A Machine Learning-Based Correction Method for High-Frequency Surface Wave Radar Current Measurements

Abstract

An algorithm based on a long short-term memory (LSTM) network is proposed to reduce errors from high-frequency surface wave radar current measurements. In traditional inversion algorithms, the radar velocities are derived from electromagnetic echo signals, with no constraints imposed by physical oceanographic processes. In this study, sea surface winds and tides are included in the LSTM algorithm to improve radar data. These physical factors provide the LSTM network with more oceanic information by which to constrain and improve its training efficiency. The results show that the domain-averaged root-mean-square errors of the radar-derived velocities are reduced from 0.22 to 0.09 m/s for the whole radar observation area. The overall correlation coefficient increases from 0.37 to 0.88. To provide a practical strategy for future field work, we conduct a set of sensitivity experiments, showing that the LSTM network based on one single point can be applied to other data points within a sub-domain.

1. Introduction

Pearl River is the second largest and the third longest river in China, with many tributaries. The Pearl River Estuary (PRE), located in the south of Guangdong Province of China, is the most important river estuary in the northern continental shelf of the South China Sea. The PRE is vulnerable to marine meteorological disasters, which can cause huge losses. Therefore, real-time monitoring of the marine environment in this area is of great significance.

As a relatively new ocean current observation technology, high-frequency (HF) surface wave radar overcomes the spatial limitations of traditional observations, such as acoustic Doppler current profiler (ADCP), and has the advantages of wide range, low cost and all-weather real-time monitoring ability. Crombie [1] and Wait [2] first discovered and proved that the resonance between electromagnetic waves and ocean waves with specific wavelengths results in Bragg scattering. Following this discovery, Barrick [3,4,5] proposed that ocean dynamic parameters such as currents, winds, and waves can be extracted from the first-order spectrum and the second-order spectrum. At present, the large-area current detection of the HF radar systems can be used for routine operational ocean observations.

Machine learning (ML) methods have been widely used in oceanography fields due to its excellent nonlinear learning ability. Fan et al. [6] and Christoph et al. [7] used a LSTM network to predict the significant wave height, improving its prediction accuracy in near-shore shallow waters. Zheng et al. [8] used a back propagation (BP) network for wave estimations to improve the accuracy. Wen et al. [9] adopted a BP network to invert the significant wave height of HF radar. Temporal convolutional network can estimate wave height from x-band radar data [10]. Convective neural networks and gated recurrent units have also achieved favorable results with respect to current prediction based on HF radar [11,12]. Huang et al. [13] applied BP to the interpolation method for a flow field mapped by HF radar. Hardman and Wyatt [14] used a neural network to infer a directional ocean spectrum from a HF radar Doppler spectrum. Shen et al. [15] used an artificial neural network to estimate wind speed by using the first-order peak energy of the backscattered HF radar Doppler spectrum. Wyatt [16] used ML to measure HF radar wind speed. In addition, ML has been involved in radar sea clutter suppression, angle estimation, and target detection [17,18,19,20,21]. It proves that ML has been widely applied to radar observation.

In traditional inversion algorithms, the HF radar current measurements are derived solely from electromagnetic echo signals, with no constraints imposed by physical oceanographic processes. The radar echoes are easily interfered with environmental noise or obstacles, such as radio broadcasting, trees, islands, and so on. All of these local interference factors will affect the quality of radar receiving echoes and the accuracy of the inversion algorithm, producing uncertain bias or errors for radar-derived currents. On the other hand, in terms of physical oceanography, the ocean currents in the PRE area are determined dynamically by winds, tides, and river discharges, as well as local topography and coastlines. Therefore, in this study, a LSTM network is used to correct the radar-derived current velocities near the PRE. Sea surface winds and tides are included in the LSTM algorithm to constrain its training process. These physical factors provide the LSTM network with ocean dynamical information and help the LSTM obtain more accurate training results.

In this section, we clarify the purpose and significance of this research. In the next section, the data and methods used in this study are introduced, and the results are presented in Section 3. A summary is given in Section 4.

