Satellite-based RAR performance simulation for measuring directional ocean wave spectrum based on SAR inversion spectrum

Some missions have been carried out to measure wave directional spectrum by synthetic aperture radar （SAR） and airborne real aperture radar （RAR） at a low incidence.Both them have their own advantages and limitations.Scientists hope that SAR and satellite-based RAR can complement each other for the research on wave properties in the future.For this study,the authors aim to simulate the satellite-based RAR system to validate performance for measuring the directional wave spectrum.The principal measurements are introduced and the simulation methods based on the one developed by Hauser are adopted and slightly modified.To enhance the authenticity of input spectrum and the wave spectrum measuring consistency for SAR and satellite-based RAR,the wave height spectrum inversed from Envisat ASAR data by cross spectrum technology is used as the input spectrum of the simulation system.In the process of simulation,the sea surface,backscattering signal,modulation spectrum and the estimated wave height spectrum are simulated in each look direction.Directional wave spectrum are measured based on the simulated observations from 0 ？ to 360 ？ .From the estimated wave spectrum,it has an 180 ？ ambiguity like SAR,but it has no special high wave number cut off in all the direction.Finally,the estimated spectrum is compared with the input one in terms of the dominant wave wavelength,direction and SWH and the results are promising.The simulation shows that satellite-based RAR should be capable of measuring the directional wave properties.Moreover,it indicates satellite-based RAR basically can measure waves that SAR can measure.

Measurements of ocean wave spectrum from airborne radar at small incidence angles

This paper proposes the retrieval method of ocean wave spectrum for airborne radar observations at small incidence angles, which is slightly modified from the method developed by Hauser. Firstly, it makes use of integration method to estimate total mean square slope instead of fitting method, which aims to reduce the affects of fluctuations superposed on normalized radar cross-section by integration. Secondly, for eliminating the noise spectrum contained in signal spectrum, the method considers the signal spectrum in certain look direction without any long wave components as the assumed noise spectrum, which would be subtracted from signal spectrum in any look direction for linear wave spectrum retrieval. Estimated v from the integration method are lower than the one from fitting method and have a standard deviation of 0.004 between them approximately. The assumed noise spectrum energy almost has no big variations along with the wave number and is slightly lower to the high wave number part of signal spectrum in any look direction, which follows that the assumption makes sense. The retrieved directional spectra are compared with the buoy records in terms of peak wavelength, peak direction and the significant wave height. Comparisons show that the retrieved peak wavelength and significant wave height are slightly higher than the buoy records but don＇t differs significantly （error less than 10%）. For peak direction, the swell waves in first case basically propagate in the wind direction 6 hours ago and the wind-generated waves in second case also propagate in the wind direction, but the 180° ambiguity remains. Results show that the modified method can carry out the retrieval of directional wave spectrum.

Three-dimensional dynamic sea surface modeling based on ocean wave spectrum

In conventional marine seismic exploration data processing,the sea surface is usually treated as a horizontal free boundary.However,the sea surface is affected by wind and waves and there often exists dynamic small-range fluctuations.These dynamic fluctuations will change the energy propagation path and affect the final imaging results.In theoretical research,different sea surface conditions need to be described,so it is necessary to study the modeling method of dynamic undulating sea surface.Starting from the commonly used sea surface mathematical simulation methods,this paper mainly studies the realization process of simple harmonic wave and Gerstner wave sea surface simulation methods based on ocean wave spectrum,and compares their advantages and disadvantages.Aiming at the shortcomings of the simple harmonic method and Gerstner method in calculational speed and sea surface simulation effect,a method based on wave equation and using dynamic boundary conditions for sea surface simulation is proposed.The calculational speed of this method is much faster than the commonly used simple harmonic method and Gerstner wave method.In addition,this paper also compares the new method with the more commonly used higher-order spectral methods to show the characteristics of the improved wave equation method.

Observed typhoon wave spectrum in northern South China Sea

To describe both the way in which a wave spectrum grows and the growth processes of realistic wave conditions,the dependence relationship between the spectrum parameters and wind parameters must be obtained. Based on data measured in 2010 by a Wave Rider buoy,which was deployed in the South China Sea at coordinates 21.89°N,115.13°E,we evaluated the wave spectrum in the sea area when affected by three typhoons:Conson,Chanthu,and Megi. The Joint North Sea Wave Project spectrum was parameterized based on the observed wave spectrum. We proposed a spectrum with three parameters:the dimensionless lowest moment of the spectrum,dimensionless peak frequency,and spectrum width. The relationships between these spectral parameters and the dimensionless fetch were also discussed.

