Enhancing Sea Surface Height Retrieval with Triple Features Using Support Vector Regression

Abstract

In Global Navigation Satellite System Reflectometry (GNSS-R), SNR spectrum analysis is widely used for surface altimetry inversion because of its low cost and easy operation. However, this method is somewhat limited in environmental situations with large tidal variations in sea level. In this paper, we implemented a machine learning approach to retrieve sea level height using three feature parameters of frequency, amplitude, and phase extracted by GNSS-R as inputs for the support vector regression (SVR) model, achieving better robustness in environments with large tidal variations. In this experiment, two stations, SC02 and BRST, were selected for research comparison, in which the sea surface fluctuation at the SC02 station was smaller at around 3 m while the sea surface fluctuation at the BRST station was larger at around 7 m. Global Navigation Satellite System (GNSS) observations were selected for 6 months for use to perform the assessment. The SC02 station improved 25.64% and 24.05% in the accuracy of RMSE (14.5 cm) and MAE (12.0 cm), respectively, using the SVR model compared to the conventional method (CM). In the environment with large sea level tidal fluctuations, the BRST station improved accuracy by 17.32% and 15.81% using the SVR model compared to the CM for RMSE (25.3 cm) and MAE (21.3 cm), respectively. It is shown that the SVR model is robust for sea level height retrieval with large tidal variations and that these three feature parameters, including frequency, amplitude, and phase extracted by GNSS-R, are crucial for optimizing sea surface height retrieval.

1. Introduction

The surveillance and investigation of sea level changes are important for the natural environment, ecosystems, and economic development of coastal areas. Traditional methods for measuring sea level height include tide gauge stations and satellite altimetry. However, satellite altimetry data can suffer from reduced accuracy in coastal regions due to the influence of land subsidence [1]. The Global Navigation Satellite System Reflectometry (GNSS-R) technology, with its benefits of low cost, abundant signal sources, and an all-weather observation capacity, can assist in providing sea level monitoring data for coastal areas [2]. Interference effects occurring between the direct and reflected signals received by Global Navigation Satellite System (GNSS) receivers can affect signal-to-noise ratio (SNR) observations [3,4,5,6]. This effect carries information about the reflective surface and can, therefore, be used for sea surface height inversion research.

The GNSS satellite signal has the signal properties of an electromagnetic wave, which provides a great deal of relevant information about the reflective surface. It is an electromagnetic wave signal made up of electric and magnetic field components. With GNSS-R technology, the reflecting surface has an impact on the amplitude, phase, frequency, and polarization features of the reflected signal, which allows the sea level height to be inverted. Right-handed circularly polarized (RHCP) antennas are now the main antenna type used in GNSS-R sea surface altimetry to receive both the direct satellite signal and the reflected signal resulting from multipath phenomena [7]. The combined SNR is the result of these two signals’ interference effects on the antenna. Spectral analysis is used to identify primary multipath signal frequencies from the SNR, and an altitude model is built to determine the sea surface height. In 2013, Larson et al. [8] extracted the dominant frequency of the oscillation term from the satellite reflection signal to invert the sea surface height. These experimental findings demonstrate that signal-to-noise data can be applied to the measurement of the sea level. This provided a contribution to the subsequent research.

