基于海面多普勒谱模型的海浪反演精度分析

Microwave remote sensing is one of the most useful methods for observing the ocean parameters. The Doppler frequency or interferometric phase of the radar echoes can be used for an ocean surface current speed retrieval,which is widely used in spaceborne and airborne radars. While the effect of the ocean currents and waves is interactional. It is impossible to retrieve the ocean surface current speed from Doppler frequency shift directly. In order to study the relationship between the ocean surface current speed and the Doppler frequency shift, a numerical ocean surface Doppler spectrum model is established and validated with a reference. The input parameters of ocean Doppler spectrum include an ocean wave elevation model, a directional distribution function, and wind speed and direction. The suitable ocean wave elevation spectrum and the directional distribution function are selected by comparing the ocean Doppler spectrum in C band with an empirical geophysical model function(CDOP). What is more, the error sensitivities of ocean surface current speed to the wind speed and direction are analyzed. All these simulations are in Ku band. The simulation results show that the ocean surface current speed error is sensitive to the wind speed and direction errors. With VV polarization, the ocean surface current speed error is about 0.15 m/s when the wind speed error is 2 m/s, and the ocean surface current speed error is smaller than 0.3 m/s when the wind direction error is within 20° in the cross wind direction.     

Application of the four models of directional spectra in the Bohai Sea

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各向异性海面全极化微波双站散射的仿真与分析

为了解各向异性随机粗糙海面的微波双站散射机制及其特性,本文利用解析近似的积分方程模型以及一种改进的半经验海浪谱模型实现了对各向异性随机粗糙海面的全极化微波散射仿真模拟,并与卫星观测数据、经验的地球物理模式函数及已有的解析近似散射模型仿真结果进行了对比,验证了仿真结果的可行性和准确性。利用该模型分析了入射波频率、入射角、极化方式、海面风速及风向等参数对各向异性海面双站散射的影响。模拟结果表明,在不同的入射角、散射角及方位角等观测几何条件下,海面不同波段的双站散射表现出不同的空间散射特性,且对风速、风向等海面动力学参数表现出不同的敏感性,以L波段为例,海面向后半球双站散射在各个极化方式下都对风速较为敏感,而在同极化方式下,其对风向的响应在中低风速和高风速条件下相反,整体而言,低风速下海面双站散射对风向更为敏感。这表明对于海面动力参数的反演,双站散射可以提供比传统单站雷达后向散射更丰富的物理信息。本文探讨了各向异性海面微波双站散射特性,为基于主动式及分布式微波传感器的海洋动力参数遥感反演提供了理论分析基础。     

Observations of the spectra of hurricane generated waves

An extensive database of one-dimensional spectra observed during the passage of hurricanes is examined. Spectra recorded within eight times the radius to maximum winds of the centers of hurricanes are unimodal and remarkably similar to previously recorded fetch limited spectra. Parametric spectral forms such as JONSWAP and that of Donelan et al. approximate the data well. In addition, the functional dependence of the spectral parameters α and γ on the inverse wave age is consistent with that observed under fetch limited conditions. It is concluded that the similarity of the hurricane wave spectra to those observed for simpler fetch limited spectra is largely due to the effects of nonlinear interactions. The shape stabilizing effects of the nonlinear interactions reshape spectra consisting of a mix of swell and wind-sea to conform with typical one-dimensional fetch limited wind-sea forms.     

Directional wave spectra measured with a cloverleaf buoy during ARSLOE

The cloverleaf buoy is designed to determine the directional wave spectra with high directional resolution by measuring the vertical acceleration, surface slope, and curvature of the ocean wave surface. This paper describes the properties of the directional wave spectra measured with the cloverleaf buoy during the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE). It is shown that the directional wave spectra measured under relatively constant wind agree fairly well with the similarity spectrum reported previously, but some differences are found in the spectral parameters. The differences in the scale parameters are attributed to unstable atmospheric conditions, though reasonable explanations for those in the shape parameters are difficult now.     

