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.

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.

A chirp signal is a large-bandwidth signal which is widely used in engineering. In many applications, it is necessary to decompose a mixed chirp signal into its components. However, the traditional Fourier transform method cannot process a mixed chirp signal when its components intersect in the joint time-frequency domain. Combining the advantages of the morphological component analysis (MCA) with multicomponent signal processing and the fractional Fourier transform (FrFT) in chirp signal processing, this letter proposes the MCA-FrFT method to decompose a multicomponent chirp signal. First, the cost function is defined using the FrFT and optimized by the split augmented Lagrangian shrinkage algorithm (SALSA), and then, all the morphological components are obtained. The proposed method is verified by simulations, and simulation results show that the proposed method has good performance in separating the multicomponent chirp signals into components. Besides, the proposed method is evaluated experimentally in the sea target detection, and the experimental results confirm that the proposed method can not only extract the low observable targets from a heavy sea-clutter environment but also separate them from each other.