1. Introduction
The wave spectrum measured at a particular position of the ocean is usually regarded as the sum of wave components generated by events separated either in frequency, direction, or both (Hanson and Mandelberg 2000; Wang and Hwang 2001; Yılmaz and Özhan 2014). When the sea state consists of more than one wave system, the spectrum is generally multipeaked, with each of them representing wind sea generated locally or swell independent of local wind. Several observations by oceanographers have shown that wind sea and swell can occur simultaneously with relatively high probability all around the world, both in the open ocean and coastal areas (Guedes Soares 1991), and Guedes Soares (1991) obtained a range of 23%–26% from the measured data in a coastal site off Portugal. Moon and Oh (1998) found the percentage of multipeaked spectra was 25% according to 17 750 nearshore wave spectra observed around the Korean Peninsula.
In general, wind sea refers to waves that are still being developed by wind or are very near to the area they were generated. While swell are waves that have propagated away from the generating region, or when the phase velocities are higher than the wind speed, far from the effect of the wind that caused them (Ewans et al. 2004; Holthuijsen 2007; Semedo et al. 2009). Separation and identification of complex wave conditions into wind sea and swell provide us with detailed wave information that is important to both scientific research and engineering applications. Wind seas are generated locally and receive momentum from the wind in their growing process; therefore, a proper estimation of the wind sea is required for the study of wind sea dynamics, validating wave models, and air–sea interaction. With the slow energy attenuation rate, swells radiating from tsunamis or storms can travel long distances across the globe ocean; can have great significance on human activities such as nearshore structure design, marine operations, offshore industry, and coastal management; and may cause sensible beach erosion (Doong and Kao 2007; Ardhuin et al. 2009; Kumar et al. 2011; de Farias et al. 2012).
The commonly used method in literature for separating wind sea and swell can be divided into two categories: one is based on 1D wave spectrum (energy spreading over frequency) and the other is based on directional wave spectrum (energy spreading over both frequency and direction). The separation from the 1D spectrum is usually aimed to obtain a cutoff frequency or separation frequency 
Concerning the identification result of wind sea and swell from the 1D spectrum, customarily used methods were sometimes found to largely differ from one another (Hwang et al. 2012). Moreover, wind sea and swell may overlap in the frequency and direction domains under changing winds; the separation and identification processes will be particularly difficult due to the complex features in the 1D spectrum. It is evident that more reliable and consistent effects can be achieved using wave age (WA) when the directional wave spectrum and wind velocity are available (Portilla et al. 2009). With the directional wave spectrum, many methods have been developed to distinguish wind sea and swell from the directional spectrum (Gerling 1992; Hasselmann et al. 1996; Hanson and Phillips 2001; Portilla et al. 2009). Among these methods, the identification results of wind sea and swell differ from each other due to the various wave age thresholds they adopted.
In this article a practical and efficient methodology based on the overshoot phenomenon (OP) in wind-generated waves is put forward that is independent of subjective selection of wave age threshold or wind information. This paper focuses on the separation and identification of wind sea and swell components from directional wave spectrum and compares the two methods. Section 2 describes the development of the two methods. Field data and the sea-state parameters of wind sea and swell acquired from an S-band Doppler radar are shown in section 3. A summary of the paper is given in the last section.
2. Extraction of wind sea and swell
A wave spectrum is composed of numerous wave systems representing different meteorological characteristics, which appear in the form of local peaks in the spectrum. The procedure of extraction usually involves the following two steps: (i) the separation of wave systems from the spectrum and (ii) the identification of wind sea and swell from wave systems. For the former step, Portilla et al. (2009) indicates that most of the separation results proposed before are very similar and that the main differences lie in the adjustment of some parameters of the algorithms, for example, the energy threshold of spurious peaks and the definition of the closeness of two peaks. But the identification of wind sea and swell is influenced by the wave age threshold selection and wind condition.
a. Separation of wave systems
Spectral separation provides a preliminary determination and isolation of spectral peaks with each peak representing a wave system. The peaks of wind sea and swell frequently mix with spectral irregularities, which constitute the local maxima in the wave spectrum resulting from artifacts of random processes. It is clear that more spurious peaks exist in the observed spectrum, such as that derived from radar or buoys, than that in the model spectrum. Therefore, it is necessary to eliminate spurious peaks that have low energy and to merge adjacent peaks that lie too close in the spectrum.
