Evaluation of Norm-Constrained Capon Method on Improving Doppler Peak Localization of Antenna-Arrayed High-Frequency Coastal Radar
1. Introduction
Among the various types of radars used for monitoring the oceanic waters, the shore-based ground wave radar (coastal radar hereafter) operating at very-high-frequency (VHF) and high-frequency (HF) bands are potent instruments for observations of the sea surface currents and ocean waves in a large sea area (Bass et al. 1968a,b; Barrick 1971; Teague et al. 1997; Gurgel et al. 1999). Depending on the transmission frequency used, the observational distance of the coastal radar can be as far as 400 km from the coastline. Additionally, coastal radar can detect the vessels on the sea surface (Khan et al. 1994; Dzvonkovskaya et al. 2009; Ponsford and Wang 2010; Vesecky and Laws 2010; Flores-Vidal et al. 2013; Chuang et al. 2015; Lu et al. 2017; Cai et al. 2021; Chen et al. 2021). The capability of over-the-horizon detection renders coastal radar an indispensable tool for every country to monitor and manage the waters of its exclusive economic zone (EEZ).
The sea echoes detected by the coastal radar are mainly attributed to the Bragg backscattering of ocean waves at the scale of half the incident radar wavelength (Crombie 1955). In the Doppler power spectrum, such sea echoes appear at around two spectral lines
Recently, the arrayed configuration has received considerable attention in establishing new coastal radars, even though the arrayed radar technology has been used for decades (Teague et al. 1997; Gurgel et al. 1999). One of the reasons for the widespread adoption of the arrayed configuration for coastal radar systems is the highly serviceable beamforming capability; i.e., the main lobe of the receiving pattern can be directed to various orientations without the need for physical rotation of the antenna array. Accurate beamforming capability benefits the sea surface current measurement and oceanic wave monitoring as the Doppler-range spectrum of different azimuthal angles is essential for the corresponding data processing. A conventional algorithm, the Fourier (F) beamformer hereafter, is commonly used to process the beamforming, which is linear and straightforward. Nevertheless, there are additional algorithms for beamforming, for example, Capon, multiple signal classification (MUSIC), and norm-constrained Capon methods (Capon 1969; Schmidt 1986; Cox et al. 1987; Li et al. 2003; De Paolo et al. 2007; Liu and Liao 2010). These algorithms are adaptive to the data and can improve range and angular resolutions when used to detect soft and hard targets. For instance, a novel application of the norm-constrained Capon method (NC-Capon beamformer hereafter) was proposed for vessel detection and tracking in the spatiotemporal domain using an arrayed HF coastal radar (Chen et al. 2021), which demonstrates that the NC-Capon beamformer outperformed the conventional Fourier beamformer by less sidelobe contamination. Based on this, more applications of the NC-Capon beamformer to the HF coastal radar are anticipated. In this study, we carried out the beamforming in the spectral domain using the NC-Capon beamformer. We demonstrated an improvement in spectral localization and its potential benefit in deriving the Doppler/radial velocity, as compared with the Fourier beamformer.
The remainder of this paper is organized as follows: Section 2a describes the HF coastal radar and an acoustic Doppler current profiler (ADCP) used in the study. The ADCP data are used as a benchmark of the sea surface current. The beamforming algorithms applied to the spectral domain are introduced and verified in section 2b. The spectral parameters, i.e., spectral peak width and spectral width and Doppler/radial velocity of the first-order echoes retrieved at several beamforming angles, are presented in sections 3a, 3b, and 3c, respectively. Comparisons between the results of the NC-Capon and the Fourier beamformers are made. Additionally, section 3d compares the radial velocities between the radar and the ADCP to validate the usability of the two beamformers. Conclusions are stated in section 4.
2. Instruments and beamforming methods
This section provides a concise introduction to two beamforming methods: Fourier and NC-Capon. Readers interested in more detailed explanations and practical applications of these beamformers in atmospheric and oceanic studies can refer to relevant literature such as Hashimoto et al. (2016), Hashiguchi et al. (2018), and Chen et al. (2021, 2022).
