Quality Control for Ocean Current Measurement Using High-Frequency Direction-Finding Radar

Abstract

High-frequency radars (HFRs) are important for remote sensing of the marine environment due to their ability to provide real-time, wide-coverage, and high-resolution measurements of the ocean surface current, wave height, and wind speed. However, due to the intricate multidimensional processing demands (e.g., time, Doppler, and space) for internal data and effective suppression of external noise, conducting quality control (QC) on radar-measured data is of great importance. In this paper, we first present a comprehensive quality evaluation model for both radial current and synthesized vector current obtained by direction-finding (DF) HFRs. In the proposed model, the quality factor (QF) is calculated for each current cell to evaluate its reliability. The QF for the radial current depends on the signal-to-noise ratio (SNR) and DF factor of the first-order Bragg peak region in the range–Doppler (RD) spectrum, and the QF for the synthesized vector current can be calculated using an error propagation model based on geometric dilution of precision (GDOP). A QC method is then proposed for processing HFR-derived surface current data via the following steps: (1) signal preprocessing is performed to minimize the effect of unwanted external signals such as radio frequency interference and ionospheric clutter; (2) radial currents with low QFs and outliers are removed; (3) the vector currents with low QFs are also removed before spatial smoothing and interpolation. The proposed QC method is validated using a one-month-long dataset collected by the Ocean State Monitoring and Analyzing Radar, model S (OSMAR-S). The improvement in the current quality is proven to be significant. Using the buoy data as ground truth, after applying QC, the correlation coefficients (CCs) of the radial current, synthesized current speed, and synthesized current direction are increased by 4.33~102.91%, 1.04~90.74%, and 1.20~62.67%, respectively, and the root mean square errors (RMSEs) are decreased by 2.51~49.65%, 7.86~27.22%, and 1.68~28.99%, respectively. The proposed QC method has now been incorporated into the operational software (RemoteSiteConsole v1.0.0.65) of OSMAR-S.

1. Introduction

High-frequency radar (HFR) has attracted extensive attention from the research community, coastal managers, and private organizations due to its ability to map ocean surface currents well beyond the horizon with fine spatial and temporal scales. It has become a valuable tool for operational oceanography [1,2,3,4,5], including ocean dynamics modeling [6], sea ice sensing [7], and other applications [8]. In recent years, there has been a growing interest in developing HFR networks [9]. These HFR networks can provide high-precision measurement of ocean surface current, which is essential for marine science, environmental protection, and maritime security, etc. As the coverage and applications of these networks continue to expand, the importance of the quality control (QC) of radar data becomes increasingly evident. The quality of the radar signal will be affected by the complexity of electromagnetic scattering, frequent external interference from other radio users and lightning, and internal signal-processing algorithms involved in current mapping. There are many uncertainties in different aspects of single-site HFR processing, such as the identification of Doppler lines in the first-order Bragg region and the averaging in the spatial and temporal domain [10]. These uncertainties will also be propagated to the final vector current estimates when multiple radar sites are used for current synthesis. Therefore, it is necessary to perform QC to ensure the reliability and accuracy of the current measurements before they are put into practical use.

Many coastal countries have developed their HFRs with different types of receiving antennas and corresponding signal-processing algorithms. For example, the SeaSonde system [11] uses a compact crossed-loop/monopole antenna (CMA), and the Wellen Radar (WERA) [12] uses a uniform linear array (ULA). For compact radar with CMA, direction finding (DF) instead of beamforming should be used to identify the direction of arrival (DOA) of each Doppler cell due to its wide beam. In general, compact direction-finding (DF) radars are somewhat inferior to beamforming radars in both the accuracy and detection range of current measurements, but they are often preferred in practical application owing to their ease of deployment. Correspondingly, different QC measures should be taken for different types of radar systems.