A wave system separation method named the “watershed algorithm” proposed by Gerling (1992) is based on the geometric characteristics of a spectrum without considering the geophysical properties. In this scheme, the lowest threshold is found when the part of the spectrum above the threshold value is disconnected. This procedure is repeated until all systems are detected. A partition is deemed significant if it is consistent in time and space. So, a practical limitation appears that it demands the availability of other wave spectra. In addition, the number of wave systems detectable in an observed spectrum by this method is representative of the order of tens, complicating the process of associating wave components with that of neighbors at different times. Following Gerling (1992), Guillaume (1994), Hasselmann et al. (1996), and Voorrips et al. (1997) add constraints of the geophysical properties of sea state to the separation and form their own methodology. In Guillaume’s (1994) method, the maximum spectral peak is selected and all the bins within a certain direction and frequency range are allocated to that peak, leading to the formation of a wave system. Then the process is iterated for the next maximum peak. The major disadvantage of this scheme is that the spread of a wave system is not taken into consideration. Hasselmann et al.’s (1996) approach is based on the steepest ascent algorithm, which in essence calculates the basins of attraction for each peak. But the criteria used for merging peaks rely on rather arbitrary parameters that need to be adjusted for different situations. Voorrips et al. (1997) simply merge partitions with low energy (i.e., lower than 0.0025 m2).
An iterative smoothing approach including successively combing neighboring peaks and removing spurious peaks has been utilized by Portilla et al. (2009) to reduce the impact of spurious peaks. The approach involves a kind of 2D discrete convolution operation that carries out a weighted average to adjacent peaks. This operation can be repeated until the number of wave systems is less than or equal to a specified threshold set by the user.
However, the directional wave spectrum could be more blurred if the convolution process is repeated excessively, which may render the wave systems indiscernible. An energy level for a noise threshold of 1% and 2% of the total energy in the spectrum is suggested by Portilla et al. (2009) to remove the noise energy, especially in the observed spectrum. Consequently, by applying the noise energy threshold and iterative convolution procedures, the noise of the spectrum is filtered out and important spectral features are preserved, alleviating the dependence of excess arbitrary parameters set by previous methods proposed by Guillaume (1994), Hasselmann et al. (1996), and Voorrips et al. (1997).
b. WA method
Thus, in the WA method, the selection of the “optimal” threshold is largely a subjective process. The threshold of 1.5 is adopted for reference to the method of Hanson and Phillips (2001) and Hessner and Hanson (2010) to extract wind sea and swell from the radar wave spectra in the nearshore region observation represented hereinafter.
c. OP method
The presence of the overshoot phenomenon in wind-generated wave was proposed by Barnett and Sutherland (1968) according to the ocean and laboratory data. During the experiment, it was found that an overshoot occurs when the energy of a spectral component first grows rapidly past its eventual equilibrium value and then decays back to this value. It is manifested in the development of wind sea, the energy of the wind sea increases with fetch until it reaches a certain maximum value at a specified fetch. Subsequently, the energy gradually decreases to a stable value and reaches the equilibrium state, which demonstrates the wave has been fully developed. The overshoot phenomenon reveals the energy variation characteristics during the growth of the wind sea system.
Portilla et al. (2009) pointed out that the overshoot phenomenon in the 1D wave spectrum means the peak amplitude of developing wind sea is greater than that of a fully developed wave with the same peak frequency. Since the PM spectrum mentioned above is a typical wave model of fully developed sea state, it is practical to identify a wave system by comparing the peak value of the corresponding 1D wave spectrum with the peak amplitude of the PM spectrum of the same peak frequency.