a. Taichung Harbor coastal radar and ADCP
The sea surface radar echoes were collected by the coastal radar following the University of Hawai’i Generic High-Frequency Doppler Radar design (Kirincich et al. 2019), located at the northern embankment of Taichung Harbor, Taiwan (24°18.591′N, 120°31.389′E). The radar system consists of 16 vertical dipole antennas aligned linearly for 16 receiving channels, and the interelement distance is 4 m. It is operated in a series of chirps using frequency-modulated continuous waves (FMCWs) with a center frequency of 27.75 MHz and a bandwidth of 300 kHz. Each chirp length is 0.216 66 s, and the radar raw data within 30 min are assembled in a file, giving at least 8192 chirp data in a file. In the following fast Fourier transform (FFT) analysis, 1024 raw data points are taken each time. The ocean-facing transmitter lobe is centered on 296° azimuth, the range cell size is 500 m, and 80 range cells are sampled in an observation (Chien et al. 2020; Dao 2022). Routine phase calibration of the antenna/receiving channels is made for operational observations. A study using the ship’s radar echoes and automatic identification system (AIS) information has also been carried out to validate the calibration results (Chen et al. 2021).
In this study, the sea surface current data utilized for comparative analysis were obtained from a Teledyne/RDI Workhorse II Sentinel 600-kHz ADCP. This device was located to the west-southwest of the coastal radar, approximately 4.5 km away. It was affixed on a steel frame on the seabed, oriented upward through a water column with a depth of about 30 m and a roll angle of 1.2°. The ADCP was configured with a vertical resolution of 1 m per cell, allowing for precise profiling of the sea current’s eastern and northern vector components. To align with the radar-derived observations, the data from the uppermost layer of the seawater measured by the ADCP were selected for comparison (Dao 2022).
b. Beamforming methods and initial comparison
In the data analysis, the Blackman–Harris window was used to get the respective spectra of receiving channels, and the Hamming window was applied to the spectra of receiving channels in the beamforming process to suppress the sidelobe level. A discussion on the sidelobe effect for our coastal radar has been made by Chen et al. (2021) using the radar echoes reflected from vessels. It showed that the NC-Capon beamformer had less sidelobe contamination than the conventional Fourier beamformer.
Figure 1 shows four examples of the Doppler spectra retrieved from the Fourier and NC-Capon beamformers, where the beamforming angle of 0° was directed to 296° azimuth. The original Doppler spectra of 16 receiving channels were obtained through the FFT with 1024 data points, resulting in 1024 spectral lines between −2.3 and 2.3 Hz. Figure 1 represents the spectral amplitude between −1 and 1 Hz, in which the Doppler spectral curves were normalized within the range cell. The Bragg-resonance frequencies were approximately fb = ±0.5372 Hz (vertical dashed lines). Black and green dotted lines denote the locations of the Doppler frequencies at
Four examples of Doppler spectra retrieved by the F and NC-Capon beamformers. The spectra are represented in amplitude and normalized in each range cell. Vertical dashed lines indicate the Bragg-resonance frequencies ± fb. Black and green dotted lines denote the locations of the Doppler frequencies at
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
Observing the separation between the first-order and some specific second-order spectral peaks was usually larger than about
In Fig. 1b, strong echoes also appeared at around zero Doppler frequency, which could be the ship echoes. It is inevitable to receive ship echoes around the harbor, and the ship echoes could contaminate the sea echoes when the ship echoes’ Doppler frequencies are in the sea echoes’ neighborhood. To discard the ship echoes as far as possible, only the spectral peak determined in the spectral region
The use of the frequency band
The NC-Capon spectra in Fig. 1 were obtained using the norm constraint parameter δ = 10. Different δ values might alter the outcome more or less; moreover, the larger the δ value, the lower the retrieved brightness. To inspect the suitability of the δ value, statistical estimates of spectral peak widths varying with the δ value and the beamforming angle were carried out; the results are shown in Fig. 2. The Fourier results (dashed lines) are also displayed for comparison, which is not related to the δ value in reality but varies slightly with the beamforming angle. There could be many peaks in the Doppler spectra. We extracted at most 10 peaks from each spectrum, and in all, 3840 spectra captured within 3 h (0200–0500 UTC 7 November 2020) were processed for each beam direction. To discard noise peaks, the peaks with a height more significant than 0.25 in a normalized spectral curve were selected. As a result, Fig. 2 shows that the mean (open circles) and standard deviation (vertical line segments) of the peak widths obtained from the NC-Capon beamformer did not vary with the δ value significantly, and in general, the mean approached a constant value as δ increased to approximately 5. The computation time could be shorter for a larger δ value, but the resultant brightness would be lower, and some minor peaks might be suppressed. Based on this, the value of 10 assigned to δ was considered suitable for the present study. Furthermore, Fig. 2 illustrates that the peak widths obtained from the NC-Capon beamformer were consistently smaller than those obtained from the Fourier beamformer. Further statistical comparisons between the spectral characteristics of the two beamformers are presented in section 3.
