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.

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.

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 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.

Validation of RADARSAT-2 fully polarimetric SAR measurements of ocean surface waves

C band RADARSAT-2 fully polarimetric (fine quad-polarization mode, HH+VV+HV+VH) synthetic aperture radar (SAR) images are used to validate ocean surface waves measurements using the polarimetric SAR wave retrieval algorithm, without estimating the complex hydrodynamic modulation transfer function, even under large radar incidence angles. The linearly polarized radar backscatter cross sections (RBCS) are first calculated with the copolarization (HH, VV) and cross-polarization (HV, VH) RBCS and the polarization orientation angle. Subsequently, in the azimuth direction, the vertically and linearly polarized RBCS are used to measure the wave slopes. In the range direction, we combine horizontally and vertically polarized RBCS to estimate wave slopes. Taken together, wave slope spectra can be derived using estimated wave slopes in azimuth and range directions. Wave parameters extracted from the resultant wave slope spectra are validated with colocated National Data Buoy Center (NDBC) buoy measurements (wave periods, wavelengths, wave directions, and significant wave heights) and are shown to be in good agreement.

On SAR wind speed ambiguities and related geophysical model functions

Recent investigations show that normalized radar cross sections for C-band microwave sensors decrease under high wind conditions with certain incident angles instead of increase, as is the case for low to moderate wind speeds. This creates the problem of ambiguities in high wind speed retrievals from synthetic aperture radar (SAR). In the present work, four geophysical model functions (GMFs) are studied, namely the high wind C-band model 4 (CMOD4HW), C-band model 5 (CMOD5), the high wind vertical polarized GMF (HWGMF_VV), and the high wind horizontal polarized GMF (HWGMF_HH). Our focus is on model behaviours relative to wind speed ambiguities. We show that, except for CMOD4HW, the other GMFs exhibit the wind speed ambiguity problem. To consider this problem in high wind speed retrievals from SAR, we focus on hurricanes and propose a method to remove the speed ambiguity using the dominant hurricane wind structure.

Speed ambiguity in hurricane wind retrieval from SAR imagery

Under strong ocean surface wind conditions, the normalized radar cross section of synthetic aperture radar (SAR) is dampened at certain incident angles, compared with the signals under moderate winds. This causes a wind speed ambiguity problem in wind speed retrievals from SAR, because two solutions may exist for each backscattered signal. This study shows that the problem is ubiquitous in the images acquired by operational space-borne SAR sensors. Moreover, the problem is more severe for the near range and range travelling winds. To remove this ambiguity, a method was developed based on characteristics of the hurricane wind structure. A SAR image of Hurricane Rita (2005) was analysed to demonstrate the wind speed ambiguity problem and the method to improve the wind speed retrievals. Our conclusions suggest that a speed ambiguity removal algorithm must be used for wind retrievals from SAR in intense storms and hurricanes.

Near-Space Wide-Swath Radar Imaging With Multiaperture Antenna

Near-space, defined as the altitude region between 20 and 100 km, offers many capabilities that are not accessible for low Earth-orbit (LEO) satellites or airplanes because it is above storm and not constrained by orbital mechanics and high fuel consumption. Hence, a high flying speed can be obtained for the maneuvering vehicles operating in near-space. This offers a promising solution to simultaneous high-resolution and wide-swath synthetic aperture radar (SAR) imaging. As such, one near-space wide-swath SAR imaging technique is presented in this letter. The system configuration, signal model, and imaging scheme are described. An example near-space SAR system is designed, and its imaging performance is analyzed. Simulation results show that near-space maneuvering vehicle SAR indeed seems to be a promising solution to wide-swath SAR imaging.

A new wind vector algorithm for C-band SAR

Ocean wind speed and wind direction are estimated simultaneously using the normalized radar cross sections or' corresponding to two neighboring (25-km) blocks, within a given synthetic aperture radar (SAR) image, having slightly different incidence angles. This method is motivated by the methodology used for scatterometer data. The wind direction ambiguity is removed by using the direction closest to that given by a buoy or some other source of information. We demonstrate this method with 11 EN-VISAT Advanced SAR sensor images of the Gulf of Mexico and coastal waters of the North Atlantic. Estimated wind vectors are compared with wind measurements from buoys and scatterometer data. We show that this method can surpass other methods in some cases, even those with insufficient visible wind-induced streaks in the SAR images, to extract wind vectors.

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.

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.

Wind-vector estimation for RADARSAT-1 SAR images: Validation of wind-direction estimates based upon geometry diversity

In this letter, a new wind-vector algorithm is presented that uses radar backscatter sigma(0) measurements at two adjacent subscenes of RADARSAT-1 synthetic aperture radar (SAR) images, with each subscene having slightly different geometry. Resultant wind vectors are validated using in situ buoy measurements and compared with wind vectors determined from a hybrid wind-retrieval model using wind directions determined by spectral analysis of wind-induced image streaks and observed by colocated QuikSCAT measurements. The hybrid wind-retrieval model consists of CMOD-IFR2 [applicable to C-band vertical-vertical (W) polarization] and a C-band copolarization ratio according to Kirchhoff scattering. The new algorithm displays improved skill in wind-vector estimation for RADARSAT-1 SAR data when compared to conventional wind-retrieval methodology. In addition, unlike conventional methods, the present method is applicable to RADARSAT-1 images both with and without visible streaks. However, this method requires ancillary data such as buoy measurements to resolve the ambiguity in retrieved wind direction.

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。

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.

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources. (c) 2006 Elsevier GmbH. All rights reserved.