Comparison of spectral partitioning techniques for wind wave and swell

The ocean waves are generally mixed with wind wave and swell. In order to separate these two kinds of ocean waves, many wave spectral partitioning techniques have been proposed. In this study, a two-dimensional（2D） and three one-dimensional （1D） wave spectral partitioning techniques （denoted as PM, WH, and JP） are examined based on the model simulations and in-situ observations. It is shown that the 2D technique could provide the most reliable results as a whole. Compared with 2D technique, PM and JP techniques obviously overestimate the wind-wave components, and the same situation happens for WH technique at low wind speed. With the adjustment of the partitioning frequency ratio, the 1D PM technique is modified, in which the result agree well with that of the 2D scheme.

Analytically Derived Wind Wave Growth Relations

By the use of the 3/2 power law presented by Toba combined with the significant wave energy balance equation for wind wave, wind wave growth at a limited fetch is analytically investigated. The new wind wave growth relations (WWGRs) are analytically derived with sheltering coefficient and wind drag coefficient as parameters. The geometrical average of observational values of sheltering coefficient and the arithmetic average of observational values of wind drag coefficient are applied to determine the new WWGRs. Comparisons with existing empirical WWGRs are made.

Low frequency shift of wind waves induced by long waves based on experimental observation data

The influence of long regular waves on wind waves are examined in the laboratory tank. The wave spectra of wind waves are compared when there is and there is not long waves. Besides the widely addressed suppression of wind waves by long waves, it is also found that, the presence of long regular wave induces low frequency shift of wind waves when long wave slope is small and also its frequencyf is quite apart from wind wave crest frequencies fp. The effect of long wave modulation on wind wave spectra is estimated according to Longuet-Higgins ＆ Stewart （1960） （abbreviated as LS60 afterwards）, which is found to be prominent at the large ratio of fp/f l. It＇s also found that, when the limitation of wave breaking on wind wave steepness is taken account of, the LS60 theory can explain the low frequency shift satisfactorily. The work suggests that, at small long wave slope and large ratio of fp/fl, the LS60 modulation mechanism together with the enhanced wave breaking may dominate the influence of long waves on wind waves.

The long-term trend of the sea surface wind speed and the wave height (wind wave, swell, mixed wave) in global ocean during the last 44 a

Utilizing the 45 a European Centre for Medium-Range Weather Forecasts （ECMWF） reanalysis wave da- ta （ERA-40）, the long-term trend of the sea surface wind speed and （wind wave, swell, mixed wave） wave height in the global ocean at grid point 1.5°× 1.5° during the last 44 a is analyzed. It is discovered that a ma- jority of global ocean swell wave height exhibits a significant linear increasing trend （2-8 cm/decade）, the distribution of annual linear trend of the significant wave height （SWH） has good consistency with that of the swell wave height. The sea surface wind speed shows an annually linear increasing trend mainly con- centrated in the most waters of Southern Hemisphere westerlies, high latitude of the North Pacific, Indian Ocean north of 30°S, the waters near the western equatorial Pacific and low latitudes of the Atlantic waters, and the annually linear decreasing mainly in central and eastern equator of the Pacific, Juan. Fernandez Archipelago, the waters near South Georgia Island in the Atlantic waters. The linear variational distribution characteristic of the wind wave height is similar to that of the sea surface wind speed. Another find is that the swell is dominant in the mixed wave, the swell index in the central ocean is generally greater than that in the offshore, and the swell index in the eastern ocean coast is greater than that in the western ocean inshore, and in year-round hemisphere westerlies the swell index is relatively low.

A hybrid model for numerical wave forecasting and its implementation-Ⅰ.The wind wave model

The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This part of the paper is devoted to the wind wave model. Both deep and shallow water models have been developed, the former being actually a special case of the latter when water depth is great. The deep water model is exceptionally simple in form. Significant wave height is the only prognostic variable. In comparison with the usual methods to compute the energy input and dissipations empirically or by 'tuning', the proposed model has the merit that the effects of all source terms are combined into one term which is computed through empirical growth relations for significant waves, these relations being, relatively speaking, easier and more reliable to obtain than those for the source terms in the spectral energy balance equation. The discrete part of the model and the implementation of the model as a whole will be discussed in the second part of the present paper.

Improved form of wind wave frequency spectrum

The lower frequency part of the theoretical wind wave spectrum proposed by the authors (Wen et al. , 1988a, b,c) has been improved and the form of spectrum is appreciably simplified. In addition to the field data collected in the Bohai Sea region and used in the previous papers, those obtained in the Huanghai Sea, the East China Sea and the South China Sea have been employed so that the improved spectra can be verified on a more extensive observational basis. Computed results agree with the observations well. Further comparisons have been made between the proposed spectra and the JONSWAP spectrum. Though the two types of spectrum are close to each other in form, the former shows, as a whole, better agreement with the observation than the latter. By introducing an improved relation between the peak-ness factor and significant wave steepness, the spectrum contains only significant wave height and period as parameters. For spectra given in this form, the computed peak frequencies coincide approximately with observed values and the computed peak magnitudes of spectra agree basically with observations, but, because of the statistic variability inherent in the measurements of significant wave heights and periods, there are certain discrepancies between computed and measured spectrum peak magnitudes.

