High-Frequency Surface Wave Radar Current Measurement Corrections via Machine Learning and Towed Acoustic Doppler Current Profiler Integration

Abstract

This paper proposes an algorithm based on the long short-term memory (LSTM) network to improve the quality of high-frequency surface wave radar current measurements. In order to address the limitations of traditional high-frequency radar inversion algorithms, which solely rely on electromagnetic inversion and disregard physical oceanography, this study incorporates a bottom-mounted acoustic Doppler current profiler (ADCP) and towed ADCP into LSTM training. Additionally, wind and tidal oceanography data were included as inputs. This study compared high-frequency radar current data before and after calibration. The results indicated that both towed and bottom-mounted ADCP enhanced the quality of HF radar monitoring data. By comparing two methods of calibrating radar, we found that less towed ADCP data input is required for the same high-frequency radar data calibration effect. Furthermore, towed ADCP has a significant advantage in calibrating high-frequency radar data due to its low cost and wide calibration range. However, as the location of the calibrated high-frequency radar data moves further away from the towing position, the calibration error also increases. This article conducted sensitivity studies on the times and different positions of using towed ADCP to calibrate high-frequency radar data, providing reference for the optimal towing path and towing time for future corrections of high-frequency radar data.

1. Introduction

Oceans and seas encompass vast ecosystems, harboring abundant biological resources and diverse natural environments. However, rapid economic development and increased human activities pose significant challenges to the marine environment. Situated in the southern part of Guangdong Province, China, the Pearl River Estuary (PRE) stands as the most crucial estuary of the continental shelf in the northern part of the South China Sea. While the PRE region holds considerable economic and ecological value, it suffers from severe marine environmental issues. An accurate and timely understanding of the changes in ocean current velocity in the Pearl River Estuary is paramount to providing essential data in order to support decision-making processes for early warning systems for marine disasters, the development and utilization of marine resources, and the prevention and control of marine pollution. Monitoring ocean current velocity data aids relevant departments in promptly detecting environmental issues, predicting and preventing potential marine disasters, planning pragmatic resource development and utilization programs, formulating scientifically grounded and effective pollution prevention and control measures, and advancing sustainable economic and social development in the Pearl River Estuary. Therefore, the significance of monitoring marine current velocity in the Pearl River Estuary is indisputable.

High-frequency (HF) radar uses microwave signals generated with a transmitter to be sent out to sea, and the return signal is received by using a receiver. The interaction of the microwave signal with the sea current causes a Doppler shift phenomenon, resulting in a change in the frequency of the echo signal. By analyzing the Doppler shift of the echo signal, it is possible to calculate the speed and direction of the sea current [1,2,3,4,5]. High-frequency radar can therefore accurately monitor large areas of ocean surface dynamics, including currents, winds, and waves, under all weather conditions. This method has the advantages of being cost-effective, having a wide range, and providing strong real-time monitoring capabilities. However, during the observation process, radar-detected current data quality may be affected by ionospheric or transient interference, power outages, hardware or software failures, vandalism, or environmental constraints. Therefore, machine learning methods are necessary to ensure the completeness and accuracy of the data across the entire detection area. Liu et al. [6] observed, compared, and evaluated sea surface currents on the West Florida Shelf using radar and Doppler tachometer systems. Mau et al. [7] demonstrated the accuracy and reliability of a three-dimensional primitive equation model by successfully simulating semidiurnal currents in the waters of New York Bay and Block Island, validating the model with measured data and radar observation. Zhu et al. [8] validated the quality of high-frequency radar data obtained from the new radar stations in the Pearl River Estuary of China, discussed the impact of coastlines and open seas on the radar data quality, and proposed an improved machine learning inversion algorithm to enhance it.

The ADCP (acoustic Doppler current profiler) is an instrument that utilizes the acoustic Doppler effect to measure the flow velocity of a body of water. It is widely used in the fields of oceanography, hydrography, and engineering. The instrument works by transmitting sound waves and measuring the change in echo frequency to determine the water flow rate and direction. Towed ADCPs have been developed over the past few years and are suitable for measurements in wide seas. They can effectively minimize the interference of carriers with the instrument. This type of ADCP shares characteristics with ROV robots; Sentchev et al. [9] discuss this in their work. The optimal interpolation (OI) method was used to determine the most probable evolution of the velocity field based on the constraints provided by the ADCP observations and their error statistics. Vennell et al. [10] observed tidal spatial patterns and vorticity by using a shipborne acoustic Doppler current meter (ADCP) measurement. Simpson et al. [11] compared shipborne acoustic Doppler current meter measurements of the flow in the waterway between Scotland and the Hebrides with large-scale numerical modeling. Candela et al. [12] used a method based on shipborne acoustic Doppler current meter (ADCP) data analysis to subtract the effect of tidal movements, obtain sub-tidal fields in marine surveys, and combine them with other current velocity observations to obtain the best description of tides and sub-tides. Zhu et al. [13] compared high-frequency radar data with ADCP at the mouth of the Pearl River and captured tidal features and flow field structures through error analysis.

