A Scheme for Credibility of Surface Currents Derived From High Frequency Radars

Large amount of real-time ocean currents measured by HF radar have been included into the ocean observation database in many countries and regions, in support of applications for various marine activities such as marine research, Oil spill detection, tsunami warning, search and rescue. However, due to the performance of inversion algorithms and radar antennas, and other reasons, there are differences in the credibility of ocean current results at different times and locations, which brings on difficulties to applications of ocean currents. This letter proposes a method for developing a credibility model of ocean current results, mainly for all-digital multi-input and multi-output (MIMO) HF radar. By comparing the model with field experimental results, it is confirmed that the method is feasible. It will be very beneficial for radar users to select and use ocean current results, greatly reducing the work of verification of newly installed radars, and will be an innovation in the application technology of over-the-horizon marine radars.


Introduction
High frequency (HF) radar currents have a wide range of applications, including ocean dynamic process studies, tsunami warnings, search and rescue, model assimilation, and oil spill and sea-ice monitoring [1,2,3].However, the accuracy of currents vary depending on the location and time within the detection range.This can result in some degrees of errors, when currents are applied to different applications as input or comparing data.Such as rescue and model assimilation, HF radar currents serve as input parameters that enhance the accuracy of assimilation model productions [4].As a result, understanding the credibilities of currents at different times and locations can greatly benefit in selecting and utilizing current data.
There are several factors that impact the credibility of ocean currents, and these factors may also vary slightly depending on the technical type of HF radar being used.For instance, when it comes to compact HF radar currents, the accuracy of antenna patterns [5,6,7] and direction-of-arrival (DOA) estimation [8,9] are the main factors that affect credibility.On the other hand, the credibility of phased-array HF radar currents may be more influenced by radio frequency interference [10,11].The geometric dilution of precision (GDOP) is a major factor that influences vector currents synthesized from radial currents obtained by two or more HF radars, no matter they are compact or phased-array HF radars [12].Additionally, the use of different radial current inversion methods can also affect the results.The performance of the MUltiple SIgnal Classification (MUSIC) algorithm, which is commonly used for DOA estimation in wide-beam HF radar, is another significant influencing factor.
In recent decades, both portable (compact) and phased-array HF radars have made significant progress and innovations.However, it is important to note that most ocean surface current data products obtained by HF radar cannot be directly used.Radar users must understand the credibility of the current data before utilizing it.A credible and reliable model for assessing radar results would be highly advantageous for radar users in selecting and utilizing results.Furthermore, it would significantly decrease the workload of comparative verification for newlyinstalled radars.This innovation would have a substantial impact on the application technology of over-the-horizon marine radar.
Wuhan University has developed a novel type of HF radar in these years [13,14], providing an opportunity to verifying the model we proposed.The authors aim to establish a credibility model for ocean current results obtained through HF radar with a phased-array configuration.The model will be based on three key factors: the signal-to-noise (SNR) ratio of the first-order spectrum, the accuracy of the array direction-finding, and the spatial coverage of the ocean current.

Theory and Method
To identify the factors that impact the credibility of radial current results, it is crucial to have a clear understanding of the radial current inversion process for a single radar site.Shown as the Fig. 1 below, the received signal undergoes double fast Fourier transformation to obtain the distance Doppler spectrum.After calibration of each receiving antenna channel, the firstorder spectra region can be extracted.The radial current was then obtained by calculating the Doppler shift of each frequency point in the first-order spectral domain; on the other hand, the direction of arrival of each spectral point was estimated using a MUSIC algorithm.Finally, the polar coordinate radial current with the radar site as the origin is obtained from the direction and velocity.Each grid point on the coordinate is represented by (r, θ), where r is the distance and θ is the azimuth.Figure 2. Credibility model.
The accuracy of radial current data is heavily reliant on the quality of the Doppler spectra.In particular, the SNR of the first order spectra region plays a crucial role in determining ocean dynamic parameters such as wind, waves, and currents [9].When the SNR is low, it becomes difficult to accurately distinguish the first-order and second-order spectrum regions, leading to a loss of useful spectrum points and ultimately a decrease in the accuracy of the inversion of ocean dynamic parameters.
In addition to target echoes and sea clutter, there are usually different types of radio frequency interferences found in radar echoes, which causing the rise of bottom noise and the decrease of SNR.Moreover, When such interferences occur in the first and second order spectrum, it not only forms a masking effect on the useful signal, but also affects the correct extraction of the first order spectra, and they also affect the DOA estimation of the spectral points in this area, leading to errors, thus affecting the credibility of the inversion results.
Ocean dynamic parameters such as wind, waves, and currents measured by radar usually present continuous distribution characteristics in space.Outliers in regional parameters can be visually identified by comparing inversion results for the same region over time.If spatial coverage is fragmented at one time, the credibility of current can be assumed to have low confidence in all grid points at this time.
Combining the above factors that affect the credibility of radar results, a simple credibility model of current results can be established.By analyzing and processing large amounts of data, SNR, DOA estimation accuracy and spatial coverage characteristics of ocean surface currents are selected as factors affecting the credibility model of radar results.The specific research ideas are shown in the Fig. 2.

