Intelligent Prediction of Sea Level in the South China Sea Using a Hybrid SSA-LSTM Model

Abstract

As an important marginal sea in the western Pacific, sea-level changes in the South China Sea not only respond to global warming but are also regulated by regional ocean dynamics and climate modes, exerting profound impacts on the socioeconomic development and engineering safety of coastal regions. To address the widespread issues of low accuracy and robustness in existing sea-level prediction models when handling nonlinear, multi-scale sequences, as well as the complexity of sea-level change mechanisms in the South China Sea, this study constructs a hybrid model combining Singular Spectrum Analysis and Long Short-Term Memory neural networks (SSA-LSTM). The coral skeletal oxygen isotope ratio (δ¹⁸O) used in this study is a key indicator for characterizing the marine environment, defined as the per mille difference in the ¹⁸O/¹⁶O ratio of a sample relative to a standard. Based on coral δ¹⁸O data from the South China Sea, the sea level from 1850 to 2015 is reconstructed. SSA is then applied to decompose the sea-level data into trend and periodic components. The trend component, accounting for 37.03%, and components 2 to 11, containing major periodic information, are extracted to reconstruct the sea-level series. The reconstructed series retains 95.89% of the original information. The trend component is modeled through curve fitting, while the periodic components are modeled using an LSTM neural network. Optimal hyperparameters for the LSTM are determined through parameter sensitivity analysis. An integrated SSA-LSTM model is constructed to predict sea level in the South China Sea, and its predictions are compared with those from a Singular Spectrum Analysis-Autoregressive Integrated Moving Average (SSA-ARIMA) model. The results indicate that from 1850 to 2015, sea level in the South China Sea exhibits periodic fluctuations with a significant overall upward trend. Specifically, the growth rate from 1921 to 1940 reaches 5.49 mm/yr. Predictions from the SSA-LSTM model are significantly higher than those from the SSA-ARIMA model. The SSA-LSTM model projects that from 2016 to 2035, sea level in the South China Sea will continue to rise at a fluctuating rate of 0.75 mm/yr, with a cumulative rise of approximately 15 mm. This study provides a novel methodology for investigating the mechanisms of sea-level change in the South China Sea and offers a scientific basis for coastal risk management.

1. Introduction

Sea-level change is recognized as a key indicator of global climate system changes, and its continuous rising trend has become a major environmental issue that is widely concerned by the international community. According to the World Meteorological Organization’s “2023 State of the Global Climate Report,” the global mean sea-level rise rate during the satellite observation era (1993–2023) was measured at approximately 3.4 mm/year and was observed to be continuously accelerating [1,2,3,4,5]. This change was mainly attributed to ocean thermal expansion and land ice melt caused by global warming. As an important semi-enclosed marginal sea in the western Pacific, the South China Sea’s sea-level change is not only influenced by the background of global sea-level rise but is also jointly regulated by multiple factors such as regional ocean circulation, monsoon systems, and the El Niño–Southern Oscillation (ENSO), forming unique spatiotemporal variation characteristics. Abnormal sea-level changes in this region can alter the marine dynamic environment, further affecting the regional water cycle and ecosystem, and are considered to have profound impacts on the socio-economic development of surrounding countries and regions [6,7,8].

Research on sea-level change in the South China Sea is regarded as particularly important in the field of marine science. Existing studies have shown that sea-level change in the South China Sea is characterized by significant regional features and complex multi-scale variability. Through the analysis of multi-source observation data, researchers such as Liu Rui found that the sea-level rise rate in the South China Sea during 1970–2013 reached 2.4 mm/year, a value slightly higher than the global average during the same period [9]. Furthermore, a study by Pan Yi et al., based on multi-generation satellite altimetry data, confirmed that the sea-level rise rate in the South China Sea remained at 2.4 mm/year during 1993–2015, indicating a continuous upward trend [10]. Additionally, significant interannual and decadal fluctuations are found in the sea-level changes in the South China Sea, which are closely related to climate modes such as the Pacific Decadal Oscillation (PDO) and ENSO. These research results provide an important scientific basis for understanding the patterns of sea-level change in the South China Sea and serve as important references for regional marine environment prediction and coastal zone management [11,12].