Means (circles) and standard deviations (vertical segments) of peak widths at various values of δ used in the NC-Capon beamformer. F results (dashed lines) are not related to δ value but slightly change with the beamforming directions. (from left to right) Beamforming angles are −60° −30°, 0°, 30°, and 60°, respectively. The 0° beamforming angle is the central direction of the ocean-facing transmitter lobe, i.e., 296° azimuth. Data time: 0200–0500 UTC 7 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
3. Comparison and discussion
To inspect the performance of the NC-Capon beamformer with respect to the improvement of the Doppler spectra, statistical comparisons of spectral peak widths and spectral widths and Doppler/radial velocities of the first-order echoes between the NC-Capon and the Fourier beamformers were carried out; these are demonstrated in sections 3a, 3b, and 3c, respectively. Herein, spectral peak width is understood as the width of half the peak prominence, and the peak prominence measures how much the peak stands out relative to other peaks (refer to the instruction of MATLAB for details). Spectral width, on the other hand, is the mean width estimated by the moment method with the spectral lines that are bounded for the first-order echo region. Finally, a comparison of radial velocities between the radar and the ADCP is shown in section 3d.
a. Spectral peak width
Figure 2 already illustrates that the mean and the deviation of the spectral peak widths produced by the NC-Capon beamformer are smaller than those of the Fourier beamformer. Distributions of spectral peak widths for two additional examples are shown in Fig. 3. The radar echoes for Fig. 3a were collected under the sea state of regular tidal motion, and the radar echoes for Figs. 3b and 3c were obtained during Typhoon Atsani passing through the southern sea area of the coastal radar. As seen in Figs. 3a and 3b, the NC-Capon beamformer yielded narrower peak widths than the Fourier beamformer, irrespective of the beamforming angle and sea state. Distributions of peak widths along the range are displayed in Fig. 3c. Notably, the NC spectral peak widths (red stairstep curve) were statistically smaller than those of the Fourier (black stairstep curves), regardless of the beamforming angle, range, and SNR (blue curves). Based on the comparison of the two beamformers shown in Figs. 2 and 3, it is evident that the NC-Capon beamformer indeed improved the resolution of the Doppler spectra. This enhancement in spectral resolution could contribute to more precise estimates of spectral width, Doppler velocity, and wave parameters for subsequent studies utilizing these spectral parameters.
(a),(b) Histograms of Doppler spectral peak widths obtained from two periods at the beamforming angles of −60° −30°, 0°, 30°, and 60°, respectively. The beamforming angle of 0° is the central direction of the ocean-facing transmitter lobe (296° azimuth). Yellow region: NC; blue region: F; brown region: overlapped. F and NC values are the weighted mean locations of peak widths estimated from the histogram numbers. (c) Range variation in the histograms of Doppler spectral peak widths, in which four range cells are integrated into one. The two profiling curves in blue denote the mean SNRs of spectral echoes retrieved by F (dotted) and NC-Capon (solid) beamformers, respectively. SNR unit is decibel (dB), as indicated at the top of the axes.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
Note that the SNR profiles in Fig. 3c were calculated from the respective spectral powers of range cells. For each range cell, the lowest 50% of the spectral powers were averaged to represent the noise level, while the spectral power lines higher than the noise level were considered as signals. As shown, the SNRs of the NC-Capon beamformer were either higher or equal to those of the Fourier beamformer in this case. The difference in SNR was more pronounced at the beamforming angles of −60°, 30°, and 60°, within about 20 km. This feature could be attributed to the more excellent behavior of the NC-Capon beamformer in suppressing the noises or signals from the sidelobes of the beamforming pattern. On the other hand, the SNR profiles yielded by the two beamformers nearly coincided at both beamforming angles of −30° and 0°; the two beamforming angles corresponded to 266° and 296° azimuth, respectively. Because the radar receiving antennas are installed linearly along the coastline, and the coastline is nearly in the north−south direction, the two azimuthal angles of 266° and 296° are oriented to the water area around the due west of the radar site, where a greater sea echo intensity is commonly produced in the beamforming of this study. Given this, we suspect the sidelobe effect on the beamforming angles of −60°, 30°, and 60° mainly originated from the more substantial sea echoes coming from the due west of the radar site or the reflected echoes from the land objects.
b. Spectral width
We estimated the spectral parameters of the first-order echoes using the moment method. The spectral region confined in the calculation was determined as follows: 1) locating the maximum spectral peak in the frequency band of
Figure 4 shows the range histograms of spectral widths for the 3-h data used for Fig. 3a. The results of the forward (positive) and backward (negative) spectral sides were presented separately. As depicted, the distributions of the NC spectral widths (red stairstep curve) generally tended to smaller values than those of the Fourier (black stairstep curves). For easy inspection, several examples are highlighted with frames.