Rainfall effect on wind waves and the turbulence beneath air-sea interface

Rainfall effects on wind waves and turbulence are investigated through the laboratory experiments in a large wind-wave tank. It is found that the wind waves are damped as a whole at low wind speeds, but are enhanced at high wind speeds. This dual effect of rain on the wind waves increases with the increase of rain rate, while the influence of rainfall-area length is not observable. At the low wind speed, the corresponding turbulence in terms of the turbulent kinetic energy （TKE） dissipation rate is significantly enhanced by rain- fall as the waves are damped severely. At the high wind speed, the augment of the TKE dissipation rate is suppressed while the wind waves are enhanced simultaneously. In the field, however, rainfall usually hin- ders the development of waves. In order to explain this contradiction of rainfall effect on waves, a possibility about energy transfer from turbulence to waves in case of the spectral peak of waves overlapping the inertial subrange of turbulence is assumed. It can be applied to interpret the damping phenomenon of gas trans- fer velocity in the laboratory experiments, and the variation of the TKE dissipation rates near sea surface compared with the law of wall.

Study on the growth of wind wave frequency spectra generated by cold waves in the northern East China Sea

The growth of frequency spectra and spectral parameters of wind waves generated by cold waves, a kind of severe weather system, in the northern East China Sea is studied in this paper. Based on a third-generation wave action model(the Simulating WAves Nearshore model), simulations were developed to analyze the spatiotemporal characteristics of wind waves and to output spectral data. It is shown that the cold wave-induced spectra can be well described by the modified Joint North Sea Wave Project spectral form. The growth of wave spectra is comprehensively reflected by the evolution of the three characteristic parameters: peak frequency, spectral peak and wave energy. Besides, the approximations of dependences between spectral parameters and the three types of universal induced factors are obtained with the least squares method and compared systematically. Fetch and peak frequency turn out to be suitable parameters to describe the spectral parameters, while the dependences on the inverse wave age vary in different sea areas. In general, the derived relationships improve on results from previous studies for better practical application of the wind wave frequency spectrum in the northern East China Sea.

Estimation of Wind Wave Frequency Spectra by Use of the Arcsine Law

In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.

A laboratory study of directional spectra with maximum likelihood method─I Developing wind wave

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.

The equilibrium range of wind wave frequency spectrum

-Theoretical form of equilibrium range is given on the basis of the wind wave frequency spectra proposed by Wenel al. (1988a,b,c, 1989a,b). The effects of peakness factor and water depth are discussed. In the case of deep water the e-quilibrium range is reduced to the form first proposed by Toba (1973) and the coefficient of the formula is shown to be the function of nondimensional fetch or peak frequency. Results of the present paper have been verified through field data.

Directional Spectrum of Wind Waves: Part Ⅱ- Comparison and Confirmation

A model on the directional frequency spectrum of wind waves for deep water is introduced. The comparisons of the proposed model with other existing models show that the proposed model is very close to the JONSWAP model and DHH model for describing the developing waves under the normal spectral bandwidth, and has a better description for the transition of the unidirectional spectrum from ω -4 to ω -5 at a position around 3ω p, i.e., three time the peak frequency. Comparisons also show that the proposed model describes closely both field data measured by a four-frequency radar and a laser-optical sensor, and laboratory data measured by a laser slope gauge and an imaging optical method. The comparisons further demonstrate that the inverse spectral bandwidth as a new wave parameter is robust for describing the spectral steepness. Finally, the formula on the local spectral-peak angular frequency is confirmed using the observed two-dimensional spectra.

On the Spectrum Width of Wind Waves

Based on the universal expression of wind wave spectra, four commonly used definitions of the spectrum width are re-examined. The results show that the non-dimensional spectrum width can measure the width of non-dimensional spectra but it does not reflect the developing state of the spectra. The dimensional spectrum width expresses the degree of concentration of wave energy of the spectrum in the process of wind wave growth. Tests show that the spectrum width presented by Wen et al. can objectively measure the degree of concentration of wave energy of the spectrum, reflect the state of wind wave growth, and provides a better result for practical application, The rules for definition of the spectrum width are discussed.

A Parameterization Scheme for Wind Wave Modules that Includes the Sea Ice Thickness in the Marginal Ice Zone

The global wave model WAVEWATCH III®works well in open water.To simulate the propagation and attenuation of waves through ice-covered water,existing simulations have considered the influence of sea ice by adding the sea ice concentration in the wind wave module;however,they simply suppose that the wind cannot penetrate the ice layer and ignore the possibility of wind forcing waves below the ice cover.To improve the simulation performance of wind wave modules in the marginal ice zone(MIZ),this study proposes a parameterization scheme by directly including the sea ice thickness.Instead of scaling the wind input with the fraction of open water,this new scheme allows partial wind input in ice-covered areas based on the ice thickness.Compared with observations in the Barents Sea in 2016,the new scheme appears to improve the modeled waves in the high-frequency band.Sensitivity experiments with and without wind wave modules show that wind waves can play an important role in areas with low sea ice concentration in the MIZ.

