Directional wave information from the SeaSonde

This paper describes methods used for the derivation of wave information from SeaSonde data, and gives examples of their application to measured data. The SeaSonde is a compact high-frequency (HF) radar system operated from the coast or offshore platform to produce current velocity maps and local estimates of the directional wave spectrum. Two methods are described to obtain wave information from the second-order radar spectrum: integral inversion and fitting with a model of the ocean wave spectrum. We describe results from both standard- and long-range systems and include comparisons with simultaneous measurements from an S4 current meter. Due to general properties of the radar spectrum common to all HF radar systems, existing interpretation methods fail when the waveheight exceeds a limiting value defined by the radar frequency. As a result, standard- and long-range SeaSondes provide wave information for different wave height conditions because of their differing radar frequencies. Standard-range SeaSondes are useful for low and moderate waveheights, whereas long-range systems with lower transmit frequencies provide information when the waves are high. We propose a low-cost low-power system, to be used exclusively for local wave measurements, which would be capable of switching transmit frequency when the waveheight exceeds the critical limit, thereby allowing observation of waves throughout the waveheight range.     

Measurement of ocean wave spectra using narrow-beam HE radar

A data interpretation algorithm is developed to extract ocean wave information from HF radar backscatter observed by a narrow-beam antenna system. The basis of this measurement is the inversion of the integral equation representing the second-order radar cross section of the ocean surface. This equation is numerically inverted by approximating it as a matrix equation and pseudoinverting the kernel matrix using a singular value decomposition. As a test of this algorithm, comparisons are made between wave spectrum estimates obtained from a WAVEC buoy and a pair of 25.4-MHz ground wave radars, using data collected during the 1986 Canadian Atlantic Storms Program (CASP). Overall, the results of this experiment have been positive and have demonstrated both the basic feasibility of the inversion algorithm and the wave sensing capability of HF radar. For example, significant wave height estimates deduced by two radars differed from the buoy, in an absolute value sense, by only 0.12 m on average. When using only one radar, the mean difference of this important parameter from the buoy was a reasonable 0.33 m     

HF radar data quality requirements for wave measurement

HF radar wave measurements are presented focussing on theoretical limitations, and thus radar operating parameters, and quality control requirements to ensure robust measurements across a range of sea states. Data from three radar deployments, off the west coast of Norway, Celtic Sea and Liverpool Bay using two different radar systems, WERA and Pisces, and different radio frequency ranges, are used to demonstrate the wave measurement capability of HF radar and to illustrate the points made. Aspects of the measurements that require further improvements are identified. These include modifications to the underlying theory particularly in high sea states, identification and removal of ships and interference from the radar signals before wave processing and/or intelligent partitioning to remove these from the wave spectrum. The need to match the radio frequency to the expected wave peak frequency and waveheight range, with lower radio frequencies performing better at higher waveheights and lower peak frequencies and vice versa, is demonstrated. For operations across a wide range of oceanographic conditions a radar able to operate at more than one frequency is recommended for robust wave measurement. Careful quality control is needed to ensure accurate wave measurements.     

Extraction of Ocean Wave Spectra From Simulated Noisy Bistatic High-Frequency Radar Data

An algorithm is developed for the inversion of bistatic high-frequency (HF) radar sea echo to give the nondirectional wave spectrum. The bistatic HF radar second-order cross section of patch scattering, consisting of a combination of four Fredholm-type integral equations, contains a nonlinear product of ocean wave directional spectrum factors. The energy inside the first-order cross section is used to normalize this integrand. The unknown ocean wave spectrum is represented by a truncated Fourier series. The integral equation is then converted to a matrix equation and a singular value decomposition (SVD) method is invoked to pseudoinvert the kernel matrix. The new algorithm is verified with simulated radar Doppler spectrum for varying water depths, wind velocities, and radar operating frequencies. To make the simulation more realistic, zero-mean Gaussian noise from external sources is also taken into account     

高频地波雷达海面有效波高探测实验研究

利用安装于福建龙海的OSMAR071高频地波雷达和位于雷达波束范围内金门料罗湾口的波浪浮标在2008年11月1日至2009年4月30日半年期间的观测结果,对Barrick波高模型进行改进和模型系数拟合、标定,讨论了改进模型系数的稳定性。结果表明,该模型能适应噪声和干扰等因素对宽波束雷达有效波高探测结果的影响。雷达观测反演回报的有效波高与浮标观测结果对比,二者时间序列的均方根误差为0.39m,相关系数为0.67。     

The role of the gravity-wave dispersion relation in HF radar measurements of the sea surface