Histograms (stairstep curves) of spectral widths of the first-order echoes at beamforming angles of −60° −30°, 0°, 30°, and 60°, respectively. Results from the (left) backward and (right) forward spectra retrieved by F and NC-Capon beamformers are shown at various ranges, in which four range cells are integrated into one. SNR profiles (dotted and solid blue curves) are the same as in Fig. 3c. Data time: 0000–0300 UTC 15 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
The one-to-one difference in spectral widths ΔW between the two beamformers was estimated, i.e., NC-Capon minus Fourier, and the resultant histograms are shown in Fig. 5a, where the forward (positive) and backward (negative) spectral sides were processed separately. In the histograms of Fig. 5a, the values in percentage at the left and right sides of the histograms denote, respectively, the negative and positive ΔW numbers. As estimated, all the numbers of negative ΔW were above 66.7%, irrespective of the beamforming angle. The range profiles illustrating the differences in mean spectral widths between the two beamformers are given in Fig. 5b. It is reasonable to discard the results in the ranges beyond ∼35 km, where the SNRs were extremely low and the spectra were characterized by white noise, leading to the differences in the mean spectral widths around zero. The results within the range of 2 km were also unreliable, as the near-field effect of the radar system and land objects could govern the echoes. Upon excluding the range cells beyond ∼35 km and less than ∼2.5 km, most of the differences were observed to be negative. A negative (positive) difference in the mean spectral widths indicates that the NC-Capon beamformer yields a narrower (broader) spectral width than the Fourier beamformer.
(a) Histograms of the differences in the first-order spectral widths between NC-Capon and F beamformers. The values in percentage at the left and right sides of the histograms denote, respectively, the relative numbers of negative and positive ΔW. Backward (negative) and forward (positive) spectral sides are processed separately. Yellow region: backward; blue region: forward; brown region: overlapped. (b) Profiles of the differences in mean spectral widths between the two beamformers. SNR profiles (dotted and solid blue curves) are the same as in Fig. 3c. Data time: 0000–0300 UTC 15 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
Further investigations using the data from different time periods revealed a similar scenario; i.e., most of the ΔW values were negative, as demonstrated in Fig. 6. In calculation, a set of histograms at five beamforming angles were produced every 3 h, similar to that illustrated in Fig. 5a. Figure 6 presents the number percentage of negative ΔW observed between 3 and 30 November 2020. Forward and backward sides are displayed, respectively. First, it is observed that the percentages were mostly larger than 50%, irrespective of beamforming angle and backward and forward spectra. This reaffirms that, in general, the NC-Capon beamformer yields smaller spectral widths than the Fourier beamformer. Second, the percentage of negative ΔW varied periodically, particularly following the departure of the typhoon from the Taiwan Strait, occurring approximately from the 238.5-h mark. The most prominent variation cycle was close to the period of the diurnal tide. A semidiurnal period was also discernible but less distinct, for example, between 286.5 and 382.5 h. These features imply that the performances of NC-Capon and Fourier beamformers might depend on the prevailing sea state. As exemplified by a 52-MHz VHF coastal radar for the northern part of the Taiwan Strait (Chen et al. 2019), the spectral widths correlated with tidal periods. This could also happen to the radar observation at the middle part of the strait.