Three JONSWAP spectra with different peak enhancement factors and the PM spectrum with the same peak frequency are shown in Fig. 1a with the condition that wind speed is 10 m s−1 at the height of 10 m and wind fetch is 30 km. As depicted by Fig. 1a, the three peak enhancement factors are 6, 4, and 1.5, and the calculated peak values 
(a) Three JONSWAP spectra with peak enhancement factors of 6, 4, and 1.5, respectively, with the condition that wind speed is 10 m s−1 and fetch is 30 km, and the PM spectrum has the same peak frequency. (b) Two JONSWAP spectra and corresponding PM spectra with wind speeds of 10 and 15 m s−1, respectively, and the peak enhancement factor is 3.3.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
3. Radar data and discussions
An S-band Doppler radar called Microwave Ocean Remote Sensor (MORSE) has been developed by Wuhan University to measure directional wave spectra, and some preliminary wave results have confirmed the performance of MORSE (Chen et al. 2012; Fan et al. 2012). The attached six horn antennas with each beamwidth of 30° can be deployed above the sea level and illuminate a region of 180°. The six antennas work in time multiplex mode, and it takes about 18 min for full six-direction measurements. For each antenna, Doppler offsets of radial ocean surface velocities derived from the estimation of Doppler spectra are used to calculate the unidirectional spectrum by means of a modulation transfer function (MTF). The unidirectional spectrum from one antenna for a footprint has a 180° ambiguity relative to wave direction. Therefore, the phase angles of radial velocities from two neighboring footprints can be calculated to resolve the ambiguity. After a full six-antenna scan, a directional wave spectrum is obtained by summing the six unidirectional wave spectra and interpolation is available to enhance the angular resolution. MORSE performs well under extreme weather conditions and during the night when visual observations are not possible.
The wave data used in this work were collected in a coastal region of the South China Sea during December 2012. During the observation, the six antennas were deployed at a height of 20 m MSL. The latitude and longitude of the radar are 22°39′25″N and 115°34′19″E, respectively. With specified transmitting power, the reliable coverage can range from 200 to 2000 m with a resolution of 7.5 m. The directional wave spectra adopted here are from the footprint of 700 m from the radar. Furthermore, an anemometer located near the radar at the height of 10 m MSL was used to record wind velocity of the area every 10 min. The main wind direction is 90° relative to north during the experiment. In the following process, the wind speed and direction are linearly interpolated in accordance with the time series of radar wave spectra. The location of the MORSE system and coverage of the six antennas are shown in Fig. 2.
Location of the MORSE system and coverage of six antennas. The position of the radar site is 22°39′25″N, 115°34′19″E.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
To analyze details, the spectrum at 0136 LST 4 December 2012 is shown in Fig. 3. The original directional spectrum in Fig. 3a is separated by the steepest ascent algorithm proposed by Hasselmann et al. (1996), exhibiting 37 peaks. It is smoother and more regular in Fig. 3b after a procedure of 2D convolution described in section 2a, during which adjacent peaks with a too-close distance in the directional spectrum are merged. By employing the noise energy threshold of 2% according to Portilla et al. (2009), the noises existing in the form of spurious peaks are filtered out in Fig. 3c compared with that in Fig. 3b. A series of gray dots constitute the separation boundaries of the wave systems, showing 10 and 4 wave systems in Figs. 3b,c, respectively.
Directional spectrum from radar at 0136 LST 4 Dec 2012. (a) Original directional spectrum. (b) Directional spectrum after convolution. (c) Directional spectrum after convolution and spurious system removal. A series of gray dots constitute the separation boundaries of the wave systems.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
The two steps of 2D convolution and noise elimination alleviate the sensitivity to parameter settings such as the threshold of merging, spread of frequency and direction, and improving the ability of the method to acquire relevant spectral features objectively. After the separation of wave systems from directional wave spectra, the identification of each wave system will be implemented. In the experiment, the wind sea and swell by the OP method presented in this paper are extracted to compare with that by the WA method with the wave age threshold of 1.5.
Figure 4a shows the separation result from the directional wave spectrum at 2133 LST 16 December 2012, in which the dashed line is the directional wave age parabola and the three wave systems with boundaries indicated by gray dots are displayed. The wind speed and direction are 6.3 m s−1 and 83°, respectively in the meantime. As seen in Fig. 4a, the three wave systems are in the external region of the wave age parabola; that is to say, every peak frequency of the three systems is lower than that of the fully developed wind sea in the same direction, demonstrating that the three systems are all swells.