The approach of retrieving sea level height from SNR signals is now the most popular. Anderson [9] found for the first time that the interferogram in the SNR originated from the interference of the reflected signal to the direct signal, which was related to the sea level altitude measurement. Due to the multipath effect, the conventional method separates the reflected signal from the direct signal [10], for the sea surface fluctuations do not change the case of the method better. However, this method has a certain error when the sea level fluctuation changes dramatically. In 2013, Larson et al. [11] experimentally tested a GPS station in Kachemak Bay, Alaska, where the tidal variation was the largest in the United States (>7 m) and extended the method by adding a correction term to the original method. This had important implications for the monitoring of large tidal fluctuations. The sea surface experienced significant fluctuations, resulting in varying levels of signal reflection. This made the traditional method limited, where the sea surface fluctuated. These fluctuations introduced additional noise and uncertainties in the SNR spectrum, making it challenging to accurately retrieve sea level height. Large tidal variations could lead to changes in the reflection patterns and signal strengths, which could interfere with the interpretation of the SNR spectrum. However, the sea surface survey not only requires the reflector height of GNSS-R, but also the height from the phase center of the reflector antenna to the hydrographic reference point. As the ground settles, the reference point also changes accordingly, or the topography of the antenna changes, which brings a lot of workload and error to the sea level height measurement. Machine learning can have a profound impact on the application of environmental monitoring. In 2022, Nutpapon Limsupavanich et al. [12] firstly utilized the recurrent neural network (RNN) as a noise model to train, preprocess and denoise SNR data. The experimental results showed that SNR denoising using RNN reduced the RMSE by 3 cm compared to the previous method and by 9 cm compared to the denoising based on the empirical mode decomposition (EMD) method, respectively. RNN-based denoising techniques are superior to EMD techniques for applications requiring short SNR data. In 2023, Ole Roggenbuck et al. [13] proposed a technique for estimation based on kernel regression and clustering methods coupled with supervised machine learning to calculate the significant wave height using a linear model as a baseline. Additionally, the best result from the artificial neural network (ANN) was that testing RMSE (0.167 m), which was reduced by 32% compared to the baseline model. Cemali Altuntas and Nursu Tunalioglu et al. [14] investigated the classification of strong and weak reflected signals by input parameters (azimuth, satellite altitude angle, year, reflected signal amplitude, number of ephemerides, etc.) using machine learning classification algorithms. The results of this research show that better retrieval results can be obtained after filtering and classifying SNR signals using machine learning classification algorithms, and their correlation was improved by 19%. The RMSE was reduced from 15.4 cm to 4.5 cm.

In the present study, the stability and accuracy of retrieval are concerned. The stronger robustness and accuracy of machine learning may have excellent performance in sea surface height retrieval. Larson et al. [15,16] demonstrated that ground information is related to the dominant frequency, phase, and amplitude of the reflected signal. Additionally, it has also been shown that, in addition to the frequency in the oscillation term of the reflected signal, both the amplitude and the phase reflect the ground characteristics. Therefore, it is possible to utilize it to obtain the sea surface height. The SVR model in machine learning has an excellent regression effect and robustness for small amounts of data [17]. The machine learning model has a mature theoretical foundation, which is equivalent to a black-box model without the need for the complicated human derivation of formulas [18]. Therefore, the frequency, amplitude, and phase extracted by GNSS-R were proposed for the first time as the input parameters of the SVR model and for the retrieval of sea surface height in this paper. This approach helps to mitigate the challenges posed by land subsidence and the need for antenna height adjustments, allowing for the effective retrieval of sea surface heights even in stations experiencing significant wave fluctuations.

To verify the conjecture of the above method, we selected two stations (SC02 station and BRST station) for the experiment. In the second chapter, we introduce the traditional sea level retrieval method and the SVR model. In the third chapter, we perform the experiments, which include the source of data, SNR quality control, a specific flow chart of the proposed method, and a comparative analysis of the proposed method and the traditional method. Finally, we draw conclusions.

2. GNSS-R Sea Surface Height Retrieval Method

2.1. Principle of GNSS Conventional SNR-Based Altimetry

As shown in Figure 1, for the geometric relationship of GNSS-R, the GNSS receiver receives the direct signal emitted by the satellite and the reflected signal reflected by the reflecting surface.

In the figure, the angle between the direct signal and the reflected surface is denoted by $\theta$, while the height of the antenna phase center to the reflective surface is denoted by $RH$.

The SNR, which measures signal quality, is frequently employed in communications. In GNSS observations, it can be used as an observed value to invert the sea level height. The oscillation term was caused by the multipath effect, which contained the physical information of the reflecting surface. This made it possible to invert the sea level height and other medium parameters. Niewinski and Larsen presented the multipath effect reflection model, which can be described as [19].

$$\{\begin{array}{c}SNR=SN{R}_d+SN{R}_{rev}\\ SN{R}_d=(w_d+w_r+w_r^l)/w_n\\ SN{R}_{rev}=2\sqrt{w_d{w}_r}\cos ({\psi }_i)/w_n\end{array}$$