Temporal variation in the number percentage of negative spectral width difference ΔW (indicated in Fig. 4a). Backward (negative) and forward (positive) spectral sides at different beamforming angles are displayed, respectively. A set of histograms at five beamforming angles were produced every 3 h. Date time: 3–30 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
To learn more about the correlation between spectral width and tidal period, Fig. 7 shows the temporal variation in spectral widths from 3 to 30 November 2020, in the range interval between 2 and 20 km where the periodic variation can be distinguished more clearly. In the calculation, eight spectra were averaged to acquire smoother Doppler spectra, giving an estimate of approximately 30 min. In Fig. 7a, the outcomes were averaged further over 3 h and four range cells. The bottom panel presents the sea level height observed by a tidal gauge at the Taichung Harbor. The tidal data indicate that the semidiurnal tide governed the sea level, and two spring tides occurred around 320 and 680 h. Inspecting the spectral widths in Fig. 7a, the most impressive variation cycle was not the semidiurnal but quasi-diurnal period, particularly apparent after 300 h. Figure 7b extends the time interval between 300 and 420 h, where the outcomes within only 1 h were averaged to yield a higher time resolution. As observed, the semidiurnal period was noticeable within the 4-km range. By contrast, five periodic cycles close to but slightly shorter than the period of the diurnal tide were predominant beyond the 4-km range; nevertheless, semidiurnal and other periodic tides also existed and modulated the five primary cycles.
Temporal variation of spectral widths at a selected range interval. (a),(b) The results of different time intervals. Results retrieved by F (blue) and NC-Capon (red) beamformers are shown, in which four range cells are averaged as one and shown in a 2-km range interval. Forward and backward sides are displayed in the upper and lower parts of the 2-km range interval, respectively. The number pair, 0.05 and 0.25, given at the lower-right sides of the upper panels, denotes the value interval of spectral width spanning in a 1-km range interval. The sea level heights observed at Taichung Harbor are displayed on the bottom panels.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
A comprehensive investigation into the intricate variations in spectral width and their correlation with the sea state is a potential avenue for research, albeit beyond the scope of the current study. Our primary focus is to compare the performances of the NC-Capon and Fourier beamformers. We demonstrate that both beamformers yielded concordant variations in spectral widths, and it is worth noting that the NC-Capon beamformer statistically generated narrower spectral widths compared to the Fourier beamformer. The comparisons presented in Figs. 4–7 provide supporting evidence for these conclusions. In addition, it is noteworthy that there were occasional distinctions between the backward and forward spectral performances. A deeper comparison of the backward and forward spectral characteristics is worthy of future exploration.
Figures 4 and 5 clearly illustrate the dynamic variation in the disparity between the spectral widths yielded by the two distinct beamformers, showcasing the influence of range, beamforming angle, and SNR. In alignment with conventional expectations, an increase in range corresponded with a typical decrease in SNR. Further statistical examination is demonstrated in Fig. 8, where the mean spectral width versus SNR is shown. The results at different beamforming angles and from forward and backward spectra are illustrated, respectively. It is observed that the spectral widths of the two beamformers tended to approach each other at lower and higher SNR conditions. The discrepancy between the two beamformers was most prominent in the middle range of SNR, where the values from the NC-Capon beamformer were smaller. Notice that the middle range of SNR depended on the beamforming angle and forward and backward spectra. In an extremely low SNR condition, noise dominates the signals, rendering the performances of the two beamformers indistinguishable. On the other hand, the signals from the sidelobes of the beamforming pattern have less contribution to the echoes from the main lobe in a significant SNR situation, diminishing the superior efficiency of the NC-Capon beamformer in suppressing the sidelobe echoes. In summary, the NC-Capon beamformer can enhance the concentration of sea echoes when the SNR decreases while the signals are still detectable, giving a narrower spectral width.
Mean spectral width vs SNR. (top) From forward spectra. (bottom) From backward spectra. Date time: 3–30 Nov 2020. Range interval: 2–40 km.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
c. Doppler and radial velocities
The Doppler and radial velocities are additional parameters for evaluating the beamformer’s performance. First, we examined the separation of the two Doppler velocities estimated from the forward and backward first-order spectra, as depicted in Fig. 9. The separation is expected to be two times the Bragg-resonance velocity [2 × λfb/2 = (300/27.75) m × 0.5372 Hz ≅ 5.81 m s−1], as indicated by the vertical dashed lines in Fig. 9. Indeed, the histograms show that the separation values were around 5.81 m s−1, except for the farther distance (>35 km) at the beamforming angles of ±30° and ±60° where the SNRs were relatively low, and the separation values were distributed more diffusively. This signifies the accuracy of the computing process, as well as the robustness of the retrieval methods. Interferences at distances beyond ∼30 km were detected by the beamforming angle −30°, as marked by the frame in green. Discarding these interferences, the NC-Capon beamformer (red curve) yielded more events concentrating on the expected location (5.81 m s−1), particularly between 20 and 35 km of the beamforming angles at ±60° and between 25 and 38 km of the beamforming angle 30° (marked by the frames in black). This feature suggests that the NC-Capon beamformer could be more effective under a larger beamforming angle or a lower SNR. Additional pieces of evidence for this comment are given below.