Sea-level prediction is considered crucial for formulating coastal climate adaptation strategies. Although important progress has been made in existing research, current studies on sea-level change in the South China Sea still face many challenges. First, sea-level time series typically contain complex nonlinear characteristics and multi-timescale variation signals, making it difficult for traditional time series analysis methods to effectively separate their trend, periodic, and noise components [13,14]. Second, sea-level prediction is affected by various uncertainty factors, including the internal variability of the climate system, climate responses under different greenhouse gas emission scenarios, the complexity of regional oceanic dynamic processes, and the selection of statistical model parameterization schemes [15,16,17]. Especially under the background of global climate change, the increased frequency of extreme sea-level events further amplifies the uncertainty in sea-level prediction. These factors collectively cause the sea-level change series to exhibit complex nonlinear and long-range dependency characteristics, meaning the current state may be influenced by climate conditions from the distant past. When capturing such long-range dependencies, traditional time series models often struggle to learn key information across time periods due to the vanishing gradient problem. These factors make accurately characterizing the patterns of sea-level change in the South China Sea and predicting its future trends a research hotspot and challenge in the interdisciplinary field of physical oceanography and coastal engineering [18,19,20,21,22]. For this purpose, the Long Short-Term Memory (LSTM) neural network is regarded as an effective solution. As a special type of recurrent neural network, LSTM uses its unique “gating mechanism” (input gate, forget gate, and output gate) to finely regulate the flow of information. Its core cell state acts like a memory corridor, enabling the network to selectively remember long-term trends (such as the slow rise driven by greenhouse gases) while forgetting short-term irrelevant fluctuations. This characteristic allows it to effectively address noise and uncertainty in sea-level prediction, opening new avenues for solving the nonlinearity and long-range dependency problems in sea-level forecasting.

In this study, coral δ¹⁸O data from the South China Sea are first obtained. Based on these data, the sea level of the South China Sea from 1850 to 2015 is reconstructed. Singular Spectrum Analysis (SSA) is then employed to decompose the South China Sea’s sea level data into trend and periodic components. The trend component is modeled through curve fitting, while the periodic component is modeled using a Long Short-Term Memory (LSTM) neural network. Through parameter sensitivity analysis, the optimal hyperparameters of the LSTM are determined. An SSA-LSTM integrated model is constructed for predicting sea level in the South China Sea. This method fully leverages the advantages of SSA in signal denoising and component extraction, while combining the powerful capability of LSTM in handling nonlinear time series prediction, aiming to effectively enhance the accuracy and reliability of sea-level prediction. The research results of this paper are expected to contribute to a deeper understanding of the mechanisms of sea-level change in the South China Sea and provide a scientific basis and technical support for assessing the impact of sea-level rise on coastal engineering, formulating adaptation management strategies, and promoting regional sustainable development.

2. Research Area, Data, and Methods

2.1. Overview of the Study Area

The South China Sea is recognized as one of the largest marginal seas in the western Pacific and the largest and deepest sea among China’s adjacent waters. The South China Sea extends in a NE-SW direction, covering an area of approximately 3.5 million square kilometers. Its main body is characterized by a vast deep-sea basin, with an average depth of about 2000 m and a maximum depth exceeding 5500 m. The sea area features a complex topographic structure, composed of a central deep-sea basin, surrounding continental shelves, seamounts, and ridges. Among these, the northern continental shelf is wide, while the southern continental shelf is relatively narrow. The South China Sea is home to one of the world’s most abundant coral reef ecosystems, which provides ideal conditions for reconstructing high-resolution environmental records using coral geochemical proxies. The geographical location of the South China Sea and its connectivity with surrounding water bodies are considered crucial for its hydrodynamics. The most significant water exchange with the western Pacific is conducted through key channels such as the Luzon Strait, and it is connected to the Indian Ocean via the Strait of Malacca in the south. Furthermore, freshwater discharge from major rivers such as the Pearl River, Mekong River, and Red River exerts significant regional influences on the salinity and sea level, particularly in the northern part of the sea. The South China Sea is located in a typical East Asian monsoon region, and its marine dynamic environment is dominated by a monsoon climate. In winter, the prevailing northeast monsoon drives the surface circulation in a cyclonic (counter-clockwise) pattern; in summer, the southwest monsoon prevails, and the circulation shifts to an anti-cyclonic (clockwise) pattern. This seasonally reversing circulation pattern not only regulates water masses and heat distribution within the South China Sea but also causes its sea-level changes to respond significantly to interannual climate variability signals such as the El Niño–Southern Oscillation (ENSO). Therefore, the sea-level series of the South China Sea incorporates the long-term trend of global sea-level rise, periodic signals driven by regional monsoons, and interannual fluctuations induced by ENSO, making it a complex and representative sea area for studying the driving mechanisms of sea-level change.