Recent experimental and theoretical findings raise interesting questions about the applicability of the normal gravity-wave dispersion relation at wave frequencies that exceed the spectral peak frequency. The use of the dispersion relation in analysis of HF radar Doppler sea echo is examined in this paper. Drawing on the results of perturbation theory for wave-wave nonlinear interactions, we show that this relation, so essential to echo interpretation in terms of current and wave information, can be employed with no degradation in accuracy for current measurement when the dominant wave frequency is considerably less (by as much as 10) than the radar Bragg resonance frequency. This finding is supported by comparisons of currents measured by HF radar with "surface truth;" the first-order echo must only be identifiable in order to be used accurately. Wave-height directional spectral information can be extracted from the second-order echo at a given radar frequency up to the point (in wave height) where the perturbation solution employed in the inversion process fails; then a lower radar frequency must be used. On the other hand, most conventional wave measuring instruments should not use the dispersion relation for interpretation of data well beyond the spectral peak, because they do not observe wave height as a function of both space and time independently, as does HF radar.     

Operational Wave, Current, and Wind Measurements With the Pisces HF Radar

This paper presents results of a trial of a Pisces HF radar system aimed at assessing its use as a component of a wave-monitoring network being installed around the coasts of England and Wales. The radar system has been operating since December 2003 and the trial continued to June 2005. The data have been processed in near-real time and displayed on a website. Radar measurements of the directional spectrum and derived parameters are compared with those measured with a directional waverider and with products from the Met Office, United Kingdom, operational wave model. Radar measurements of currents and winds are also compared with Met Office model products and, in the case of winds, with the QuikSCAT scatterometer. Statistics on data availability and accuracy are presented. The results demonstrate that useful availability and accuracy in wave and wind parameters are obtained above a waveheight threshold of 2 m and at ranges up to 120 km at the radar operating frequencies (7-10 MHz) used. Waveheight measurements above about 1 m can be made with reasonable accuracy (e.g., mean difference of 2.5% during January-February 2004). Period and direction parameters in low seas are often contaminated by noise in the radar signal. The comparisons provide some evidence of wave model limitations in offshore wind and swell conditions     

利用高频雷达海面回波中奇异峰估计浪高的方法

The popular methods to estimate wave height with high-frequency(HF) radar depend on the integration over the second-order spectral region and thus may come under from even not strong external interference. To improve the accuracy and increase the valid detection range of the wave height measurement, particularly by the smallaperture radar, it is turned to singular peaks which often exceed the power of other frequency components. The power of three kinds of singular peaks, i.e., those around ±1,±2~(1/2) and ±1(2~(1/2)) times the Bragg frequency, are retrieved from a one-month-long radar data set collected by an ocean state monitoring and analyzing radar,model S(OSMAR-S), and in situ buoy records are used to make some comparisons. The power response to a wave height is found to be described with a new model quite well, by which obvious improvement on the wave height estimation is achieved. With the buoy measurements as reference, a correlation coefficient is increased to 0.90 and a root mean square error(RMSE) is decreased to 0.35 m at the range of 7.5 km compared with the results by the second-order method. The further analysis of the fitting performance across range suggests that the peak has the best fit and maintains a good performance as far as 40 km. The correlation coefficient is 0.78 and the RMSE is 0.62 m at 40 km. These results show the effectiveness of the new empirical method, which opens a new way for the wave height estimation with the HF radar.     

Comparison of inversion algorithms for HF radar wave measurements

All ocean wave components contribute to the second-order scattering of a high-frequency (HF) radio wave by the sea surface. It is therefore theoretically possible to estimate the ocean wave spectrum from the radar backscatter. To extract the wave information, it is necessary to solve the nonlinear integral equation that describes the relationship between the backscatter spectrum and the ocean wave directional spectrum. Different inversion techniques have been developed for this problem by different researchers, but there is at present no accepted “best” method. This paper gives an assessment of the current status of two methods for deriving sea-state information from HF radar observations of the sea surface. The methods are applied to simulated data and to an experimental data set with sea-truth being provided by a directional wave buoy     

X-波段雷达近海海浪频谱反演的神经网络模型

X-波段雷达作为国内海浪观测的一种新工具,在海浪频谱获取和有效波高反演方面仍存在较多问题.本文利用非线性回归方法,将现场实测浮标数据频谱和雷达一维图像谱分别与标准频谱模型进行拟合,发现浮标频谱和一维图像谱具有标准频谱的特征,能够较准确地获取相应的谱参数.提出了建立由雷达一维图像谱参数反演海浪频谱参数的神经网络模型,同时在模型中加入影像序列信噪比,进而反演有效波高,并将反演结果与现场实测数据和传统算法(建立影像序列信噪比与有效波高之间的线性回归方程)进行了对比,结果表明,获取谱参数的误差和反演有效波高的平均误差在20％以内,而传统算法计算有效波高平均误差在20％以上.     