Artificial neural networks have become increasingly popular due to their immunity to subjective and objective factors such as time, space, and technology. They are capable of processing large amounts of data at high speeds and are fault- and error-tolerant. Neural networks have been utilized to predict wave heights in various studies [14,15,16,17]. Lee et al. [18] employed backpropagation neural networks to efficiently forecast long-term tidal levels using short-term measurements. Deo et al. [17] utilized a neural network approach to predict the wave height and breaking water depth during wave breaking. Liang et al. [19] accurately predicted tide levels, including tidal water levels under strong meteorological influences, using a backpropagation neural network (BPNN) approach through the concepts of iterative multi-step prediction and cycle analysis. Xiao et al. [20] employed a machine learning approach that combines a long short-term memory (LSTM) deep recurrent neural network model with an AdaBoost-integrated learning model to predict the daily mean sea surface temperatures in the short- and medium-term. The LSTM method was used by Fan et al. [21] to quickly predict nearshore effective wave height with improved accuracy. Machine learning was utilized to predict short- and medium-term daily mean sea surface temperature, nearshore effective wave height, radar sea clutter suppression, angle estimation, and target monitoring [22,23,24,25,26]. Wong et al. [27] used the Princeton Ocean Model to study the circulation features in the Pearl River Estuary and their responses to various factors, successfully simulating the seasonal distribution of salinity and hydrodynamic processes. Pan et al. [28] conducted a survey of navigation and numerical simulation research on the Pearl River Estuary and adjacent waters, revealing the characteristics of circulation and salinity structure, as well as changes in ebb tidal current velocity.

The purpose of this study was to use six HF radar stations established in the Pearl River Estuary, towed ADCP data from 7 June 2023 to 9 June 2023, and bottom-mounted ADCP data from 8 June 2023 to 29 June 2023, and introduce two physical factors, namely, the wind and tide, to control the training and correction process and build LSTM network models in order to compare the correction effect of towed ADCP on the radar. The correction effect of ocean current data was compared with the correction effect of bottom-mounted ADCP on radar data, and the optimal number of days for model application was obtained, which improved the quality and applicability of the radar data. The results of this study are of great significance to the future path planning of towed ADCP and improving the correction effect on radar data.

2. Materials and Methods

2.1. High-Frequency Radar

The OSMAR-S100 compact HF surface wave radar [29] developed by Wuhan University was used in this study. This type of radar has several advantages over large-scale array-type surface wave radars, including equipment miniaturization, high frequency, small antenna aperture (less than a few hundred meters), low power consumption, and the easy installation and maintenance of antenna equipment. The OSMAR-S100 HF radar is a networked radar that operates within the 13–16 MHz range. It has a synthesized detection area spanning 113.38° E to 114.32° E and 21.52° N to 22.54° N (Figure 1). Six radar systems have been installed at Wushunde (Zhuhai), Hengqin, Hengshan, Guishan, Miaowan, and Tandang Island. Radar data were collected between 7 June and 29 June 2023 at a spatial resolution of 0.02° × 0.02° and at 20-min intervals. Radar data may be incomplete or of lower quality due to weather conditions, equipment failure or maintenance, and environmental interference. To ensure data reliability, only points with a data collection rate of over 80% were selected. The machine learning model was trained and predicted using hourly radar data to align with other time series.

2.2. Wind and Tide Data

ERA5 is a global reanalysis dataset developed by the European Center for Medium-Range Weather Forecasts (ECMWF) that provides a range of meteorological and climatic variables [30]. One of these variables is the 10 m height standard wind, which describes wind speed and direction conditions in the atmosphere 10 m above sea level. The experiment’s 10 m height standard wind speed is derived from data with a resolution of 0.25° × 0.25°. TPXO7.2 is a global ocean tidal model that predicts and simulates tidal variations in various ocean areas of the Earth. It was developed by Thaddeus P. Y. Fan and Prof. Shi-Ming Chau of Oregon State University, USA, among others. The model is based on global ocean observation data and numerical computation methods, providing high-spatial and high-temporal-resolution tidal information. The tide data of the corresponding TPXO7.2 were extracted from the coordinate points passed by the towed ADCP in this experiment.