2. Materials and Methods

2.1. Data

The HF radars used in this study are OSMAR-071G high-frequency surface wave radars developed by Wuhan University of China. OSMAR-071G HF radars operate at a frequency of 9.355 MHz and detect ocean surface currents and wave heights in the ranges of 100–150 km. A pair of HF radars were deployed at Shangchuan and Wanshan Islands to the west of the PRE outlet in southeastern China. Their total detection range is 112.4° E–114.7° E, 20.2° N–22.0° N, with a detection area of nearly 40,000 km². The radar data used in this study span from 1–30 March 2020, with a time interval of 10 min and a spatial resolution of 5 km.

The standardized winds at 10 m were obtained from the ERA5 dataset, which is the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate (ERA5|ECMWF). The wind data had a spatial resolution of 0.25° × 0.25°. Tidal data were taken from the TPXO7.2 global tidal model developed by Egbert and Erofeeva [22] of Oregon State University. Model data were simulated using a regional PRE model with a minimum model grid size of 100 m in the radar observation area. The model-simulated currents were validated against the radar and ADCP measurements in our previous study [23]. In order to coincide with the radar data, wind, tide, and model data from 1–30 March 2020 were used in this study. Note that all the above data were averaged to hourly data and smoothed using a four-hour running mean to eliminate very-high-frequency signals.

2.2. LSTM Neural Network

LSTM was first proposed by Hochreiter and Schmidhuber [24] and its structure is shown in Figure 1. LSTM is a special form of recurrent neural network (RNN). Unlike the traditional RNN, LSTM adds memory cell blocks to each neuron of the hidden layer, and these determine the degree of memory for forgetting of information through input gates, forget gates, and output gates. LSTM has a long-term memory function and can be effectively used with respect to regression problems for time series. The main formulas are as follows:

$$\begin{array}{c}{f}_t=\sigma \left(W_f·\left[h_{t-1},x_t\right]+b_f\right)\end{array}$$

(1)

$$\begin{array}{c}{i}_t=\sigma \left(W_i·\left[h_{t-1},x_t\right]+b_i\right)\end{array}$$

(2)

$$\begin{array}{c}{\tilde{C}}_t=\tan h\left(W_c·\left[h_{t-1},x_t\right]+b_c\right)\end{array}$$

(3)

$$\begin{array}{c}{C}_t=f_t·C_{t-1}+i_t·{\tilde{C}}_t\end{array}$$

(4)

$$\begin{array}{c}{o}_t=\sigma \left(W_o·\left[h_{t-1},x_t\right]+b_o\right)\end{array}$$

(5)

$$\begin{array}{c}{h}_t=o_t·\tan h\left(C_t\right)\end{array}$$

(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 the neural network algorithms.

The LSTM network used in this study included three layers. The input layer contains the original HF radar currents, surface winds, and tides. The output layer is the “true” currents, which were set to the u- and v-component of the model-simulated currents. The LSTM layer comprises 128 neurons. Through the training process, the LSTM network built a nonlinear regression between the input factors and the model currents (outputs) by minimizing the radar–model errors. In other words, the LSTM training process rectifies the radar data deviations against the model currents by means of wind and tidal information. The data between 1–25 March were taken as the training set, and the data between 26–30 March were used as the validation set. Note that in this study, we treat the model currents as the true values, considering that no current in situ observations are available in this area. The results of this study will be useful for designing observation strategies for future field work.

2.3. Empirical Orthogonal Function (EOF) Ellipse

To compare two time series of radar and model velocities, an ellipse is derived from EOF analysis. First, a data matrix is built as the first column comprising the u-component velocity and the second column comprising the v-component velocity. Second, this velocity matrix is decomposed by EOF analysis into 1st and 2nd modes. Third, the ellipse is determined as follows: its major axis is set to the 1st mode of eigenvalues representing the largest standard deviation of total velocities, and its minor axis is set to the 2nd mode of eigenvalues. The orientation of the ellipse is calculated by $\theta =arctan\left(\frac{v_2}{v_1}\right)$, where v₁ and v₂ are the 1st and 2nd modes of the eigenvectors.

3. Results

3.1. Corrections for Two Single Points

Figure 2a shows a comparison of EOF ellipses calculated from the HF radar and model currents. It can be seen that the degree of agreement between the HF radar and model ellipses can be divided into three regions: (1) Along the coast, the EOF ellipses are quite different in their sizes and orientations, which indicates that the complex coastline and islands might be the key factor causing these discrepancies. (2) In the region between 21° N and 21.5° N, with the influence of islands and coastlines decreases. The radar and model ellipses almost overlap with each other, indicating that the current fields derived from HF radars and model simulations are well consistent; (3) Further offshore, between 20.5° N and 21° N, the two sets of EOF ellipses are not well matched. The orientations of the radar ellipses in some areas are opposite to those of the model.