2.2. Data Source and Processing

Corals are regarded as ideal archives for recording marine environments due to their long lifespan, clear annual bands, and sensitivity to environmental changes. The oxygen isotope ratio (δ¹⁸O) in their skeletons is influenced by factors such as seawater temperature and salinity. During global warming, sea-level rise is caused collectively by thermal expansion of seawater and ice sheet melting. Simultaneously, increased seawater temperature and the input of meltwater enriched in light isotopes lead to more negative (lower) δ¹⁸O values in coral skeletons. Consequently, a significant negative correlation is observed between the coral δ¹⁸O series and sea-level change, allowing it to be used as an effective proxy for reconstructing historical sea-level variations. In this paper, coral skeletal oxygen isotope (δ¹⁸O) data measured by our team [4] and obtained from the literature [23,24,25,26,27] were adopted to reconstruct the sea level. The data records cover the period from 1850 to 2015.

To construct a uniform sea-level indicator that can represent the overall signals of the South China Sea, the coral δ¹⁸O series mentioned above were processed by arithmetic averaging in this study, resulting in a 166-year coral δ¹⁸O time series for the South China Sea. This averaged series effectively reduced the local noise that may be present in individual coral records and more clearly reflected environmental changes at the overall basin scale of the South China Sea. Subsequently, based on the transfer function (Equation (1)) established by Tao et al. (2022) [4] between coral δ¹⁸O and relative sea-level height in the South China Sea, the averaged coral ^δ18O series was converted into a relative sea-level series for the South China Sea. To eliminate the impact of inconsistent baselines on sea-level trend analysis, the sea-level data were standardized in this study. First, the mean sea level over the 36-year period from 1980 to 2015 was calculated and defined as the baseline value. Then, the sea-level data were uniformly converted into an anomaly series relative to this baseline, thereby producing a standardized anomaly series. This standardized anomaly series was used as the direct input data for Singular Spectrum Analysis (SSA) and LSTM.

Sea Level (mm) = −259.52 × δ¹⁸O (‰) + 0.017 (r = −0.87, p < 0.0001)

(1)

Figure 1 presents the relationship between the mean coral δ¹⁸O and the tide gauge mean sea level (TMSL). In this figure, the mean coral δ¹⁸O is represented by the blue line, and the TMSL is represented by the red line. Figure 2 displays a scatter plot illustrating the negative correlation between δ¹⁸O and TMSL. Based on the data from Figure 1 and Figure 2, the statistical correlation between the δ¹⁸O series and the TMSL was calculated. A significant negative correlation was revealed (r = −0.87, p < 0.0001). These results indicate that the δ¹⁸O series can effectively reflect sea-level change signals, supporting its applicability in sea-level reconstruction research. The coral δ¹⁸O data and tide gauge sea-level data used in this paper were derived from multiple sampling sites in the South China Sea. The values represent the arithmetic means of the δ¹⁸O series and sea-level series from all sites, rather than records from a single location. Hence, the relationships presented in Figure 1 and Figure 2 were between the spatially averaged coral δ¹⁸O and the TMSL. The objective of this paper is to reveal the average hydrological environmental characteristics on a regional scale in the northern South China Sea.