2.3. Mooring Data

This study employed Teledyne RD Instruments’ Workhorse II Sentinel ADCP (600 K) (

Table 1. Specifications of the Workhorse II Sentinel ADCP provided by Teledyne RD Instruments.

Frequency	600 kHz
Max profiling range	70 m
Max bottom tracking range	N/A
Velocity accuracy (typical)	±0.3% of measured velocity +0.3 cm/s
Velocity range	+5 m/s (default) to +20 m/s
Ping rate	2 Hz (typical)
Beam angle	20°
Depth rating	200 m (optional 500 m or 6000 m)
Standard sensors	Temperature, tilt, compass
Communications	Serial RS-422 or RS-232 ASCll or binary

) and designed a route for the towed ADCP in the Pearl River Estuary, starting at 113.66° E, 22.36° N and ending at 113.70° E, 22.04° N. The data were collected over a period of nearly three days, with a temporal resolution of 2 min and a vertical resolution of 0.5 m between the adjacent layers in the vertical direction. An ADCP was deployed at 113.66° E, 22.2° N to collect data for 21 days. The temporal resolution was 5 min, and the vertical resolution was 0.5 m between the adjacent layers. The collected data were processed as hourly data to align with the other time series.

2.4. LSTM Neural Network

Long short-term memory (LSTM) neural networks are a variant of RNNs with long- and short-term memory cells. They can forget information using the forgetting gate and choose to remember or forget the long-term information [17,20]. LSTM is a good solution to solve the problems of an RNN’s gradient disappearance and explosion, as well as the lack of long-term memory capacity. This makes recurrent neural networks effective in using long-distance temporal-order information [21]. The main formulas are as follows:

$$f_t=\sigma \left(W_f·\left[h_{t-1}, x_t\right]+b_f\right),$$

(1)

$$i_t=\sigma \left(W_i·\left[h_{t-1}, x_t\right]+b_i\right),$$

(2)

$${\tilde{C}}_t=\mathit{tan}h\left(W_C·\left[h_{t-1}, x_t\right]+b_C\right),$$

(3)

$$C_t=f_t·C_{t-1}+i_t·{\tilde{C}}_t,$$

(4)

$$o_t=\sigma \left(W_o·\left[h_{t-1}, x_t\right]+b_o\right),$$

(5)

$$h_t=o_t·\mathit{tan}h\left(C_t\right),$$

(6)

where t is the time step; f_t is the forget gate; i_t is the input gate; o_t is the output gate; C_t is the final cell output; h_t is the final state; X_t is the input; W_f, W_i, W_o, and W_C are the weights; b_f, b_i, b_o, and b_C are the biases; and σ is the sigmoid function, which increases the nonlinearity of neural network algorithms.

The LSTM network used in this study consists of three layers: an input layer, a hidden layer, and an output layer. As shown in Figure 2, the input layer includes the HF radar velocity, ERA5 dataset’s 10 m standard wind, and TPXO7.2 tidal data. This study tested the parameters of LSTM, compared the results through multiple experiments, and ultimately determined that the hidden layer of LSTM contains 128 neurons, while the output layer represents the true ocean current data measured by the bottom-mounted ADCP. During the training process, a bottom-mounted ADCP and towed ADCP were used as target values to determine the LSTM training parameters. In the prediction process, their respective parameters were used to validate the correction effect on radar data. Previous experiments conducted by Zhu et al. [31,32] have shown that the model’s correction of radar data is a function of time. Therefore, this study also conducted sensitivity experiments on the time of the input data in order to obtain the optimal tow route and towing time for correcting radar data.

2.5. Empirical Orthogonal Function (EOF) Ellipse

EOF analysis is a statistical method used for the downscaling and extracting modes from multidimensional datasets. The main objective of EOF analysis is to identify the primary spatial modes in the dataset, which are the modes with the largest variations in the data. The primary process involves constructing a data matrix with the u-component in the first column and the v-component in the second column. This matrix is then decomposed into the first and second modes using EOF analysis. The eigenvalues of the first mode are assigned to the long axis of the ellipse, and the eigenvalues of the second mode are assigned to the short axis of the ellipse. Finally, the orientation of the ellipse was calculated by $\theta =\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left(\frac{v2}{v1}\right)$, where $v_1$ and $v_2$ are the first and second eigenvector modes, respectively.