(1)

where $SN{R}_d$ is the trends term, and $SN{R}_{rev}$ is the oscillation term. $w_d$ is the direct signal power, $w_r$ is the reflected signal power, $w_n$ is the noise signal power, and $w_r^l$ is the incoherent signal power, while ${\psi }_i$ is the interferometric phase. Since $w_d$>>$w_r$, the trend term can be removed by polynomial fitting, because the trend term has almost no effect on the sea surface height inversion [20]. In terms of writing, the multipath frequency modulates of $SN{R}_{rev}$ are:

$$SN{R}_{rev}=A\cos \left(2\pi f_{x}x+\mathsf{\Phi }\right)$$

(2)

where $A$ is the oscillation amplitude, $\mathsf{\Phi }$ is the initial phase of the multipath oscillation term and $f_x$ is the oscillation frequency of the SNR oscillation term. In most cases, Lomb–Scargle periodogram (LSP) analysis is utilized to evaluate the frequency [21]. Sea surface height was retrieved with the following methods:

$$RH=\frac{\lambda f_x}{2}$$

(3)

where $\lambda$ is the wavelength of the satellite. The amplitude, phase, and frequency can be extracted by the LSP method [22]. After the trend term is removed by the LSP, the SNR residual term can be expressed by Equation (4), which is derived from a nonlinear least squares fit between the sinusoidal parameters and the non-smooth signal-to-noise ratio samples [23]. The following is an expression for the LSP function:

$$SN{R}_{rev}(t)=X\cos (2\pi f_{x}t)+Y\sin (2\pi f_{x}t)+Z$$

(4)

where $t$ refers to the sine of the elevation angle, $X$ and $Y$ terms refer to numerical terms for the inversion instead of the amplitude and phase of nonstationary samples of $SN{R}_{rev}$. $Z$ represents the average deviation, which is generally a very small value because of the trend in $SN{R}_{rev}$, which is removed. Using the extracted frequencies and Equation (3), we obtained the reflector height, which is a universal sea surface altimetry method [24,25]. Additionally, it has been demonstrated that the amplitude is determined by the reflector’s dielectric constant and the roughness of the reflecting surface, whereas the phase shift is connected to the satellite signal’s stated reflectivity depth [26]. As a result, when we receive the SNR oscillation term, we can extrapolate the signal’s properties from the reflector’s environment.

2.2. Support Vector Regression (SVR) Retrieval Principle

Support vector machine regression, first proposed by Vapnik [27,28], can be applied to pattern classification and nonlinear regression, just like multilayer perceptron networks and radial basis function networks. Compared to logistic regression and neural networks, SVR provides a clearer and more powerful approach to learning complex nonlinear equations. The fundamental goal of SVR is to construct a hyperplane that optimizes the isolated edge between positive and negative samples as a decision surface. SVR is an approximate implementation that minimizes the risk of the outcome. The SVR hyperplane is shown in Figure 2.

3. Experiments and Analysis

3.1. Data Sources and Processing

For our studies, we relied on data from the SC02 station (latitude: 48°32′46.302″, longitude: −123°0′27.396″), which is situated on the spit of land in Friday Harbor, Washington, USA. The EarthScope Plate Boundary Observation (PBO) includes the SC02 station [29]. The SC02 station, which is situated on the water’s edge and can pick up a variety of GPS reflection signals, makes it easier to conduct experimental research. The position of the SC02 station receivers and the surrounding area are shown in Figure 3. The station has a choke coil antenna and a TRIMBLE NETR9 geodetic receiver with a 15-s sample interval. The antenna is typically 5.5 m perpendicular to sea level on average. The sea level varies by around 3 m. Additionally, this study employed measured data from the tidal gauge station at Friday Harbor (latitude: 48°32′48.001″, longitude: −123°0′36″), which is located 359 m from SC02, as a reference to confirm the precision of GNSS observational technology. The tidal datum of the gauge is mean lower low water (MLLW). The National Oceanic and Atmospheric Administration provided the tide gauge data, which were sampled every 6 min.