DOA estimation
When the number of receiving array element M is greater than the input signal p, and the steering vector α(θ i ), (i = 0, 1, ...p − 1) with p different directions are linearly independent, the estimation error ( θi − θ i ) of the MUSIC estimator for the azimuth angle θ obeys a zero-mean Gaussian distribution, according to [15] by Stoica and Nehora.Its variance can be expressed as below.
where, || ii represents the diagonal element of the matrix, L is the number of snapshots, A represents array manifold, SN R = |x| 2 /σ represents the signal-to-noise ratio of the signal, d(θ) = dα(θ)/d(θ) is the first derivative of the steering vector.
Here the variance of the estimator is a function of the azimuth θ, which we use to qualitatively and quantitatively describe the azimuth accuracy of the array.The smaller the estimated variance of the estimator, the better the performance of parameter estimation and the higher the credibility of DOA.We use error ( θi − θ i ) to represent ∆θ.

Accuracy of vector currents
In consideration of relationship between SNR of first order spectra and the accuracy of radial current velocity, SNR can represents ∆v, which is the accuracy of radial current velocity for a single radar.Given with two pairs of ∆v and ∆θ, according to [16], accuracies of vector current is.
the error of the vector current can be calculated as where, v is the magnitude of vector current velocity.v 1 and v 2 are the radial current velocities measured by two radar sites respectively, and θ 1 and θ 2 are the angles between the measurement point and the lines connecting the two radars (to the north direction).Radial current errors ∆v 1 and ∆v 2 are characterized by the first-order spectral SNR corresponding to the single radar site radial current.The angle errors ∆θ 1 and ∆θ 2 between radial current and the north direction are characterized by the array's directional accuracy.

Ocean vector current spatial coverage
The HF radar can invert ocean dynamic parameters such as wind, waves, and currents, showing both temporal continuity and spatial distribution.By comparing inversion results of the same area over time, we can easily identify abnormal values in the radar footprint.It is important to distinguish between abnormal values and sudden changes.Sudden will impact the values in the subsequent period of time.These abnormal values lack continuous change before or after that moment, making them stand out.To identify abnormal values, we calculate the difference between the abnormal value and the average value of a given time period.If the absolute value of this difference is greater than twice the standard deviation of the time series during that period, we classify it as an abnormal value.
We use U (x, y, t) to represent the vector current at coordinates (x, y) on a grid divided by longitude and latitude at time t.T represents a specific time period, and Std represents the standard deviation of the time series during that period.As δ(x, y, t) increases, the credibility of the results decreases.And one grid point at a time (x 0 , y 0 , t 0 ) would be removed when δ(x 0 , y 0 , t 0 ) is positive.When detecting wind, waves, and currents, fragmented spatial coverage indicates low credibility, as illustrated in the Fig. 3.We propose three steps to calculate the degree of spatial coverage fragmentation of the vector currents are: (1) Count the number of currents located at the edge position J(t) at a certain time t.
(2) Count the total number of all currents Q(t).
As Z(t) increases, the current field's spatial coverage becomes more concentrated and fragmentation decreases, indicating a higher credibility of the current value.On the other hand, as Z(t) decreases, fragmentation increases, indicating a lower credibility of the current value.The finally credibility could be calculated as below:

Experiemnt and Results
To verify this model, we conducted a field experiment in

SNR
Using the radial velocity obtained from Longhai and Dongshan radar site at 06:50 on August 23, 2021, we can observe the SNR spatial distribution of the first-order spectrum at that time (Fig. 5).The figure below displays this distribution, which generally indicates that the closer to radar, the higher the SNR.The highest SNR within 100 kilometers of Dongshan radar site can reach up to 50 dB.

