Relationship between wave steepness and wave age in the course of wind wave growth

It is traditionally assumed that the relationship between wave steepness and wave age is independent of the wind wave growth state. In fact, the traditional relationship can not describe the whole course of wind wave growth. This paper assumes that the relationship between wave steepness and wave age changes with the variety of dimensionless fetch. Based on the relationship proposed by Hou and Wen (1990), a new relationship in the course of wind wave growth is revealed. Comparisons between the present study and other previous relationships show that this new relationship explains better the observations than the other existing relationships.In the case of small fetch, wave age value increases more quickly than other models while it is in opposition to that in the case of large fetch. The result in present paper can clearly reflect the whole course of wind wave growth, it is an improvement for traditional results.     

Parameter identification of JONSWAP spectrum acquired by airborne LIDAR

In this study, we developed the first linear Joint North Sea Wave Project (JONSWAP) spectrum (JS), which involves a transformation from the JS solution to the natural logarithmic scale. This transformation is convenient for defining the least squares function in terms of the scale and shape parameters. We identified these two wind-dependent parameters to better understand the wind effect on surface waves. Due to its efficiency and high-resolution, we employed the airborne Light Detection and Ranging (LIDAR) system for our measurements. Due to the lack of actual data, we simulated ocean waves in the MATLAB environment, which can be easily translated into industrial programming language. We utilized the Longuet-Higgin (LH) random-phase method to generate the time series of wave records and used the fast Fourier transform (FFT) technique to compute the power spectra density. After validating these procedures, we identified the JS parameters by minimizing the mean-square error of the target spectrum to that of the estimated spectrum obtained by FFT. We determined that the estimation error is relative to the amount of available wave record data. Finally, we found the inverse computation of wind factors (wind speed and wind fetch length) to be robust and sufficiently precise for wave forecasting.     

Analysis of Wave Distributions Using the WAVEWATCH-Ⅲ Model in the Arctic Ocean

In this work, we examined long-term wave distributions using a third-generation numerical wave model called WAVE- WATCH-Ⅲ(WW3) (version 6.07). We also evaluated the influence of sea ice on wave simulation by using eight parametric switches. To select a suitable ice-wave parameterization, we validated the simulations from the WW3 model in March, May, September, and December 2017 against the measurements from the Jason-2 altimeter at latitudes of up to 60?N. Generally, all parameterizations ex-hibited slight differences, i.e., about 0.6 m root mean square error (RMSE) of significant wave height (SWH) in May and September and about 0.9 m RMSE for the freezing months of March and December. The comparison of the results with the SWH from the European Centre for Medium-Range Weather Forecasts for December 2017 indicated that switch IC4_M1 performed most effec-tively (0.68 m RMSE) at high latitudes (60?– 80?N). Given this finding, we analyzed the long-term wave distributions in 1999 – 2018 on the basis of switch IC4_M1. Although the seasonal variability of the simulated SWH was of two types, i.e., 'U' and 'sin' modes, our results proved that fetch expansion prompted the wave growth. Moreover, the interannual variability of the specific regions in the 'U' mode was found to be correlated with the decade variability of wind in the Arctic Ocean.     

A relationship between wave steepness and wave age for wind waves in deep water

Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.     

A mechanism of the effect of non-uniform current on the spectrum of short wind waves

A mechanism is suggested in this paper concerning the effect of non-uniform current on the spectrum of short wind waves. According to this mechanism, a non-uniform current brings changes to the breaking criteria of short wind waves through modulating the surface drift, and hence enhances or weakens wave breaking. Some modification is proposed to the source term, which represents the spectral rate of wave energy dissipation due to wave breaking so that the source term can incorporate this mechanism. In order to illustrate whether this mechanism is significant, a real case is studied, in which the wind waves propagate on a tidal current flowing over the sea bottom covered with sand waves. Finally, the effect of the new mechanism on the equilibrium spectrum of small scale gravity waves is discussed. Numerical estimates suggest that, for water depths less than 50 m and wavelengths less than 1 m, this current field may result in distinct spatial variations of the wave breaking criteria, the spectral rate of wave energy dissipation and the equilibrium spectrum of short gravity waves.     