Utilizing the SNR data from February to July of 2022 (DOY 32-212), the performance of GNSS-R was evaluated. To ensure that the SNR data came from sea-level reflections, the elevation angle range for this station was set to 5°–30°, the azimuth angle range was set to 50°–240°, and the maximum amplitude of the LSP spectrum was set to more than twice the average background noise.

To determine the sea level, the BRST station (latitude:48°22′49.776″, longitude:-4°29′47.743″) in Brest, France, near the mouth of the Penfeld River (see Figure 4) was chosen. A Trimble TRM57971.00 choke antenna, installed on the receiver, offered high-speed observation at 1-s sample intervals. The average vertical distance of the antenna at this site from the sea surface was about 17 m and was accompanied by a tidal fluctuation of about 7 m [30]. The station data can be obtained from the IGS website (http://www.igs.org). The reference values of sea level change used in this experiment were obtained from the BREST harbor tide gauge station (latitude:48°22′58.26″, longitude:−4°29′41.417″) located 500 m north of the BRST station with a sampling rate of 1 min, and these observations could be downloaded from the official REFMAR website (http://refmar.shom.fr/ (accessed on 1 September 2022)). The tidal datum of the gauge is the Lowest Astronomical Tide (LAT).

SNR data were taken from DOY 1-181 in the first half of 2021. We employed various quality control metrics to choose the optimal SNR signal. This station’s elevation angle range was 5° to 25°, its azimuth angle range was 135° to 330°, and its maximum LSP spectral amplitude was greater than 3 times the background noise average.

3.2. Retrieval Process of SVR Model

The experiment used the SVR model compared with the conventional method (CM) to retrieve two stations, including SC02 half-yearly data from 2022 (DOY32-212) and BRST six-monthly data from 2021 (DOY1-181), respectively. The SNR data of the GPS L1 band were extracted from the frequency, amplitude, and phase (Fre, Amp, Pha) by the LSP method after removing the trend term by binomial fitting. The corresponding frequency, amplitude, and phase data were normalized to the 0–1 range based on the frequency retrieval performance results with the following equations.

$$x^{*}=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$$

(5)

where $x$ is the original value of a feature, $x_{\min }$ is the minimum value of that feature in all samples, $x_{\max }$ is the maximum value of that feature among all samples, and $x^{*}$ is the normalized value of the feature ∈ (0, 1). Frequency, amplitude, and phase were used as the input parameters for the SVR model, and tide gauge reference data were used as the corresponding target labels. The extracted frequency, phase, and amplitude were used as the three characteristic inputs to the SVR for the retrieval of surface height. The most widely used kernel function was the radial basis function (RBF), where the SVR model utilized RBF as the kernel function in this paper. C and gamma are crucial parameters in SVR. C is the penalty coefficient, and gamma is the kernel coefficient. C determines the balance between fitting the training data tightly and allowing errors, affecting overfitting and underfitting. On the other hand, gamma controls the influence range of data points in the higher-dimensional space, impacting the sensitivity to nearby support vectors. The proper tuning of these parameters is essential for optimizing the SVR model’s performance and generalization. The SVR model for the SC02 station was set to C = 5 and gamma = 0.166. The SVR model for the BRST station was set to C = 5 and gamma = 4.188. Normalized data were cross-validated using the SVR model in five folds obtained the final inversion results for comparison with the CM. We used five-fold cross-validation by dividing the dataset randomly multiple times and performing a model evaluation, which could more accurately assess the performance of the model. Each subset acted as a validation set once, which could reduce the dependence on specific divisions and improve the reliability of the evaluation results. Additionally, it was possible to fully utilize 6 months of data so that inverse results were available on a daily basis. The specific flow chart is shown in Figure 5.

3.3. Results and Analysis

3.3.1. Retrieval Experiment of SC02 Station

GPS L1-band data of DOY 32-212 in 2022 obtained from the SC02 station were analyzed, and the experiment compared the SVR model with CM. As seen in Figure 6, a graph displaying the temporal fluctuations of these findings from the CM and SVR algorithms and the measured data from the tide gauge was provided. The dates are portrayed by the horizontal axis, while the height beyond sea level is denoted by the vertical axis. The results retrieved by both methods appeared to be in general high agreement with tide gauge data. The specific retrieval results are presented in

Table 1. Comparison of the SC02 station retrieval results.

