• Ardhuin, F., , Chapron B. , , and Collard F. , 2009: Observation of swell dissipation across oceans. Geophys. Res. Lett., 36, L06607, doi:10.1029/2008GL037030.

    • Search Google Scholar
    • Export Citation
  • Barnett, T. P., , and Sutherland A. J. , 1968: A note on an overshoot effect in wind-generated waves. J. Geophys. Res., 73, 68796885, doi:10.1029/JB073i022p06879.

    • Search Google Scholar
    • Export Citation
  • Bidlot, J. R., 2001: ECMWF wave-model products. ECMWF Newsletter, No. 91, ECMWF, Reading, United Kingdom, 9–15.

  • Chen, G., , and Ma J. , 2002: Identification of swell zones in the ocean: A remote sensing approach. IGARSS ’02: 2002 IEEE International Geoscience and Remote Sensing Symposium/24th Canadian Sympoisum on Remote Sensing, Vol. 2, IEEE, 946–948, doi:10.1109/IGARSS.2002.1025738.

  • Chen, Z., , Fan L. , , Zhao C. , , and Jin Y. , 2012: Ocean wave directional spectrum measurement using microwave coherent radar with six antennas. IEICE Electron. Express, 9, 15421549, doi:10.1587/elex.9.1542.

    • Search Google Scholar
    • Export Citation
  • Churchill, J. H., , Plueddemann A. J. , , and Faluotico S. M. , 2006: Extracting wind sea and swell from directional wave spectra derived from a bottom-mounted ADCP. WHOI Tech. Rep. WHOI-2006-13, 41 pp., doi:10.1575/1912/1372.

  • de Farias, E. G. G., , Lorenzzetti J. A. , , and Chapron B. , 2012: Swell and wind-sea distributions over the mid-latitude and tropical North Atlantic for the period 2002–2008. Int. J. Oceanogr., 2012, 306723, doi:10.1155/2012/306723.

    • Search Google Scholar
    • Export Citation
  • Doong, D.-J., , and Kao C.-C. , 2007: Typhoon induced swell. Proceedings of East Asian Workshop for Marine Environments, National Chen Kung University, 163–175.

  • Earle, M. D., 1984: Development of algorithms for separation of sea and swell. National Data Buoy Centre Tech. Rep. MEC-87-1, 53, pp.

  • Ewans, K. C., , Bitner-Gregersen E. M. , , and Guedes Soares C. , 2004: Estimation of wind-sea and swell components in a bimodal sea state. J. Offshore Mech. Arct. Eng., 128, 265270, doi:10.1115/1.2166655.

    • Search Google Scholar
    • Export Citation
  • Fan, L., , Chen Z. , , Chen X. , , and Yan J. , 2012: S-band radar measurement of correlation between coastal wave and tide. Int. J. Digital Content Technol. Appl., 6, 503510, doi:10.4156/jdcta.vol6.issue19.61.

    • Search Google Scholar
    • Export Citation
  • Gerling, T., 1992: Partitioning sequences and arrays of directional ocean wave spectra into component wave systems. J. Atmos. Oceanic Technol., 9, 444458, doi:10.1175/1520-0426(1992)009<0444:PSAAOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gilhousen, D. B., , and Hervey R. , 2002: Improved estimates of swell from moored buoys. Ocean Wave Measurement and Analysis, B. L. Edge and J. M. Hemsley, Eds., ASCE, 387–393, doi:10.1061/40604(273)40.

  • Guedes Soares, C., 1991: On the occurrence of double peaked wave spectra. Ocean Eng., 18, 167171, doi:10.1016/0029-8018(91)90040-W.

  • Guillaume, A., 1994: Analyzing directional evolution ocean waves for operational research applications. Preprints, Second Int. Conf. on Sea-Air Interaction and on Meteorology and Oceanography of the Coastal Zone, Lisbon, Portugal, Amer. Meteor. Soc., 151–153.

  • Hanson, J. L., , and Phillips O. M. , 1999: Wind sea growth and dissipation in the open ocean. J. Phys. Oceanogr., 29, 16331648, doi:10.1175/1520-0485(1999)029<1633:WSGADI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hanson, J. L., , and Mandelberg M. D. , 2000: Ocean surface waves: Automated analysis of directional spectra. Oceans 2000 MTS/IEEE Conference and Exhibition, Vol. 3, IEEE, 1753–1759, doi:10.1109/OCEANS.2000.882194.