Numerous efforts have been made to enhance QC methods for current measurements using HFR. Lipa described the methods to derive the uncertainties of the radial and vector current for the SeaSonde and provided suggestions to minimize these uncertainties [13]. Laws et al. reported how to estimate and assess the current measurement errors related to antenna pattern distortion (APD) for the SeaSonde [14]. They also introduced a model for assessing HFR current measurement error based on subperiod measurement variance [15], which was demonstrated to be able to improve the assessment of current measurement uncertainty. Kirincich et al. developed QC thresholds by examining signal-to-noise ratio (SNR)-related radial metrics and DF quality metrics, which improved the root mean square error (RMSE) of current measurement by up to 2 cm/s based on a two-month-long dataset [16]. Roarty et al. continuously worked on the development of operational QC methods and laid out the framework for quality assurance (QA) methods and QC tests for the entire data processing chain [17,18]. Kim presented examples of the data quality assessment of radial currents obtained by HFR using statistical and dynamical approaches in a hindcast mode [19]. Paolo et al. examined the use of radial metrics outputs from the SeaSonde to enhance the accuracy of radial current measurements and reduce error [20]. Haines et al. implemented a QC method using non-velocity metrics of the signal quality and solutions to address the challenge of the coexistence of high and low currents [21]. Ren et al. applied a nudging data assimilation algorithm to incorporate real-time HFR current measurements into a numerical model, which improved the predictive capability of the numerical model [22]. Cosoli et al. developed a real-time and offline QC methodology based on the determination of Doppler line SNR values that contribute to hourly radial current at each range-bearing pair for the SeaSonde [23,24]. Doppler velocities are weighted by their SNR values and spectral quality factors. Velocities are then averaged to produce a final output. Michael et al. developed a unified radial data delay mode QC method, which consists of a five-step QC process [25]. The effectiveness of the method was verified by comparing the post-processed radial current with the original radial file generated by the remote site. Lorente et al. [26] proposed a combined quality control methodology and applied it to real-time web monitoring of nonvelocity-based diagnostic parameters to infer both radar site status and HF radar system performance. The validation of HF radar data with independent in situ observations from a moored current meter was conducted. The results show that the accuracy assessment of radial and total vectors is highly consistent. Lipa et al. developed a QC method for broad-beam HFR current measurements, which involves an internal consistency check between the measured Doppler spectra and the values predicted from fundamental equations [27]. Emery and Washburn concluded that the main sources of error in oceanographic HFR came from DF uncertainties and that these DF uncertainties were suitable for assimilation into numerical models [28]. Due to a vested interest in collecting high-quality national scale data, the United States Integrated Ocean Observing System (U.S. IOOS) continued to develop QC protocols for real-time HFR measurements [29]. Previous studies on wide-beam radar have shown that the QC methods based on the SNR and spatial–spectral metrics can improve the quality of radar current data. However, the QC methods mentioned above mainly provide quality flags such as pass, not evaluated, suspected, failed, and missing. No quality factors (QFs) based on the quantified relation between the SNR and spatial–spectral metrics as well as the reliability factor have been used. Moreover, the connection between the quality of vector current and that of radial current has not been investigated yet. As a result, it is a challenge for different users to select radials and vectors of specific quality levels that meet their needs using these existing QF models.

Extensive evaluations and comparisons with in situ observations including drifters, acoustic Doppler current profilers, buoys, and point-based current meters [30,31,32,33,34,35,36] have demonstrated that HFR can accurately measure ocean surface currents. A series of field experiments have shown that the root mean square error (RMSE) between radar and in situ current measurements typically falls within the range of 5 to 67 cm/s, and the correlation coefficient (CC) often remains below 0.92, as shown in

Table 1. Radar accuracies in references.

Reference	Radar and Freq. (MHz)	Period and Validation	QC	CC	RMSE
Emery et al. [30]	CODAR 13	June 1997–November 1999 Radials	No	0.62–0.88	7–19 cm/s
Kaplan et al. [31]	CODAR 12.5	May–December 2001 Total	No	0.59–0.92	5–15 cm/s
Cosoli et al. [32]	CODAR 25–36	August–September 2005 Radials	No	0.14–0.84	8–20 cm/s
Paduan et al. [33]	CODAR 13–25	July–September 2003 Radials	No	0.25–0.81	9–28 cm/s
Rubio et al. [34]	CODAR 4.5	2009 Totals	No	0.21–0.91	8–27 cm/s
Solabarrieta et al. [35]	CODAR 4.5	January 2009–September 2011 Totals	Yes	0.27–0.86	8–16 cm/s
Lorente et al. [36]	CODAR 5	January–December 2012 Radials + Totals	No	0.32–0.74	8–17 cm/s
Haines et al. [21]	CODAR 5	September–December 2014 Radials	No	0.46–0.82	14–67 cm/s
Haines et al. [21]	CODAR 5	September–December 2014 Radials	Yes	0.51–0.86	12–55 cm/s

. In addition, some other factors such as radio frequency interference (RFI), impulse interference (IMI), and ionospheric clutter can also affect the quality of the surface current. Thus, there is still much room to further improve the quality of radar measurements.

Aiming at QC for the current measured by compact DF HFRs, this study proposes QF models for radial current and vector current, respectively, which provide a basis for the presented QC method. Firstly, signal preprocessing is performed to remove IMI and RFI that frequently occur in the HF band. Then, the QF for each radial current is calculated based on signal metrics, including the SNR and angular spectrum. Finally, in the synthesis of vector current, the QF for each vector current is obtained via an error propagation model according to the geometric dilution of precision (GDOP). Based on the proposed model, more effective data can be achieved for both radial and vector currents. The proposed QC method is validated using a one-month-long HFR dataset collected by the Ocean State Monitoring and Analyzing Radar, model S (OSMAR-S) [37] in comparison with buoy measurements.

The remainder of this paper is organized as follows: Section 2 describes the proposed QF models for radial current and vector current, and the QC method. Section 3 shows the improvement in radar current measurements resulting from QC. Section 4 provides some discussions and Section 5 draws the conclusion.

2. QF Models and QC Method

To address the challenge of evaluating and improving HFR current measurements, a QC method is developed for radial current and vector current, respectively. Within the QC method, a QF is calculated for each radial current or vector current to indicate its reliability level. Data users can then select currents of certain qualities for different marine applications.

