Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

On the nonlinear integral transform of an ocean wave spectrum into an along-track interferometric synthetic aperture radar image spectrum

We present a new nonlinear integral transform relating the ocean wave spectrum to the along-track interferometric synthetic aperture radar (AT-INSAR) image spectrum. The AT-INSAR, which is a synthetic aperture radar (SAR) employing two antennas displaced along the platform's flight direction, is considered to be a better instrument for imaging ocean waves than the SAR. This is because the AT-INSAR yields the phase spectrum and not only the amplitude spectrum as with the conventional SAR. While the SAR and AT-INSAR amplitude spectra depend strongly on the modulation of the normalized radar cross section (NRCS) by the long ocean waves, which is poorly known, the phase spectrum depends only weakly on this modulation. By measuring the phase difference between the signals received by both antennas, AT-INSAR measures the radial component of the orbital velocity associated with the ocean waves, which is related to the ocean wave height field by a well-known transfer function. The nonlinear integral transform derived in this paper differs from the one previously derived by Bao et al. [1999] by an additional term containing the derivative of the radial component of the orbital velocity associated with the long ocean waves. By carrying out numerical simulations, we show that, in general, this additional term cannot be neglected. Furthermore, we present two new quasi-linear approximations to the nonlinear integral transform relating the ocean wave spectrum to the AT-INSAR phase spectrum.

Ocean wave imaging mechanism by imaging radar

Analytical representations of the high frequency spectra of ocean wave and its variation due to the variation of ocean surface current are derived from the wave-number spectrum balance equation. The ocean surface imaging formulation of real aperture radar (RAR) is given using electromagnetic wave backscattering theory of ocean surface and the modulations of ocean surface winds, currents and their variations to RAR are described. A general representation of the phase modulation induced by the ocean surface motion is derived according to standard synthetic aperture radar (SAR) imaging theory. The detectability of ocean current and sea bottom topography by imaging radar is discussed. The results constitute the theoretical basis for detecting ocean wave fields, ocean surface winds, ocean surface current fields, sea bottom topography, internal wave and so on.

A parametric method of retrieving ocean wave spectra from synthetic aperture radar images

A parametric method that extracts the ocean wave directional spectra from synthetic aperture radar (SAR) image is presented. The 180 degrees ambiguity of SAR image and the loss of information beyond the azimuthal cutoff can be overcome with this method. The ocean wave spectra can be obtained from SAR image directly by using iteration inversion mapping method with forward nonlinear mapping. Some numerical experiments have been made by using ERS-1 satellite SAR imagette data. The ocean wave direction retrieved from SAR imagette data is in agreement with the wind direction from the scatterometer data.

Measurements of ocean wave and current field using dual polarized X-band radar

A new ocean wave and sea surface current monitoring system with horizontally-(HH) and vertically-(VV) polarized X-band radar was developed. Two experiments into the use of the radar system were carried out at two sites, respectively, for calibration process in Zhangzi Island of the Yellow Sea, and for validation in the Yellow Sea and South China Sea. Ocean wave parameters and sea surface current velocities were retrieved from the dual polarized radar image sequences based on an inverse method. The results obtained from dual-polarized radar data sets acquired in Zhangzi Island are compared with those from an ocean directional buoy. The results show that ocean wave parameters and sea surface current velocities retrieved from radar image sets are in a good agreement with those observed by the buoy. In particular, it has been found that the vertically-polarized radar is better than the horizontally-polarized radar in retrieving ocean wave parameters, especially in detecting the significant wave height below 1.0 m.

Remote sensing of ocean waves by along-track interferometric synthetic aperture radar

A new wave retrieval method for the Along-Track Interferometric Synthetic Aperture Radar (AT-InSAR) phase image is presented. The new algorithm, named parametric retrieval algorithm (PRA), uses the full nonlinear mapping relations. It differs from previous retrieval algorithms in that it does not require a priori information about the sea state or the wind vector from scatterometer data. Instead, it combines the observed AT-InSAR phase spectrum and assumed wind vector to estimate the wind sea spectrum. The method has been validated using several C-band and X-band HH-polarized AT-InSAR observations collocated with spectral buoy measurements. In this paper, X-band and C-band HH-polarized AT-InSAR phase images of ocean waves are first used to study AT-InSAR wave imaging fidelity. The resulting phase spectra are quantitatively compared with forward-mapped in situ directional wave spectra collocated with the AT-InSAR observations. Subsequently, we combine the parametric retrieval algorithm (PRA) with X-band and C-band HH-polarized AT-InSAR phase images to retrieve ocean wave spectra. The results show that the ocean wavelengths, wave directions, and significant wave heights estimated from the retrieved ocean wave spectra are in agreement with the buoy measurements.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Numerical simulation and validation of ocean waves measured by an Along-Track Interferometric Synthetic Aperture Radar

