditions worsen, the peak frequency of the wave spectrum moves to the left and the energy is concentrated in the low-frequency part. As the typhoon weakens, the spectrum peak reduces and peak frequency moves to the right.

Fig. 2 Wave spectra during passage of Typhoon Conson

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Fig. 3 Wave spectra during passage of Typhoon Chanthu

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Fig. 4 Wave spectra during passage of Typhoon Megi

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Typhoon wave fields include wind waves and swell. The energy corresponding to the spectral peak is generated mainly by wind waves. If wind continues to support that part of the energy composition that belongs to wind waves, the wind waves will continue to grow or maintain an unchanged state. The remainder of the energy spectrum belongs to swell, which will decay during propagation. If the observation point is far from the center of a typhoon, the generated swell will be significantly weakened when it arrives at the observation point. Therefore, the local wind field during the passage of a typhoon is the most important factor governing the growth of waves. In the early stages of wind wave growth, the spectral energy is concentrated in the peak frequency. With an increase in the fetch or wind duration, after the passage of a typhoon, the spectrum peak frequency range of energy distribution become increasingly wide (Figs.5-7; Tables 1-3).

Fig. 5 Peak frequency distribution during passage of Typhoon Conson

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Fig. 6 Peak frequency distribution during passage of Typhoon Chanthu

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Fig. 7 Peak frequency distribution during passage of Typhoon Megi

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Table 1 Peak frequency distribution during passage of Typhoon Conson

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Table 2 Peak frequency distribution during passage of Typhoon Chanthu

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Table 3 Peak frequency distribution during passage of Typhoon Megi

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In the 1970s, based on the 2 500 limited fetch wave spectra of JONSWAP, Hasselmann et al. (1973) built the JONSWAP spectrum. The spectrum contains four parameters: peak frequency ω₀, peak enhancement factor γ, nondimensional factor α, and acceleration of gravity g. The value of γ ranges from 1.5 to 6 with an average of 3.3. The optimum value of γ varies with different sea conditions.

We fitted the typhoon wave spectra using the JONSWAP form, based on the data when the three typhoons had their greatest influence on the observation point (Typhoon Conson: July 16, Typhoon Chanthu: July 22, and Typhoon Megi: October 21; Figs.8-10, respectively). It can be seen that the typhoon spectra fit the JONSWAP spectrum well. The maxima of the measured spectra and fitting spectrum are at similar frequencies and the two spectral forms are very similar. However, in the high-frequency part, the measured spectra are larger than the fitting spectrum. In general, the JONSWAP spectrum is suitable for the growth state of wind waves and therefore, the typhoon waves belong to growth waves.

Fig. 8 Comparison of measured spectrum of Typhoon Conson and fitting spectrum at specified hours Blue line: measured spectrum; red line: fitting spectrum.

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Fig. 9 Comparison of measured spectrum of Typhoon Chanthu and fitting spectrum at specified hours Blue line: measured spectrum; red line: fitting spectrum.

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Fig. 10 Comparison of measured spectrum of Typhoon Megi and fitting spectrum at specified hours Blue line: measured spectrum; red line: fitting spectrum.

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The JONSWAP spectrum can be described as follows:

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If ω = ω₀, then

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For the best result when using the JONSWAP spectrum to fit the typhoon wave spectrum, the value of γ should be calculated appropriately. In this paper, we import a parameter called the spectrum width B = m₀/(ω₀S(ω₀)), which was proposed by Hou and Wen (1990). Hou and Wang (1993) conducted a further study on the relationship between the spectrum parameters and wind parameters. The traditional relationship between wave steepness and wave age depends upon the spectrum width in the developing states of the wave. Liu et al. (2014) introduced a wave-spectrum-width parameter B into the JONSWAP spectrum, based on which the probability density distributions of the wind wave heights were studied statistically.

It can be seen from Table 4 that the spectrum width B and γ are monotone decreasing. The γ is confirmed when spectrum B is confirmed and therefore, we can confirm γ by means of calculating spectrum width B ( Fig. 11).

Table 4 Spectrum width B and γ

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Fig. 11 Dependence relationship between B and γ

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To describe the way in which a wave spectrum grows and the growth processes of realistic wave conditions, the dependence relationship between spectrum parameters and wind parameters needs to be obtained. Because of a lack of observational data on fetch, in this paper the fetch was inverted from the existing growth relationship. Wang and Hou (2008) used dynamics theory calculating the dependence relationship between spectrum parameters and wind parameters. Hasselmann et al. (1980) proposed and based on JONSWAP. In this paper, after calculating the fetch using the growth relationship above, we took the average of . For wind speed data, the Cross-Calibrated Multi- Platform (CCMP) was used to calculate the dimensionless parameters. CCMP remotely sensed wind has much higher spatial and temporal resolution and can cover the entire ocean surface. However, the temporal resolution is only six hours; therefore, the resolution was improved using the method of interpolation. The dimensionless lowest moment of spectrum and dimensionless peak frequency . Then, we obtain the results: and . The corresponding correlation coefficients of m₀, ω₀, and B are 0.94, -0.985, and 0.864, respectively. Thus, the dependence relationships between the spectrum parameters and wind parameters are reliable (Figs.12-14).

Fig. 12 Growth relationship between dimensionless lowest moment of spectrum and dimensionless fetch x

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Fig. 13 Growth relationship between dimensionless peak frequency and dimensionless fetch x

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Fig. 14 Growth relationship between spectrum width B and dimensionless fetch x

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Based on data measured by the Wave Rider buoy in 2010, which was deployed in the SCS at coordinates 21.89°N, 115.13°E, we obtained the wave spectra during the passage of three typhoons: Conson, Chanthu, and Megi. The wave spectra from the three typhoons share the same characteristics in terms of frequency. The typhoon wave spectra fitted the form of the JONSWAP spectrum well. However, the optimal γ varies under different sea conditions. We selected different γ to fit the wave spectra of the different typhoons by calculating the spectrum width B . The growth relationship between the spectrum parameters and wind parameters was established, and the relationships between the spectrum parameters and dimensionless fetch were , , and .