2.3. Research Methods

A hybrid modeling framework combining SSA and LSTM is employed in this study to predict the South China Sea’s sea-level time series. The core of this method lies in first using SSA for the decomposition and denoising of the sea-level time series signal. The South China Sea’s sea-level time series signal is decomposed into trend and periodic components. The trend component is modeled through curve fitting, and the periodic component is modeled using LSTM, thereby constructing an SSA-LSTM integrated model for sea-level prediction in the South China Sea.

(1) SSA

SSA is a non-parametric time series analysis technique suitable for decomposing trend, periodic, and noise components in complex sequences without requiring any prior model assumptions. Its processing mainly involves four steps:

Embedding: A one-dimensional sea-level time series of length N is embedded into a trajectory matrix X with a window length of L:

$$X=\left[X_1,X_2\dots X_K\right]=\left(\begin{array}{cccc}{f}_1& f_2& \dots & f_K\\ f_2& f_3& \dots & f_{K+1}\\ ⋮& ⋮& \ddots & ⋮\\ f_L& f_{L+1}& \dots & f_N\end{array}\right)$$

(2)

where L is the window length, K = N − L + 1.

Singular Value Decomposition (SVD): Singular Value Decomposition is performed on the trajectory matrix X:

$$X=US{V}^T={\displaystyle \sum _{i=1}^R\sqrt{{\lambda }_i}}{U}_i{V}_i^T$$

(3)

where U and V are the left and right singular vector matrices, respectively, S is the diagonal matrix containing singular values $\sqrt{{\lambda }_i}$, and R is the rank of matrix X. Each $\sqrt{{\lambda }_i}{U}_i{V}_i^T$ constitutes an elementary matrix of rank 1, representing an independent component of the original series.

Grouping: Based on the research objectives, the decomposed R elementary matrices are grouped. Typically, the first few components with large contribution rates correspond to the trend and main periodic components, while subsequent components with small contribution rates are regarded as noise. The elementary matrices within the selected groups are summed to obtain the composite matrix Yc.

Diagonal Averaging: Each composite matrix Yc is transformed back into a one-dimensional time series Fc of length N through the diagonal averaging method, which is the reconstructed signal component.

(2) LSTM

LSTM (Figure 3) is a special type of recurrent neural network (RNN). The problems of vanishing/exploding gradients during the training of traditional RNNs are effectively solved through the introduction of a gating mechanism, making it particularly adept at learning and predicting long-term dependencies in long time series. The core of LSTM is three gating structures:

Forget Gate: Determines which information is discarded from the cell state Ct−1 of the previous time step.

Input Gate: Controls how much information from the current input xt needs to be updated into the cell state.

Output Gate: Determines the output ht for the current time step based on the current cell state Ct.

Its forward propagation process is defined by the following set of formulas:

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

(4)

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

(5)

$$c_t=f_t·c_{t-1}+i_t·{\tilde{c}}_t$$

(6)

$${\tilde{c}}_t=\tanh \left(W_c·\left[h_{t-1},x_t\right]+b_c\right)$$

(7)

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

(8)

$$h_t=o_t·\tanh \left(C_t\right)$$

(9)

where σ is the Sigmoid activation function, tanh is the hyperbolic tangent activation function, ⊙ denotes the element-wise multiplication, and W and b are the weight matrices and bias terms for the respective gates, respectively.

(3) SSA-LSTM Hybrid Model Construction

The main process of the SSA-LSTM hybrid model constructed in this study is as follows:

SSA Preprocessing: First, SSA is applied to the sea-level time series of the South China Sea, decomposing it into trend, periodic, and noise components. By analyzing the contribution rates of the different components, the noise components with smaller contribution rates are eliminated. The remaining main components (trend and periodic components) are then reconstructed into a new sea-level series with a significantly improved signal-to-noise ratio.

LSTM Prediction: Subsequently, the periodic component data are used as the input for the LSTM model. Key hyperparameters of the LSTM (such as the number of hidden units, training epochs, and initial learning rate) are optimized using the grid search method. The coefficient of determination and root mean square error are used as evaluation metrics, leading to an optimal model which is then used for training and predicting the periodic component.

Trend Integration: The trend component is modeled through curve fitting, and the periodic component is modeled using LSTM. The trend model and the periodic model are then added together to obtain the complete future sea-level prediction values, which include both the long-term trend and periodic fluctuations.