Histograms (stairstep curves) of the separation between the two first-order Doppler velocities estimated from forward and backward spectra, respectively. Beamforming angles are −60° −30°, 0°, 30°, and 60°. Results from the spectra retrieved by F and NC-Capon beamformers, in which four range cells are integrated into one, are shown. SNR profiles (blue curves) are the same as in Fig. 3c. Data time: 0000–0300 UTC 15 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
Figure 10 displays the histograms of Doppler velocities obtained from the backward and forward sides of the spectra for the data examined in Fig. 9. As shown, the disparity was minor in the histograms between the two beamformers (black and red stairstep curves) at shorter distances, say, within ∼15 km from the coastal line. In contrast, the difference between the two stairstep curves became visible at farther ranges, particularly notable at the beamforming angles of ±60° and ±30°, where the NC-Capon beamformer yielded more concentrated Doppler velocities than the Fourier beamformer (marked by the frames in black). Additional case studies yielded similar consequences (not shown). Based on these examinations, the NC-Capon beamformer is expected to provide superior outcomes to the Fourier beamformer for retrieving the sea surface current at larger beamforming angles or lower SNR conditions. In addition, it is observed that the histogram peaks of the two beamformers could be slightly different, as marked by the green frames, for example. This suggests that the retrieved Doppler velocities could sometimes differ between the two beamformers. The correctness of the two retrieved Doppler velocities can be validated by comparing the radar observation with the in situ measurement of sea current; unfortunately, this cannot be achieved in this study because of the lack of in situ measured data in these range intervals.
Histograms (stairstep curves) of the Doppler velocities estimated from the first-order spectra at beamforming angles of (a) −60°, (b) −30°, (c) 0°, (d) 30°, and (e) 60°. Results from the forward and backward spectra retrieved by F and NC-Capon beamformers, in which four range cells are integrated into one, are shown. SNR profiles (blue curves) are the same as in Fig. 3c. Data time: 0000–0300 UTC 15 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
For a more comprehensive examination of the divergence in the Doppler/radial velocities obtained through the two beamformers, Fig. 11 provides insightful comparisons. Figures 11a and 11b show the temporal fluctuations in radial velocities (upper panels) alongside their associated standard deviations (lower panels) for the beamforming angles of −60° and 30°, respectively, and both encompass the same range interval of 8 km between 24 and 32 km. Note that each data point presented in the plots was an outcome estimated from the measurements over 3 h and four range cells (equating to a 2-km range interval). In the chosen range interval, the histograms detailing the Doppler velocities exhibited a discernible contrast between the NC-Capon and Fourier beamformers, as shown in Fig. 10. Forward and backward sides are displayed in the upper and lower parts of the 2-km range interval, respectively. The value scales are given at the lower-right side of the panels (marked with shadow): from −1 to 1 m s−1 for Doppler velocity and 0–1 m s−1 for standard deviation.
(a),(b) The temporal variations of radial velocities and (c) the corresponding standard deviations at a chosen range interval. Results retrieved by the F (blue) and NC-Capon (red) beamformers are shown, in which four range cells are integrated into one and shown in a 2-km range interval. Forward and backward sides are displayed in the upper and lower parts of the 2-km range interval, respectively. The numbers at the lower-right side of the panel (marked with shadow) denote the value intervals of the parameters. (c) The histograms (stairstep curves) of differences between the two standard deviations of radial velocities (NC minus F).
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
The upper panels of Figs. 11a and 11b show consistency between the radial velocities yielded by the two beamformers over a prolonged temporal span, and the tidal currents riding on the long-term variation are visible. Nevertheless, disparities are also observable in certain instances. The standard deviation of the radial velocities can further reveal the difference in radial velocities, as shown in the lower panels of Figs. 11a and 11b. Overall, the standard deviations from the NC-Capon beamformer were smaller than those from the Fourier beamformer for the beamforming angle of −60°. For the beamforming angle of 30° in Fig. 11b, however, the standard deviations of the radial velocities given by the two beamformers were very small and close to each other during the time interval of 300 and 450 h, irrespective of forward or backward sides. In addition, we can observe in Fig. 11b that the radial velocities and their standard deviations estimated from the forward spectra had minor differences between the two beamformers. This raises the question again that the forward and backward spectra could perform differently, which may depend on beamforming angle, range, sea state (e.g., direction and spreading of Bragg waves and wave–current interactions), and so on.