3. Results

3.1. Radar and ADCP Comparisons

In order to assess the correction effect on radar data, the radar data at the coordinates of 113.66° E, 22.2° N were initially compared with bottom-mounted ADCP measurements. Note that the above data were averaged to hourly data and smoothed using a four-hour running mean to eliminate very-high-frequency signals. The analysis, shown in Figure 3 and Figure 4, indicated a notable resemblance in the variations between the bottom-mounted ADCP and radar data. Specifically, the correlation between radar and bottom-mounted ADCP exceeded 0.4 for the first five days, but decreased to 0.2665 on the tenth day, followed by a marginal recovery. The abrupt decline in radar data correlation during the period of 14–15 June in the graph could potentially be attributed to anomalies in the radar station or the interpolation process. Subsequently, as the radar data returned to normal, the correlation also demonstrated a slight recovery.

3.2. Experimentation with Inputs

In our previous study, we concluded that adding wind and tide to the input term can improve the training of the LSTM model. However, at that time, we used the flow velocity of the Finite-Volume Coastal Ocean Model (FVCOM) as the true value [32]. Therefore, as the closest approximation to the true ocean current data, obtained from ADCP measurements, we are curious as to whether incorporating wind and tidal factors can improve the correlation between the predicted values and the ADCP data. Experiments were conducted using four groups. The first group used radar flow velocity, wind, and tide as the input terms simultaneously. The second group used radar flow velocity and tide as the input terms simultaneously. The third group used radar flow velocity and wind as the input terms simultaneously. The fourth group made a direct comparison. According to Figure 5, the first three groups of experiments had a positive effect on radar correction. The correlation coefficients of the corrected radar flow velocities were higher than the initial radar flow velocities, and the root-mean-square errors were lower than the initial radar flow velocities. It is evident that the correlation decreases as the number of days of corrected radar increases. Although the radar effect improves from 15 to 21 days, the correction effect decreases with the increase in correction time.

3.3. Comparison of Radar Altimeter Correction for Bottom-Mounted ADCP and Towed ADCP

When we discovered that the wind and tide can simultaneously affect the radar correction, we used radar current speed, wind, and tide as the input terms. We employed two methods for correction: the first method trained the bottom-mounted ADCP current speed as the target term; and the second method trained the towed ADCP as the target term. Both methods resulted in improved radar data correction, as shown in Figure 6. Figure 7 presents a comparison of the correlation coefficients and RMSEs for two methods of correcting different radar flow times. The correlation coefficients for the first ten days of training used the bottom-mounted ADCP flow rate as the target value, which ranged from 0.7728 to 0.8342. However, the correlation coefficients for training using the towed ADCP flow rate as the target value are slightly lower, ranging from 0.6965 to 0.7209. The correlation coefficients for both methods decrease for the radar correction time. However, the second method decreases more gently than the first. By day 15, the correlation coefficient for the second method of correcting the radar flow velocity exceeds that of the first. It is worth noting that both methods have decreasing correlation coefficients. This suggests that using a short-duration towed ADCP is cost-effective and profitable for correcting radar flow velocities over relatively long periods of time.

3.4. Time Sensitivity Experiment of Bottom-Mounted and Towed ADCPs

It is widely acknowledged that the training of neural networks improves with increased quantities of data. As shown in

Table 2. Sensitivity experiment of training data quantity for towed and bottom-mounted ADCPs.

Experiment	Target Value Time Length	Correlation Coefficient	RMSE(m/s)
Exp 1	Towed ADCP (1.5 d)	0.49	0.21
Exp 2	Towed ADCP (2 d)	0.57	0.18
Exp 3	Towed ADCP (3 d)	0.64	0.17
Exp 4	Bottom-mounted ADCP (3 d)	0.59	0.15
Exp 5	Bottom-mounted ADCP (5 d)	0.65	0.14
Exp 6	Bottom-mounted ADCP (10 d)	0.75	0.13

, this study comprised six experiments using the towed ADCP data of 1.5, 2, and 3 days as the target value, and the sit-on-the-bottom ADCP data of 3, 5, and 10 days, respectively. The table below shows that as the length of time of the target value increases, the correlation of the corrected 21-day radar current data increases with the amount of data learned by the LSTM, resulting in smaller errors. It can be observed that the correlation coefficient increases by 0.15 when the time of the towed ADCP data is changed from 1.5 to 3 days. In contrast, the correlation coefficient only increases by 0.16 when the time of the bottom-mounted ADCP data is changed from 3 to 10 days. This suggests that to improve the correction of the same radar data, the towed ADCP needs to acquire less data in time.