To quantify the difference between the radar and model ellipses, Figure 2b shows their errors formulated by

$\sqrt{{\left(\mathrm{L}ma{j}_{radar}-\mathrm{L}ma{j}_{model}\right)}^2+{\left(\mathrm{L}mi{n}_{radar}-\mathrm{L}mi{n}_{model}\right)}^2}$. According to the error distributions, the radar observing area can easily be marked by three regions from north to south. As shown, area B denotes the minimum errors and the best agreement between the radar and model ellipses. The errors in areas A and C are relatively large, and these will be the targeting areas for the error corrections.

We selected two typical points (marked by A and B in Figure 2a) with relatively large errors for testing the correction process. Figure 3 shows the comparison of velocities at point A with the radar, model, and LSTM training results. We can see that, in the training period from 1–25 March, the v-component of the radar and model velocities at point A do not match well with a Pearson correlation coefficient (PCC) of 0.15 and a root-mean-square error (RMSE) of 0.47 m/s (Figure 3a). That is the reason why the two EOF ellipses do not match each other in point A. The training set of LSTM velocities (dashed red line) shows a very good agreement with the model velocities, with a PCC of 0.99 and RMSE of 0.01 m/s. Note that we used 128 neurons in the LSTM network, and therefore the model currents can be exactly reproduced by the LSTM training process. To validate the effectiveness of the LSTM training process, the trained regression weights between the input factors and model (outputs) were examined during the validation period 26–30 March. That is, given the radar velocities, the trained weights saved in the LSTM were used to calculate the validation set of the velocities and this was compared with the model. It can be seen that the LSTM velocities in the validation period (purple line) also shows good agreement with the model, with a PCC of 0.88 and RMSE of 0.06 m/s. This is acceptable, as all validation data were not used in the training process. The u-component shows the same features and the LSTM can also produce good training and validating sets of velocities, compared to the model currents (Figure 3b).

Figure 4 is the same comparisons as in Figure 3, but for point B in area C. It is noteworthy that the u-component shows almost opposite phase difference between the radar and model currents during the training period (Figure 4b). This is the reason why the EOF ellipses of the radar and model show opposite orientations at point B (Figure 2a). In our previous research [23], we found that the Shangchuan station showed large errors in area C, whereas the Wanshan station did not. Compared with the model, the radar velocities at Shangchuan station were systematically underestimated by half. Moreover, the currents were mainly determined by tides and winds in this region, which can be adequately captured by Doppler spectra, therefore, the HF radar should have been able to resolve the currents. Therefore, the errors in the area C might originate from the radar systematical bias of the Shangchuan station. After correction by the LSTM, the validation sets of LSTM velocities show a PCC of 0.94 and RMSE of 0.05 m/s compared to the model values.

3.2. Corrections for the Whole Domain

Since the LSTM enabled successful error correction at sites A and B, we applied this algorithm to the whole radar observing area. Figure 5 shows the comparison of the EOF ellipses between the model velocities and the LSTM results. Compared to Figure 2a, all ellipses in the three areas have been corrected to some extent.

Table 1. Domain-averaged PCCs and RMSEs in areas A, B, and C.

Area	PCCs		RMSEs (m/s)
	Radar	LSTM-Corrected	Radar	LSTM-Corrected
A	0.3848	0.7614	0.2739	0.1381
B	0.4759	0.8843	0.1838	0.0906
C	0.2706	0.9167	0.2108	0.0749

shows the area-averaged PCCs and RMSEs for the three areas. Overall, the LSTM-corrected velocities show significant improvement in the three areas, compared with the original radar velocities. The LSTM-corrected velocities obtain the smallest RMSE and highest PCC in area C, and the highest RMSE and smallest PCC in area A. This implies that, with physical information with respect to winds and tides, the LSTM works effectively in area C, where the current variability is mostly modulated by tides and winds. In contrast, the current variability in area A is much more complicated. In addition to the winds and tides, the Pearl River runoff and the local topography and coastlines are also important influencers of the currents in area A.