  • Hanson, J. L., , and Phillips O. M. , 2001: Automated analysis of ocean surface directional wave spectra. J. Atmos. Oceanic Technol., 18, 277293, doi:10.1175/1520-0426(2001)018<0277:AAOOSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., and et al. , 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project. Deutches Hydrographisches Institut Ergänzungsheft 8-12, 95 pp.

  • Hasselmann, S., , Brüning C. , , Hasselmann K. , , and Heimbach P. , 1996: An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra. J. Geophys. Res., 101, 16 61516 629, doi:10.1029/96JC00798.

    • Search Google Scholar
    • Export Citation
  • Hessner, K., , and Hanson J. L. , 2010: Extraction of coastal wavefield properties from X-band radar. 2010 IEEE International Geoscience and Remote Sensing Symposium, IEEE, 4326–4329, doi:10.1109/IGARSS.2010.5650134.

  • Holthuijsen, L. H., 2007: Waves in Oceanic and Coastal Waters.Cambridge University Press, 387 pp.

  • Hwang, P. A., , Teague W. J. , , Jacobs G. A. , , and Wang D. W. , 1998: A statistical comparison of wind speed, wave height, and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region. J. Geophys. Res., 103, 10 45110 468, doi:10.1029/98JC00197.

    • Search Google Scholar
    • Export Citation
  • Hwang, P. A., , Ocampo-Torres F. J. , , and García-Nava H. , 2012: Wind sea and swell separation of 1D wave spectrum by a spectrum integration method. J. Atmos. Oceanic Technol., 29, 116128, doi:10.1175/JTECH-D-11-00075.1.

    • Search Google Scholar
    • Export Citation
  • Komen, G. J., , Hasselmann K. , , and Hasselmann K. , 1984: On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr., 14, 12711285, doi:10.1175/1520-0485(1984)014<1271:OTEOAF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kumar, V. S., , Singh J. , , Pednekar P. , , and Gowthaman R. , 2011: Waves in the nearshore waters of northern Arabian Sea during the summer monsoon. Ocean Eng., 38, 382388, doi:10.1016/j.oceaneng.2010.11.009.

    • Search Google Scholar
    • Export Citation
  • Moon, I. J., , and Oh I. S. , 1998: A study of the characteristics of wave spectra over the seas around Korea by using a parametric spectrum method. Acta Oceanogr. Taiwan, 37, 3146.

    • Search Google Scholar
    • Export Citation
  • Pierson, W. J., Jr., , and Moskowitz L. , 1964: A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res., 69, 51815190, doi:10.1029/JZ069i024p05181.

    • Search Google Scholar
    • Export Citation
  • Portilla, J., , Ocampo-Torres F. J. , , and Monbaliu J. , 2009: Spectral partitioning and identification of wind sea and swell. J. Atmos. Oceanic Technol., 26, 107122, doi:10.1175/2008JTECHO609.1.

    • Search Google Scholar
    • Export Citation
  • Semedo, A., , Sušelj K. , , and Rutgersson A. , 2009: Variability of wind sea and swell waves in the North Atlantic based on ERA-40 Re-analysis. Proc. Eighth European Wave and Tidal Energy Conf., Uppsala, Sweden, Uppsala University, 119–129.

  • Toba, Y., 1978: Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanogr., 8, 494507, doi:10.1175/1520-0485(1978)008<0494:SFOTGO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Tracy, B., , Devaliere E. , , Hanson J. , , Nicolini T. , , and Tolman H. , 2007: Wind sea and swell delineation for numerical wave modeling. Proc. 10th Int. Workshop on Wave Hindcasting and Forecasting/Coastal Hazard Symp., North Shore, Oahu, HI, WMO, IOC, and U.S. Army Corps of Engineers, P12. [Available online at ftp://www.wmo.int/Documents/PublicWeb/amp/mmop/documents/JCOMM-TR/J-TR-44/WWW/Papers/10th_wave_paper_tracy_dhnt.pdf.]

  • Voorrips, A. C., , Makin V. K. , , and Hasselmann S. , 1997: Assimilation of wave spectra from pitch-and-roll buoys in a North Sea wave model. J. Geophys. Res., 102, 58295849, doi:10.1029/96JC03242.

