Wave Extraction with Portable High-Frequency Surface Wave Radar OSMAR-S

ZHOU Hao, ROARTY Hugh, and WEN Biyang

1) School of Electronic Information, Wuhan University, Wuhan 430072, P. R. China

2) Suzhou Institute of Wuhan University, Suzhou 215123, P. R. China

3) Institute of Marine and Coastal Sciences, Rutgers, The State University of New Jersey, New Brunswick 08904, USA

Wave Extraction with Portable High-Frequency Surface Wave Radar OSMAR-S

ZHOU Hao1),2),*, ROARTY Hugh3), and WEN Biyang1)

1) School of Electronic Information, Wuhan University, Wuhan 430072, P. R. China

2) Suzhou Institute of Wuhan University, Suzhou 215123, P. R. China

3) Institute of Marine and Coastal Sciences, Rutgers, The State University of New Jersey, New Brunswick 08904, USA

High frequency surface wave radar (HFSWR) has now gained more and more attention in real-time monitoring of sea surface states such as current, waves and wind. Normally a small-aperture antenna array is preferred to a large-aperture one due to the easiness and low cost to set up. However, the large beam-width and the corresponding incorrect division of the first- and second-order Doppler spectral regions often lead to big errors in wave height and period estimations. Therefore, for the HFSWR with a compact cross-loop/monopole antenna (CMA), a new algorithm involving improved beam-forming (BF) and spectral division techniques is proposed. On one hand, the cross-spectrum of the output sequence by the conventional beam-forming (CBF) with all the three elements and the output with only the two loops is used in place of the CMA output self-spectrum to achieve a decreased beam-width; on the other hand, the better null seeking process is included to improve the division accuracy of the first- and second-order regions. The algorithm is used to reprocess the data collected by the portable HFSWR OSMAR-S during the Sailing Competition of the 16th Asian Games held in Shanwei in November 2010, and the improvements of both the correlation coefficients and root-mean-square (RMS) errors between the wave height and period estimations and in situ buoy measurements are obvious. The algorithm has greatly enhanced the capabilities of OSMAR-S in wave measurements.

HFSWR; wave height; wave period; in situ comparison; beam-forming; cross-loop

1 Introduction

Sea surface current, wind and waves are important dynamic factors to describe sea states and for marine and coastal activities of human beings (Dong et al., 2012; Li et al., 2012; Wyatt, 2012; Wang et al., 2012). For sea state monitoring, high frequency surface wave radar (HFSWR) has received much attention in the past few decades due to its capabilities in over-the-horizon (OTH), all-weather, and real-time detection. According to the first- and second-order scattering theory established by Barrick (1972a, 1972b), the underlying current, waves and wind can be extracted from sea echo Doppler spectra. The current field has now been a robust data product of HFSWR due to the simple and direct relationship between current velocity and the Doppler shift of the Bragg peaks. However the method for wave and wind extraction is still in the developing stage because the complicated second-order electromagnetic (EM) scattering is involved. The error of the inversion method mainly arises from the inherent inaccuracy of theoretical models, the insufficient spatial resolution of radar and noise. Narrow-beam phased array radar, e.g., WERA with a 16-antenna configuration (Gurgel et al., 1999), generally has small range/azimuth cells, therefore the inversion process is direct and the wave parameters extracted have relatively high reliability and accuracy (Gurgel et al., 2006). However, for small- aperture radars such as the SeaSonde, larger error will arise from the spatial aliasing of directional wave spectra within a bigger radar cell (Long et al., 2011). Although previous experiments have shown good consistence between wave and wind parameters measured by HFSWR and in situ buoys, there is still much room for further improvement of the wave extraction method with a small- aperture radar (Hilmer, 2010; Wyatt, 2011; Wyatt et al., 2011).

In this paper, the wave extraction with OSMAR-S, a portable HFSWR developed by Wen et al. (2009), is demonstrated. OSMAR-S uses a linear frequency- modulated interrupted continuous wave (FMICW) for range/ Doppler processing and a compact cross-loop/monopole receiving antenna for angular processing. During the Sailing Competition in the 16thAsian Games held at Shanwei, Guangdong Province, in November 2010, OSMAR-S, together with other in situ instruments, was deployed to provide sea state information for marine weather forecast services. Significant wave heights and peak wave periods measured by the instrument were compared with those byin situ buoys, and general coincidence was achieved. The system description and preliminary error analysis were reported (Zhou et al., 2012), however, a detailed reexamination of the Doppler spectra reveals that the improper separation of the first- and second-order spectral regions is a major source of big error due to spectral spreading. To reduce this error, the beamforming and the first/second-order spectral separation algorithms are revised, and great improvements are gained in both wave height and period estimates. The measurements at two radar sites show similar results, which demonstrate the internal consistency of the system.

