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  • View in gallery

    Power spectrum density estimation by (a) AR and (b) AR-z. The two Bragg peaks are seen wider than the peak at zero-Doppler frequency associated with the direct-path power or radar echo backscattered from the earth. The corresponding Doppler frequencies of the five large peaks are pointed by the arrow and indicated by the text in (b).

  • View in gallery

    PDF fitting with Rayleigh and Weilbull distribution: (a) , using the whole time record; and (b) , using the third segment of the time record.

  • View in gallery

    Power spectrum estimated from the three segments and the whole sequence. Spectra estimated by (left) the Welch method and (right) the AR method. In (e) the Welch spectrum shows no split of the positive Bragg peak, while in (f) the AR spectrum displays a split of the positive Bragg peak.

  • View in gallery

    Locations of the two buoys (dots) and a single radar site (star). The top-right buoy is at a distance of 10 km from the site, while the bottom-left buoy is at a distance of 63 km from the site. This figure is plotted using the M_Map mapping package for MATLAB.

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    Comparisons of radial current speed obtained from the HF radar (triangles) and the current meter (circles) over the period from 29 Nov 2012 to 21 Aug 2013.

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High-Resolution Spectral Estimation of HF Radar Data for Current Measurement Applications

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  • 1 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador, Canada
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Abstract

This paper presents a comparative study of high-resolution methods for high-frequency radar current mapping. A z-domain transformation and auxiliary z-domain manipulation of the autoregressive method is proposed for this comparison. A Weibull distribution test is recommended to justify the Rayleigh distribution of the sea clutter for quality control. Upon the power spectrum estimation, a conventional centroid method and a new symmetric-peak-sum method for the identification of current Doppler shift are proposed as another comparison. HF radar data were collected over the period from November 2012 to August 2013 at Placentia Bay, Newfoundland, Canada, and were compared with measurements from an acoustic Doppler current meter. This comparison is used to study the utility of high-resolution spectrum estimation and Bragg identification methods for surface current mapping. Results show promising use of these methods in different current scenarios and suggest combined applications to improve accuracy.

Corresponding author address: Wei Wang, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, P.O. Box 63, St. John’s NL A1B 3X5, Canada. E-mail: weiw@mun.ca

Abstract

This paper presents a comparative study of high-resolution methods for high-frequency radar current mapping. A z-domain transformation and auxiliary z-domain manipulation of the autoregressive method is proposed for this comparison. A Weibull distribution test is recommended to justify the Rayleigh distribution of the sea clutter for quality control. Upon the power spectrum estimation, a conventional centroid method and a new symmetric-peak-sum method for the identification of current Doppler shift are proposed as another comparison. HF radar data were collected over the period from November 2012 to August 2013 at Placentia Bay, Newfoundland, Canada, and were compared with measurements from an acoustic Doppler current meter. This comparison is used to study the utility of high-resolution spectrum estimation and Bragg identification methods for surface current mapping. Results show promising use of these methods in different current scenarios and suggest combined applications to improve accuracy.

Corresponding author address: Wei Wang, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, P.O. Box 63, St. John’s NL A1B 3X5, Canada. E-mail: weiw@mun.ca

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 , where , 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 , where the positive and negative signs correspond to waves moving toward and away from the radar, respectively. The Doppler shifts of these echoes are known as Bragg frequencies because of the direct analogy of the backscatter mechanism with Bragg’s law of diffraction developed in 1913, and are widely applied to X-ray crystallography.

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 , predicted from Bragg waves moving over still water. They showed that the observed differences resulted from near-surface ocean currents. When the Bragg wave train in the radar footprint propagates through a surface current, this results in an additional Doppler shift, , of the entire Doppler spectrum (including higher-order contributions) by an amount determined by the radial surface current velocity along the radar look direction. Hence, the current mapping capabilities of HF radar are highly dependent on the Doppler frequency resolution of the spectrum and the accurate identification of the Bragg frequency. These two issues constitute the major focus of this paper.

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 in a Doppler spectrum are proposed. It is well known that when the maximum-peak method is applied, errors will arise at least partly due to the often-variable width of the Bragg peaks, which may arise due to current fluctuations and other environmental effects, such as contamination by ionospheric scattering. Sometimes, the broadening of the spectral peaks, due to such influences as current variations in a resolution cell, can be very pronounced (Barrick 1980). It is noted that, even in ideal conditions, there is an inherent randomness associated with the Doppler spectral amplitudes (more details are available at Barrick and Snider 1977; Gill and Walsh 2008), and this, therefore, also translates into a randomness in as well as in the location of the peak frequencies. Any statistical error in determining the latter will affect the subsequent estimation of the radial current velocities.