    • Search Google Scholar
    • Export Citation
  • Wang, D. W., , and Hwang P. A. , 2001: An operational method for separating wind sea and swell from ocean wave spectra. J. Atmos. Oceanic Technol., 18, 20522062, doi:10.1175/1520-0426(2001)018<2052:AOMFSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yılmaz, N., , and Özhan E. , 2014: Characteristics of the frequency spectra of wind-waves in Eastern Black Sea. Ocean Dyn., 64, 14191429, doi:10.1007/s10236-014-0756-z.

    • Search Google Scholar
    • Export Citation
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    (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.

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    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.

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    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.

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    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 by Hwang et al. (2012) of the three systems in (a), respectively. (f)–(h) The 1D spectra, PM spectra, and by Hwang et al. (2012) of the three systems in (b), respectively.

  • View in gallery

    (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 by Hwang et al. (2012) of the two systems in (a), respectively.

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    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.

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    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.

  • View in gallery

    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.

  • View in gallery

    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 (°).

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    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.

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    Wind sea scatterplot and regression result by Hwang et al. (1998) using the WA and OP methods: (a) vs using the WA method and (b) vs using the OP method.

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A Practical Method of Extracting Wind Sea and Swell from Directional Wave Spectrum

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  • 1 School of Electronic Information, Wuhan University, Wuhan, China
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Abstract

Wind sea and swell representing different weather conditions generally coexist in both open waters and coastal areas, which results in bimodal or multipeaked features in directional wave spectrum. Because they make wave parameters such as significant wave height and mean wave period of the mixed sea state less meaningful, the processes of separation and identification of wind sea and swell are crucial. Consistent wind sea and swell results can be obtained by a commonly used method based on wave age (WA) with the directional wave spectrum and wind velocity. However, the subjective dependence of wave age threshold selection and the required wind information restrict the application of this method. In this study, a practical method based on the overshoot phenomenon (OP) in wind-generated waves is proposed to extract wind sea and swell from the directional wave spectrum without any other meteorology information. Directional wave spectra derived from an S-band Doppler radar deployed on the coast of the South China Sea have been utilized as the datasets to investigate the performance of both methods. The proposed OP method is then validated by comparing it with the WA method and the verifying results are presented.

Corresponding author address: Chen Zhao, School of Electronic Information, Wuhan University, LuoJia Hill, Wuhan, Hubei 430072, China. E-mail: zhaoc@whu.edu.cn

Abstract

Wind sea and swell representing different weather conditions generally coexist in both open waters and coastal areas, which results in bimodal or multipeaked features in directional wave spectrum. Because they make wave parameters such as significant wave height and mean wave period of the mixed sea state less meaningful, the processes of separation and identification of wind sea and swell are crucial. Consistent wind sea and swell results can be obtained by a commonly used method based on wave age (WA) with the directional wave spectrum and wind velocity. However, the subjective dependence of wave age threshold selection and the required wind information restrict the application of this method. In this study, a practical method based on the overshoot phenomenon (OP) in wind-generated waves is proposed to extract wind sea and swell from the directional wave spectrum without any other meteorology information. Directional wave spectra derived from an S-band Doppler radar deployed on the coast of the South China Sea have been utilized as the datasets to investigate the performance of both methods. The proposed OP method is then validated by comparing it with the WA method and the verifying results are presented.

Corresponding author address: Chen Zhao, School of Electronic Information, Wuhan University, LuoJia Hill, Wuhan, Hubei 430072, China. E-mail: zhaoc@whu.edu.cn

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 for a given wave spectrum. Wave components at frequencies lower than are considered as swell and the higher ones correspond to wind sea. For the 1D wave spectrum, Chen and Ma (2002) use a typical frequency of 0.1 Hz (corresponding to a wave period of 10 s) as the separation frequency and study the evolution of swell energy. But they indicate that this simple method performs well only in the conditions that wind sea and swell are apparently distinguished in frequency domain. Earle (1984) puts forward an empirical relation between the cutoff frequency and the local wind speed. In his method, can be expressed as , in which is the wind speed at 10-m height and the typical value of is 1.02. The disadvantage of this method is leaving out spectral information. Wang and Hwang (2001) determine assuming that wave phase velocity corresponding to the frequency of is equal to , in which is calculated by fitting the wave steepness function with the Pierson–Moskowitz (PM) spectrum (Pierson and Moskowitz 1964). According to Portilla et al. (2009), the wind sea and swell can be separated from a 1D spectrum through comparing the wave spectrum energy to an appointed PM spectrum; they found that the method Wang and Hwang (2001) proposed tends to underestimate wind sea, especially when the wind sea is dominated. The method of Wang and Hwang (2001) is revised by Hwang et al. (2012) through modifying the steepness function and yields a good result for a wide range of wind sea wave age. Gilhousen and Hervey’s (2002) scheme is based on a hypothesis that the steepness of wind sea is larger than that of swell, and the maximum steepness appears in the wave spectrum near the peak of wind sea energy. This method improves the performance of swell estimate significantly and has been implemented by NOAA’s National Data Buoy Center (NDBC).

