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.     

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.     

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     

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.     

Mapping wind by the first-order Bragg scattering of broad-beam high-frequency radar

Mapping wind with high-frequency(HF) radar is still a challenge. The existing second-order spectrum based wind speed extraction method has the problems of short detection distances and low angular resolution for broad-beam HF radar. To solve these problems, we turn to the first-order Bragg spectrum power and propose a space recursion method to map surface wind. One month of radar and buoy data are processed to build a wind spreading function model and a first-order spectrum power model describing the relationship between the maximum of first-order spectrum power and wind speed in different sea states. Based on the theoretical propagation attenuation model, the propagation attenuation is calculated approximately by the wind speed in the previous range cell to compensate for the first-order spectrum in the current range-azimuth cell. By using the compensated first-order spectrum, the final wind speed is extracted in each cell. The first-order spectrum and wind spreading function models are tested using one month of buoy data, which illustrates the applicability of the two models. The final wind vector map demonstrates the potential of the method.     

Statistical characteristics of individual waves in laboratory wind waves I. Individual wave spectra and similarity structure

Statistical characteristics of individual waves in laboratory wind waves have been studied by use of a wind-wave tunnel. The individual waves are defined by actual undulations of the water surface at any instant, and are characterized by concentrated shearing stress and strong vorticity at their crests. A conspicuous self-similarity structure is found in the individual wave field. The similarity manifests itself as a simple spectral form, and as the statistical 3/2-power law between nondimensional wave height and wave period, and further as the -1/2-power relationship between nondimensional phase speed and frequency, for waves of the high frequency side. The normalized energy spectrum, specially defined for individual waves, has a form practically equivalent to the traditional spectrum for component waves in the main frequency range from 0.7 to 1.5 in the frequency normalized by the peak frequency, but does not have secondary peaks at harmonics. The phase speed of individual waves also coincides with that of component waves in the main frequency range.     

Measurement of oceanic wind speed from HF sea scatter by skywave radar

Remote measurements of the spatial mean ocean wind speeds were obtained using Doppler spectra resolved to 0.08 Hz from high-resolution HF skywave-radar backscatter measurements of the ocean surface. A standard deviation of 2.4 m/s resulted from the correlation of observed winds over the ocean and the broadening of the Doppler spectra in the vicinity of the higher first-order Bragg line. This broadening, for Doppler spectra unperturbed by the ionospheric propagation, is proportional to the increase in power caused by higher order hydrodynamic and electromagnetic effects in the vicinity of the Bragg line and inversely proportional to the square root of the radio frequency. A lower bound on the measure of wind speed was established at 5 m/s by the low resolution spectral processing and low second-order power. An upper limit is suggested by the steep slope in the region of the sea backscatter spectrum outside the square root of two times the first-order Bragg line Doppler.     

Frequency management support for remote sea-state sensing using the JINDALEE skywave radar

Successful operation of a skywave (over-the-horizon, OTH) radar in a remote sea-state sensing mode is critically dependent upon the application of comprehensive frequency management techniques. In addition to the problem of selecting a frequency yielding an adequate signal-to-noise ratio in the geographical area under investigation, attention must be paid to minimization of ionospheric multimode and other phenomena capable of distorting or convoluting the sea backscatter spectrum. This paper describes the manner in which these problems have been addressed in the JINDALEE skywave radar, and relates the practical difficulties inherent in the task of frequency management in support of an OTH radar involved in sea-state sensing. Measurement techniques include backscatter and oblique-incidence sounding, HF spectral surveillance, and a low-powered frequency-agile "miniradar" capable of operating in either a conventional backscatter or alternate oblique-incidence mode. In addition to providing the main radar with real-time frequency management advice, a principal emphasis has been the acquisition of a synoptic data base suitable for off-line statistical analysis.     

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.     

Quantitative seafloor characterization using a bathymetric sidescansonar

Bathymetry and backscatter measurements from a 120-kHz phase-difference sonar are analysed in terms of statistical and spectral characteristics. Data from a multisensor, multiscale survey of the Juan de Fuca Ridge are compared across three distinct geological provinces: sediment pond, ridge flank, and axial valley. The detrended bathymetry follows a Gaussian distribution; the power spectral density can be approximately described by a power law. The composite multiscale power spectrum demonstrates a similar slope spanning a spatial frequency range from about 0.005 to 50 cycles/m, corresponding to a range of geological features from a few hundred meters down to several centimeters. The backscattering strength and grazing-angle dependencies agree with previous empirical studies; data from a sediment-pond region are shown to match theoretical predictions of the composite-roughness model. Histograms of the echo amplitude are characterized by a multimodal Rayleigh probability density function. For all analyses, the data show distinct differences among the three provinces     

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.     

Experimental research on the statistical characteristics of radar signal spikes at small grazing angles

The results of research into the characteristics of spikes in a radar signal scattered by the sea surface at small grazing angles and horizontal polarization of radiation are reported. Studies were carried out at wind speeds of 4.4–10.3 m s^–1. It is shown that the experimental distribution of the amplitudes of the radar signal spikes is described well by an exponential function. The distribution of the amplitudes of spikes, normalized to their average value for the measurement cycle, is of universal character. It does not depend on the observational conditions. The relationship between the average level of signal and the wind speed agrees with the results of computation on the model suggested.Translated by Mikhail M. Trufanov.     

Studies of backscattered sea return with a CW, dual-frequency,X-band radar

A coherent, CW, dual-frequency,X-band radar was used to study microwave sea return from the Chesapeake Bay. It is shown that the product of the backseattered fields depends strongly on long surface wave properties. In particular, a sharp line is found in the product power spectrum whose frequency is that of the water wave whose wavelength is in resonance with the spatial period of the beat frequency between the two transmitted signals and whose wave vector is parallel to the horizontal line of sight. Thus, gravity wave dispersion relations can be obtained with the system. Furthermore, the degree of modulation of short waves by long ones is given by the intensity of the line. A broad background corresponding to the convolution of the single-frequency Doppler spectra is also seen in the product power spectrum. These results are shown to be interpretable by composite surface scattering theory.     