Separation and identification results from two-directional wave spectra at (a) 2133 LST 16 Dec 2012 and (b) 1557 LST 10 Dec 2012, in which the dashed line is the directional wave age parabola and the wave system with boundaries indicated by gray dots is swell and open circles correspond to wind sea. (c)–(e) The 1D spectra, PM spectra, and 
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
For the OP method, each of the three wave systems has been integrated over direction to obtain the corresponding 1D spectrum. The comparison with the PM spectra of the same peak frequencies are shown in Figs. 4c–e. The peak frequencies of the three wave systems in Figs. 4c–e are 0.12, 0.11, and 0.22 Hz, respectively, and the relevant ratio 
The example of the directional wave spectrum referenced above involves only swell systems. A wave spectrum consisting of both wind sea and swell at 1557 LST 10 December 2012 is given as a typical example in order to investigate other circumstances, and the identification is shown in Fig. 4b. The wind speed and direction recorded meanwhile are 7.5 m s−1 and 117°, respectively. There are also three wave systems in the spectrum, and they appear distinctly in both the frequency and direction domains.
The peak of the wave system with the boundaries indicated by the gray dots is in the internal region of the directional wave age parabola in Fig. 4b; hence, this wave system is identified as wind sea by the WA method. The remaining two systems are considered swell because they not “included” by the parabola. The identification in Fig. 4b using the OP method presents the same result as that by the WA method, and the corresponding 1D spectra are delineated in Figs. 4f–h. The peak frequencies of the three wave systems in Figs. 4f–h are 0.13, 0.11, and 0.23 Hz, respectively, and the relevant ratio 
A typical example of the directional wave spectrum at 2315 LST 10 December 2012, which has a different identification result, is displayed in Fig. 5a. The wave system with boundaries indicated by gray dots is swell and the other is wind sea by the WA method. But Figs. 5b,c exhibit another result, in which the two systems are both considered to be swells by the OP method. The separation by Wang and Hwang (2001) supports the WA method, indicating there is probably something wrong with the OP method.
(a) Separation and identification results from the directional wave spectrum at 2135 LST 10 Dec 2012, in which the dashed line is the directional wave age parabola and the wave system with boundaries indicated by gray dots is swell and the open circles correspond to wind sea. (b),(c) The 1D spectra, PM spectra, and 
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
In addition to the results of the two methods used in one directional wave spectrum, detailed identification is implemented by adopting the directional wave spectra from 0100 LST 4 December 2012 to 2000 LST 19 December 2012 during which the time series of directional wave spectra and wind velocity are both linearly interpolated every hour.
Figures 6–8 show the comparison of significant wave height (Hs), and mean period and mean direction of wind sea and swell by the WA and OP methods separately. During the observation, the wind speed and direction at the height of 10 m MSL are plotted in Fig. 9. The wind directions are less than 130° at all times during the observation, indicating the wind always blows toward the six antennas. The two sequences of significant wave height of swell by the two methods both have larger value than that of wind sea from Fig. 6, with the same characteristics of the value of the mean period in Fig. 7. This phenomenon illustrates that swell has larger energy than wind sea during the observation. As for the mean direction, the result of wind sea in Fig. 8a by the OP method systematically has larger value than that by the WA method, demonstrating larger error than that of swell in Fig. 8b.
Time series of Hs of wind sea and swell using the WA (plus signs) and OP (open circles) methods, and each horizontal axis is labeled with “day.” (a) Significant wave height of wind sea. (b) Significant wave height of swell.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
Time series of the mean period of wind sea and swell using the WA (plus signs) and OP open circles) methods, and each horizontal axis is labeled with “day.” (a) Mean period of wind sea. (b) Mean period of swell.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
Time series of the mean direction of wind sea and swell using the WA (plus signs) and OP (open circles) methods, and each horizontal axis is labeled with “day.” (a) Mean direction of wind sea. (b) Mean direction of swell.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
Time series of wind speed and direction at the height of 10 m MSL, and each horizontal axis is labeled with “day”: (a) wind speed (m s–1) and (b) wind direction (°).