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.

The 2D discrete convolution is described by
e1
where is the raw spectrum and is the spectrum after convolution, both having dimensions . The sign indicates a convolution process. The convolution kernel chosen as a constant matrix of 3 × 3 seems to perform well in most circumstances (Portilla et al. 2009), which can be expressed by
e2

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

When the directional spectrum and wind velocity are available, a brief step to identify wind sea and swell is the utilization of wave age criteria. Wave age is an important parameter describing the development status of ocean wave, which is defined as follows:
e3
where is the wave age, denotes the phase speed of the wave corresponding to the maximum energy, is the wind speed at 10-m height, and and are the wave direction and the wind direction, respectively. A threshold can be given to determine that a wave system is wind sea if and swell when (Komen et al. 1984). When the wind direction is fluctuating significantly, however, young swell components that are no longer driven by local wind still have the characteristic of wind sea and may be estimated as wind sea improperly. Accordingly, Hanson and Phillips (2001) presented that for a wind sea condition, the direction of wave is expected in a region of a 180° cone centered in the wind direction—that is, 90° at each side relative to the prevailing wind direction. The aforementioned constraint condition for the angle of wind sea can be expressed as
e4
where is the direction of a certain wave system relative to wind. Equation (4) ensures the consistency of the direction of the wind sea and the wind. Considering and the dissipation relation of wave, , the phase speed can be expressed as
e5
where and are the wavelength and frequency of the spectrum corresponding to peak energy, respectively. Substituting Eq. (5) into Eq. (3) and considering Eq. (4), the identification criteria of wind sea can be expressed by
e6
where is the separation frequency and is the direction series of the wave spectrum. A wave portion with a frequency higher than is considered wind sea and the others are swell. The identification methods commonly used are based on Eq. (6), but researchers have adopted their own threshold according to some physical properties of wind and waves that can lead to significant differences in the identification results (Portilla et al. 2009). Bidlot (2001) uses the threshold 1.3 in the analysis of wind sea and swell in the Wave Model (WAM) operated by ECMWF. Tracy et al. (2007) employ 1.7 as the threshold value and apply this algorithm called Wave Spectrum Energy Partitioning (WaveSEP) written in FORTRAN to MIKE2008 and to WAVEWATCH III (WW3) model. Through an observation experiment, Hanson and Phillips (2001) indicate that all possible wind sea peaks in the directional wave spectrum can be included in the wind sea portion when the threshold is 1.5. de Farias et al. (2012) present a value of 1.2 on the basis of the PM spectrum because the wave age can be calculated by the fully developed PM spectrum expression. A succession of sensitivity tests of the threshold have been carried out by Churchill et al. (2006) through directional wave spectra from bottom-mounted ADCP at the Martha’s Vineyard Coastal Observatory. They suggest this value to be ranging from 1.4 to 1.9 and implement the software system from the Applied Physics Laboratory (APL) of the Johns Hopkins University APL-WAVES using the moderate value of 1.6, demonstrating the capability of ADCP to separate wind sea and swell. Hessner and Hanson (2010) developed an ocean surface wave analysis system named XWaves by integrating the WA method with the Wave and Surface Current Monitoring System (WaMoS II) radar employing the threshold of 1.5 and indicate that this system is capable of capturing the evolution of wind sea and swell in the surf zone through an experiment of monitoring the north coast of California.

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.