Method	RMSE/cm	MAE/cm	Correlation Coefficient	a	b
CM	19.5	15.8	0.971	0.9535	0.0969
SVR	14.5	12.0	0.981	0.9976	0.0077

. Most of the CM results (green dots) are not as excellent as those of the SVR (orange dots) in the marginal part of the retrieval, as shown in the red frame. This shows that the SVR model had higher superiority in surface altimetry retrieval performance compared with CM.

In this experiment, RMSE, MAE, and R were used as the evaluation criteria for the accuracy of sea level retrieval. Figure 7 displays the correlation analysis for the two techniques of measuring sea level height, tide gauge, and monitoring, respectively. Additionally, we gave the line form $y=ax+b$ to describe the linear relationship between the tide gauge and the two methods. The linear correlation equation between the tide gauge and CM was solved as $y=0.9535x+0.0969$ (see Figure 7a). It has a few discrepancies in the figure. However, in Figure 7b, we found that the linear correlation equation between the SVR model and the tide gauge was $y=0.9976x+0.0077$, which was corrected for deviations compared to the CM. This deviation was more concentrated, the linear relationship more similar to $y=x$, and there was not a very large deviation value. The RMSE, MAE, and R correspondingly decreased and increased, respectively. Thus, as has been said, the results obtained from the SVR model retrieval based on the frequency, amplitude, and phase inputs can be better than the results obtained from CM.

Figure 8 shows the residual of the SC02 station for SVR versus CM. This figure compares the residuals produced by the two methods on a daily basis from February to July, where the green color is the residuals produced by CM, and the orange color is the residuals produced by SVR. The variations between the two techniques are very obvious, and the SVR model had a significant positive impact on the retrieval accuracy of sea surface height.

In Table 1, the specific statistics are displayed. The SVR’s RMSE value is 14.5 cm, and the correlation between the measured sea level and the SVR is 0.981. The RMSE value of CM is 19.5 cm, and the correlation coefficient with the measured sea level is 0.971. The MAE values of CM and SVR are 15.8 cm, 12.0 cm, respectively. Compared to CM, RMSE and MAE decreased by nearly 25.64% and 24.05%, respectively. Noteworthy is the fact that the regression line of SVR was $y=0.9976x+0.0077$. Compared with that of CM, $a$ was towards 1 and $b$ was closer to 0.

The residuals between the tide levels obtained by the inversion of the two methods and the measured tide levels are presented in Figure 9. The residual difference between the observed value and the inverse sea level is denoted by the horizontal axis, and the vertical coordinate represents the data obtained from the tide gauge. It is obvious to notice that the residuals of the CM inverse performance were concentrated around the value of 0, and some residuals were outside the value of 0.3 m. By contrast, the residuals of the SVR inversion were more concentrated than those of the CM, and there were fewer values outside 0.3 m. It can be seen that the SVR model combining frequency, amplitude, and phase had a better inversion effect.

3.3.2. Retrieval Experiment of BRST Station

The experimental data were GPS L1-band signals from DOY 1-181 at the BRST station. With the same approach as above, we tested the BRST station to demonstrate the reliability of the SVR model effect (see Figure 10). In the case of high tidal variations, SVR also had a very good performance. In the marginal part of the retrieval, most of the SVR results (orange dots) were closer to the tide gauge data, as shown in the red box. In addition, the missing part was the part where tide gauge data and observations were not available. As shown in the diagram, SVR still exhibited robustness to large tidal variations at the monitoring stations.

Figure 11 represents the correlation analysis diagram between tide gauge and two methods. The linear relationship of Figure 11a is $y=0.9730x+0.1010$, and Figure 11b is $y=0.9996x-0.0092$. We found that the SVR was more able to concentrate the deviation values compared to the CM (see the lower left dark blue part of Figure 11b), in addition to the $a$ of the SVR, which reached 0.9996 (almost one) and the $b$ of the SVR was also very close to 0. Similarly, the residual analysis in Figure 12 shows that the residuals generated by the SVR method were not as prominent as those of the SC02 station but could still be seen to be significantly superior in effect.