2.1. QF Model for Radial Current

The radial currents are extracted from the Doppler lines in the first-order Bragg region in the HFR range–Doppler spectrum. Correspondingly, an empirical QF model is constructed here using the underlying signal indices, including the SNR- and DF-related metrics.

2.1.1. SNR-Related QF

As described in [14], the SNR plays a key role in identifying each Doppler line in the first-order Bragg region and subsequent DOA estimation. Therefore, the SNR of each Doppler line is taken as a major quality metric. In this study, the noise floor is estimated by averaging the spectrum in the region beyond ±1.8 times the Bragg frequency at each range bin. Using an SNR reference value of 12 dB, the SNR-related QF is given by

$$q_{snr}=\min (10\lg (P_S/P_N)/12,1),$$

(1)

where $P_S$ is the power of the Doppler line and $P_N$ is the power of the noise floor.

To strike a balance between the radial current qualities and detection range, an empirical range-dependent SNR threshold [37], η, is used to select strong Doppler lines in the first-order Bragg region for further current extraction, and it is given by

$$\eta =\left\{\begin{array}{c}10\mathrm{dB},\\ (12-r/20)\mathrm{dB},\\ 8\mathrm{dB},\end{array}\right.\begin{array}{c}\hfill 0<r<40\mathrm{km}\\ \hfill 40\mathrm{km}\le r<80\mathrm{km}\\ \hfill r\ge 80\mathrm{km}\end{array},$$

(2)

where $r$ is the radar range.

2.1.2. DF-Related QF

For each Doppler line in the first-order Bragg region, DF is used to estimate the DOA of the radial current. Errors in the DOA will cause biases in the estimated radial velocity and thus degrade the accuracy of the final estimates of the vector current field. Consequently, the quality of the radial current measurement also highly relies on the accuracy of the DOA estimation.

In this study, the MUltiple SIgnal Classification (MUSIC) algorithm is used to calculate the spatial spectrum and determine the DOA. The DOA variance associated with MUSIC in the case of a single source can be found in [38], which is given by

$$\mathrm{var}(\stackrel{\wedge }{\theta })=\frac{1}{2K\cdot \mathrm{SNR}}\left\{1+\frac{{[a^H(\theta )a(\theta )]}^{-1}}{\mathrm{SNR}}\right\}/h(\theta ),$$

(3a)

$$h(\theta )={\dot{a}}^H(\theta )\{\mathrm{I}-a(\theta ){[a^H(\theta )a(\theta )]}^{-1}{a}^H(\theta )\}\dot{a}(\theta ),$$

(3b)

where $\theta$ is the incident azimuth, $a(\theta )$ is the steering vector, $\dot{a}(\theta )$ is the derivative of $a(\theta )$, $a^H(\theta )$ is the transposition of $a(\theta )$, and $K$ is the number of snapshots.

The use of measured antenna patterns has been reported to be beneficial to the accuracy of current measurements [39], but it may also result in blanking regions in the radial current map. When measured patterns are available, they can be substituted into (3), and correspondingly the variance should be calculated numerically. Otherwise, an analytical solution can be sought using the ideal model.

For the CMA antenna used in this study, the ideal steering vector can be expressed as [39]

$$a(\theta )=[1,\cos (\theta +\pi /4),\sin (\theta +\pi /4)],$$

(4)

and the corresponding DOA variance estimation is given by [40]

$$\mathrm{var}(\stackrel{\wedge }{\theta })=\frac{1}{2K\cdot \mathrm{SNR}}(1+\frac{1}{2\mathrm{SNR}}).$$

(5)

This DOA variance is independent of the actual DOA and decreases monotonically as the SNR increases, as shown in Figure 1. In OSMAR-S, the number of snapshots is 17, so at the SNR threshold for radial current extraction (≥8 dB) the standard deviation of the DOA error is less than 4.1° in theory. This error is relatively small and acceptable for radial current mapping, but it has a significant effect on the overall error in the vector current measurements.

The DF error-related QF is written as

$$q_{doa}=\min (\frac{2.5}{\sqrt{\mathrm{var}(\hat{\theta })}},1),$$

(6)

where 2.5° is the standard deviation of the DOA estimation when the SNR is 12 dB. As described in (5), the DF-related QF also relies on the SNR value but in an indirect way.

The DOA can be determined according to the peak of the MUSIC spectrum. Because the MUSIC algorithm decomposes the data into signal and noise subspaces, the prominence of the eigenvalue(s) can also serve as an indicator of quality. Thus, the ratio of the eigenvalue(s) of the signal subspace to that of the noise subspace can be used to form an eigenvalue-related QF. In the case of a single source, the eigenvalue-related QF is given by

$$q_{ev}=\min (\lg [2{\lambda }_1/({\lambda }_2+{\lambda }_3)],1),$$

(7)

while in the case of dual sources, it is calculated as

$$q_{ev,i}=\min (\lg ({\lambda }_i/{\lambda }_3),1),(i=1,2),$$

(8)

where ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ are the three eigenvalues sorted in a descending order.