A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar (ATI-SAR) image spectra is described. ATI-SAR phase image spectra are calculated for various sea states and radar configurations based on the nonlinear integral transform. The numerical simulations show that the slant range to velocity ratio (R/V), significant wave height to ocean wavelength ratio (H-s/lambda), the baseline (2B) and incident angle (theta) affect ATI-SAR imaging. The ATI-SAR imaging theory is validated by means of Two X-band, HH-polarized ATI-SAR phase images of ocean waves and eight C-band, HH-polarized ATI-SAR phase image spectra of ocean waves. It is shown that ATI-SAR phase image spectra are in agreement with those calculated by forward mapping in situ directional wave spectra collected simultaneously with available ATI-SAR observations. ATI-SAR spectral correlation coefficients between observed and simulated are greater than 0.6 and are not sensitive to the degree of nonlinearity. However, the ATI-SAR phase image spectral turns towards the range direction, even if the real ocean wave direction is 30 degrees. It is also shown that the ATI-SAR imaging mechanism is significantly affected by the degree of velocity bunching nonlinearity, especially for high values of R/V and H-s/lambda.

Remote sensing of ocean waves by polarimetric SAR

A new method to measure ocean wave slope spectra using fully polarimetric synthetic aperture radar (POLSAR) data was developed without the need for a complex hydrodynamic modulation transform function. There is no explicit use of a hydrodynamic modulation transfer function. This function is not clearly known and is based on hydrodynamic assumptions. The method is different from those developed by Schuler and colleagues or Pottier but complements their methods. The results estimated from NASA Jet Propulsion Laboratory (JPL) Airborne Synthetic Aperture Radar (AIRSAR) C-band polarimetric SAR data show that the ocean wavelength, wave direction, and significant wave height are in agreement with buoy measurements. The proposed method can be employed by future satellite missions such as RADARSAT-2.

Experimental investigation on low-temperature fatigue crack propagation in offshore structural steel A131 under random sea ice loading

An apparatus of low-temperature controlling for fatigue experiments and its crack measuring system were developed and used for offshore structural steel A131 under conditions of both low temperature and random sea ice. The experimental procedures and data processing were described, and a universal random data processing software for FCP under spectrum loading was written. Many specific features of random ice-induced FCP which differed with constant amplitude FCP behaviours were proposed and temperature effect on ice-induced FCP was pointed out with an easily neglected aspect in designing for platforms in sea ice emphasized. In the end, differences of FCP behaviours between sea ice and ocean wave were presented.

Depth inversion in coastal water based on SAR image of waves

Wave-number spectrum technique is proposed to retrieve coastal water depths by means of Synthetic Aperture Radar (SAR) image of waves. Based on the general dispersion relation of ocean waves, the wavelength changes of a surface wave over varying water depths can be derived from SAR. Approaching the analysis of SAR images of waves and using the general dispersion relation of ocean waves, this indirect technique of remote sensing bathymetry has been applied to a coastal region of Xiapu in Fujian Province, China. Results show that this technique is suitable for the coastal waters especially for the near-shore regions with variable water depths.