In the above experiments, since we treated the model currents as the true values, we had enough targeting outputs in each data point for the LSTM training processes, which meant that we could build one LSTM network for one individual data point. This also implies that in future field work, we need in situ measurements at all data points, which is infeasible in practical situations. To provide a feasible observing strategy for the field work, we performed the following experiment: building the LSTM training network at certain points to see if this well-trained network could be applied to other points in areas A to C.

The experiment was first carried out in area C. We tested LSTM corrections at each point and used the one-point LSTM trained network for all other points in the whole of domain C. As a result, we found that the LSTM network built at point C obtained a PCC of 0.92 and an RMSE of 0.08 m/s (Figure 6). If the LSTM network at point C was applied to the whole of area C, it obtained the smallest domain-averaged RMSE. In view of the good results in area C, this experiment was further carried out in area B. The best site is point D, which produced PCCs between 0.74 and 0.93 for the other points in area B except one point. The worst correction point is located in the upper-left one in area B, near the island in the northwest corner. This point is most likely affected by the island. This experimental strategy does not work for area A (not shown), which implies that local factors such as topography, surrounding islands and coastlines, and their interactions with winds and tides, play more important roles in determining the current variability at each point of area A, so that a single-point LSTM network cannot be used for correcting other points.

3.3. Sensitivity Experiments

In order to explore the relative contributions of winds and tides to the LSTM training network, we tested a set of inputs including different physical factors: (1) Exp. 1: radar and winds; (2) Exp. 2: radar and tides; (3) Exp. 3: radar, winds, and tides.

Table 2. Domain-averaged PCCs and RMSEs for the sensitivity experiments.

Experiments	Inputs	PCCs	RMSEs (m/s)
Exp. #1	Radar + Winds	0.7482	0.1222
Exp. 2	Radar + Tides	0.7696	0.1312
Exp. 3	Radar + Winds + Tides	0.8794	0.0902
Reference	Original radar data	0.3734	0.2174

shows the domain-averaged PCCs and RMSEs for the sensitivity experiments. The original radar data without correction were listed as reference. In the cases of Exp. 1 and 2, we see that including one physical factor (winds or tides) can significantly reduce the domain-averaged RMSEs, from 0.22 m/s to 0.12 and 0.13 m/s, respectively. This indicates that both winds and tides are almost equally important in respect of modulating the current variability in the whole region. In Exp. 3, both winds and tides were included in the LSTM network; the domain-averaged PCC increased to 0.88 and the RMSE decreased to 0.09 m/s. It is known that the HF radar current data were inverted from original electromagnetic echo signals, without any constraints from ocean physical processes in the traditional inversion algorithms. Our results showed that a LSTM correction algorithm combining ocean physical factors can effectively reduce radar data errors. This provides useful guidance for radar raw data quality control.

4. Conclusions

In this study, we proposed a LSTM algorithm to reduce velocity errors from HF surface wave radar current measurements. Sea surface winds and tides are included in the LSTM algorithm to provide ocean physical information by which to constrain and improve its training efficiency. The results showed that the LSTM algorithm is able to significantly improve radar data quality. The model-simulated velocity fields were treated as the targeting outputs (true values) for the LSTM training process, as no current in situ observations are available at this stage. A practical observation strategy for future field work was tested based on a set of sensitivity experiments.

The results of this study show that the improvement of the radar current data in the whole domain through the LSTM correction is obvious (Table 1 and Table 2). The degree of improvement varies in the three sub-domains, in which the current variability is dominated by different physical factors. Note that in this study we treated the model currents as the true values, which provided us with enough training data for testing various sensitivity experiments. In reality, the deployment of in situ measurements at certain points of this area is necessary for validating the radar data. Therefore, a hypothesis was proposed to test; that is, whether a well-trained LSTM network at one single point could be applied to the whole domain. Testing such a hypothesis has provided a low-cost and feasible observing strategy for future field work. As we can see, this hypothesis applies in areas B and C, where the current variability is determined by large-scale winds and tides. In contrast, the hypothesis does not apply in area A, as the local bathymetry and coastlines are the major interference factors along the coastal area. This implies that an LSTM network including more local factors or sufficient observations might provide a better correction solution for coastal area.