Since the CMA has three elements, the maximum number of sources resolvable at the same Doppler frequency is two. Considering that the DF accuracy in the case of dual sources is lower than that of a single source, an extra QF is introduced as

$$q_{nos}=\left\{\begin{array}{l}1,\mathrm{for}\mathrm{single}\mathrm{source}\\ 0.9,\mathrm{for}\mathrm{dual}\mathrm{sources}\end{array}\right..$$

(9)

Based on the above analyses, the overall DF-related QF is

$$q_{df}=q_{doa}\times q_{ev}\times q_{nos}.$$

(10)

2.1.3. Overall QF of Radial Current

The overall QF for radial current is obtained as the product of $q_{snr}$ and $q_{df}$, i.e.,

$$q_{RC}=q_{snr}\times q_{df}.$$

(11)

Note $0\le q_{RC}\le 1$.

This QF can also serve as a model for error propagation in radial current extraction. The variance of the initial speed quantization error can be determined in terms of the Doppler resolution as

$${\sigma }_v^2=var({\delta }_v)=var(\frac{\lambda \Delta f}{2})=\frac{{\lambda }^2}{48{(MT)}^2},$$

(12)

where ${\sigma }_v$ is the standard deviation of radial current speed, and ${\delta }_v$ is the quantization error of speed, $T$ is the sweep period and M is the number of points in the window for calculating the power spectrum, and $\lambda$ is the wavelength of radar wave. Taking OSMAR-S as an example, M is 1024, T is 0.38 s, when the system operates at 13 MHz, the standard deviation ${\sigma }_v$ is 1.71 cm/s.

The variance in radial current speed is a key contributor to the accuracy of the HFR surface current. The question is how to establish a relationship between QF and the variance of a given radial current. Assuming this relation is deterministic, then the variance propagation factor, k, is a function of the radial current QF, $q$,

$$k=f(q).$$

(13)

Thus, if the base variance is ${\sigma }^2$ (for $q$ = 1), the propagated variance for an arbitrary q becomes $k{\sigma }^2$. This relation enables a quantized description of the QF propagation from the radial current to the vector current.

2.2. QF Model for the Vector Current

Generally, a vector current is synthesized using the radial currents derived from two or more stations [41]. As a result, any estimation error from the radial current will be propagated to the vector current. The GDOP plays a key role in this propagation, and it consists of various factors [42] such as spatial geometry and errors in radial currents from each station. Large GDOP values often appear in the radar baseline area as well as at the edge of the vector grid.

Considering the dataset used in this study was collected from two radar stations, we will present the analysis and expression for the case with two radars here. Those for the case involving three or more radars can be derived in a similar way.

2.2.1. Principle of Vector Current Synthesis

Figure 2 shows a schematic diagram of synthesizing two radial currents into a vector current. Assume the two radial speeds are $v_{r1}$ and $v_{r2}$, their directions are ${\theta }_1$ and ${\theta }_2$ (angle to the north and positive angle runs clockwise), and the vector current speed and direction are $V$ and $\theta$, respectively. The east–west and south–north components can be determined as

$$u=\frac{v_{r1}\cos {\theta }_2-v_{r2}\cos {\theta }_1}{\sin ({\theta }_1-{\theta }_2)},$$

(14a)

$$v=\frac{v_{r2}\sin {\theta }_1-v_{r1}\sin {\theta }_2}{\sin ({\theta }_1-{\theta }_2)}.$$

(14b)

Thus, the vector current speed and direction are $V=\sqrt{u^2+v^2}$, $\theta =\arctan \frac{u}{v}$, respectively.

2.2.2. QF of the Vector Current

Using the function theory of random variables [43], we can derive the variance in the vector current from those in the radial currents as

$$\begin{array}{c}{\sigma }_S^2=\frac{{(u\cos {\theta }_2-v\sin {\theta }_2)}^2{\sigma }_1^2+{(u\cos {\theta }_1-v\sin {\theta }_1)}^2{\sigma }_2^2}{V^2{\sin }^2({\theta }_1-{\theta }_2)}\\ =\frac{{\sin }^2(\theta -{\theta }_2){\sigma }_1^2+{\sin }^2(\theta -{\theta }_1){\sigma }_2^2}{{\sin }^2({\theta }_1-{\theta }_2)}\hfill \end{array},$$

(15)

where ${\sigma }_1^2$ and ${\sigma }_2^2$ are the variances in radial currents obtained from two stations, respectively. Once the variances in the radial currents involved in the vector synthesis are obtained, the final vector current variance can be calculated by considering the geometry. It should be noted that the effects of the distances of the grid point to the radar sites have been implied in the radial variances ${\sigma }_1^2$ and ${\sigma }_2^2$.

Equation (15) depicts the GDOP for vector synthesis, but besides the geometry of the grid cell and the radars, it is also dependent on the radial current speed variance and vector current direction. This means the GDOP varies with current distribution, environmental noise level, and radar parameters, etc. In other words, the GDOP should not be determined only according to the geometry.