The ratio of the two peak values is defined as follows:
e7
where is the peak value of the corresponding 1D wave spectrum of a target wave system with a peak frequency and is the peak value of the PM spectrum with the same peak frequency. A wave system is considered to be wind sea if , illustrating that the wave system meets the condition of the overshoot phenomenon; otherwise, it is swell. The target wave system must be transformed to the corresponding 1D spectrum by integrating over the direction domain before the identification process. It should be noted that this method is based on the condition that a wave system is overshot rather than the wave growth status defined by wave age; thus, the advantage is that it does not require wind information.
The Joint North Sea Wave Project (JONSWAP) spectrum (Hasselmann et al. 1973) is usually utilized to modal a growing wind sea, which is expressed as
e8
where is the energy spectrum with frequency , is the Phillips constant concerned with wind fetch, is the acceleration of gravity, is the peak frequency, is the peak enhancement factor describing the developing status with a range of 1.5–6, and is the spectral width factor defined as follows:
e9

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 are 4.19, 1.75, and 0.39, respectively, indicating the different developing state in the same wind condition. The peak value of the corresponding PM spectrum is 0.11. It is observed that the energy of the peak frequency of these JONSWAP spectra are greater than that of the PM spectrum even when the peak enhancement factor is the minimum value of 1.5, demonstrating the existence of the overshoot phenomenon in the wind-generated wave. In Fig. 1b, two JONSWAP spectra are plotted in different wind speed conditions with the same peak enhancement factor , and the line with the plus sign in different colors are PM spectra corresponding to each JONSWAP spectrum. The figure indicates that the peak frequency of a wind sea and the relevant fully developed state is connected with wind information.

Fig. 1.
Fig. 1.

(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.

Fig. 2.
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.

Fig. 3.
Fig. 3.

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.

Fig. 4.
Fig. 4.

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 by Hwang et al. (2012) of the three systems in (a), respectively. (f)–(h) The 1D spectra, PM spectra, and by Hwang et al. (2012) of the three systems in (b), respectively.

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 proposed in section 2c for the three wave systems are 0.12, 0.02 and 0.55, respectively, in which the overshoot phenomenon is not manifested for the three wave systems. The three by Hwang et al. (2012), which are specially used for the 1D spectrum, are shown with the dashed line in the plot. The peak values of the three spectra (solid line) are all lower than that of the PM spectra (dotted line) and the peaks are all in the left position to , declaring that the three wave systems are all swells, which yield the same identification effects as the WA method.

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 for the three wave systems are 0.44, 0.07, and 2.26, respectively, in which the overshoot phenomenon appears only in the third wave system, plotted in Fig. 4h. The identification also coincides exactly with the results of Hwang et al. (2012).

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.

Fig. 5.
Fig. 5.

(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 by Hwang et al. (2012) of the two systems in (a), respectively.

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 68 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.

Fig. 6.
Fig. 6.

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

Fig. 7.
Fig. 7.

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

Fig. 8.
Fig. 8.

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

Fig. 9.
Fig. 9.

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.

Table 1.

Statistics of the wave parameters of wind sea and swell by the OP method compared with that by the WA method.

Table 1.

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.

Fig. 10.
Fig. 10.

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

It is generally considered that there is a close correlation among wind speed, wave height, and wave period in a wind-generated wave system (Hwang et al. 1998). Hwang et al. (1998) simplifies the wave growth function by eliminating the dimensionless energy and fetch parameters, obtaining Eq. (10) based on several groups of experiment data:
e10
where is wind speed at the height of 10 m, is the acceleration of gravity, is the peak period, and is the significant wave height. Hwang also found the tight correlation between and in the Gulf of Mexico wave data. Equation (10) is in accordance with the 3/2 power law of dimensionless significant wave height and period proposed by Toba (1978), which describes the growing wind waves. The relation of dimensionless significant wave height and period used by Toba (1978) is expressed as follows:
e11
where , , and are friction velocity. Equation (11) is rarely used in observation data due to the friction velocity being complex and difficult to obtain.
The wind sea scatterplot and regression results by Hwang et al. (1998) using the WA and OP methods during the observation are shown in Fig. 11. The parameter versus using the WA method is depicted in Fig. 11a and the OP result is described in Fig. 11b. The best fit between and for the WA and OP methods can be indicated by Eqs. (12) and (13), respectively:
e12
e13
Fig. 11.
Fig. 11.

Wind sea scatterplot and regression result by Hwang et al. (1998) using the WA and OP methods: (a) vs using the WA method and (b) vs using the OP method.

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).

REFERENCES

  • Ardhuin, F., , Chapron B. , , and Collard F. , 2009: Observation of swell dissipation across oceans. Geophys. Res. Lett., 36, L06607, doi:10.1029/2008GL037030.

    • Search Google Scholar
    • Export Citation
  • Barnett, T. P., , and Sutherland A. J. , 1968: A note on an overshoot effect in wind-generated waves. J. Geophys. Res., 73, 68796885, doi:10.1029/JB073i022p06879.

