For shipboard coherent S-band radar, the shadow modulation phenomenon happens at large sea surface undulations or small grazing angles. As the ship speed increases or the sea state rises, the shadow modulation leads to an increase in the peak value of the wave spectrum, which results in inaccurate wave parameter inversion. In order to achieve accurate wave detection in high sea state or high ship speed scenarios, a shadow modulation correction method based on velocity-fitting relationship and Hermite interpolation is presented. First, the variable range of radial velocity is computed using the simulated sea surface’s velocity fitting relation. The anomalous Doppler velocity is then rectified by applying the modified Akima piecewise cubic Hermite interpolation (MAPCHI) algorithm. The MAPCHI algorithm is appropriate for complex nonlinear curves and is not prone to abrupt fluctuations or flattening issues. The implementation of this interpolation algorithm can alleviate the problem of anomalous fluctuations in Doppler velocities induced by shadow modulation. Finally, the nondirectional wave spectrum and wave parameters are calculated. Numerical simulation experiments show that the proposed method can rectify the influence of shadow modulation at various speeds and sea state backdrops. Meanwhile, comparing the radar measurements in the South China Sea with the buoy results, the mean absolute error (MAE) of significant wave height and mean wave period are 0.21 m and 0.34 s, respectively. The results demonstrate that the proposed method can successfully remove shadow modulation interference with high robustness.

In the study of deterministic sea waves, the predictable zone refers to the area where the phase-resolvable wave field can be fully reconstructed and accurately predicted based on measured data. Under certain marine environmental and radar measurement parameter conditions, expanding the predictable zone is of great significance for domains such as quiescent period prediction (QPP) for ships and optimizing wave energy harvesting. Prior research on the predictable zone mostly relied on either temporal or spatial measurements, significantly constraining the range of the predictable zone. In this paper, based on coherent microwave radar, we present a novel method combining spatial and temporal measurements to expand the predictable zone. Firstly, the boundary of the predictable zone under a single spatial measurement and multiple spatial measurements (spatial-temporal measurement) are analyzed, and the closed-form expressions for the predictable zone are derived for both unidirectional and multidirectional wave fields. The quantitative relationship between the predicted time at the desired spatial location and the radar parameters and wave spectra is obtained. Subsequently, the theoretical analysis of the predictable zone is validated using the numerical simulation by comparing the theoretically predictable zone with the error distributions for the unidirectional and multidirectional wavefield cases. Finally, the analysis of experimental data from Weihai in 2021 also indicates that the joint spatial-temporal measurements can effectively expand the predictable zone.

The reconstruction and prediction of deterministic sea waves are important for increasing the safety of offshore operations and improving the efficiency of wave energy conversion. Coherent microwave radar, as a commonly used instrument for sea surface observation, can directly reconstruct deterministic sea waves based on the Doppler echo. However, its reconstruction performance relies heavily on the accuracy of the velocity measurements and is severely limited in a high sea state or the presence of hard target clutter. In this work, we propose a robust deterministic wave reconstruction and prediction scheme to reduce the influence of velocity measurement anomalies on the reconstruction and prediction results. First, the spatial-temporal velocities are obtained from the coherent microwave radar, followed by the least absolute deviation (LAD) method for solving the parameters of the wave motion model, and the deterministic wave is reconstructed and predicted based on the obtained model parameters. The deterministic wave reconstruction and prediction under long-crested and short-crested sea states with broken waves are simulated, and the results confirm the effectiveness of the scheme. Simultaneously, the scheme is verified using the experimental data collected with a coherent S-band radar in Weihai in December 2021. First, the significant wave height is reconstructed using the scheme, and the correlation with thein-situdata reaches 0.97. Then, the prediction performance of deterministic sea waves is compared with the velocity potential function method, and these results confirm the effectiveness of the scheme.

Accurate prediction of the ship motion attitude in the future period is important to ensure the safety of offshore operations and sea navigation. Coherent S-band radar is a novel wave monitoring device that can be applied to advance the development of ship motion attitude prediction. In this study, we propose a method for realizing ship motion attitude prediction from radial velocity of water particle using coherent S-band radar. First, the parameters of the wave motion model (WMM) are estimated using the regularized least squares (RLS) method, which can solve the ill-conditioning matrix on the estimation accuracy under the short-crested wave sea state. Then, a predictable zone model considering radar dwell time is proposed based on coherent S-band radar, which can improve the traditional predictable zone. Finally, the deterministic sea waves in the predictable zone are input into the ship response amplitude operator (RAO) to realize the ship motion attitude prediction. The performance of the proposed method for ship motion attitude prediction in short-crested wave condition is analyzed through simulation. Meanwhile, the proposed method is validated using real data from the sea trial experiment in December 2019 in the South China Sea. The prediction results obtained by the proposed method are compared with the measured data from the MTi-G-710 instrument, and the two trends are consistent with a correlation coefficient of 0.7564. The results show that the proposed method can effectively realize ship motion attitude prediction using coherent S-band radar.

The peak wave direction is a crucial parameter to quantify the physical characteristics of the ocean waves. For shipboard coherent microwave radar, the radar-illuminated space changes with the movement of the ship, and this fact leads to an unsolved problem for wave direction estimation. To address the issue, an approach is proposed to estimate peak wave direction using shipboard coherent microwave radar. After estimating water particles’ radial velocity and obtaining the peak wave energy from the radar echoes received with antennas, the 180° ambiguity is removed by comparing the variance of the left and right boundaries of sea echoes in the range-Doppler spectrum. The approach is validated using the datasets collected with a shipboard coherent S-band wave radar and a wave buoy in the South China Sea in 2019. The comparison with the wave buoy data shows that the root-mean-square error (RMSE) of peak wave direction is 10.6°. This result indicates that the method can work effectively.