The QF calculation process for the vector current is shown in Figure 3. The variance in the radial current is calculated using (13). Then the variance in the vector current is obtained from (15). Finally, an empirical reference variance is selected, and the QF of the vector current is calculated based on the ratio of the vector current variance to the reference variance.

2.3. QC Method

The accuracy and reliability of HFR measurements may be decreased by strong external noises such as interference and ionospheric clutter, which can result in raised noise levels and a reduced detection range. Particularly, when the interference and clutter overlap with the Bragg peak, they can lead to erroneous measurements of ocean surface currents.

In the OSMAR-S system, the effective detection range is up to 150 km when operating with an average transmission power of 100 W at 13 MHz. For a range resolution of 2.5 km, the maximum number of range bins with radial current information is 60.

2.3.1. Interference Detection and Suppression

Because IMI often has a strong effect on both range and Doppler dimensions, it may severely contaminate useful signals. Therefore, it is essential to detect and suppress IMI to ensure the accuracy and reliability of the received signals.

The steps of IMI suppression are illustrated as follows. Firstly, the time series of the average power for the range bins greater than 60 (i.e., reserved range bins) is obtained. Secondly, the histogram of the series is generated and a reference power is determined as the value at which the cumulative percentage exceeds a specified threshold (e.g., 70%). Thirdly, the power threshold is calculated as the summation of the reference value and a preset SNR threshold (e.g., 10 dB). Finally, samples exceeding this power threshold are identified as IMI and set to zero. To avoid the negative effect due to truncating the data over a long interval, it is necessary to check the duration of IMI. If it exceeds a certain number of points (e.g., 200 points), only those IMI samples near the peak power are removed to avoid high sidelobes caused by the nulling.

Figure 4 shows an example of IMI suppression. Figure 4a depicts a range–Doppler (RD) spectrum containing severe interference. Strong IMI overlaps with the negative Bragg peak and it significantly affects the extraction of sea state information. The range–time spectrum is displayed in Figure 4b, where strong IMI is observed across the range bins. Figure 4c illustrates the histogram and cumulated percentage of the range–time spectra. The corresponding threshold obtained is presented in Figure 4d. After nulling of the frames containing IMI, the resulting RD spectrum is displayed in Figure 4e. Notably, Figure 4e clearly demonstrates the effectiveness of IMI suppression, the negative Bragg peak, previously overwhelmed by interference, is now visible, and the noise level also drops. Figure 4f illustrates the Doppler spectra at the 30th range bin before and after IMI suppression, from which the Bragg peaks can be easily observed after IMI suppression. However, some RFIs still exist at around −1.095 Hz, −0.6735 Hz, −0.3907 Hz, and 0.7763 Hz.

RFI detection is then performed on the mean Doppler spectrum across the reserved range bins using a similar decision-making process to that used for IMI. After that, the orthogonal projection filter in the range domain [37] is used to suppress RFI. The RFI suppression results are displayed in Figure 5. Comparing Figure 5a with Figure 4e, we can see those RFIs are almost completely suppressed while the noise level remains low and flat. The Doppler spectra at the 30th range bin before and after RFI suppression are shown in Figure 5b for a more detailed comparison.

2.3.2. Ionospheric Clutter Detection and Exclusion

Ionospheric clutter is another factor that can significantly degrade the performance of HFR in the surface current measurement. Therefore, it is necessary to identify and suppress the ionosphere clutter. Various methods for detecting ionospheric clutter have been developed, e.g., [44]. Considering the difficulty in efficient suppression of ionospheric clutter with a compact radar, those range bins containing ionospheric clutter are typically excluded to prevent large errors.

An example of radar data containing ionospheric clutters is shown in Figure 6a, in which strong ionospheric clutters appear near the 16th, 110th, and 125th range bins. Figure 6b illustrates the spectrum at the 16th range bin, where the negative Bragg peak is contaminated by the ionospheric clutter.

2.3.3. Flow of QC

HFR performance can be easily affected by the external environment if no QC measure is taken. To improve the reliability of radar data, preprocessing of the radar signals is essential to suppress interference and exclude the ionospheric clutter regions. The flow charts for the radial current mapping and signal preprocessing are depicted in Figure 7. The processing for the radial current extraction with OSMAR-S is shown in Figure 7a. Further details on the mapping of the radial and vector currents can be found in [37]. Figure 7b shows the flow of RFI and ionospheric clutter suppression. Here, QC measures are taken in every module throughout the current extraction, including the radial and vector currents mapping.

3. Experimental Results

3.1. Description of Experiment

The proposed QC method was validated using the datasets collected from a field experiment that involved two HFRs at SHLI and XIAN, respectively. The HFRs were OSMAR-S, whose parameters are listed in

Table 2. Radar parameters.