A physics-based dual-frequency approach for altimeter wind speed retrieval

The altimeter normalized radar cross section(NRCS) has been used to retrieve the sea surface wind speed for decades, and more than a dozen of wind speed retrieval algorithms have been proposed. Despite the continuing efforts to improve the wind speed measurements, a bias dependence on wave state persists in all wind algorithms. On the basis of recent evidence that short waves are essentially modulated by local winds and much less affected by wave state, we proposed a physics-based approach to retrieve the wind speed from the dual-frequency difference in terms of the mean square slope of short waves. A collocated dataset of coincident altimeter/buoy measurements were used to develop and validate the approach. Validation against buoy measurements indicates that the approach is almost unbiased and has an overall root mean square error of 1.24 m s-1, which is 5.3% lower than the single-parameter algorithm in operational use(Witter and Chelton, 1991) and 2.4% lower than another dual-frequency approach(Chen et al., 2002). Furthermore, the results indicate that the new approach significantly improves the wave-dependent bias compared to the single-parameter algorithm. The capacity of altimeter to retrieve sea surface wind speed appears to be limited for the case of winds below 3 m s-1. The validity of the approach at high winds needs to be further examined in the future study.     

Wave assimilation and numerical prediction

ＩＮＴＲＯＤＵＣＴＩＯＮＤａｔａａｓｓｉｍｉｌａｔｉｏｎｗａｓｕｓｅｄｉｎｅａｒｌｙｎｕｍｅｒｉｃａｌｗｅａｔｈｅｒｐｒｅｄｉｃｔｉｏｎｔｏｉｍｐｒｏｖｅｆｏｒｅｃａｓｔａｃｃｕｒａｃｙ.Ｆｏｒｅｃａｓｔｅｒｒｏｒｓｒｅｓｕｌｔｆｒｏｍｓｅｖｅｒａｌｍａｉｎｒｅｓｏｕｒｃｅｓ:ｔｈｅｆｉｒｓｔｉｓｐｈｙｓｉｃａｌａｐｐｒｏｘｉｍａｔｉｏｎｉｎｔｈｅｄｙｎａｍｉ ｃａｌｅｑｕａｔｉｏｎｓｏｆｔｈｅｍｏｄｅｌ;ｔｈｅｓｅｃｏｎｄｉｓｔｈｅｌｏｗｑｕａｌｉｔｙｏｆｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｓａ…     

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.     

A temporal sliding procedure for ocean wave variational data assimilation and its application

For sequential performance of wave variational data assimilation, we proposed a temporal sliding method in which the temporal overlap is considered. The advantage of this method is that the initial wave spectrum of the optimization process is modified by the observations in latter and former times. This temporal sliding procedure is important for marginal region, such as the China seas, where the duration of assimilation effectiveness is 2-3 days. Experiments were performed in the whole course of Cyclone 9403 (Russ). Around the cyclone center, the maximum value of wave elements did not change much by assimilation, because the extreme value was determined by wind energy input that was not yet optimized. In the area outside the cyclone center, this modification is evident especially for wind wave growth.     

若尔盖等地风能资源评价

本文用平均风速和最大风速法对若尔盖等三地的韦伯分布参数k、c进行估算,并用韦伯分布计算风能的指标。计算表明:若尔盖、红原属风能可利用区,用风力发电是有利用价值的;阿坝属风能贫乏地区。     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study, typhoon waves generated during three typhoons(Damrey(1210), Fung-wong(1416), and Chan-hom(1509)) in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN) model, and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model. Various parameters, such as the Holland fitting parameter(B) and the maximum wind radius(R), were investigated in sensitivity experiments in the Holland model that affect the wind field construction. Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements. The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied, including wind input, whitecapping, and bottom friction. Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation) and the JONSWAP scheme(dissipation of bottom friction) resulted in good reproduction of the significant wave height of typhoon waves. A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon, while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves. The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.     

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.     

两种海浪模式对一次台风浪过程的模拟分析

以CCMP（Cross—Calibrated,Multi—Platfoml）风场为驱动场,分别驱动目前国际先进的第3代海浪模式ww3（WAVEWATCH—III）、SWAN（Simulating WAves Nearshore）,对2010年9月发生在东中国海的台风“圆规”所致的台风浪进行数值模拟,就台风浪的特征进行分析,并对比分析两个海浪模式的模拟效果。结果表明：1）以CCMP风场分别驱动WW3、SWAN海浪模式,可以较好地模拟发生在东中国海的台风浪,风向与波向保持了大体一致,波高与风速的分布特征保持了很好的一致性;2）综合相关系数、偏差、均方根误差、平均绝对误差来看,两个模式模拟的有效波高（SWH—Significant Wdve Height）都具有较高精度,SWAN模拟的SWH略低于观测值,WW3模拟的SWH与观测值更为接近;3）台风浪可给琉球群岛海域带来5m左右的大浪,台风浪进入东海后,波高、风速都有一定程度的增加,当台风沿西北路径穿越朝鲜半岛时,受到半岛地形的巨大影响,风速和波高都明显降低。     

A proposed frequency spectrum for fully developed wind waves by revisiting P-M spectrum

It is generally believed that the equilibrium range of wind wave spectrum is in the form of the −4 rather than −5 power law. However, in the widely applied P-M spectrum the equilibrium range is given in the form of −5 power law. In the present paper, a spectrum for full development of wind waves is proposed using the form of the Neumann spectrum, but adopting the −4 power law for the equilibrium range. The proposed spectrum has been verified with NDBC buoy data and could be a substitute for the P-M spectrum.     