The Research on Typhoon Wave Spectrum in Northwestern South China Sea

Based upon the one-year wind wave measurement data, collected from the South China Sea(SCS) at coordinates 20? 36.298?N, 110?45.433?E. by Acoustic Wave And Current(AWAC), we analyzed the wave characteristics and concluded that the most common wave direction was E and the second most common direction was ENE,the mean and the maximum values of significant height was 1.2 m and 4.36 m, respectively. The mean period was 4.0 s. We also evaluated the wave spectrums under conditions existing in three typhoons: Rumbi, Jeti and Utor. We found that unimodal spectrums occurred more often than others, and the maximum spectrum peak was 30.7911 m2 s. The minimum peak frequency was 0.0625 Hz, and the mean peak frequency was 0.126 Hz. The wave period is important for the design of marine structures, especially the position of peak frequency had a great influence on the stress calculation. Spectral analysis showed that the values of peak frequency distributed between 0.063 Hz and 0.217 Hz, with the mean value 0.114 Hz. We fit the normalized spectrum with 6 theoretical spectral models, out of which, the Wen spectrum, JONSWAP spectrum and Wallops spectrum were proved to give the best fit. What distinguished the Wen Spectrum from the rest was that it does not rely on the measured spectrum for parameter estimation. Hence, we recommend that the Wen spectrum should be widely used in marine construction.

Effect of wave spectrum width on the probability density distribution of wind-wave heights

The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights,derived from this distribution,are widely used for the treatment of realistic wind waves. However,the bandwidth of wave frequency influences the probability distribution of wave heights. In this paper,a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages,based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B. The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for B ≥0.3,and the difference between them increased with the threshold value. The relation between the H s /σ ratio and B was investigated statistically,which revealed that the H s / σ ratio deviated from 4.005 and declined with B. When B reached 0.698 1,the H s / σ ratio was 3.825,which is about 95.5% of its original value. This indicates an overestimation in the prediction of H s from H s =4.005 σ,and provides a potential method for improving the accuracy of the H s remote sensing retrieval algorithm,critical for extremely large waves under severe sea states.

An Appropriate Unidirectional Wave Spectrum Model for the Strait of Hormuz

这份报纸的目的是为 Hormuz 的海峡介绍一个适当单向性的波浪光谱模型。研究集中于在这个区域估计标准波浪光谱模型的性能。由基于最近出版的珍贵测量数据评估如此的模型，刻度过程在如此的标准模型上被进行了到达在一个修改标准之间的一个更好的词语索引光谱模型和观察领域系列。刻度开始关于与四个可得到的测量车站有关的四个不同方向被执行。那么，它为一个提名的模型导致系数的四个集合。下次，它继续被到达就对方向感觉迟钝的一个模型。结果清楚地证明国际拖引坦克会议(ITTC ) 模型在这个区域是比联合诺思海波浪工程(JONSWAP ) 和 Pierson 和 Moskowitz (下午) 模型更适当的，甚至没有任何刻度。然而，修正在改进模型的一致上是成功的。

Photo-stimulation effect on the human EEG alpha-wave spectrum

The EEG α wave mode shows chaotic characters and the frequency spectrum is entrained to the external photo-stimulation peak. This effect was observed exceedingly in the photo-sensitive children as compared with the normal adults. The α spectrum shows asymmetric components with lower frequency-side tail. This spectrum shape could be realized from the computation in terms of the McCulloch-Pitts model and presented in comparison with the observed result. From this analysis, it turns out that the frequency spectrum analysis is most essential for the investigation of the EEG characteristics in comparison with simple waveform inspections in the time-passage. When light flashing frequencies come close to the alpha peak, the both peaks are fused in a giant single peak. These phenomena cannot be understood by the simple mechanical resonant theory but as discussed from the viewpoint of the soft chaotic dynamics of the neural network. Here the both peak intensities Iα and Iex are investigated under different conditions of ωex ωα, and ωα ωex, and it is shown that the entrainment effect is remarkably different in both cases. This result can be understood from the relating neuronal numbers and discussed.

QUADRATIC CORRECTION TO THE LINEAR WAVE SPECTRUM OF TWO-DIMENSIONAL RANDOM WAVES

A perturbation expansion method’s first three order solutions of two-dimensional random gravity waves in finite uniform depth were used as bases to derive the quadratic correction to the linear wave spectrum (ie., the quadratic spectrum ). For infinite water depth, the expression of the quadratic spectrum given in this paper is much simpler then that of Sclavounos (1992) and Olemz and Milgram (1995).

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.

PLANE WAVE SPECTRUM AND BORESIGHT ERROR OF RADOME-ENCLOSED ANTENNAS

The plane wave spectrum surface integration (PWS SI) is a practical and efficient method for antenna radome system analysis, especially for determining the boresight error (BSE) in the system. But it is only used for sum pattern calculation till now, and BSE is calculated by the beam maximum searching method. In this paper, the aperture distribution for difference pattern is formulated as the product of that for sum pattern and a two dimensional periodic window function. A series representation for the spectrum of difference pattern is then obtained according to the convolution theorem. The truncation error of the series has been analyzed by introducing the coverage radius of the spectrum of sum pattern. Based on this representation, the PWS SI technique is extended to difference pattern calculation of radome enclosed antennas. The BSE of a three dimensional multilayered radome, with thickness tapers in all layers, is calculated through the difference pattern null searching. Owing to the steep slope of difference pattern near the nulls, this method for BSE calculation is more stable and reliable than the original beam maximum searching method in PWS SI analysis. The results are compared with those from aperture integration surface integration (AI SI) analysis and the measured ones.