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
The error statistics of the wave parameters of wind sea and swell by the OP method compared with that by the WA method are shown in Table 1. The significant wave heights of both wind sea and swell calculated by the two methods have a high correlation coefficient and small RMSE. The correlation coefficients of the mean period of wind sea and swell are relatively lower than that of wave height. In regard to the mean direction, the correlation coefficient of wind sea is only 0.30, far less than the value of 0.92 for swell. The RMSE presents a worse value of 21.34° as well. This is probably because of the different energy of wind sea and swell in the data used here. During the observation, wave systems that are always below the wave age parabola are generally identified as swells for both the WA and OP methods. These swells have large energy in most cases. Wave systems with higher peak frequencies often give different identification results by the WA and OP methods, and they usually have lower energy than swells. So these “unstable” wave systems will have a smaller influence on swells than wind seas, manifesting the consistent statistic values of swells in Table 1. However, the mean direction of wind sea is calculated by averaging the weighted energy over the direction cell. So, it could be affected largely by the unstable identification result.
Statistics of the wave parameters of wind sea and swell by the OP method compared with that by the WA method.
In the WA method, the criterion of wind and swell depends only on the separation parabola calculated by wind speed and direction without consideration of the characteristics of ocean waves themselves. It means that there will be more wave systems contained within the parabola when the wind speed is larger. The theory of this method determines the strong correlation between wind sea and wind speed than the OP method, as can be seen in Fig. 10. The correlation coefficient between wind speed and the significant wave height of wind sea is 0.89 by the WA method in Fig. 10a, while the value is 0.73 by the OP method in Fig. 10b.
Time series of Hs of wind sea and wind speed at the height of 10 m MSL, and each horizontal axis is labeled with “day”: (a) Hs of wind sea by the WA method and wind speed and (b) Hs of wind sea by the OP method and wind speed.
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
Wind sea scatterplot and regression result by Hwang et al. (1998) using the WA and OP methods: (a) 
Citation: Journal of Atmospheric and Oceanic Technology 32, 11; 10.1175/JTECH-D-15-0092.1
Equations (12) and (13) are both very close to Eq. (10). The correlation coefficient of the results by the WA and OP methods are 0.88 and 0.90, respectively, and the RMSE values are 0.06 and 0.07, respectively. Compared with the WA method, the OP method has a better correlation coefficient but worse RMSE. The two fitting coefficients of wind sea results by the WA and OP methods are 0.62 and 0.63, respectively, which coincide well with the 2/3 power law of wind-generated waves by Toba (1978). It demonstrates that the wind sea from both the WA and OP methods conforms to wind-wave growth function.
4. Conclusions
A practical method based on the overshoot phenomenon (OP) in wind-generated waves used for extracting wind sea and swell from directional wave spectrum has been proposed and investigated in this paper, which utilizes the characteristics of the directional wave spectrum rather than wind information. This scheme has been applied to the directional wave spectra obtained from the S-band Doppler radar developed by Wuhan University, and the results were compared with another commonly used method based on directional wave age. Before the identification of wind sea and swell, a simple 2D convolution put forward by Portilla et al. (2009) and a noise filtering procedure aiming to remove spurious peaks and to merge adjacent peaks have been described to separate the directional wave spectrum into several wave systems. This process reduces the sensitivity to threshold value settings.
The reference method named WA adopted in this study demands the directional wave spectrum plus wind speed and direction, using all available information and giving the most consistent effects. In contrast, the sea-state parameters such as significant wave height and mean period of wind sea and swell extracted by the OP method show good agreement with the results of the WA scheme. The deviation of the mean direction of wind sea between the WA and OP methods probably lies in the different identification of wave systems with higher frequencies. The distinction result by OP under this circumstance remains questionable. Finally, the regression results of wind sea results obtained from the WA and OP methods coincide well with the power law of wind-generated waves, validating the performance of this method.
In contrast to the WA method, the OP method is independent of wind information or the artificial selection of wave age threshold. It could be widely used to separate and extract wind sea and swell, especially when the reliable wind information is difficult to obtain.
Acknowledgments
This work was supported by the Public Science and Technology Research Funds Projects of Ocean (201205032), the National Natural Science Foundation of China (41376182), Fundamental Research Funds for the Central Universities (2012212020203), and the Project of Hubei Province Science and Technology Support Program (2014BEC057).
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