合成孔径雷达提取海面风、浪信息研究

传统海洋测量方法例如岸基观测站、船只和浮标等方式只能对海面进行单点观测，存在很多不足之处：观测点少，只能获得有限的点的资料，无法得到大范围的海面信息；费用较高，无法大范围的密集观测；传统方法受天气影响较大，无法长时间的连续观测；星载合成孔径雷达能全天候、全天时、高分辨率对海面成像，能实现多波段、多极化、多视角得观测海面，提供大范围、高精度的实时动态海面信息。同时，这种全天候、全天时和高分辨率观测海洋的优势是可见光和红外传感器所没有的。总之研究如何从SAR影像中有效地获取海面信息具有重要的科学和实用意义。 自从1978年Seasat卫星发射以来SAR图像就广泛的应用于海洋要素的反演如海面风场、波高、平均周期。其中对海面风场的反演研究的最多，一般的方法是首先对SAR图像进行快速傅立叶变换得到SAR图像谱，通过图像谱的峰值信息能够得到具有180°模糊的风向，利用SAR图像的条纹或者浮标等外部信息来消除180°模糊确定风向，其次把风向和图像的正交后向散射截面数值(NRCS)带入经验函数CMOD4通过迭代计算得到风速。这种方法得到的海面风场需要外部信息的辅助，不利于大范围的业务化的反演海面风场。因此本文试图直接通过SAR图像来反演海面风场而不利用其他外部信息的帮助。2002年3月1日发射的ENVISAT卫星所获得的ASAR图像具有不同于ERS系列的SAR图像的新特点：不同入射角的情况下获得ASAR图片、双极化数据以及可以获得更宽的带幅的图像。双极化数据可以同时地提供同极化和交错极化的影像，两种极化的数据能够增加分辨目标的能力和提供目标更多的信息，这方面的优势也使得利用双极化的数据来消除SAR图像反演风场中的180º模糊问题提供了可能。本文推导了利用双极化的ASAR图像反演海面风场的新函数，该函数是在同极化和交错极化函数的基础上推导出来的，有效的消除了只用一副ASAR图片反演风场所固有的180º模糊现象。风速和风向的反演结果与Quikscat数据之间的均方根误差分别为0.53 m/s和2.21º。该方法与传统方法的比较可以看出新方法与浮标数据以及Quikscat数据符合的更好。 利用SAR图像来反演海浪的波高也是一个研究的比较多的领域。比较传统的方法是由SAR图像得到的海浪谱计算出波高，目前国际上比较流行的SAR图像反演海浪谱的模式有两种：一种是Hasselmann（1991）提出的在Max－Planck Institute（MPI）发展起来的方法，Hasselmann（1996）进行了改进和完善。另一种是Mastenbroek和de Valk（2000）提出的半参数化反演方法。这两种方法的最主要的缺点就是需要引进外部信息(WAM模式结果或者散射计的风的信息)来消除图像所固有的180°方向模糊问题。而本文应用的经验函数方法(CWAVE)不需要引进任何外部信息而直接得到海浪的重要参数－有效波高(Hs)，输入该经验函数的参数主要有：波模式图像的雷达截面、图像方差以及由SAR谱得到的20个参数。这些参数的选择是通过逐步回归方法进行筛选的。CWAVE经验函数的系数是通过6000幅全球分布的ERS-2波模式的图像谱拟合同时同地点的WAM模式结果得到的。利用CWAVE经验函数反演了1998年9月到2000年11月两年多的全球接近一百万的ERS-2 SAR图像的有效波高，利用NOAA浮标数据对反演结果进行了验证，他们之间的相关系数为0.83, 均方根误差为0.61m，偏差为0.02 m；反演结果也与欧洲中长期预报中心(ECMWF)的ERA-40有效波高资料和高度计资料进行了比较，结果表明该方法是通过SAR图像反演Hs的一种有效方法。 SAR的反演结果也应用于有效波高的非线性统计分布的研究。结合动力学和随机统计学原理推导了海面高度、波高和有效波高的非线性统计分布，同时利用了NOAA浮标数据、华师大的波高数据以及SAR的有效波高数据分别对推导出的非线性统计分布函数进行了检验。 SAR的结果也用来反演新的风浪成长关系： ，与已有的风浪成长关系的比较表明该成长关系与已有的结果比较一致。

星载散射计海浪参数提取方法研究

海浪是重要的海洋动力环境参数之一,迄今为止，合成孔径雷达是唯一测量海浪谱的传感器，然而，由于它存在方位波数的截止和能量短缺，限制了其应用。卫星高度计可以测量全球有效波高，但其二维空间分辨率低，其应用也受到了限制。因此，发展一个能够全天候全天时测量海浪参数的有效方法迫在眉睫。 本论文希望利用散射计提取波浪参数,主要研究工作如下： 1、利用二尺度理论模拟了涌浪对C-波段后向散射系数的影响，并与前人在L-波段 和 Ku-波段模拟的结果进行了比较，验证了涌浪对雷达后向散射截面的影响随雷达频率增加而减小，同样也随入射角增大而减小。 2、根据浮标和散射计匹配的数据发现，当海浪参数和雷达入射角给定后，雷达后向散射截面同方位角的关系显示二阶余弦函数关系，为此建立了一种BP神经网络波浪参数反演模式。 3、分别发展了ERS卫星和QuikSCAT卫星散射计资料反演海浪参数的方法，利用NDBC浮标数据分别对它们反演的波浪参数进行了验证。并发现风浪占优势时反演有效波高的结果好于涌浪占优势；C-波段反演有效波高的结果要好于Ku波段,且在Ku波段，水平极化好于垂直极化；波陡反演的结果不受海况影响。 关键词：散射计，风浪，涌浪，有效波高，平均周期，波陡，神经网络