All analysis, modeling, and visualization in this paper are conducted on the MATLAB R2023b platform, encompassing key steps such as data preprocessing, SSA decomposition and reconstruction, and LSTM model construction and hyperparameter optimization.

3. Results and Analysis

3.1. Characteristics of Sea-Level Change in the South China Sea

The averaged coral δ¹⁸O series is converted into a relative sea-level series for the South China Sea using the transfer function proposed by Tao et al. [4] (Figure 4). As can be seen from Figure 4, against the background of a significant overall upward trend, the South China Sea level is characterized by superimposed pronounced periodic fluctuations, demonstrating a pattern of “fall-rise-rise-rise-rise”. Specifically, during the period 1850–1897, the sea level slightly declined at an average rate of −0.15 mm/yr, reaching its lowest value in 1897. Thereafter, the trend was reversed, with the rate of rise reaching 5.49 mm/yr, particularly during 1921–1940. From 1950 to 2015, the sea level continued to rise at a rate of 1.58 mm/yr. Over the entire period from 1900 to 2015, the South China Sea’s sea level was observed to have risen cumulatively by approximately 141 mm. Spectral analysis was performed on the sea-level data, as shown in Figure 5. From Figure 5, the main periodic components of the South China Sea’s sea-level time series are identified as 71 years, 33 years, 18 years, 14 years, and 12 years (Figure 6).

3.2. Sea-Level SSA Decomposition and Reconstruction

In this study, SSA is employed for the decomposition and reconstruction of sea-level data. The window length L is set to 60, and the original series is decomposed into 60 components. The contribution rate of each component is shown in Figure 7. Within the framework of SSA, the selection of the trend component is primarily based on the mathematical principles of SSA, the defining characteristics of a trend, and the frequency properties of the components. SSA extracts the core structure of a sequence through SVD, where the magnitude of singular values directly corresponds to a component’s contribution to the original sequence. In this study, the contribution of the first component (approximately 40%, see Figure 7 and Figure 8) is significantly higher than that of subsequent components, indicating that the first component represents the most dominant structural information in the original sequence. In terms of frequency properties, the initial high-contribution component in SSA typically corresponds to the dominant low-frequency portion of the sequence. The essence of a trend is precisely the “slow, systematic long-term pattern of change,” which is characterized primarily by low-frequency features (in contrast to the medium-to-high-frequency fluctuations of periodic components and the high-frequency random fluctuations of noise). Considering the definition of a trend as “slowly varying and non-oscillatory,” this dominant low-frequency component perfectly matches the core characteristics of a trend. This approach also aligns with the established practice in SSA-based time series analysis, where the first one or two high-contribution components are typically identified as the trend. Therefore, in this paper, the first component is selected as the trend component. Within the analytical logic of SSA component separation, periodic components correspond to the oscillatory structures of a sequence. They are typically characterized by “moderate contribution and a tendency to appear in pairs” (due to the conjugate pairs often formed by the SVD eigenvectors of periodic components), and their frequency properties correspond to medium-to-high-frequency fluctuations (distinct from the low-frequency nature of the trend). As seen in the contribution distribution in Figure 5, the contributions of components 2 to 11 fell within a “secondary dominant range” (significantly lower than the first trend component but notably higher than subsequent noise components). Furthermore, the contributions of these components exhibited a pattern of “minor fluctuations with relative concentration,” which is consistent with the structural feature of periodic components involving “superimposed multiple oscillatory modes.” Simultaneously, from the perspective of frequency properties, these components corresponded to the medium-to-high-frequency portions of the sequence, precisely matching the essence of periodic components as “cyclical fluctuations” (distinguished from the low-frequency, slow variation in the trend and the high-frequency randomness of noise). So, in this paper, components 2 to 11 were selected as the periodic components. The remaining components, with a low contribution rate (approximately 4.02%), were regarded as noise and are eliminated. The South China Sea-level time series was reconstructed using the periodic components and the trend component. The reconstructed time series retained 95.89% of the original information (Figure 9).