EFFECTS OF WIND SHEAR ON ATMOSPHERIC GRAVITY WAVE SPECTRUM

The effects of constant wind shear on atmospheric gravity wave spectrum are examined.At first a three- dimensional equilibrium spectral model of gravity waves is established in which wind shear rate β is implicit. Based on this model,the expressions for one-dimensional frequency spectrum of atmospheric gravity waves are derived in which β is explicit.Numerical results show that (1) if we assume that mean wind U(z)=βz (z represents the altitude) and the internal gravity wave spectrum at the altitude of U=0 (that is,z=0) is VanZandt one,then the effect of Doppler shifting due to mean wind may be ignored;(2) when Richardson number J(J=N^2/β~2,N is Brunt-V(?)is(?)l(?) frequency,and is equal to 10^(-2)s^(-1) in this paper) satisfies J≥10.0,the effects ofwind shear arealso ignored;(3)for f^2(?)ω~2(?)N^2 (f is the inertia frequency,and f=10^(-4)s^(-1) in this paper,and co is the observed frequency),the wind shear only affects the spectral amplitude,and does not alter the spectral shape;and (4) as wind shear becomes strong,a part of wave potential energy turns into wave kinetic one,and a part of the vertical kinetic energy further turns into the horizontal one.

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.

Parameterized first-guess spectrum method for retrieving directional spectrum of swell-dominated waves and huge waves from SAR images

从 SAR 检索海浪系列的一个方法想象，命名 ParameterizedFirst 猜测光谱方法(PFSM ) ，在理论的解释以后被建议到海浪成像和通常使用的检索模型的缺点的分析。在这个方法，与另外的信息和卫星参数，分开的波浪数字首先被计算决定线性关系能在以外被使用的最大的波浪数字。separatingwave 数字能用风速度和参数 ofSAR 卫星的另外的信息被计算。然后 SAR 光谱能根据分开波浪数字的结果被划分成风波浪并且 swell 的 SAR 光谱。SAR 光谱的部分由风波浪产生了，被用来寻找海洋风波浪光谱的最合适的参数包括海浪的繁殖方向，分阶段执行统治传播的波浪和角度的速度系数。swell 光谱被获得由直接到给 SAR 光谱的部分的 SAR 光谱的海浪光谱的线性关系产生了由的 inversing 胀大。我们使用了建议方法从华南海从 ERS-SAR 数据检索海浪光谱并且把结果与高度表数据作比较。协议显示 PFSM 是可靠的。

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.

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.

Experimental Study of Wave Energy Spectrum in Shallow Water

Wave energy spectrum in shallow water can be studied in wind wave channel in combination with irregular wave- maker. Fetch length is successfully extended and by 'Relay' method the corresponding spectrum pattern and the wind velocity scale are obtained.

Transformation of Wave Energy Spectrum in Shallow Water

Combined with irregular wave-maker, the growing process of Wave Energy Spectrum in shallow water can be studied in wind wave channel on different water depth conditions, and its transformation characteristics and rules can be obtained.

EFFECT OF WATER DEPTH ON WIND-WAVE FREQUENCY SPECTRUM Ⅰ.SPECTRAL FORM

Wen et al.’s odhed dewiogh to obtain wind-wave frequency spectrum in deep was used toderive the spectrum in finite depth water. The spedrum S（ω） （ω bein angular frequency） when normalizedwith the zeroth moment m and peak frequercyω。 contains in adrition to the peakness factor P=ω。S（ω。）/m。, a twth parameter n=（2πm。）1/2d （d being water depPth）, so the spatrum behavior can bestudies for different ware growth stages and water depths.

Wave decomposition phenomenon and spectrum evolution over submerged bars

Wave decomposition phenomenon and spectrum evolution over submerged bars are investigated by a previously developed numerical model. First, the computed free surface displacements of regular waves at various locations are compared with the available experimental data to confirm the validity of the numerical model, and satisfactory agreements are obtained. In addition, variations of decomposition characteristics with incident wave parameters and the change of energy spectrum for regular waves are also studied. Then the spectrum evolution of irregular waves over submerged bars, as well as the influence of incident peak wave period and the steepness of the front slope of the bar on spectrum evolution, is investigated. Wave decomposition and spectral shape are found to be significantly influenced by the incident wave conditions. When the upslope of the bar becomes 1：2, the length of the slope becomes shorter and will not benefit the generation of high frequency energy, so spectrum evolution is not significant.