The Equilibrium Range of Wind Wave Spectra: an Explanation Based on White Noise

Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral space by many researchers. In this paper we point out that white noise on an oscillation system can also lead to a similar inverse power law in the corresponding displacement spectrum, implying that the – 4 power law for the equilibrium range of wind wave spectra may probably only reflect the randomicity of the wind waves rather than any other dynamical processes in physical space. This explanation may shed light on the mechanism of other physical processes with spectra also showing an inverse power law, such as isotropic turbulence, internal waves, etc.

Interannual Variability of SST,SLA and Wind Waves in the Hawaii Area and Their Responses to ENSO

Time series of sea surface temperature （SST）, wind speed and significant wave height （SWH） from meteorological buoys of the National Data Buoy Center （NDBC） are useful for studying the interannual variability and trend of these quantities at the buoy areas. The measurements from 4 buoys （B51001, B51002, B51003 and B51004） in the Hawaii area are used to study the responses of the quantities to El Nino and Southern Oscillation （ENSO）. Long-term averages of these data reflect precise seasonal and climatological characteristics of SST, wind speed and SWH around the Hawaii area. Buoy observations from B51001 suggest a significant warming trend which is, however, not very clear from the other three buoys. Compared with the variability of SST and SWH, the wind speeds from the buoy observations show an increasing trend. The impacts of EI Nifio on SST and wind waves are also shown. Sea level data observed by altimeter during October 1992 to September 2006 are analyzed to investigate the variability of sea level in the Hawaii area. The results also show an increasing trend in sea level anomaly （SLA）. The low-passed SLA in the Hawaii area is consistent with the inverse phase of the low-passed SOI （Southern Oscillation Index）. Compared with the low-passed SOl and PDO （Pacific Decadal Oscillation）, the low-passed PNA （Pacific-North America Index） has a better correlation with the low-passed SEA in the Hawaii area.

The Fractional Power Law of Wind Wave Growth in Deep Water for Short Fetch

Combining the 3/2 power law proposed by Toba with the significant wave energy balance equation for wind waves, wave growth in deep water for short fetch is investigated. It is found that the variations of wave height and period with fetch have the form of power function with fractional exponents 3/8 and 1/4 respectively. Using these exponents in the power functions and through data fitting, the concise wind wave growth relations for short fetch are obtained.

Composite Type Wind Wave Frequency Spectrum

Based on the P-M spectrum and improved theoretical wind wave frequency spectrum, this paper presents the composite type wind wave frequency spectrum, which is given by 2 pieces and satisfies 4 conditions: the spectrum peak passes through a given point; spectral area m0 and significant wave height H have the relationship H = 4.0 ; at the piecewise point, the values of spectrum and slope are contin-

Elimination of Wind Wave Effects on Sub-Bottom Profiler Record

With the presence of wind waves, the swaying of survey vessel may effect the quality of sub-bottom profiler records and, therefore, it is necessary to correct the distortions induced by wave action. A major issue is to distinguish wind wave effect and real bedforms such as sand waves. In this paper, a bandstop filter is designed according to the frequency features of wind wave effect to treat the distortion of seabed topography by wind waves. The technique is used to correct the sub-bottom profile in order to eliminate the wave-induced distortions for the sub-bottom profile records from the Yangtze Estuary. This study shows that the undulate seabed record is resulted from wave action, rather than the presence of sand waves, and the filtration technique helps to eliminate the wave effect and recover the real morphology of seabed and the sediment sequence underneath. In addition, a method for data processing is proposed for the case that the record indeed represents a combination of wave effects and real bedforms.

Numerical simulation of non-gaussian process of wind waves

In this paper further mathematical analysis on 'correlation transfer technique' by Polge el al. is carried out, the tenable conditions and the extent of suitability for the said method are proved as well. In consideration of the influence of skewness of the sea surface elevation on spectral shape, a 'quasi-correlation transfer techique' is developed by the modification of the simulated target spectrum. Meanwhile, the numerical simulation of the non-Gaussian process of wind waves is carried out in view of the two conditions of the surface elevation probability distribution and the spectrum. By using its simulated results, the influence of skewness of the sea surface elevation on two parameters in the distribution of wave heights (which had been fitted by using the Weibull distribution) is analysed. The 'quasi- correlation tranfer technique' is verified and compared with the selection wave data observed in the Jiaozhou Bay in the period of 1980 to 1981. Results make clear (hat, as far as the statistical distribution of the wave heights and the distribution of the maximum (minimum) values of the sea surface elevation are concerned, the said method is obviously superior to the conventional mothed of the linear wave superposition, and that the simulated results are closer to the observation data.