干涉合成孔径雷达海浪遥感理论与应用研究

干涉合成孔径雷达 (Interferometric Synthetic Aperture Radar，InSAR) 是以合成孔径雷达复数据提取的相位为信息源获取地表三维信息和海表散射体运动信息的新型微波成像雷达。 InSAR通过两幅天线同时观测 (单轨模式)，或两次近平行的观测 (重复轨道模式)，获取地面或海面同一景观的复图像对。20世纪90年代以来，InSAR陆地和海洋研究成为微波遥感的热点，广泛应用于地表变形监测、南极冰流测量、地面或海面慢速运动目标检测等领域。 近年来，国际上逐渐应用机载顺轨或交轨干涉合成孔径雷达进行海表面流速测量以及海面波成像机制研究。相对于传统单天线合成孔径雷达 (Synthetic Aperture Radar, SAR)，双天线干涉合成孔径雷达 (InSAR) 测量海表面波有着独特的优势： (1) InSAR复图像的相位近似正比于海面散射体的径向速度，这种内在的成像机制提供了直接测量海表面动态运动的机会。 (2) 真实孔径雷达调制传递函数几乎对InSAR相位图像没有影响，而对传统SAR图像影响较大。 基于干涉合成孔径雷达测量海浪的优势，本文做了一些干涉合成孔径雷达海浪遥感理论与应用研究工作，主要内容大致可归纳如下： (1)基于新建立的顺轨干涉合成孔径雷达 (Along-Track Interferometric Synthetic Aperture Radar，ATI-SAR) 相位谱与海浪谱之间的非线性映射关系，通过数值模拟研究了不同雷达参数和海况参数对应的ATI-SAR相位谱。数值模拟结果表明：距离速度比率、雷达入射角、天线间距和有效波高和波长比率是影响ATI-SAR海浪成像的重要因素。进一步，利用机载X波段水平极化相位图像和机载C波段水平极化相位图像谱结合方向波骑士浮标测量的海浪方向谱验证了ATI-SAR相位谱与海浪谱之间的非线性映射关系。结果显示用前向映射关系计算的相位谱与实际观测的相位谱较为一致，二者相关系数总体大于0.6，而且对成像非线性不敏感. (2)建立了包含海表面高度和速度聚束的交轨干涉合成孔径雷达 (Across-Track Interferometric Synthetic Aperture Radar，XTI-SAR) 涌浪干涉相位模型，得到了涌浪成像的解析表达式，进一步研究了XTI-SAR沿方位向传播的涌浪成像机制。定义二次谐波振幅与基波振幅比率来表征成像非线性，通过比较XTI-SAR和ATI-SAR相位的二阶调和分量，分析不同海况和干涉SAR参数情况下的数值模拟，结果表明：当速度聚束弱时，XTI-SAR相位比ATI-SAR相位具有较强的非线性，ATI-SAR比XTI-SAR更适合测量海浪。当速度聚束强时，XTI-SAR相位比ATI-SAR相位具有较弱的非线性，XTI-SAR比ATI-SAR更适合测量海浪。 (3)基于包含海表面高度和速度聚束的交轨干涉合成孔径雷达 (XTI-SAR) 涌浪干涉相位模型，结合多维高斯变量的特征函数方法建立了新的XTI-SAR相位谱与海浪谱非线性积分变换。新积分变换不同于Bao (1999) 建立的积分变换，两者形式上区别在于新积分变换中包含了长波径向轨道速度一阶倒数项。数值模拟显示：通常情况下，长波径向轨道速度一阶倒数项不能忽略。进一步，我们针对不同雷达参数和海况结合新非线积分变换对XTI-SAR海浪成像进行了数值模拟，结果表明：同顺轨干涉合成孔径雷达 (ATI-SAR) 海浪成像一致，距离速度比率 和有效波高与波长比率 是影响XTI-SAR海浪成像的重要因子。 (4)基于新的ATI-SAR相位谱与海浪谱之间的非线性映射关系，发展了利用ATI-SAR相位图像反演海浪方向谱的参数化反演模式，并由此得到海浪波长、波向和有效波高。反演结果与现场浮标观测结果比较一致。相对于其它反演模式，参数化反演模式的优点在于：(1) 不需要任何附加信息如初猜海浪谱、散射计提供的风速风向等信息。 (2) 不需要对相位图像进行辐射定标，可以由反演的海浪谱直接计算有效波高。(3) 反演结束后还可以得到成像区域的局地风速信息。因此，参数化反演模式可以实现风、浪信息的联合反演。

The induced flow field by internal solitary wave and its action on cylindrical piles in the stratified ocean

The induced flow fields by internal solitary waves and its actions on cylindrical piles in density stratified ocean with a basic density profile and a basic velocity profile are investigated. Some results, such as the time evolution of flow fields and hydrodynamic forces on the piles are yielded both by theoretical analysis and numerical calculation for general and specific cases. Several kinds of ambient sea conditions of the South China Sea are specified for numerical simulation. Moreover, the effects of relative density difference, depth ratio and wave steepness on maximal total force and total torque are analyzed.