    • Search Google Scholar
    • Export Citation
  • Bidlot, J. R., 2001: ECMWF wave-model products. ECMWF Newsletter, No. 91, ECMWF, Reading, United Kingdom, 9–15.

  • Chen, G., , and Ma J. , 2002: Identification of swell zones in the ocean: A remote sensing approach. IGARSS ’02: 2002 IEEE International Geoscience and Remote Sensing Symposium/24th Canadian Sympoisum on Remote Sensing, Vol. 2, IEEE, 946–948, doi:10.1109/IGARSS.2002.1025738.

  • Chen, Z., , Fan L. , , Zhao C. , , and Jin Y. , 2012: Ocean wave directional spectrum measurement using microwave coherent radar with six antennas. IEICE Electron. Express, 9, 15421549, doi:10.1587/elex.9.1542.

    • Search Google Scholar
    • Export Citation
  • Churchill, J. H., , Plueddemann A. J. , , and Faluotico S. M. , 2006: Extracting wind sea and swell from directional wave spectra derived from a bottom-mounted ADCP. WHOI Tech. Rep. WHOI-2006-13, 41 pp., doi:10.1575/1912/1372.

  • de Farias, E. G. G., , Lorenzzetti J. A. , , and Chapron B. , 2012: Swell and wind-sea distributions over the mid-latitude and tropical North Atlantic for the period 2002–2008. Int. J. Oceanogr., 2012, 306723, doi:10.1155/2012/306723.

    • Search Google Scholar
    • Export Citation
  • Doong, D.-J., , and Kao C.-C. , 2007: Typhoon induced swell. Proceedings of East Asian Workshop for Marine Environments, National Chen Kung University, 163–175.

  • Earle, M. D., 1984: Development of algorithms for separation of sea and swell. National Data Buoy Centre Tech. Rep. MEC-87-1, 53, pp.

  • Ewans, K. C., , Bitner-Gregersen E. M. , , and Guedes Soares C. , 2004: Estimation of wind-sea and swell components in a bimodal sea state. J. Offshore Mech. Arct. Eng., 128, 265270, doi:10.1115/1.2166655.

    • Search Google Scholar
    • Export Citation
  • Fan, L., , Chen Z. , , Chen X. , , and Yan J. , 2012: S-band radar measurement of correlation between coastal wave and tide. Int. J. Digital Content Technol. Appl., 6, 503510, doi:10.4156/jdcta.vol6.issue19.61.

    • Search Google Scholar
    • Export Citation
  • Gerling, T., 1992: Partitioning sequences and arrays of directional ocean wave spectra into component wave systems. J. Atmos. Oceanic Technol., 9, 444458, doi:10.1175/1520-0426(1992)009<0444:PSAAOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gilhousen, D. B., , and Hervey R. , 2002: Improved estimates of swell from moored buoys. Ocean Wave Measurement and Analysis, B. L. Edge and J. M. Hemsley, Eds., ASCE, 387–393, doi:10.1061/40604(273)40.

  • Guedes Soares, C., 1991: On the occurrence of double peaked wave spectra. Ocean Eng., 18, 167171, doi:10.1016/0029-8018(91)90040-W.

  • Guillaume, A., 1994: Analyzing directional evolution ocean waves for operational research applications. Preprints, Second Int. Conf. on Sea-Air Interaction and on Meteorology and Oceanography of the Coastal Zone, Lisbon, Portugal, Amer. Meteor. Soc., 151–153.

  • Hanson, J. L., , and Phillips O. M. , 1999: Wind sea growth and dissipation in the open ocean. J. Phys. Oceanogr., 29, 16331648, doi:10.1175/1520-0485(1999)029<1633:WSGADI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hanson, J. L., , and Mandelberg M. D. , 2000: Ocean surface waves: Automated analysis of directional spectra. Oceans 2000 MTS/IEEE Conference and Exhibition, Vol. 3, IEEE, 1753–1759, doi:10.1109/OCEANS.2000.882194.

  • Hanson, J. L., , and Phillips O. M. , 2001: Automated analysis of ocean surface directional wave spectra. J. Atmos. Oceanic Technol., 18, 277293, doi:10.1175/1520-0426(2001)018<0277:AAOOSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., and et al. , 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project. Deutches Hydrographisches Institut Ergänzungsheft 8-12, 95 pp.