Retrieval of surface wave parameters from sar images and their validation in the coastal seas around Japan

We have developed a scheme to retrieve surface wave parameters (wave height and wave propagation direction) from European Remote-Sensing Satellite (ERS) Synthetic Aperture Radar (SAR) image mode data in coastal seas around Japanese coastlines. SAR spectra are converted to surface wave spectra of swell-dominated or wind-wave dominated cases. The SAR spectrum and SAR-derived wind speed are used to derive the surface wave spectrum. The wind-wave dominated case and swell-dominated case are differentiated by a wind speed of 6 m/s, and processed in different ways because of their different degree of nonlinearity. It is indicated that the cutoff wavelength for retrieval of the wind-wave dominated spectrum is proportional to the root of significant wave height, which is consistent with the results of previous studies. We generated 66 match-ups using the SAR sub-images and the in-situ surface wave parameters, which were measured by wave gauges installed in near-shore seas. Among them, there are 57 swell-dominated cases, and 9 wind-wave dominated cases. The significant wave heights derived from SAR and from in-situ observation agree with the bias of 0.09 m, the standard deviation of 0.61 m and the correlation coefficient of 0.78. The averaged absolute deviation of wave propagation directions is 18.4°, and the trend of the agreement does not depend on the wave height. These results demonstrate that the SAR surface wave spectrum retrieved by the present system can be used to observe the surface wave field in the coastal seas around Japan.     

A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory

A state of wind waves at a fetch is assumed to be transformed into another state of wind waves at a different fetch by the renormalization group transformation. The scaling laws for the covariance of water surface displacement and for the one-dimensional and two-dimensional spectrum and the power law for the growth relation are derived from the fact that the renormalization group transformation constitutes a semigroup. The scaling relation or the relation among the exponents of the power law is also derived, using the two assumptions that the renormalization group transformation is applicable to fetch-limited wind waves and that the saturated range exists, which implies that the directional distribution function of energy in the wave number region much larger than the peak wave number does not depend on wave number.     

Modification of SAR spectra associated with surface wind fields in the sea off the Kii Peninsula: A case study

Using surface wave parameters and a high-resolution surface wind field derived from Synthetic Aperture Radar (SAR) image mode data, we have investigated the spatial modification of SAR spectra. We found a surface wind front, formed by sheltering effect of the Kii Mountains, separating high and low wind-speed regions in a sea area of an European Remote-Sensing Satellite (ERS) SAR image off the Kii Peninsula. A swell system propagating westward dominates in the whole sea area covered by the SAR image. The wavelength retrieved from the SAR spectra in the sheltered (non-sheltered) region is longer (shorter). Since the distributions of surface wave parameters and surface wind speed are so well correlated, it can be considered that the SAR spectra are modified differently by the sheltered/non-sheltered surface winds. In order to examine the phenomena observed on the SAR image we have estimated the wind-wave SAR spectrum using the SAR surface winds, a wind-wave spectrum model and a SAR wave imaging model. We assume that the SAR spectrum related to the swell is homogeneous in the area imaged by SAR, and that the SAR spectrum of the wind-wave components causes the observed SAR spectra modification. Differences between the observed SAR spectra and the estimated SAR spectra in the sheltered and non-sheltered regions agree well with each other. In the present case, it can be concluded that the observed SAR spectra can be regarded as a linear combination of the wind-wave SAR spectra and the swell SAR spectra.     

Parameters in wind-wave frequency spectra and their bearings on spectrum forms and growth

The spectrum variance m0, peak frequency ω0 and peakness factor p are expressed in terms of nondimensional fetch and duration by making use of relations which are derived through comparing and analyzing existing empirical formulas for the growth of significant wave height and period. The main features of spectrum growth as specified by these parameters agree with those of the JONS-WAP experiments. For given wind speed and fetch, the high frequency parts beyond the peaks of shallow water spectra almost coincide with that of the corresponding deep water spectrum, whereas the low frequency parts differ appreciably. The method developed in this paper predicts smaller significant wave height as well as smaller wave period for shallow water spectra in contrast to the theoretical result of Kitaigorodskii ef al, in which the peak frequency, and consequently the significant wave period, remains basically unchanged for different water depths. Spectra are further reduced to a form in which only significant wave h     

关于风浪预报公式和风区宽度的注记

从定常波的风浪波高随风距成长的预报公式出发 ,在一定条件下 ,导出各波向上风浪波高分量与该波向上的风距之间的关系 ,以便在不规则风区上推算风浪波高和平均波向 ;同时 ,对风区宽度作了定量化的分析。     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.     

A Whitecap Coverage Model Based on the Surface Slope For Criterion of Wave Breaking

Using the limit surface slope as a criterion of wave breaking,a simple model for estimatingthe spatial fraction of breaking surface of sea at an instant,which is regarded as the whitecap coverge inthis paper,is analytically derived from the probability density of surface slope based on Gaussianstatistics.The resulting fraction is found depending on the fourth moment of wave spectum,m_4,as well asthe critical threshold of surface slope.By expressing the fourth moment in terms of the Neumannspectrum,a formula linking the fraction and wind speed for fully developed sea states is obtianed.Anotherformula relating the fraction to both wind speed and fetch(or duration)is achieved by expressing m_4 interms of the Krylov spectrum and applying the empirical relationships used in the SMB ocean wave pre-dicting technique.A comparison between these results and the field data of whitecap coverage collected byMonahan and O＇Muircheartuigh shows an encouraging agreement.     