Table 2. Comparison of the BRST station retrieval results.

Method	RMSE/cm	MAE/cm	Correlation Coefficient	a	b
CM	30.6	26.0	0.985	0.9730	0.1010
SVR	25.3	21.3	0.990	0.9996	−0.0092

presents the results of the experiment. The RMSE value of the SVR was 25.3 cm, and the correlation coefficient with the measured sea level was 0.990. The RMSE of the GNSS-R was 30.6 cm, while the correlation between the observed sea level and that value was 0.985. The accuracy of RMSE improved by nearly 17.32% compared to that of CM. The accuracy of MAE also showed a significant improvement of 15.81%.

It is obvious from Figure 13 that the residuals of the CM inverse performance were also concentrated around the value of 0, with some residual values outside of 0.4 m, which was slightly larger compared to the residuals of the SC02 station. The residuals of the SVR inverse performance were more concentrated at 0.4 m compared to the CM.

3.4. Discussion

Errors in GNSS sea level measurements can arise due to various factors, including the large distance between the illuminated area, the antenna, and the tide gauges. If the distance between the tide gauge station and the GNSS station is very far, it is possible that the fluctuation of the water measured by the tide gauge station is not the same as the fluctuation of the water at the GNSS station, which can result in errors. However, the locations of the tide gauges selected are the closest ones to the station (359 m and 500 m between them, respectively), which adequately reflect water level changes near the coastline and do not give rise to very large errors. From the Fresnel zone, it can be seen that the SC02 station covers the majority of the water surface information and adequately reflects tidal changes near the coast, but the BRST station is a narrow channel, so the maximum elevation angle is set to 5 degrees less than that set at the SC02 station in order to minimize the error of the ground or buildings due to the multipath effect. Even so, narrow channels are still subject to errors due to reflections from land or buildings due to multipath effects. It can be found in the experiments at the SC02 station that the number of reflection points at the low water level was less compared to that at a high-water level, while this distribution was not obvious in the experiments at the BRST station. From the point of view of the elevation angle of the reflection signal, we considered the sea level as a fluctuating process, and when the tidal wave fluctuated to low water, the elevation angle of the same reflection surface was greater than the limit of the set elevation range, which was filtered out as an outlier. Therefore, it is a common phenomenon that the number of low-water reflection points is less than the number of high-water reflection points. However, at the BRST station, this phenomenon was less pronounced due to the high-water level at that location.

4. Conclusions

In this paper, the BRST and SC02 station were experimented separately and produced different results for stations with different sea level fluctuations. It can be found that the retrieval results of the SVR model based on three feature inputs had higher accuracy and better stability than CM. In particular, the residuals of the GNSS-R-based SVR for SC02 and BRST stations were lower than CM, respectively, demonstrating a better fit that closely matched the tide gauge data. For a station with large sea level fluctuations, it would be desirable to make the retrieval more stable, and the SVR model can retrieve a more stable result when faced with frequent and large sea level fluctuations. At the same time, this makes it possible to invert the sea surface height by machine learning using three parameters: frequency, amplitude, and phase. Since the SVR model has a mature theoretical foundation, this makes it show high accuracy in the process of sea surface level retrieval. It is shown that a good agreement can be achieved compared to the nearby tide gauge, with a 25.64% decline in RMSE and a 24.05% decline in MAE for the SC02 station. In addition, it was found that there was a 17.32% and 15.81% decline in the BRST station RMSE and MAE, respectively, which demonstrated the high feasibility of our method even in a large tidal variation environment. This proves that the method has good robustness and accuracy in sea level height monitoring.

In conclusion, the frequency, amplitude, and phase can serve as effective machine learning features for sea level height monitoring, which can significantly contribute to the development of GNSS-based sea surface monitoring and related scientific application infrastructure. The application of machine learning in environmental monitoring, including sea level height retrieval, has the potential to enhance accuracy, reduce manual efforts, and streamline data analysis processes. By leveraging the strengths of machine learning models, researchers can achieve outstanding performance and gain valuable insights into environmental changes and phenomena. Moreover, in the future, this strategy might be used in different situations, such as soil water content monitoring and snow depth estimation.