  • Hasselmann, S., , Brüning C. , , Hasselmann K. , , and Heimbach P. , 1996: An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra. J. Geophys. Res., 101, 16 61516 629, doi:10.1029/96JC00798.

    • Search Google Scholar
    • Export Citation
  • Hessner, K., , and Hanson J. L. , 2010: Extraction of coastal wavefield properties from X-band radar. 2010 IEEE International Geoscience and Remote Sensing Symposium, IEEE, 4326–4329, doi:10.1109/IGARSS.2010.5650134.

  • Holthuijsen, L. H., 2007: Waves in Oceanic and Coastal Waters.Cambridge University Press, 387 pp.

  • Hwang, P. A., , Teague W. J. , , Jacobs G. A. , , and Wang D. W. , 1998: A statistical comparison of wind speed, wave height, and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region. J. Geophys. Res., 103, 10 45110 468, doi:10.1029/98JC00197.

    • Search Google Scholar
    • Export Citation
  • Hwang, P. A., , Ocampo-Torres F. J. , , and García-Nava H. , 2012: Wind sea and swell separation of 1D wave spectrum by a spectrum integration method. J. Atmos. Oceanic Technol., 29, 116128, doi:10.1175/JTECH-D-11-00075.1.

    • Search Google Scholar
    • Export Citation
  • Komen, G. J., , Hasselmann K. , , and Hasselmann K. , 1984: On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr., 14, 12711285, doi:10.1175/1520-0485(1984)014<1271:OTEOAF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kumar, V. S., , Singh J. , , Pednekar P. , , and Gowthaman R. , 2011: Waves in the nearshore waters of northern Arabian Sea during the summer monsoon. Ocean Eng., 38, 382388, doi:10.1016/j.oceaneng.2010.11.009.

    • Search Google Scholar
    • Export Citation
  • Moon, I. J., , and Oh I. S. , 1998: A study of the characteristics of wave spectra over the seas around Korea by using a parametric spectrum method. Acta Oceanogr. Taiwan, 37, 3146.

    • Search Google Scholar
    • Export Citation
  • Pierson, W. J., Jr., , and Moskowitz L. , 1964: A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res., 69, 51815190, doi:10.1029/JZ069i024p05181.

    • Search Google Scholar
    • Export Citation
  • Portilla, J., , Ocampo-Torres F. J. , , and Monbaliu J. , 2009: Spectral partitioning and identification of wind sea and swell. J. Atmos. Oceanic Technol., 26, 107122, doi:10.1175/2008JTECHO609.1.

    • Search Google Scholar
    • Export Citation
  • Semedo, A., , Sušelj K. , , and Rutgersson A. , 2009: Variability of wind sea and swell waves in the North Atlantic based on ERA-40 Re-analysis. Proc. Eighth European Wave and Tidal Energy Conf., Uppsala, Sweden, Uppsala University, 119–129.

  • Toba, Y., 1978: Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanogr., 8, 494507, doi:10.1175/1520-0485(1978)008<0494:SFOTGO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Tracy, B., , Devaliere E. , , Hanson J. , , Nicolini T. , , and Tolman H. , 2007: Wind sea and swell delineation for numerical wave modeling. Proc. 10th Int. Workshop on Wave Hindcasting and Forecasting/Coastal Hazard Symp., North Shore, Oahu, HI, WMO, IOC, and U.S. Army Corps of Engineers, P12. [Available online at ftp://www.wmo.int/Documents/PublicWeb/amp/mmop/documents/JCOMM-TR/J-TR-44/WWW/Papers/10th_wave_paper_tracy_dhnt.pdf.]

  • Voorrips, A. C., , Makin V. K. , , and Hasselmann S. , 1997: Assimilation of wave spectra from pitch-and-roll buoys in a North Sea wave model. J. Geophys. Res., 102, 58295849, doi:10.1029/96JC03242.

    • Search Google Scholar
    • Export Citation
  • Wang, D. W., , and Hwang P. A. , 2001: An operational method for separating wind sea and swell from ocean wave spectra. J. Atmos. Oceanic Technol., 18, 20522062, doi:10.1175/1520-0426(2001)018<2052:AOMFSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yılmaz, N., , and Özhan E. , 2014: Characteristics of the frequency spectra of wind-waves in Eastern Black Sea. Ocean Dyn., 64, 14191429, doi:10.1007/s10236-014-0756-z.

    • Search Google Scholar
    • Export Citation
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