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 of the required FFT limits the precision of the current estimate. The performance degrades as the signal-to-noise ratio (SNR) and data range decrease. Since the 1990s, a number of studies (more details are available at Bouchard et al. 1994; Hickey et al. 1995; Martin and Kearney 1997; Vizinho 1998) have been conducted to address the problem of selecting an optimal high-resolution SE method as a viable alternative to the conventional periodogram method.

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 of the input random noise (Marple 1987) of the linear system that hypothetically generates the signal. The detailed mathematical model will be given in Eq. (3) in section 3. The modified covariance (MCOV) and Yule–Walker methods, among others, may be used for this parameter and variance estimation. It is worth noting that traditional periodogram methods have resolutions that are, on the average, roughly the reciprocal of the observation interval and can be determined by a factor of the initial phases of the signal. The AR spectrum estimator can, in principle, perfectly resolve any two sinusoids if the autocorrelation function is perfectly known and the SNR is high. Even at a low SNR, spectral resolution provided by the AR method is as good as that of the conventional periodogram methods. It may also be noted that the AR spectral estimate has a resolution that varies mainly as a function of SNR rather than the time series length (Marple 1977). As such, for short time series, the AR method with small values of the model orders (Martin and Kearney 1997; Vizinho 1998) is found to produce more stable and accurate Bragg estimates than the classical periodogram method. Also, the MCOV method is found to be able to reduce the number of split Bragg peaks arising from current variability in short time series. This indicates the potential for the application of AR methods in areas of rapidly varying current conditions. However, AR methods are subject to errors from model misspecification.

The MUSIC method (Schmidt 1986) is an example of a subspace method. It is used to generate frequency component estimates for a signal based on an eigenanalysis of the autocorrelation matrix. The MUSIC frequency estimator, which is based on the noise subspace eigenvectors and a vector of complex sinusoidal components, is given by
e1
where represents the conjugate transpose. One problem encountered in applying the MUSIC method in HF radar sea sensing is that it is sensitive to the ill-conditioned autocorrelation matrix (Bouchard et al. 1994). In particular, under low-SNR conditions, if the signal subspace is small, then the MUSIC algorithm may generate false spectral peaks.

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

AR is a model-based method, the parameters of which are estimated from a given data sequence . The data can be modeled as output of a causal, all-pole, discrete filter whose input is white noise, given by
e2
where is the AR parameter and is the white noise of variance . The power spectral density (PSD) estimate is then computed from and , as given by
e3
where T is the sample period. Having obtained for the time sequence, a z transform is performed to give a z-domain representation of the signal as
e4
where . The PSD can be then expressed in terms of the z variable as
e5
In this paper, the time sequence is the time series of the sea echo backscattered from a certain range bin and azimuth direction. Term T is the sampling period of the radar. The two dominant Bragg peaks have corresponding z values of
e6
Auxiliary AR processes are defined as and , respectively, where and are then created to remove the component out of the phase of the z variable. By multiplying with , the AR-z spectrum is obtained as
e7
This process is hereafter termed auxiliary z-domain manipulation.
Since the radar echoes backscattered from the earth or the direct-path power also produce a peak at zero-Doppler frequency, there are consequently three peaks in the , as shown in Fig. 1a. After auxiliary z-domain manipulation, five large peaks, as shown in Fig. 1b, will appear on the unit circle corresponding to frequency lines at
e8
Fig. 1.
Fig. 1.

Power spectrum density estimation by (a) AR and (b) AR-z. The two Bragg peaks are seen wider than the peak at zero-Doppler frequency associated with the direct-path power or radar echo backscattered from the earth. The corresponding Doppler frequencies of the five large peaks are pointed by the arrow and indicated by the text in (b).

Citation: Journal of Atmospheric and Oceanic Technology 32, 8; 10.1175/JTECH-D-14-00191.1

Among these, the largest peak arises from the Doppler shift generated by the radial current velocity. This is because both and contain large power at , and they are added constructively. Presently, the task is to identify, from N bins, the frequency shift of the largest peak from zero Doppler. Since , where is the resolution of the radial current speed, current speed will be calculated by
e9

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 . After z-transforming and auxiliary z-domain manipulation, the Doppler line of the maximum magnitude is found to be at bin 1032 in Fig. 1b. This is an eight-bin shift (i.e., 1032 − 1024 = 8) to the positive Doppler from zero Doppler. Therefore, an approaching radial current with speed is obtained.

Figure 1b shows that the two peaks for are sharp, while the remaining three peaks are wider. This is expected because the peaks correspond to the zero-Doppler peaks in the original AR spectrum, while other wider peaks correspond to Bragg frequencies that are broadened (the detailed reason will be discussed in section 5). In this case, instead of using simply the maximum magnitude criterion to find the frequency of , the centroid of is a more reasonable estimate, given by
e10
where is the AR-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.