Figure 11c provides the histograms (stairstep curves) depicting the differences between the two standard deviations of radial velocities (NC minus Fourier) from the whole data. The two examples shown in Figs. 11a and 11b are framed in the plot. As seen in the framed region of the −60° beamforming angle, most standard deviations were negative, irrespective of forward and backward sides. This feature was similarly observed in the 60° beamforming angle within the same range interval. By contrast, in the framed region of the 30° beamforming angle, most standard deviations from the backward spectra were negative, while those from the forward spectra were nearly symmetrically distributed around and close to zero. Apart from the regions mentioned above and ignoring the places at farther ranges where SNRs were relatively low, the histograms of differences between the two standard deviations of radial velocities were nearly symmetric to zero. These observations imply that the two beamformers generally yielded concordant Doppler velocities but might sometimes produce discrepant outcomes at different sea states, ranges, and beamforming angles.
d. Comparison of radial currents
In the previous sections, we demonstrate that in contrast to the Fourier beamformer, the NC-Capon beamformer statistically yields narrower spectral widths and could effectively produce more outcomes of Doppler velocity under a larger beamforming angle or a lower SNR. Demonstrating the NC-Capon beamformer’s optimal performance requires comparing the radar outcomes and in situ measurements of sea surface currents through buoys or other measurement instruments at farther distances from the radar site, where the low SNR conditions are typically encountered. Regrettably, the absence of such measurement campaigns in the period of radar data collection and the foreseeable future makes such comparison unavailable. Despite this difficulty, we indeed compared the radar outcomes with the in situ measurements of an ADCP lying to the west-southwest of the radar, approximately 4.5 km away from the radar (see section 2a for the description of the instruments).
Figures 12a–c show the hourly variations of radial velocities retrieved by the NC-Capon and Fourier beamformers with the radar data in 3–30 November 2020 and in the range cell 10 where the ADCP was approximately located. The radial velocity measured by the ADCP is a projection along the direction of the line connecting the radar and the ADCP. In producing the radial velocity from the radar data, a beamforming angle step of 1° was conducted, and one of the radial velocities having more considerable spectral power from the backward and forward spectra was adopted. Finally, the outcomes of four beam angles centering on the ADCP direction were averaged to increase reliability. In this comparison, a three-point running mean (∼3 h) was executed to smooth the curve. Then, correlation coefficients with a running window of 36 h were calculated through the data series, as indicated by the black curve. Scattering plots of the radar versus the ADCP outcomes are also provided in the right panels. Two findings and discussion for Fig. 12 are described below:
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Overall, the radial velocities of the radar and the ADCP varied concordantly in the cases of both beamformers. Figures 12a and 12b show that the Fourier beamformer seems marginally closer to the ADCP results even though the NC-Capon beamformer yielded a slightly greater portion of correlation coefficients above 0.5, i.e., 96.3% > 95.4%. In reality, the two beamformers’ performances at this place were similar, as shown in Fig. 12c.
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The scatterplots in Figs. 12a and 12b show that the slopes of the regression lines were smaller than one, indicating that the magnitudes of the radar-measured radial velocities were smaller than those of the ADCP-measured; i.e., the amplitude variation in the radar-measured radial velocity was more moderate than that of the ADCP, as observed in the hourly variations of radial velocities in the left panels. Despite the discrepancy in magnitude, the correlation coefficients (CCs) were mostly larger than 0.5, except around 120 h (7 November 2020) when Typhoon Atsani was passing through the southern part of the sea area and around 390 h when the retrieved radial velocities had more significant differences between radar and ADCP. The difference between radar and ADCP measurements could be mainly attributed to two reasons. The first is the different water depths at which the two instruments are measuring, even when the ADCP data closest to the sea surface are used in comparison with the radar measurement. The ADCP surface velocities adopted here refer to the location approximately 4–5 m below the sea surface, but the radar measures the current velocity near the sea surface ranging from 0 to about 1 m in depth. Second, the coverage water area of the radar measurement in a range cell is considerably more extensive than that of the fixed-point ADCP record, and moreover, the outcomes of three radar beams around the ADCP direction were averaged in our calculation for comparison with ADCP measurement. Therefore, each radar velocity was a smoothed average of the sea state covered by a much wider water area than the ADCP location.