Parameters	Values
Working frequency	13.37 MHz
Bandwidth	60 kHz
Sweep duration	0.256 s
Sweep repetition period	0.3799 s
Period of gate signal	1.28 ms
Duty ratio	50%
Coherent integration time	6.48 min (1024 sweeps)
Range resolution	2.5 km

. Four buoys (A, B, D, and E) were deployed within the overlapping coverage areas of the two radars to provide in situ current velocity measurements. The map of the investigated sea area is shown in Figure 8, in which the position of the radar stations and buoys are marked. The red dots represent the locations of the two radar stations, while the red triangles indicate the positions of the buoys. The maximum range of surface current mapping reaches 100 km and is denoted by the black dotted line.

Table 3. Distances between the radars and buoys and water depths at the buoy locations.

Station	SHLI (km)	XIAN (km)	Water Depth(m)
SHLI	-	60.5	-
XIAN	60.5	-	-
Buoy A	42.5	44	38
Buoy B	47	83	46
Buoy D	85.5	80.5	38
Buoy E	83	48	29

shows information about the distances between the radar and buoys, as well as the water depth. The dataset was collected over one month from 1 February 2013 to 28 February 2013.

3.2. Radial Current

The proposed QF modeling and QC methods were incorporated into the OSMAR-S software (RemoteSiteConsole v1.0.0.65) for current extraction. The QF for each current also enables a detailed evaluation of the various QFs involved.

Table 4. Statistics of the radial currents within different QF intervals at the SHLI station.

Buoy	QF	Samples	CC	RMSE (m/s)
A	0~0.4	0	-	-
	0.4~0.6	29	0.7757	0.2755
	0.6~0.8	278	0.8146	0.1833
	0.8~1.0	1707	0.8734	0.1256
B	0~0.4	0	-	-
	0.4~0.6	37	0.3177	0.2227
	0.6~0.8	321	0.4273	0.1326
	0.8~1.0	1653	0.5570	0.1117
D	0~0.4	60	0.6765	0.1955
	0.4~0.6	713	0.7889	0.1708
	0.6~0.8	702	0.9286	0.1018
	0.8~1.0	533	0.9497	0.0801
E	0~0.4	27	0.5418	0.2983
	0.4~0.6	699	0.8386	0.1818
	0.6~0.8	794	0.9195	0.1379
	0.8~1.0	488	0.9429	0.1140

and

Table 5. Statistics of the radial currents within different QF intervals at the XIAN station.

Buoy	QF	Samples	CC	RMSE (m/s)
A	0~0.4	0	-	-
	0.4~0.6	5	0.9355	0.1924
	0.6~0.8	38	0.8806	0.1265
	0.8~1.0	1972	0.9469	0.1145
B	0~0.4	26	0.8712	0.1557
	0.4~0.6	721	0.8824	0.1511
	0.6~0.8	864	0.8905	0.1343
	0.8~1.0	418	0.9062	0.1171
D	0~0.4	13	0.7752	0.1492
	0.4~0.6	481	0.6678	0.1502
	0.6~0.8	870	0.6637	0.1410
	0.8~1.0	650	0.7006	0.1204
E	0~0.4	0	-	-
	0.4~0.6	20	0.4913	0.2320
	0.6~0.8	119	0.5374	0.1821
	0.8~1.0	1876	0.3982	0.1913

show the CC and RMSE results over different QF intervals for the radial currents derived by the SHLI and XIAN radars, respectively. The data presented in these tables reveal that the current cells whose QFs are greater than 0.6 account for the vast majority of all the data and generally have higher CCs and smaller RMSEs. The rest of the current cells whose QFs are below 0.6 often display either low CCs or large RMSEs. In addition, although point B is closer to the SHLI station than other buoy locations (say, A, D, and E), its CC is much lower. This is because the radial current speed values at point B are much smaller than those at other points (see Figure 9). A similar phenomenon can be observed at point E for the XIAN station.

According to the above analysis, only those current cells whose QFs are above 0.6 are retained for further processing, and this is a core criterion for the QC in this study.

Table 6. Accuracy of the OSMAR-S radial current incorporating different QF components.