A wave modulation model of ripples over long surface waves

A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modulation model is proposed. In this model, the wind surface stress modulation is related to the modulation of ripple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the ripple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves.     

Wind-forced equatorial wave dynamics of the Pacific Ocean during 2014/2015 and 2015/2016 E1 Ni?o events

The equatorial wave dynamics of interannual sea level variations between 2014/2015 and2015/2016 El Nino events are compared using the Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics Climate Ocean Model(LICOM) forced by the National Centers for Environmental Prediction(NCEP) reanalysis I wind stre s s and heat flux during 2000-2015.In addition,the LICOM can reproduce the interannual variability of sea surface temperature anomalies(SSTA) and sea level anomalies(SLA) along the equator over the Pacific Ocean in comparison with the Hadley center and altimetric data well.We extracted the equatorial wave coefficients of LICOM simulation to get the contribution to SLA by multiplying the meridional wave structure.During 2014/2015 El Nino event,upwelling equatorial Kelvin waves from the western boundary in April2014 reach the eastern Pacific Ocean,which weakened SLA in the eastern Pacific Ocean.However,no upwelling equatorial Kelvin waves from the western boundary of the Pacific Ocean could reach the eastern boundary during the 2015/2016 El Nino event.Linear wave model results also demonstrate that upwelling equatorial Kelvin waves in both 2014/2015 and 2015/2016 from the western boundary can reach the eastern boundary.However,the contribution from stronger westerly anomalies forced downwelling equatorial Kelvin waves overwhelmed that from the upwelling equatorial Kelvin waves from the western boundary in 2015.Therefore,the western boundary reflection and weak westerly wind burst inhibited the growth of the 2014/2015 El Nino event.The disclosed equatorial wave dynamics are important to the simulation and prediction of ENSO events in future studies.     

Numerical simulation of scatterometer assimilated wind and ocean wave in eastern China seas and adjacent waters

Using the latest version of Mesoscale Modeling System (MM5v3), we assimilated wind data from the scatterometer and built a model to assimilate the wind field over eastern China seas and adjacent waters and applied the wave model WAVEWATCH-Ⅲ to test the sea area with assimilative wind and blended wind of QSCAT and NCEP as driving forces. High precision and resolution numerical wave results were obtained. Analysis indicated that if we replace the model wind result with the blended wind, better sea surface wind results and wave results could be obtained.     

Laboratory Experiment on Wave Induced Turbulence

A laboratory experiment was conducted inside a wind wave tank to investigate the wave induced turbulence. In this experiment, the wave surface elevation and velocity beneath the water surface were measured simultaneously to investigate the relation between the wave status and wave induced turbulence. The profile of the turbulent dissipation rate and Reynolds stress were calculated using experimental data. The effect of the wave status on turbulence is investigated with regard to the wind wave, swell, and mixed wave conditions. It was depicted that the turbulence decreased with increasing depth from the water surface and that the turbulence that was induced by a wave with larger wavelength and wave height is much stronger for the same wave status. Finally, we observed that the wind wave is more effective in activating the wave induced turbulence.     

ON LONG-WAVES BREAKING Ⅱ.IN A HALF INFINITE CHANNEL WITH BOTTOM SLOPE

The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.     

NUMERICAL STUDY OF THE INFLUENCE OF WAVES AND TIDE-SURGE INTERACTION ON TIDE-SURGES IN THE BOHAI SEA

Abstract The author‘s combined numerical model consisting of a third generation shallow water wave model and a 3-D tide-surge model with wave-dependent surface wind stress were used to study the influence of waves on fide-surge motion. For the typical weather case, in this study, the magnitude and mechanism of the influence of waves on tide-surges in the Bohai Sea were revealed for the first time. The results showed that although consideration of the wave-dependent surface wind stresses raise slightly the traditional surface wind stress, due to the accumulated effects, the computed results are improved on the whole. Storm level maximum modulation can reach 0.4 m. The results computed by the combined model agreed well with the measured data.