2 Principles for Wave Inversion

Sea surface echoes in the HF band are dominated by the Bragg scattering. Barrick (1972a, 1972b) derived the first- and second-order cross section equations for narrow-beam HF radars, which established the theoretical basis for wave and wind inversion. He also derived an efficient method to calculate the root-mean-square (RMS) wave height via the first- and second-order spectral powers (Barrick, 1977), i.e.,

where ω is the circular Doppler frequency, σ1and σ2are the first- and second-order spectral power density, respectively, k0is the incident EM wavenumber, W is a dimensionless weighting function, and Ω1and Ω2are the firstand second-order spectral integral intervals, respectively. The significant wave height is then given by

with β being the calibration factor, and the wave period is given by

Usually only the spectral side with the stronger Bragg peaks is involved in the above integrations. The Barrick’s method allows wave inversion from the radar spectrum alone, without a priori knowledge of the sea state, so up till now it has routinely been used in a variety of oceanographic radars.

The beamwidth, signal-to-noise ratio (SNR), and sea level are the main factors impacting the accuracy of wave estimation in the Barrick’s method. Particularly, as the beamwidth increases, both the first- and second-order spectral regions will spread in frequency due to the Doppler modulation by underlying currents. This makes the determination of integral intervals more difficult, and a wrong integral interval may lead to much greater errors than spatial blur.

OSMAR-S can provide high-quality sea echo spectra, usually more than 40 dB SNR for the Bragg peaks at short ranges (Fig.1). However, the large beamwidth of antenna is a disadvantage for wave extraction. As can be seen from Fig.1, spreading and aliasing of characteristic spectra occur frequently.

Fig.1 Range/Doppler spectrum (left) and Doppler spectrum at the 10th range cell (right) recorded by OSMAR-S on November 16, 2010 at 09:58. The radar frequency is 25 MHz.

3 Beamforming with a Cross-Loop/Monopole Antenna

Beamforming is a necessary step for wave extraction. The elemental patterns of a cross-loop/monopole antenna are given by

respectively, where the angle θ is defined clockwise relative to the cosine loop plane. Each loop has an equal half-power beamwidth, θl=π/2. When a beam is directedat an angle of α, the conventional beamforming (CBF) weights with respect to each element are given by

Assume that the signals of elements are sk(t) (k=1, 2, 3, t=0, …, N-1) with N being the number of temporal samples, then the weighted sum of the array is given by

the power spectrum of which, P(f), is used for wave extraction. Regularly the Welch method is used to calculate power spectrum (Welch, 1967). The original sequence is first divided into K subsequences of M points with an overlap of Q points, which are denoted by xk(t) (k=1, …, K, t=0, …, M-1). Then the Fourier transform is performed and the periodograms, i.e., the squares of the moduli of the Fourier spectra, Xk(f), are averaged over the subsequences, which can be expressed as

By the CBF the synthesized beam pattern in the modulus sense is

To decrease the beamwidth while maintaining the scanning ability of antenna, an alternative method is used referring to the beamforming of the acoustic vector sensor (Hui and Hui, 2009). First a two-sided cosine beam, at an angle of α, is formed by combination of the signals on the loops, that is,

Then the modulus of the cross-spectrum of y(t) and x(t) is used in place of the power spectrum, PXX(f), for wave extraction. The cross-spectrum can be written as

where the superscript * denotes the complex conjugate and Yk(f) is the moduli of the Fourier spectra obtained by dividing y(t) into K subsequences and performing the Fourier transform on the subsequences. The corresponding synthesized beam pattern in the power sense is

and the half-power beamwidth is

Particularly, in the case that the look angles are less than 180 degrees, e.g., in a gulf or on the coast with a straight coastline, the monopole can be abandoned and (9) can be directly used to form a beam as a rotated loop. The beam pattern in the modulus sense is given by

Although there exists a strong back lobe (equal to the front lobe), the absence of sea echoes in the back direction guarantees the efficiency of such a method.

The synthesized patterns mentioned above are shown in Fig.2. It can be seen that the cross-spectrum method can effectively improve the directional pattern with slightly increased sidelobes, which generally have a smaller impact on the signal of interest than the large beamwidth of the mainlobe. The pattern synthesized with loops only has the smallest beamwidth. Therefore, when sea echoes arrive from directions greater than 180 degree, the cross-spectrum method is preferred, while the loop beamforming can give the best performance for a look angle less than 180 degree.

Fig.2 Synthesized patterns in the modulus sense.

4 First/Second-Order Spectral Region Location

As can be seen from Equations (1) and (3), the locations of first- and second-order Doppler spectral regions may have a crucial impact on wave extraction. Usually there is more than one peak in the first-order (Bragg) spectral regions due to the large beamwidth. If some firstorder peaks are mistakenly included in second-order spectra, wave heights will be greatly overestimated, and vice versa. Thus, besides seeking the steepest null around the first-order peaks by the spectral shape, more strict tests should be performed to find a more accurate location.