Buoy	Station	-	-	CC	RMSE (m/s)	Change
						CC Increase (%)	RMSE Reduction (%)
A	SHLI	Before QC		0.8478	0.1431	-	-
		After QC	$q_{snr}$	0.8594	0.1381	1.37	3.49
			$q_{df}$	0.8647	0.1350	1.99	5.66
			$q_{RC}$	0.8639	0.1351	1.90	5.59
	XIAN	Before QC		0.9396	0.1212	-	-
		After QC	$q_{snr}$	0.9461	0.1150	0.69	5.12
			$q_{df}$	0.9462	0.1151	0.70	5.03
			$q_{RC}$	0.9463	0.1147	0.71	5.36
B	SHLI	Before QC		0.4793	0.1352	-	-
		After QC	$q_{snr}$	0.5201	0.1183	8.51	12.50
			$q_{df}$	0.5342	0.1155	11.45	14.57
			$q_{RC}$	0.5343	0.1153	11.48	14.72
	XIAN	Before QC		0.7097	0.2216	-	-
		After QC	$q_{snr}$	0.8893	0.1376	25.31	37.91
			$q_{df}$	0.8978	0.1292	26.50	41.70
			$q_{RC}$	0.8961	0.1288	26.26	41.88
D	SHLI	Before QC		0.7373	0.1849	-	-
		After QC	$q_{snr}$	0.8711	0.1297	18.15	29.85
			$q_{df}$	0.9349	0.0941	26.80	49.11
			$q_{RC}$	0.9367	0.0931	27.04	49.65
	XIAN	Before QC		0.3338	0.2112	-	-
		After QC	$q_{snr}$	0.6743	0.1371	102.01	35.09
			$q_{df}$	0.6786	0.1345	103.30	36.32
			$q_{RC}$	0.6773	0.1326	102.91	37.22
E	SHLI	Before QC		0.8105	0.1973	-	-
		After QC	$q_{snr}$	0.8899	0.1529	9.80	22.50
			$q_{df}$	0.9246	0.1340	14.08	32.08
			$q_{RC}$	0.9269	0.1293	14.36	34.47
	XIAN	Before QC		0.3599	0.1991	-	-
		After QC	$q_{snr}$	0.3770	0.1945	4.75	2.31
			$q_{df}$	0.3781	0.1945	5.06	2.31
			$q_{RC}$	0.3755	0.1941	4.33	2.51

depicts the comparison of the CC and RMSE results between the radar-derived and buoy-measured currents before and after QC incorporating different QF components.

As can be seen from Table 6, before QC, the RMSEs between the radar-derived and buoy-measured radial current generally range from 0.12 to 0.22 m/s, whereas the CCs vary from 0.33 to 0.94. By a detailed observation of the time series (see Figure 9 and Figure 10), it can be found that the CCs below 0.5 mainly occur when the radial current speeds are small (within ±0.4 m/s, see point B for SHLI and points D and E for XIAN) and a relatively weak tidal property is seen. After QC, all the corresponding CCs and RMSEs were improved. Particularly with respect to point D, which is more than 80 km from both radar stations, the CCs increased by 27.04% and 102.91%, respectively, and the RMSEs reduced by 49.65% and 37.22%, respectively.

Since the proposed QF model consists of both SNR- and DF-related components, to find out their respective contribution to the QC performance, the CCs and RMSEs are calculated after QC according to $q_{snr}$ and $q_{df}$ separately. A threshold of 0.6 is also used for both cases. It can be easily seen that the DF-related component leads to a greater improvement than the SNR-related one. This suggests that more work should be focused on decreasing the DF error in the radial current measurement. However, the combination of both components generally leads to the best performance (especially the smallest RSMEs), which confirms the validity of the proposed QF model.

Figure 9 and Figure 10 show the time series of the radial currents of buoy data and the radar-derived results before and after QC for the SHLI and XIAN stations. These figures highlight a strong agreement between the radar-derived radial currents and buoy data, characterized by a fairly high correlation. Furthermore, the radial current velocities appeared smoother and more consistent with the buoy data after QC.

Figure 11 and Figure 12 show the scatter plots of the radial current. The plots include the linear fit line (black line) and ideal relationship (red line) between radar and buoy data, as well as the frequency of different current speeds. The results demonstrate that the radar current result is generally consistent with the buoy data, with slightly less accuracy observed at buoy B for SHLI and buoy E for XIAN due to the small magnitudes of radial current speed. After QC, the radar radial current results and buoy data are more consistent.

3.3. Vector Current

To obtain the ocean surface current field, relying solely on radial current information from a single radar station is insufficient as it cannot provide a comprehensive view of the current distribution. Therefore, we need to use two or more radar stations to obtain the vector current map. A vector current map obtained is shown in Figure 13a. Figure 13b shows the QFs corresponding to the vector current field. As can be seen from Figure 13b, buoy A is located at the position with a relatively high QF, and the QFs gradually decrease with the increase in the distance from the two radar stations. In addition, there are a few points at the edge of the overlapping region with high QFs, possibly due to target signals such as ships.

The QC method proposed in this paper was applied to the radar-measured data to evaluate its effectiveness. Figure 14 shows the time series of the buoy data and radar current after QC. As can be seen, the current speed and direction obtained from the radars are in good agreement with the buoy data. Especially the data at points A and B show a better consistency with the buoy data.

Figure 15 displays the scatter plots of the current speed and directions after QC. In the plots, the red line represents the ideal relationship, while the black line represents the linear fit. As can be seen, the consistency between the radar-derived current speed and buoy data at point A is the best, while the consistency for point B, point D, and point E is slightly poor. The radar-derived currents are mainly concentrated in two directions, i.e., −120° and 60°, differing by 180°, which is a typical tidal current feature.

To further validate the effectiveness of the QC method,

Table 7. Current accuracy statistics of OSMAR-S radar.