An approximate solution of wave-modified Ekman current for gradually varying eddy viscosity

An approximate steady solution of the wave-modified Ekman current is presented for gradually varying eddy viscosity by using the WKB method with the variation of parameters technique. The parameters involved in the solution can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water. The solution reduces to the exact solution when the eddy viscosity is taken as a constant. As illustrative examples, for a fully developed wind-generated sea with different wind speeds and a few proposed gradually varying eddy viscosities, the current profiles calculated from the approximate solutions are compared with those of the exact solutions or numerical ones by using the Donelan and Pierson wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. It is shown that the approximate solution presented has an elegant form and yet would be valid for any given gradually varying eddy viscosity. The applicability of the solution method to the real ocean is discussed following the comparisons with published observational data and with the results from a large eddy simulation of the Ekman layer.     

Discussion on the critical wind speed for wind-wave generation on the basis of shear-flow instability theory

Observed critical wind speeds for the generation of wind waves are compared with those derived from a shear-flow instability theory. The theory predicts that the critical wind speed depends on the fetch and, for the case of infinite fetch, it is 93 cm s^–1 at 30 cm above the mean water surface, which agrees well with observations at sufficiently large fetch. For water containing soap, the much larger critical wind speeds which are observed cannot be explained by the reduction of surface tension alone. A qualitative discussion suggests that the elasticity of surface films of soap can effectively increase the critical wind speed.     

基于拟层流风波生成机制的海浪谱模型

海浪谱的能量可以视为由具有不同相速度的谐波携带的能量所组成。基于对风波形成、发展过程的认识,认为各组成谐波的能量由谐波自平均风摄取而来,由此根据拟层流模型推导出谐波能量密度的计算公式,建立以等效风速和峰值频率等为基本参数的海浪谱模型——随机Fourier函数模型,并给出了确定谐波频率、波长、相速度、振幅以及等效风速等模型参数的原则和计算方法。在59个实测样本谱基础上,采用随机建模方法确定模型参数的取值及其概率分布。结果表明,海浪谱模型可以很好地预测谱能,所计算的物理谱与实测谱均值吻合良好。     

Triple diagram method for the prediction of wave height and period

Many formulations have been developed so far to predict the wave height and period from fetch length and wind blowing duration for a constant wind speed. This study aimed to predict wave parameters from fetch length and meteorological factors by using triple diagram methodology based on Kriging principles. Proposed model results were compared with Joint North Sea Wave Project (JONSWAP) model which is used so commonly in the ocean and coastal engineering studies. For the implementation of the methodology hourly wave and wind data were obtained from a buoy located in Lake Ontario. Numerical and graphical comparisons demonstrated that the proposed method outperforms the classical formulation.     

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied.     

基于选定风浪方向谱的海浪模拟方法(英文)

简要回顾当前第三代海浪模式中的困难。为避开这些困难,作者提出一种新的海浪模拟方法,其中特定定义的风浪组成波依常风下随时间成长的方向谱计算,而涌浪组成波藉考虑涡动黏性和底摩擦加以计算。并进行了常风场和变风场下系统的数值试验。在常风速情形中,模拟结果能精确地化为建立模拟所根据的谱和风浪成长关系。计算显示出台风中心附近浪场的极端复杂的谱结构。当风速骤然降低时,模拟的波高减小与观测符合。在风向逐渐或骤然改变情形下,计算的时间响应尺度与海上观测符合,而且演化中的二维谱结构得到良好刻画。对于涌浪在无风下的传播,模拟结果合理,包括波参量及谱结构的变化。后报得到的波高、周期和海上资料符合。与第三代模式相比,文中提出的方法较易改进,需用的计算机时间显著减少。最后讨论采用一个已知谱来建立谱形式的海浪预报模型的合理性以及有关的问题。     

海浪方向谱阵列资料实例分析

根据傅氏级数展开法和贝叶斯方法,对现场获得的阵列资料进行了方向谱实例分析。结果表明,实测风浪方向谱能量的相对分布与相应的波场类型密切相关。涌浪和由稳定风场引起的风浪方向谱各组成波能量相对于方向呈单峰对称分布。大风引起的风浪方向谱能量的相对分布,虽也近似为单峰,但对称性差。不同波场类型的风浪方向谱各组成波的谱密度极值方向不同,表明不同频率的组成波有不同的主方向。     

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift.