## 1. Introduction

High-frequency (HF; 3–30 MHz) surface wave radar systems, by virtue of their over-the-horizon capacity and large area of coverage abilities, are particularly attractive for remote sea-state sensing. The basis of HF technology for ocean remote sensing was laid by Crombie (1955) when he correctly postulated that the primary scattering mechanism for radio waves interacting with the ocean surface is that of Bragg scattering; that is, at grazing incidence, the radio signal interacts resonantly with ocean waves whose wavelengths are half that of the incident radiation. At HF wavelengths, these so-called Bragg waves are generally deep-water waves that travel at a speed of *c*, and *g* are radar operating frequency, the speed of light, and the acceleration due to gravity, respectively. Radio echoes backscattered from these waves will be Doppler shifted from the carrier frequency by an amount

The power spectrum of the received signal, which for these coherent radars is a Doppler spectrum, provides potentially useful information about the ocean surface. The dominant features of such Doppler spectra typically consist of two large spectral peaks at the Bragg frequencies, surrounded by four continuous sidebands resulting from higher-order hydrodynamic and electromagnetic scattering effects. An early important study (Stewart and Joy 1974) showed that there are often small frequency differences between the observed Bragg frequencies and the Doppler shift

First, the performance of various high-resolution spectral estimation (SE) methods for estimating the Doppler spectrum is evaluated. Then, rather than finding the maximum peak, two methods to identify the current-associated shift

The high-resolution SE techniques applied in HF radar current sensing are briefly reviewed in section 2. In section 3, in order to improve the accuracy of Doppler spectrum estimation, a *z* transform used in conjunction with an autoregressive (AR) method is introduced. Physical reasons for the variations in the Bragg frequency are then analyzed in section 4. Based on Doppler spectra estimated using the high-resolution techniques mentioned above, two Bragg peak identification algorithms are proposed. These algorithms are intended to mitigate the impact of Bragg frequency fluctuations on the subsequent current measurements. In the supporting experiment, HF radar data were collected from November 2012 to August 2013 at Placentia Bay, Newfoundland, Canada. The mooring data (SmartAtlantic Alliance 2013) used in this paper for comparisons with the radar data are from an acoustic Doppler current meter. In section 5, preliminary results for the comparison between radial currents from the single radar and the current meter are presented and discussed. RMS differences between the radar- and current meter–derived currents are evaluated. Conclusions are given in section 6.

## 2. High-resolution spectrum estimation methods

The first issue associated with the accuracy of the radar current measurements is the Doppler spectrum estimation. HF radars used for mapping surface currents may be classified as beamforming or direction finding (see, e.g., Paduan and Washburn 2013). Although they are different in terms of the techniques used to determine directions of arrival, they both commonly apply periodogram methods—that is, fast Fourier transform (FFT) or Welch (1967) methods—to the radar backscatter from the ocean surface for spectral analysis. An early example of the simple FFT approach for beamforming pulse radar is found in Prandle and Ryder (1985). More recently, Wyatt et al. (2007) utilizes the Welch method, which is an overlapped and averaged periodogram method, for both current and wave measurements. The most common direction-finding radar is the Coastal Ocean Dynamics Applications Radar (CODAR) SeaSonde, which implements the FFT and the multiple signal classification (MUSIC) algorithm for spectral analysis and direction finding, respectively (see, e.g., Barrick 2008).

However, for typical sampling intervals, the frequency resolution

High-resolution SE methods can be classified into two main categories: the parametric AR and subspace methods. The power spectrum of a *p*-order AR process is determined by the AR parameters and the variance

## 3. A *z* transform with autoregressive method and superresolution method

In this section, a *z* transform based on the AR estimate of the Doppler spectrum (termed AR-*z*) is introduced to examine the performance with respect to the estimation of the Bragg peaks.

### a. AR-z method

*T*is the sample period. Having obtained

*z*transform is performed to give a

*z*-domain representation of the signal aswhere

*z*variable asIn this paper, the time sequence

*T*is the sampling period of the radar. The two dominant Bragg peaks have corresponding

*z*values ofAuxiliary AR processes

*z*variable. By multiplying

*z*spectrum is obtained asThis process is hereafter termed auxiliary

*z*-domain manipulation.

*z*-domain manipulation, five large peaks, as shown in Fig. 1b, will appear on the unit circle corresponding to frequency lines at

*N*bins, the frequency shift of the largest peak from zero Doppler. Since

To illustrate the current estimation using the AR-*z* method, field data collected on 24 July 2013, from a site at Placentia Bay are used. A 2048-sample time sequence of sea echoes is taken as the input *z*-transforming and auxiliary *z*-domain manipulation, the Doppler line of the maximum magnitude

*z*power spectrum of Eq. (7) and the integration is performed within a few bins around the zero-Doppler bin.

### b. Effect of signal stationarity in the AR-z algorithm

AR models are either nonadaptive or adaptive. The relative simplicity and reliability of the Levinson–Durbin and Burg algorithms (Ljung 1987) have made the nonadaptive model by far the more popular of the two and is the one used in this paper. Nonadaptive AR models choose the parameters that give the best fit to a given time sequence and require the signal to be stationary. Therefore, in order to confidently apply the AR method, close attention will be paid to the level of stationarity of the data in this paper.

*c*; if

*λ*and

*b*are the scale parameters,

*c*is the shape parameter, and

The second step in the analysis consists of dividing the data into shorter segments and checking whether the whole data can be modeled with the same model parameters as extracted from the shorter segment, that is, examining whether the model parameters are unchanged with time. If this is the case, then the stationarity of the data is assumed to be validated. As a proof of concept, a time sequence *c* to be further from 2 instead of closer, as compared to *c* for the first two segments. Thus, checking the value of *c* using short time sequences may provide a means of revealing otherwise obscured current shear or possible sidelobe contamination of the signal.

To sum up, the above-mentioned test is recommended both for the quality control on the cleanness of the sea echoes and for the examination of the time stationarity of the total radar echoes. When the quality control test shows the estimated *c* to be close to 2, the radar data will be considered as “clean,” that is, consisting mainly of sea echoes. Any bimodality observed in this clean data could indicate spatial variability of the currents within in the cell, or changes in the currents over the period of the measurement, or, more likely, an antenna sidelobe issue in which different current vectors in sidelobe directions from the same range arc are combined with the currents in the mainlobe direction. Subsequent to the quality control test, the time stationarity test is applied. If this test indicates stationarity (i.e., the estimated *c* in each segment does not vary appreciably), the AR estimator can be applied with more confidence.

## 4. Bragg frequency identification algorithms

In view of the fact that surface currents are deduced from the shifts of the Bragg spectral peaks from their theoretical values, it is critical to accurately determine these shifts. By far, the most common and popular Bragg identification methods include the peak search method (Ha 1979) and the centroid method (Barrick 1980). If the Bragg region is broad and noisy, the identification of an appropriate single value to be assigned as *the Bragg frequency* may be biased. This is why the peak search method was more often used at the early stage of the development of the radar technique. Therefore, the centroid method will be included in the comparison to show the significant improvement provided by the proposed symmetric-peak-sum (SPS) method relative to this standard.

The Bragg Doppler shift in a real scenario exhibits time-varying and width-broadening features. One possible reason why the Bragg frequency continuously changes is that the velocity of the ocean gravity waves giving rise to the Bragg scatter may be affected by other waves, such as swell on the patch (Haykin 2007). Another reason is the random phases of the ocean surface waves on the scattering surface cause the amplitude of the backscattered complex signal to be a Rayleigh random process (Zhang et al. 2012). Regarding the width-broadening feature, there are three main issues. 1) Irrespective of the waveforms used, the transmitted signal is spread over a bandwidth. This will cause a certain degree of Bragg broadening determined by the pulse width or sweep bandwidth. For example, a bandwidth of 50 kHz will correspond to a spread of 0.022 Hz for the Bragg frequency. 2) The total effect of the orbital velocities of the intermediate waves (wavelength smaller than the range resolution but longer than the Bragg waves) causes a spectral broadening around the Bragg lines. 3) An increase of the half-power beamwidth of the receiving antenna will broaden the Bragg frequency (Georges and Maresca 1979).

Next, by considering the time-varying and width-broadening features discussed above, two methods are proposed to deal with the problem of accurate identification of the Bragg Doppler shift.

### a. Centroid method

The commonly used centroid method is implemented here as follows: 1) A 150 cm s^{−1} (the largest expected current velocity assumed to be present in the scattering region) isolation window is placed around

### b. SPS method

Since the ocean surface is composed of not only local wind waves but also ocean swell, the latter contribution will cause narrow peaks adjacent to the first-order peaks. As such, the presence of the swell peaks could potentially affect the SNR values at the frequencies in the isolation window during weighting and thus may affect the centroid Bragg peak identification based on the centroid algorithm.

Here, a modification of the centroid method involving a peak detection scheme is implemented with a view toward reducing the impact of swell. Although it is intuitive to locate the maximum power and calculate its corresponding Doppler shift, according to the previous discussion on the Bragg frequency, a maximum power does not always indicate the true Bragg location. For example, interference signals or strong noise may produce a local maximum that may exceed the power of the actual Bragg frequency. Fluctuations in the Bragg peaks as discussed above may also invalidate this maximum criterion. Considering these features, the principle of the SPS method is to add a pair of spectral values with the same Doppler shift from

The particulars of the SPS method are as follows: 1) the still water theoretical Bragg frequencies

## 5. Ground-truth data validation

As validation of the above-mentioned procedures, tests were conducted to compare the performance of the AR (or MCOV), AR-*z*, and MUSIC methods, together with the centroid and SPS identification methods, using field data. HF radar data were collected from an experiment, which commenced on 29 November 2012. The radar system consisted of eight receiving elements and operated at 13.385 MHz with a 50-kHz bandwidth, yielding a theoretical 3-km range resolution. This does not account for any reduction in spatial resolution as a result of the windowing conducted in the frequency-to-range transform. The broadside half-power beamwidth is approximately 16.3°, or 0.28 rad, and this degrades by a factor of 2 at beam-steering angles of ±60°. It is to be expected that such a coarse azimuthal resolution may contribute significantly to differences between radar-deduced currents and those obtained from in situ instruments (Chen et al. 2008). Individual time series, collected along each radar beam, consist of 2048 samples collected at a sampling frequency of 2.56 Hz.

Because of the random nature of the ocean surface, spectral measurements are subject to random variability. To reduce this variability, the common procedure is to calculate each spectrum by averaging a number of FFT estimates obtained from, for example, the Welch spectrum estimator. In rapidly varying sea conditions, for example, successive FFT estimates may be quite inconsistent with each other if carried out over long time series, and then the spectrum estimate obtained by averaging is not only difficult to interpret, but it may also be distorted. To examine the performance of the various techniques with short time series, each radial current speed is retrieved within 13-min data segments without further temporal averaging.

Two instrumented buoys were deployed during the period of the radar experiment. The more distant buoy (46°58.8′N, 54°41.1′W) is about 60.36 km from the radar site and close to the maximum range of radar coverage. Because of the low SNR, data from this deployment are not used in the comparison. At position 47°19.6′N, 54°07.7′W (about 10 km from the radar site) shown in Fig. 4, a NORTEK AquaDopp acoustic Doppler single-point current meter moored at a depth of 0.5–1 m in about 153 m of water and operating at a frequency of 2 MHz is used in the current speed comparisons. This instrument provided current velocity every half an hour on a daily basis.

A number of comparison studies have examined the ability of HF radars for surface current measurements. Moored current meters have been used for validation. Differences between HF radar– and current meter–derived velocities near 10–15 cm s^{−1} have been reported by Holbrook et al. (1982), Janopaul et al. (1982), and Schott et al. (1986). More recently, Chapman et al. (1997) used shipborne current meter data to suggest that the upper bound of HF radar accuracy is 7–8 cm s^{−1}. The most recent comparisons between HF radar velocities and point measurements show RMS differences between 7 and 19 cm s^{−1} (more details available at Essen et al. 2000; Paduan et al. 2006; Lorente et al. 2014).

The comparison of the buoy currents with those obtained from the radio scatter requires care (Graber et al. 1997). The radar measures the weighted average of the current with depth, while the current meter measures the current at a particular depth (Stewart and Joy 1974). For the 13.385 MHz used in this experiment, the Stewart and Joy analysis indicates that the radar will provide a current averaged over approximately 1 m and thus the buoy and the radar sampled essentially the same oceanographic regime. According to the technical specification of the current meter, the range of the water velocity measurement is ±5 m s^{−1} with an accuracy of 1%.

Figure 5 shows the radar- and buoy-derived radial currents for the entire experiment period. Results obtained using the three spectral estimation methods are depicted in rows and each column shows a comparison of the centroid and SPS methods. The optimal model orders have been tested using the radar data. Figures 5a–c indicate that the AR-*z* method provides the best current results when the current is relatively stable (data in time point regions 1–10, 30–50, and 60–70), but it tends to lose track of currents when the latter change abruptly. The agreement between the current meter and radar results is found to be poor for the case of the centroid method used with the MUSIC method (see Fig. 5a). The reason might be that the MUSIC spectrum provides two peaks with much narrower widths than those produced by the other spectral estimation methods. Using the centroid method, which is designed for the identification of noisy and broad peaks, would lead to bias error in this case. On the other hand, the SPS method, which searches for the maximum peak, is expected to exhibit significantly better performance than the centroid method over the entire dataset. This expectation is confirmed in Figs. 5a,d in that, in comparison to results from the centroid method, a 6 cm s^{−1} reduction is realized in the RMS difference and the correlation coefficient is roughly doubled when the SPS method is applied. Figures 5b,e also confirm better performance of the SPS method by showing a 4% increase in correlation and 4 cm s^{−1} reduction in the RMS difference. Figures 5d,e reveal that the AR method performs slightly better than the MUSIC method in terms of RMS difference and correlation, while both methods are able to track rapid current changes (e.g., see estimates in the time intervals 10–30 and 80–90). These results imply that a combination of the AR and AR-*z* methods may improve current measurements; we mean 1) each method is applied individually to the entire radar dataset; 2) these initial applications show that the AR-*z* method outperforms the AR method for steady currents, while the opposite is true for fast-changing currents; and 3) the final algorithm output consists of the relatively steady currents found from the AR-*z* method and the fast-changing currents determined from the AR method. Using the combination, the RMS difference is reduced to 7.61 cm s^{–1} and the correlation coefficient is increased to 82% (see Fig. 5f). A summary of the comparison results discussed above is provided in Table 1.

Comparison of various settings of the parameters in the SE methods. Symbols include the model order *p* the correlation coefficient cc, the centroid method c-, the SPS method s-, Welch is for “modified periodogram,” and “—” means not applicable.

The significant wave height is around 0.5–2 m more than 90% of the time of the experiment, except for being 3–4.5 m during several days in January 2013. In the former case in which the sea state is moderate—that is, <2 m—the agreement associated with the SPS method is found to be better than the centroid method. In the latter case of high sea states, the agreement resulting from both the SPS and the centroid methods is significantly reduced, and this indicates a negative impact of high sea states on the current estimation using HF radar.

## 6. Conclusions

In this paper, three high-resolution spectral estimation methods (i.e., AR, MUSIC, and AR-*z*) are investigated in conjunction with two Bragg identification methods. Besides the conventional AR and MUSIC methods, the AR-*z* technique is introduced to estimate current Doppler shift directly by removing still water Bragg wave components from the Bragg offset in the *z* domain. Also, instead of applying the AR method directly and assuming the data are stationary, it is recommended to fit radar data with a Weibull distribution and to check a model parameter *c*. The data are divided into subsegments to extract the *c*. If the differences in *c* for different segments are small, then the data are assumed to be stationary. It is noted that when *c* = 2, the Rayleigh distribution is established; otherwise, the existence of interference, which is likely to follow a different distribution, is indicated.

Based on the power spectrum estimated from the three methods, the centroid and symmetric-peak-sum (SPS) techniques are proposed to identify Bragg frequencies. SPS is introduced here as a simple but novel method to mitigate adverse contributions from swell and hard targets by destructive summation of their nonsymmetric signals in the positive and negative first-order regions.

Comparing field data with buoy measurements, the AR-*z* method is shown to provide the best current estimates in stable current scenarios, while the AR and MUSIC methods are shown to track sudden changes more accurately. The new SPS Bragg identification method exhibited significant improvements over the centroid method. A combination of AR and AR-*z* methods for spectral estimation and the SPS method is recommended for current retrieval. Results showed that an 82% correlation with buoy measurements and an RMS difference of 7.61 cm s^{−1} could be achieved. Future work will involve further validation using more field data under a variety of current and sea states.

## Acknowledgments

This work was supported by an Atlantic Innovation Fund (AIF) award to Memorial University of Newfoundland (E. W. Gill, principal investigator) and by a Natural Sciences and Engineering Research Council Discovery Grant (NSERC 238263-10) to E. W. Gill.

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