Sea surface radial currents observed by ADCP and retrieved by (a) F and (b) NC-Capon beamformers. (c) The comparison of F and NC-Capon results. CCs are between ADCP and radar measurements, and the percentage indicates the amount of CC values larger than 0.5. The two values given in the scatterplot are the slope and intercept of the regression line (solid). Data time: 3–30 Nov 2020.
Citation: Journal of Atmospheric and Oceanic Technology 41, 11; 10.1175/JTECH-D-23-0046.1
In short, Fig. 12 demonstrates that both beamformers yielded similar radial velocities, and the variations of radial velocities were generally accordant with those of the ADCP readings approximately 4.5 km from the radar site. Nonetheless, more work and comparison are needed in the future to see the main differences between the two beamformers at farther distances and in lower SNR conditions.
4. Conclusions
The primary purpose of this study was to assess the efficacy of the NC-Capon beamformer in enhancing Doppler spectral resolution, a factor crucial for ocean current monitoring. This assessment was achieved through a comparative analysis of the spectral peak widths in the Doppler spectra and the spectral width and Doppler/radial velocity of the first-order sea echoes, in contrast to those computed using the Fourier beamformer, a widely adopted method for coastal HF radar applications. The results demonstrate that the NC-Capon beamformer yielded narrower spectral peaks, which is indicative of improved Doppler spectral resolution. Consequently, the NC-Capon beamformer generally gave narrower spectral widths for the first-order sea echoes, especially in lower signal-to-noise ratio (SNR) conditions. Furthermore, the NC-Capon beamformer generated more reliable Doppler/radial velocities for the first-order sea echoes, characterized by smaller standard deviations, particularly under the circumstances of lower SNR and larger beamforming angle. In sum, the NC-Capon beamformer enhanced the concentration of the first-order sea echoes and delivered more dependable estimations of Doppler/radial velocity in the conditions of lower SNR or larger beamforming angle, as compared with the Fourier beamformer. This enhancement is anticipated to significantly contribute to deriving the sea surface current field. It is also expected that the second- and higher-order sea echoes could be extracted more efficiently through the improved Doppler spectral resolution yielded by the NC-Capon beamformer. This issue requires more effort and space to discuss; it is left for future work.
This study also highlighted discrepancies in the performance of forward and backward spectra in deriving spectral parameters. These discrepancies could potentially be attributed to various factors, including sea surface wind conditions, SNR, wave characteristics at different beamforming angles, and other related parameters. Furthermore, the spectral parameters exhibited variations in response to tidal phase and meteorological conditions such as the passage of typhoons, leading to corresponding variations in the performance of the two beamformers. The underlying physical mechanisms responsible for these observations, however, have not been comprehensively investigated or discussed in this study. To address these gaps and enhance the robustness of the NC-Capon beamformer when applied with antenna-arrayed coastal radar, further comparisons between radar-observed current velocities, wave parameters, and in situ measurements are required. Present, we made an initial comparison of the radar radial velocities with the in situ measurements of an ADCP located approximately 4.5 km from the radar. It shows that the NC-Capon and Fourier beamformers yielded similar radial velocities, and the variations of radial velocities were generally accordant with those of the ADCP. This supports the usability of the NC-Capon beamformer. For lack of in situ measurements at farther distances from the radar site where the low SNR conditions are typically encountered and could verify the optimal performance of NC-Capon beamformer, collections of in situ marine data in the farther sea area are needed in the future.
Acknowledgments.
This research received partial support from Grant IOT-111-H2D018, provided by the Transportation Technology Research Center (TTRC; formerly known as the Harbor and Marine Technology Center), Institute of Transportation, Ministry of Transportation and Communications, Taiwan. Additional funding was obtained from the National Science and Technology Council of Taiwan through Grants NSTC112-2111-M-039-001 and NSTC113-2111-M039-001 from the China Medical University of Taiwan under Grant CMU111-MF-76. The authors express sincere gratitude to the colleagues at the TTRC for their invaluable assistance, facility support, and contributions to the provision and validation of the coastal radar data. The authors also thank Dr. Pierre Flament for his continuing contribution to instrument installation, monitoring, and improving data quality for our coastal radar.
Data availability statement.
The coastal radar data used in this study were generously provided by the Transportation Technology Research Center, Institute of Transportation, Ministry of Transportation and Communications, Taiwan. For inquiries regarding access to the radar data, please contact the corresponding authors.
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