		Current Speed		Current Direction
Buoy		CC	RMSE(m/s)	CC	RMSE(°)
A	Before QC	0.9380	0.0776	0.8192	28.3850
	After QC	0.9478	0.0715	0.8290	27.9082
	Change (%)	1.04	−7.86	1.20	−1.68
B	Before QC	0.5706	0.1899	0.5791	34.2272
	After QC	0.7903	0.1382	0.6758	29.9925
	Change (%)	38.50	−27.22	16.70	−12.37
D	Before QC	0.4137	0.2563	0.4414	36.6953
	After QC	0.7891	0.1944	0.7005	26.0591
	Change (%)	90.74	−24.15	58.70	−28.99
E	Before QC	0.4547	0.1961	0.2660	46.1500
	After QC	0.5982	0.1755	0.4327	44.7313
	Change (%)	31.56	−10.50	62.67	−3.07

summarizes the CC and RMSE of the radar-measured vector current before and after QC compared with the buoy data. As can be seen, the radar-derived vector current had the highest correlation with buoy A. This is because location A is relatively close to SHLI and XIAN, thus in positions with high radar measurement accuracy. The performance of buoy locations B, D, and E is slightly worse. However, after QC, the CCs of the radar-derived current speed at these three locations are increased by 38.50%, 90.74%, and 31.56%, respectively, and the RMSEs are decreased by 27.22%, 24.15%, and 10.50%, respectively. The CCs of the current direction are increased by 16.70%, 58.70%, and 62.67%, respectively. The RMSEs of the current direction are decreased by 12.37%, 28.99%, and 3.07%, respectively. This shows that the accuracy of the radar-derived ocean currents was greatly improved after QC.

4. Discussion

Researchers have shown that when interference or ionospheric clutter overlaps with the Bragg peak in the RD spectrum, it can result in inaccurate measurements of ocean surface currents [37,44]. In this work, we propose a preprocessing procedure to suppress interference and exclude ionospheric clutter regions, which can reduce outliers and avoid strong interference or clutter, improving the accuracy of the radial current estimation.

Over the past decades, the SNR and spatial–spectral metrics have been proven effective in improving the data quality of wide-beam radars [24,27]. However, these studies mainly focus on the qualitative evaluation of the quality of ocean current data. Specifically, the collected data after applying the QF model are labeled with “pass”, “not evaluated”, “suspected”, “failed”, and “missing”, i.e., lacking a quantitative relationship with the SNR and spatial–spectral metrics. Moreover, the relationship between the quality of the vector current and that of the radial current has not been fully explored. In this work, we propose a QC method for both radial and vector currents. We build a radial current quality model and use the SNR and spectral QFs to determine radial current quality. By setting the SNR threshold, we can select strong sea echoes to provide more stable estimates of ocean currents. Moreover, we build a relationship between the radial current quality and vector current quality based on the GDOP. The effectiveness of the proposed method is verified using radar-derived and buoy-measured currents.

The QF model and the corresponding QC method can be applied to three or more radars. Here, we only focus on the expressions and results associated with two radars since the data used were collected from two radar stations. However, the method can be applied to the case with three or more radars. In the future, we will analyze the error in synthesizing the vector currents in the multiple station case to further evaluate the effectiveness of the proposed QC technique.

In this work, we use the SNR and spatial–spectral metrics as the indicators of data quality. With a lower SNR threshold, the number of sea echo spectral points available for calculation increases, but lower SNR values may lead to abnormal radial current speed. However, with a higher SNR threshold, the number of available spectral points decreases dramatically, which can result in a large number of blank areas in the ocean current map. In addition, the QF of the spatial–spectral metrics is also affected by the SNR (e.g., $q_{doa}$). Therefore, the setting of the SNR threshold will affect the QF of ocean currents, thereby affecting the mapping results of ocean currents. When setting the SNR threshold in the model, we need to adopt empirical values of the radar system for various environmental conditions.

The QF model in this study is semi-empirical, and there are some preset key parameters that will affect the final quality factors of currents. The optimization of their values will be further studied via more field experiments with in situ measurements. Improvement of the QC measures should also be accomplished through collaboration between oceanographic researchers and users.

In the future, we will apply the QF model and the QC measure to other HFR data products, such as wave height, wave period, and wind speed.

5. Conclusions

To improve the performance of the compact HFR system OSMAR-S in ocean surface current measurement, a QC method was developed. The QC process involves several key steps: (1) Data preprocessing, mainly to suppress IMI and RFI and exclude ionospheric clutter. By removing the data with interference, the quality of the radar signals is improved. (2) Create quantifiable quality models for the radial current and vector current. QFs in these quality models can be used to evaluate data quality. The effectiveness of the radial current and vector current QF model was verified by comparing the results before and after QC. After QC, the accuracy of the OSMAR-S-derived ocean currents was improved due to the removal of the radial current and vector current with low QFs. Compared with buoy data, after applying QC, the CCs of radial current, vector current speed, and vector current direction were increased by 4.33~102.91%, 1.04~90.74%, and 1.20~62.67%, respectively, and the RMSEs were decreased by 2.51~49.65%, 7.86~27.22%, and 1.68~28.99%, respectively. These results prove that the application of QC significantly improved the data quality.