3.5. Spatial Comparison of Bottom-Mounted and Towed ADCPs

This study aimed to correct the radar data effect on the towed ADCP by identifying the best route based on a spatial and temporal scale. The towed ADCP was used as the target value of the LSTM output for the corrected u-component and v-component radar data. The corrected radar oceanic current u-component and v-component were used as the target value for the LSTM output. The radar provided the original flow rate of the u-component and v-component, while the original bottom-mounted ADCP flow rate yielded the EOF ellipse, as shown in Figure 8. At the coordinate points of our experiments, it was evident that the ellipse using bottom-mounted ADCP as the target value was similar to the original ellipse of the bottom-mounted ADCP, while the ellipse using the towed ADCP as the target value was almost identical to the ellipse of the original bottom-mounted ADCP currents. The reason for the difference in the LSTM output when using the bottom-mounted ADCP as the target value was likely due to the limited amount of data used, which was only 3 days. This highlights the superiority of radar data, which, when corrected by using towed ADCP data, can capture the magnitude and direction of ocean currents more accurately. In our previous study, we obtained ADCP-corrected radar data within a specific spatial range. However, we were unable to obtain additional ADCP data for validation during the same time period. Therefore, we conducted an experiment to randomly compare the ellipses of six other points in the existing radar data after correcting them using the previous training parameters of the LSTM. It is evident that both training methods produce errors larger than the experimental points, and these errors tend to increase as the distance from the experimental points increases. Therefore, the closer the corrected radar data align with the towed ADCP trajectory, the better the result is.

4. Conclusions

On the one hand, ocean current data derived from high-frequency radar are obtained via electromagnetic inversion, which has high-resolution and long-distance detection capabilities. However, it also has the characteristics of being insensitive to physical oceanography and susceptible to electromagnetic interference. On the other hand, bottom-mounted acoustic Doppler current profilers (ADCPs) can allow for the real-time monitoring of ocean currents at a single point. However, bottom-mounted ADCPs require installation on the seafloor, which may increase the difficulty of equipment deployment in certain sea areas. In addition, maintenance is relatively difficult due to the high cost. In this study, we proposed a method by which to monitor a relatively large area at a lower cost by using the ocean current data obtained from a towed ADCP and training them with a long short-term memory (LSTM) algorithm to reduce the error of the high-frequency radar monitoring of ocean currents.

By adjusting the input parameters and introducing wind and tide information, we demonstrated that the addition of this missing oceanographic information can supplement radar flow speed and improve the training efficiency of the LSTM algorithm, thereby improving the effectiveness of the radar monitoring of ocean currents. By training the LSTM algorithm using ocean current data of the same length obtained from both bottom-mounted and towed ADCPs, we found that as the time for correcting the radar increased, the correction effect became worse. However, the reduction in towed ADCP training was more gradual than that of the bottom-mounted ADCP. Through experiments on the time sensitivity of the bottom-mounted and towed ADCPs as the target values, we found that both became more effective in correcting radar currents as more data were available for LSTM learning. However, compared to the bottom-mounted ADCP, the towed ADCP could achieve better radar current correction effects with shorter periods of data.

Furthermore, by constructing an EOF ellipse from the corrected 21-day radar currents obtained from bottom-mounted and towed ADCPs, as well as the original ocean currents from bottom-mounted ADCPs and untrained radar currents, we found that the towed ADCP data for 3 days could obtain the magnitude of and variation in the spatial ocean currents for 21 days; in contrast, a bottom-mounted ADCP required more time. However, for a specific area, we could not provide a specific range of the size of the area that the LSTM model trained with towed ADCP data can be used for, as we lacked more bottom-mounted ADCP data for different areas at the same time. Nevertheless, from Figure 8, we can see that as the correction area moved further away from the training area, the effect became worse.

In summary, although training with a bottom-mounted ADCP to explore ocean currents can achieve good results in a specific area, it requires a long detection time and has a high cost, as well as a risk of equipment loss. In contrast, training with a towed ADCP to explore ocean currents can improve the correction area of the radar and obtain the magnitude and direction of the ocean currents in this area. Therefore, as long as we can reasonably calculate the time and space scales for towing to correct the radar ocean currents according to our needs, we can obtain safe, low-cost, and high-yield corrected radar ocean current data.