Coherent microwave radar processes sea echoes by using a direct relationship between wave orbital velocity and wave spectrum instead of backscattered intensity to obtain wave parameter. However, the measurements of wave orbital velocity are susceptible to ocean conditions (e.g., low sea state and interference), and thus the method’s performance is often uneven under the mixed conditions. To solve this problem, a novel method for wave parameter inversion based on spectral proper orthogonal decomposition (SPOD) is proposed. The spatial–temporal series of the wave orbital velocities are first processed using SPOD, and a series of expansion coefficients, modes, and eigenvalues can be obtained. Later, the ocean conditions are classified according to the distribution of the eigenvalues, and the truncated frequencies and modes are used to remove nonwave contributions. Finally, wave parameter inversion is performed using the reconstructed spatial–temporal velocities. The proposed method is validated by data from two ocean observation experiments, including coherent S-band radar wave echoes and buoy measurements. The results indicate that the proposed method can discard nonwave contribution and obtain wave parameters in good agreement with buoy measurements regardless of low sea state or mixed ocean conditions.

Coherent microwave radar is one of the effective devices for ocean wave measurements. However, the accuracy of wave inversion is significantly affected by the non-gravity wave components (referred to as non-wave components in this work) such as broken waves and shadows in the sea echoes. In this article, a new method based on the Radon transform and discrete Fourier transform (DFT) is proposed to suppress the non-wave components. First, the spatial-temporal velocities are calculated based on the raw data obtained from coherent microwave radar. Second, the Radon transform and DFT are performed on the spatial-temporal velocities to obtain the distribution of the spatial-temporal velocities in the Radon-Fourier transform domain. Following this, non-wave components are eliminated in accordance with the phase velocity and frequency distribution of the wave components. To validate the method, we analyzed the experimental data collected with a coherent S-band radar in Weihai in December 2021. After removing the non-wave components from the radar echoes, we invert three wave parameters including peak wave period, peak wave direction, and significant wave height, and compare them with thein-situdata. The results indicate that the method can effectively remove the non-wave components from the wave echoes without any empirical parameters.

Deterministic sea wave prediction (DSWP), which aims to predict instantaneous elevation of the ocean surface, can facilitate the safe implementation of many wave height limited maritime operations. Coherent microwave radar is an emerging tool for accurate wave measurements and could be utilized for the advance of DSWP. To address this issue, a method is proposed to estimate the phase-resolved model coefficients and predict the instantaneous wave elevation using coherent microwave radar. The least square with regularization is adopted to estimate phase-resolved model coefficients from radial velocities of water particles extracted from radar echoes. Then instantaneous wave elevation is predicted according to the linear wave propagation model in terms of phase-resolved model coefficients. Simulation analysis is carried out to evaluate the performance of the proposed method under long-crested and short-crested sea states. Subsequently, the proposed method is validated using the dataset collected with a coherent S-band radar. The radar-measured wave spectrum is consistent with the WaveRider data. A comparison between the predicted wave elevation at the location of ship and the phase-shifted roll angle are conducted, and the trends are in an agreement with a correlation coefficient 0.69. In addition, the significant wave height derived from the predicted wave elevation is close to that of the buoy. These results indicate that the proposed method is effective for DSWP using coherent microwave radar.

Shore-based coherent microwave radar and high-frequency (HF) surface wave radar are two components of a rapidly emerging set of technologies suitable for ocean wave remote sensing. To investigate their differences, this paper describes and analyzes the relationship between the water particle velocity and the wave height spectrum based on linear wave theory which underpins the algorithms developed for the analysis of data collected by coherent microwave radar. The backscatter mechanism which addresses the interaction of the HF radio waves with the ocean surface waves, as well as the empirical method adopted in our HF radar is also presented. The wave characteristics observed by the shore-based coherent S-band radar [Microwave Ocean Remote SEnsor (MORSE)] are analyzed. A multifrequency HF (MHF) radar based on a circular receiving array, which is capable of sensing waves up to 100-km offshore, is also introduced. An intercomparison of the wave height measurements obtained from the MORSE, MHF radar, and wave buoy is made. The comparison indicates that the wave heights measured by the MORSE and the MHF radar are consistent with the buoy-derived wave heights, with the root-mean-square differences (RMSDs) of 0.27 and 0.37 m, respectively.

Recent studies indicate that the poor antenna sidelobe level of phased-array high-frequency (HF) radars degrades the performance of Bragg ratio estimation for wind direction measurements. To explore this issue, this paper improves the previous model of wind direction estimation for phased-array HF radars, and the effect of unsatisfactory array patterns on Bragg ratio estimation is theoretically analyzed. Moreover, a hybrid beam-forming and direction-finding method, in which wind direction is measured by reducing the influence of unsatisfactory array patterns on Bragg ratio estimation, is proposed for multifrequency HF radars installed along the coast of Zhejiang Province in China. The procedure for implementing this scheme is also presented in detail. Wind directions derived from 8.05-, 10.7-, 16.8-, and 19.2-MHz radar data are compared with measurements collected with anemometers at three sampling locations to verify the proposed method, and the measurements with root-mean-square errors from 19.5° to 26.6° show that this strategy is effective for wind direction measurements. We recommend adopting the proposed method or using similar approaches to estimate wind direction based on HF radars, especially in situations where the array pattern is not sufficiently narrow.