基于SVM回归模型的SAR图像有效波高估测

A new method for estimating significant wave height(SWH) from advanced synthetic aperture radar(ASAR) wave mode data based on a support vector machine(SVM) regression model is presented. The model is established based on a nonlinear relationship between σ0, the variance of the normalized SAR image, SAR image spectrum spectral decomposition parameters and ocean wave SWH. The feature parameters of the SAR images are the input parameters of the SVM regression model, and the SWH provided by the European Centre for Medium-range Weather Forecasts(ECMWF) is the output parameter. On the basis of ASAR matching data set, a particle swarm optimization(PSO) algorithm is used to optimize the input kernel parameters of the SVM regression model and to establish the SVM model. The SWH estimation results yielded by this model are compared with the ECMWF reanalysis data and the buoy data. The RMSE values of the SWH are 0.34 and 0.48 m, and the correlation coefficient is 0.94 and 0.81, respectively. The results show that the SVM regression model is an effective method for estimating the SWH from the SAR data. The advantage of this model is that SAR data may serve as an independent data source for retrieving the SWH, which can avoid the complicated solution process associated with wave spectra.     

Data assimilation of partitioned HF radar wave data into Wavewatch III

In this study the assimilation of HF radar data into a high resolution, coastal Wavewatch III model is investigated. An optimal interpolation scheme is used to assimilate the data and the design of a background error covariance matrix which reflects the local conditions and difficulties associated with a coastal domain is discussed. Two assimilation schemes are trialled; a scheme which assimilates mean parameters from the HF radar data and a scheme which assimilates partitioned spectral HF radar data. This study demonstrates the feasibility of assimilating partitioned wave data into a coastal domain. The results show that the assimilation schemes provide satisfactory improvements to significant wave heights but more mixed results for mean periods. The best improvements are seen during a stormy period with turning winds. During this period the model is deficient at capturing the change in wave directions and the peak in the waveheights, while the high sea state ensures good quality HF radar data for assimilation. The study also suggests that there are both physical and practical advantages to assimilating partitioned wave data compared to assimilating mean parameters for the whole spectrum.     

Measurement of ocean wave spectra using a ship-mounted HF radar

The work describes an inversion algorithm for HF radar measurement of nondirectional wave spectra using an omnidirectional receive/transmit antenna. Such a radar would be suitable for deployment on a stationary ship or drill rig. In this approach, wave information is extracted from the radar observations by numerically inverting the integral equation representing the backscatter return from the ocean. Test results of this technique applied to data collected using a 25.4-MHz radar installed on a ship have been very positive. For the two measurements collected, there is a high degree of correlation between the radar wave estimates and those of a WAVE-TRACK buoy     

Detection of nonlinear waves and their contribution to ocean wave spectra Part I: Theoretical consideration

This is a Part I of a paper of nonlinearities of wind waves in the deep open ocean. First, considerations are given in order to verify the theoretical expression for bound waves from observed data. We compare the contribution of bound waves and double Bragg scattering to the second-order scattering, and we show that the contribution of bound waves is larger, and that bound waves can be detected by measuring the Doppler spectra of HF (high-frequency) radio wave scattering from the sea surface. Moreover, if the theory of the HF radio wave scattering from the sea surface is verified, so is the second-order perturbation theory for bound waves. Then, the contributions of bound waves to ocean wave spectra are investigated on the basis of the nonlinear theory. The bound waves are shown to modify frequency spectra and wave directional distributions at higher frequencies, and it is shown that although the modifications of frequency spectra are smaller for a two-dimensional field case than for a one-dimensional field case, they are not negligible at higher frequencies. On the other hand, the modifications of wave directional distributions are shown to be significant at higher frequencies. These discussions become significant only when bound wave predictions are verified in the open ocean. Consequently, it is shown that nonlinearities of water waves are important in considering both radio wave scattering from the sea surface and the detailed structures of ocean wave spectra at high frequencies.     

Directional sea spectrum determination using HF Doppler radar techniques

Second-order features in HF radar Doppler spectral data are compared with a theoretical model of the radar spectrum. The model is the corner reflector double-scatter model which employs a more realistic directional sea spectrum model than those used in earlier works. It includes a frequency-dependent angular spreading function and assumes the existence of spectral energy over a full360degarising from an apparent second-order wave-wave interaction. Comparison is made with ground wave data collected at the NRL/NOAA/ITS San Clemente Island HF radar.     