Herein, a more sophisticated algorithm is proposed to locate the spectral regions with a stronger Bragg peak. For simplicity and without loss of generality the positive Bragg peak is assumed to be stronger than the negative one in the following description of the algorithm.

Initialization: Set the maximum radial velocity of the surface current, vmax, the maximum wave spectral shift, fw, the Bragg peak SNR threshold, ηB, and the null-to-peak power ratio threshold, ηn;

Step 1: Estimate the averaged noise power, Pn, and the corresponding Bragg peak threshold, γB=Pn·ηB;

Step 2: Calculate the candidate Doppler interval of the first-order (Bragg) region using the maximum radial current velocity, and find the strongest spectral peak within the interval, which gives {Pmax, fmax} and the null power threshold, γn=Pmax/ηn;

Step 3: Find the null below the threshold, γn, between the strongest Bragg peak and the half maximum wave spectral shift, which is expressed as fn∈ (fmax, fmax+fw/2);

Step 4: Find another lower null on the right side of the previous null if possible as in Step 3, and, if the peak value between the successive nulls exceeds the Bragg peak threshold γB, the interval between the nulls is included in the first-order region and the new null is considered as a valid null;

Step 5: Repeat Step 4; The right-side null is fn,rand the second-order region is [fn,r, fn,r+fw];

Step 6: Determine the left-side null fn,lin the range of (fmax-fw/2, fmax) following Steps 3 to 5.

Comparing to the conventional method the additional evaluation of neighboring nulls as implemented in steps 4 and 5 can effectively avoid the split first-order peaks to be improperly included in the second-order region.

5 Experimental Results

The new wave extraction algorithm, including the improved beamforming and spectral division, is used to reprocess the data collected by OSMAR-S during the Sailing Competition of the 16thAsian Games held in Shanwei, Guangdong Province in November 2010. Fig.3 shows the observation system.

Fig.3 The observation system.

The two radar sites are GUAO (22? 41.2?N, 115?29.8?E) and ZHEL (22?39.5?N, 115?32.2?E), and in situ wave parameters are also measured by buoys A (22?39.5?N, 115?32.2?E) and C (22?36.0?N, 115?32.9?E), which are about 5 and 11 km from the GUAO site, respectively. Using the original wave extraction algorithm, the OSMAR-S measurements show similar trends of wave heights and periods to those with the buoys, but relatively large fluctuations and errors (Zhou et al., 2012). However, the new algorithm greatly improves the estimates of wave heights and periods. Figs.4 and 5 show the results by the GUAO and ZHEL radars, respectively. Here the parameters at the locations of buoys A and C are independently estimated by the two radar sites, but the original wave measurements at buoy C by the GUAO radar are not shown for clarity. Table 1 shows the RMS errors of wave height and period estimates using the original and latest algorithms; the improvement of accuracy is obvious. The correlation coefficients between radar- and buoy-measured wave heights are improved from below 0.6 to above 0.8 by the latest algorithm. Besides, similar wave parameters measured at the two radar sites demonstrate the system stability and dependability. Site ZHEL generally has a relatively worse performance due to the attenuation and distortion of radar signals by the islet in front of the site.

6 Conclusions

A latest algorithm with improved beamforming and first/second-order spectral region division techniques is used in the HFSWR OSMAR-S for wave extraction. Remarkable improvements on wave height and period estimates are achieved, which greatly enhances the capability of portable radars in wave measurements. Future studies are needed to further improve wave extraction techniques of and to obtain more accurate wave measurements from the portable HFSWR system.

Table 1 Comparisons of wave heights and periods estimated by the original and latest algorithms

Fig.4 Comparisons of wave heights and periods estimated by the radar at site GUAO and measured at buoys A and C. (a) Wave height sequences; (b) Wave period sequences; (c) Scatter map of wave heights at buoy A; (d) Scatter map of wave periods at Buoy A; (e) Scatter map of wave heights at Buoy C; (f) Scatter map of wave periods at buoy C.

Fig.5 Comparisons of wave heights and periods estimated by the radar at the ZHEL site and those measured by buoys A and C. (a) Wave height sequences; (b) Wave period sequences; (c) Scatter map of wave heights at buoy A; (d) Scatter map of wave periods at Buoy A; (e) Scatter map of wave heights at Buoy C; (f) Scatter map of wave periods at buoy C.

Acknowledgements

This work was supported by the Natural Science Foundation of China under Grant 61371198, the Ocean Public Welfare Scientific Research Project 201205032-3, and the Natural Science Foundation of Jiangsu Province under Grant SBK201240419. The authors thank the South Sea Forecast Center of the State Oceanic Administration of China for supporting the radar observations and providing the buoy data, and the Wuhan Devices Electronic Technology Company for conducting the observations.

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(Edited by Xie Jun)

(Received April 10, 2013; revised September 2, 2013; accepted October 14, 2014)

? Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2014

* Corresponding author. E-mail: zhou.h@whu.edu.cn