An Empirical Method to Derive Ocean Waves From Second-Order Bragg Scattering: Prospects and Limitations

High-frequency (HF) radar wave processing is often based on the inversion of the Barrick-Weber equations, introduced in 1977. This theory reaches its limitations if the length of the Bragg-scattering wave raises to the order of the significant waveheight, because some assumptions are no longer met. In this case, the only solution is moving to lower radar frequencies, which is not possible or desirable in all cases. This paper describes work on an empirical solution which intends to overcome this limitation. However, during high sea state, the first-order Bragg peaks sometimes could not be clearly identified which avoids the access to the second-order sidebands. These cases cause problems to the algorithm which have not been solved yet and currently limit the maximum significant waveheight to about the same values as reported for the integral inversion method. The regression parameters of the empirical solution calibrated from the European Radar Ocean Sensing (EuroROSE) data set are constant values for the complete experiment and when applied to the HF radar data they reconstruct the measurements by a colocated wave buoy quite well. When including a radar-frequency-dependent scaling factor to the regression parameters, the new algorithm can also be used at different radar frequencies. The second-order frequency bands used for the empirical solution are sometimes disturbed by radio interference and ship echoes. Investigations are presented to identify and solve these situations     

Tidal Current Measurements Using VHF Radar and ADCP in the Normand Breton Gulf: Comparison of Observations and Numerical Model

Performance and operational feasibility of very high-frequency (VHF) Doppler radar have been demonstrated in a region dominated by strong tidal currents. An analysis of remote measurements of sea surface currents acquired by Courants de Surface MEsureacutes par Radar (COSMER)-pulsed Doppler radar during Evaluation et Preacutevision de l'Environnement Littoral (EPEL) experiment (supported by the French Navy) is presented in this paper. The VHF COSMER radar was deployed to provide continuous sea surface current measurements within an area of about 25 km times 25 km in the Normand Breton Gulf, France. This paper presents VHF measurement comparisons with observations such as acoustic Doppler current profiler (ADCP), as well as comparisons with numerical model TELEMAC 2-D. Results of tidal waves extraction, using harmonic analysis and residual currents, are shown in this paper. We also present a case where radar method is limited, due to the presence of additional peaks in the Doppler spectrum     

Spectrum of mesoscale sea level oscillations in the northern Black Sea: Tides,seiches, and inertial oscillations

Long-term data from 23 tide gauges were used to analyze the spectrum of mesoscale sea level variability of the Black Sea. The tides have sharp spectral peaks, and they are detected at diurnal and semidiurnal frequencies for all stations. A local wide spectral peak associated with inertial oscillations is located between the diurnal and semidiurnal tidal peaks. This peak is well known in the spectra of the current velocity variations of the Black Sea, but in the sea level spectrum it has been identified for the first time. At frequencies of >3 cpd, sea level spectra of the Black Sea have (1) wide maxima in the continuous spectrum, which correspond to the main eigenmodes of the sea with periods of 5.6, 4.8, 4.1, and 3.1 h, and (2) sharp peaks of radiational harmonics S₃, S₄, S₅, and S₆. The periods of seiches calculated in this study are close to the periods of eigenmodes of the Black Sea, obtained by the numerical modeling of other authors. The main factors influencing the formation of radiational tides in the Black Sea are presumably breezes and runoff from large rivers. The significant predominance of a harmonic with frequency of 5 cpd (S₅) over other radiational harmonics is caused by the influence of an eigenmode, with a frequency of about 5 cpd. The proximity of the periods of these oscillations leads to resonant amplification and to a corresponding increase in amplitude of the radiational harmonic S₅.     

Range and Doppler information from fourth-order spectra

In an active sonar system setting, a novel method is evaluated that extracts range and Doppler information from a Doppler-spread active sonar echo. The Doppler spreading is based on H. Van Trees' (1971) Gaussian amplitude modulating model, and the new method is based on the Fourier transform of a special case of the fourth-order cumulant. Specifically, from the envelope of the Gaussian amplitude modulated echo of a transmitted coded pulse train, the second-order spectrum and the Fourier transform of a special case of the fourth-order cumulant are derived and analyzed for this ability to extract range and Doppler information. It is shown that the method can theoretically extract range and Doppler information without degradation. The reason for this result is that a special case of the fourth-order cumulant is independent of the covariance of the Gaussian amplitude modulating function. These methods are also simulated and compared with the simulated results of the range-Doppler ambiguity function. This shows that the ambiguity function and the second-order spectrum are degraded due to the Gaussian amplitude modulation. The results are further demonstrated by simulating the three range-Doppler extraction methods for the received echo in noise     

X波段雷达海面回波谱宽特征研究

海面电磁回波频谱宽度与海浪波高密切相关，可应用频谱宽度进行海浪有效波高反演。本文应用线性滤波法仿真出了海表散射面元在雷达视向上的投影速度，建立了回波谱宽模型，分析了雷达空间分辨率、回波时间序列长度及海洋环境参数等因素对频谱宽度的影响，同时还针对如何在实际观测过程中选择回波时间序列长度、观测方位角等参数进行了讨论。最后还将理论结果与CSIR-X波段雷达实测数据谱宽估计结果进行了比较。结果表明，剔除雷达噪声以及频率泄露的影响后，基于高斯分布标准偏差的谱宽估计方法所得结果与理论结果吻合很好，这从而证明了理论结果的可靠性。本文所得结果对海浪有效波高反演具有一定参考价值。     

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