Direction finding accuracy
Fig. 6 displays the estimation errors of the DOA using the real receiving arrays.As the angle deviates further from -70°(LH) and -30°(DS), the error increases.Fig. 7 shows the DOA error

Vector current
Taking the vector current measured by Dongshan and Longhai radar sites at 06:50 on August 23 as an example, combined with the spatial coverage situation, the spatial distribution of the credibility of the vector current at that time is shown in the Fig. 8. Credibility values range from 0 to 1, with '1' indicating the highest credibility and '0' indicating the lowest.In the edge area, the credibility values do not exceed 0.3.However, as we move towards the central area of the common coverage, the credibility values increase, reaching up to 0.9.The ocean current arrows in the edge area appear disorganized, with some outliers and sudden changes.The continuity of arrow directions is weak and disorderly.In contrast, the ocean current arrows in the central area show no outliers, and the continuity of arrow directions is strong, resulting in a more logical streamline.

Verification with Drift Buoy
Comparison between surface ocean currents measured by drift buoy and radar derived ocean currents can be used to verify the credibility of the model.The Fig. 4a shows the trajectory of the drift buoy from 0:00 on August 23, 2021, to 15:00 on August 25, covering a displacement of   As shown in the Fig. 9, the magnitudes and trends of the velocities measured by both methods are consistent with a root mean square error of 9.5 cm/s and a correlation coefficient of 0.92.We compared the results of the credibility model using the difference between the two, as shown in the Fig. 10.The blue curve represents the velocity difference between the drift buoy and radar ocean currents, ranging from 0 to 30 cm/s; the red dots represent the results of the credibility model.It can be seen that as the error increases, the credibility results decrease, and as the error decreases, the credibility results increase.The two are negatively correlated.

Conclusion and Disscussion
Studies on the credibility model is a novel field of high-frequency surface wave radar.The credibility models for different types and technical characteristics of HF radar detection results vary.This letter foucuses on the phased-array HF radar and presents a simulation case analysis.The analysis is based on the inversion process of radial current and vector current, radar echo characteristics, and spatial distribution characteristics of ocean current results.The aim is to establish a credibility model for vector ocean current results.
To validate this model, the paper compares and analyzes the results of the credibility model with the measured ocean currents.The study also verifies the continuous time and space credibility model by using synchronous observations of ocean currents by drift buoys.
The proposed credibility model, as demonstrated through comparison with measured current results and drift buoys, is rational and therefore applicable.It's important to note that the main influencing factors discussed in this article are not independent, but rather coupled together.For instance, SNR impacts not only the accurate extraction of the spectrum, but also the performance of the MUSIC algorithm, which ultimately affects the accuracy of DOA.Future work could focus on developing a more comprehensive and accurate credibility model by exploring various types of ocean current inversion techniques.

Figure 3 .
Figure 3. Ocean vector current spatial distribution.J represents the number of currents located at the edge in the current pattern, Q is the total number of all currents in this pattern.

Figure 4 .Figure 5 .
Figure 4. (a) The location of the radar site and the drift buoy moved from red dot to black dot.The receiving array at (b) Longhai and (c) Dongshan.Dash lines are the borders of radar station.
August 6-25 2021 at the Dongshan (23.6575 • N, 117.4863 • E) and Longhai (24.2674 • N, 118.1353 • E) radar sites along the Fujian coast.The geography map and location of the receiving array are displayed in Fig. 4. Two HF radars operated at 7.94 MHz [13].The transmitting antenna array consisted of two antenna elements.The receiving array employed an four-element array, and locations of array are in the Fig. 4. The maximum detection range was 200 km, with a range resolution of 5 km and a time resolution of 10 minutes.

Figure 6 .Figure 7 .
Figure 6.The standard error of DOA in real receiving array under different SNR (dB) values.(a) Longhai and (b) Dongshan.

Figure 10 .
Figure 10.Comparision between credibility and ocean current deviation from drift buoy.