便携式高频地波雷达台湾海峡浪高观测

As an important equipment for sea state remote sensing, high frequency surface wave radar(HFSWR) has received more and more attention. The conventional method for wave height inversion is based on the ratio of the integration of the second-order spectral continuum to that of the first-order region, where the strong external noise and the incorrect delineation of the first- and second-order Doppler spectral regions due to spectral aliasing are two major sources of errors in the wave height. To account for these factors, two more indices are introduced to the wave height estimation, i.e., the ratio of the maximum power of the second-order continuum to that of the Bragg spectral region(RSCB) and the ratio of the power of the second harmonic peak to that of the Bragg peak(RSHB). Both indices also have a strong correlation with the underlying wave height. On the basis of all these indices an empirical model is proposed to estimate the wave height. This method has been used in a three-months long experiment of the ocean state measuring and analyzing radar, type S(OSMAR-S), which is a portable HFSWR with compact cross-loop/monopole receive antennas developed by Wuhan University since 2006. During the experiment in the Taiwan Strait, the significant wave height varied from 0 to 5 m. The significant wave heights estimated by the OSMAR-S correlate well with the data provided by the Oceanweather Inc. for comparison, with a correlation coefficient of 0.74 and a root mean square error(RMSE) of 0.77 m. The proposed method has made an effective improvement to the wave height estimation and thus a further step toward operational use of the OSMAR-S in the wave height extraction.     

A Spectral Approach for Determining Altimeter Wind Speed Model Functions

We propose a new analytical algorithm for the estimation of wind speeds from altimeter data using the mean square slope of the ocean surface, which is obtained by integration of a widely accepted wind-wave spectrum including the gravity-capillary wave range. It indicates that the normalized radar cross section depends not only on the wind speed but also on the wave age. The wave state effect on the altimeter radar return becomes remarkable with increasing wind speed and cannot be neglected at high wind speeds. A relationship between wave age and nondimensional wave height based on buoy observational data is applied to compute the wave age using the significant wave height of ocean waves, which could be simultaneously obtained from altimeter data. Comparison with actual data shows that this new algorithm produces more reliable wind speeds than do empirical algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于SAR图像速度聚束调制的海浪反演研究

本文首先对合成孔径雷达（SAR）海浪成像中的3种调制（倾斜调制、流体力学调制与速度聚束调制）的影响进行了对比分析,结果显示:速度聚束调制对SAR图像的影响最为显著。另外,由于SAR图像中固有相干斑噪声的存在,较低波数范围的噪声难以滤除或抑制,利用经典MPI方法反演海浪谱会造成低波数范围谱值偏大。基于此,本文借鉴经典MPI海浪谱反演算法,建立了基于速度聚束调制的海浪方位向斜率谱和有效波高的反演算法。通过将经典MPI方法、同极化调制法及本文算法等3种海浪反演方法所得有效波高与浮标数据进行比较,结果显示:本文方法反演得到的海浪有效波高与浮标数据获得的有效波高之间的均方误差为0.79 m,为3种方法中最小。     

CODAR wave measurements from a North Sea semisubmersible

CODAR, a high-frequency (HF) compact radar system, was operated continuously over several weeks aboard the semisubmersible oil platform Treasure Saga for the purpose of wave-height directional measurement and comparison. During North Sea winter storm conditions, the system operated at two different frequencies, depending on the sea state. Wave data are extracted from the second-order backscatter Doppler spectrum produced by nonlinearities in the hydrodynamic wave/wave and electromagnetic wave/scatter interactions. Because the floating oil rig itself moves in response to long waves, a technique has been developed and successfully demonstrated to eliminate to second order the resulting phase-modulation contamination of the echo, using separate accelerometer measurement of the platform's lateral motions. CODAR wave height, mean direction, and period are compared with data from a Norwegian directional wave buoy; in storm seas with wave heights that exceeded 9 m, the two height measurements agreed to within 20 cm RMS, and the mean direction to better than 15° RMS     

基于VMD对SAR海洋内波参数的自动反演

经验模态分解(empirical mode decomposition,简称EMD)是反演海洋内波参数的有效方法之一,但由于EMD存在模态混叠等问题,对海洋内波进行参数反演时会产生一定误差。相比较于EMD,变分模态分解(variational mode decomposition,简称VMD)能够有效地抑制模态混叠现象。为了更好地对海洋内波进行参数反演,提出了一种基于VMD对合成孔径雷达(synthetic aperture radar,简称SAR)遥感图像中的内波参数进行自动反演的方法。该方法先对SAR图像进行Canny处理,获取图像中的内波条纹信息,再根据内波传播方向自动选取灰度剖面;然后利用集合经验模态分解(ensemble empirical mode decomposition,简称EEMD)信号特征自适应分解模态函数的特点,再将分解得到的有效模态数作为VMD中参数K的参考值;最后利用VMD分解后的数据进行内波参数反演。试验结果表明:通过对Canny预处理后的条纹信息进行灰度剖面自动选取,解决了人为选取剖面所可能导致的误差;通过对剖面信号进行VMD处理不仅解决了EMD模态混叠的问题,成功地反演出内波的前导波振幅,而且所反演的结果与EEMD反演参数以及实测资料数据吻合得很好。