Scattering from a given ocean surface patch illuminated by an HF electromagnetic wave can be viewed as consisting of a large number of scattering events. Because of the central limit theorem, which explains that the sum of many different random variables tend to be close to the normal distribution, the sea clutter may be taken to be a Gaussian process and its amplitude should follow a Rayleigh distribution. For this reason, the first step in the stationarity analysis is to ensure the data contain mainly sea clutter (if they are contaminated by interference or ionospheric clutter, the distribution may be different) by evaluating the empirical amplitude probability density function (PDF) and comparing it with a Rayleigh distribution model. To test the goodness of fit, a simple, yet useful, method is suggested as follows: the Weibull distribution model is fitted to the radar data; the test is then characterized by the estimated Weibull model parameter c; if , then the Weibull model coincides with the Rayleigh model; otherwise, a poor fit is observed and it implies the existence of interference. The expressions of the Rayleigh and Weibull distribution models are given by
e11
e12
where λ and b are the scale parameters, c is the shape parameter, and is the unit step function. The Rayleigh distribution is a special case of the Weibull distribution for . An example is shown in Fig. 2a, where indicates that the sea clutter is approximately Rayleigh distributed.
Fig. 2.
Fig. 2.

PDF fitting with Rayleigh and Weilbull distribution: (a) , using the whole time record; and (b) , using the third segment of the time record.

Citation: Journal of Atmospheric and Oceanic Technology 32, 8; 10.1175/JTECH-D-14-00191.1

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 containing 2048 field data samples is equally divided into three segments. Using the three segments and the whole sequence, four values of the Weilbull parameters—namely, , , , ; and , 1.92, 1.96, 1.86—were estimated. As may be observed from Fig. 2b, the third segment, for which , follows the Rayleigh distribution most closely, while the whole sequence, as indicated in Fig. 2a, shows a larger deviation. These results imply that the third segment alone may better represent a pure sea clutter signal than does the whole sequence. In fact, it may be seen from Fig. 3, that the power spectrum from the third sequence reveals a split Bragg peak. This feature is lost when the whole sequence is used. One might intuitively conclude that the split is a result of the sudden appearance of a moving target. However, if this were the case, one would expect the value of 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.

Fig. 3.
Fig. 3.

Power spectrum estimated from the three segments and the whole sequence. Spectra estimated by (left) the Welch method and (right) the AR method. In (e) the Welch spectrum shows no split of the positive Bragg peak, while in (f) the AR spectrum displays a split of the positive Bragg peak.

Citation: Journal of Atmospheric and Oceanic Technology 32, 8; 10.1175/JTECH-D-14-00191.1

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 , such that the positive and negative first-order Doppler regions may be isolated. The maximum powers in the two windowed regions are taken as approximate peaks. For example, for a radar operating frequency of 13.385 MHz, an isolation window of ±0.1375 Hz, is placed about the Bragg frequency. 2) Two noise floors are calculated from the average power in the regions Hz of the Doppler spectrum. Then, two SNR values are calculated, based on the two approximate peaks and the two noise floors. 3) The isolated region with the higher of the two SNRs is chosen as the candidate first-order region for the radial current measurement. 4) The centroid frequency for this Doppler region is calculated by weighting the frequency components (the spectral values with SNR above 10 dB are used in the weighting) with the SNR values in the isolation window.

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 in the positive and negative isolation windows one by one. The reason for this calculation is that it is assumed that no matter how many factors are involved—for example, underlying current, interacting waves, and wind drift—both Bragg frequencies are similarly shifted. Based on this idea, even if interference or noise causes a local maximum on one side of the spectrum, it cannot produce another peak with the same Doppler shift on the other side, and therefore it will not generate a maximum in the summed signal. In the case of fluctuations, since both peaks fluctuate, the standard deviation of their average will reduce by an order of the square root of 2 if the peaks are of equal amplitude. When the peak amplitudes differ significantly, the SPS method will become as effective as the maximum-likelihood method using the dominant Bragg peak.

The particulars of the SPS method are as follows: 1) the still water theoretical Bragg frequencies are calculated, 2) the isolation windows mentioned above are centered at and , and 3) the two spectral values at each frequency point in the two isolation windows are summed and divided by a factor of 2. The maximum in this averaged signal is considered to be at the true Bragg frequency.

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.

Fig. 4.
Fig. 4.

Locations of the two buoys (dots) and a single radar site (star). The top-right buoy is at a distance of 10 km from the site, while the bottom-left buoy is at a distance of 63 km from the site. This figure is plotted using the M_Map mapping package for MATLAB.

Citation: Journal of Atmospheric and Oceanic Technology 32, 8; 10.1175/JTECH-D-14-00191.1

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.

Fig. 5.
Fig. 5.

Comparisons of radial current speed obtained from the HF radar (triangles) and the current meter (circles) over the period from 29 Nov 2012 to 21 Aug 2013.

Citation: Journal of Atmospheric and Oceanic Technology 32, 8; 10.1175/JTECH-D-14-00191.1

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.

Table 1.

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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