The trend component is fitted using a fourth-degree polynomial function, with the detailed fitting equation provided in Equation (10). The fitted curve is characterized by a coefficient of determination (R²) of 0.9997 and a Root Mean Square Error (RMSE) of 1.1271, indicating that the fitting performance is considered excellent (Figure 10).

$$\mathrm{y} = 4.291\times {10}^{-7}{\mathrm{x}}^4-0.0002004{\mathrm{x}}^3+0.02886{\mathrm{x}}^2-0.372\mathrm{x}-157.6$$

(10)

3.3. SSA-LSTM Model Optimization and Validation

In this paper, the periodic component is predicted using LSTM. The input and output for the LSTM are constructed by the sliding window method, where standardized sea-level data from the previous consecutive 60 years are used as input features, and the data from the immediate following 61st year are used as the prediction target, thereby transforming the time series into a supervised learning problem. This structure enables the model to automatically learn the internal patterns and long-term dependencies of sea-level change from historical data. The model ultimately performs recursive prediction based on the last 60 years of data in the series. During the model construction phase, systematic hyperparameter optimization and validation are conducted for the LSTM model. The initial structure and parameters of the LSTM are detailed in

Table 1. Initial LSTM architecture and hyperparameters.

Parameter	Value	Parameter	Value
Time Steps	60	Number of Hidden Units	100
Optimizer	Adam	Epochs	100
Number of LSTM Layers	1	Initial Learning Rate	0.001

.

The results of the LSTM parameter sensitivity analysis are detailed in

Table 2. Comparison of R² and RMSE for the SSA-LSTM model with different numbers of hidden units.

Number of Hidden Units	R2	RMSE
100	0.655	13.538
105	0.461	14.599
110	0.651	13.463
115	0.533	14.546
120	0.681	15.311
125	0.623	13.701
130	0.704	12.854
135	0.587	14.388
140	0.627	13.547
145	0.600	13.562
150	0.632	14.416

,

Table 3. Comparison of R² and RMSE for the SSA-LSTM model with different numbers of epochs.

Number of Hidden Units	Epochs	R2	RMSE
130	80	0.659	13.196
	90	0.654	13.011
	100	0.704	12.854
	110	0.713	12.305
	120	0.726	12.127
	130	0.748	11.947
	140	0.741	11.856
	150	0.737	11.928

and

Table 4. Comparison of R² and RMSE for the SSA-LSTM model with different initial learning rates.

Number of Hidden Units	Epochs	Initial Learning Rate	R2	RMSE
130	130	0.001	0.748	11.947
		0.002	0.761	12.003
		0.003	0.697	12.430

. They indicate that, as can be seen from Table 2, when the number of hidden units is increased from 100 to 150, the model performance changes accordingly, and an optimal state is reached at 130 units (R² = 0.704, RMSE = 12.854). Subsequently, with the number of hidden units fixed and the number of training epochs adjusted (Table 3), it is found that when the number of training epochs is set to 130, the model performance is further improved (R² = 0.748, RMSE = 11.947). Finally, with both the number of hidden units and training epochs set to 130, the effects of different initial learning rates are compared (Table 4). An initial learning rate of 0.002 is identified as providing the best model performance, with a goodness-of-fit R² of 0.761 and a root mean square error (RMSE) of 12.003.

To evaluate the effectiveness of SSA preprocessing, the prediction performance of the SSA-LSTM model is compared with that of a standard LSTM model under the same optimal parameters. The results are shown in

Table 5. Comparison of R² and RMSE between LSTM and SSA-LSTM models under identical training parameters.

Number of Hidden Units	Epochs	Initial Learning Rate	Model	R2	RMSE
130	130	0.002	LSTM	0.650	12.159
			SSA-LSTM	0.761	12.003

. As can be seen from Table 5, the R² of the SSA-LSTM model (0.761) is higher than that of the LSTM model (0.650), and the RMSE of the SSA-LSTM model (12.003) is lower than that of the LSTM model (12.159). These results indicate that by filtering out noise and retaining effective periodic components, SSA significantly enhances the prediction accuracy and robustness of the LSTM model.

3.4. Comparison of SSA-ARIMA and SSA-LSTM Results

The SSA-ARIMA hybrid model is recognized as a time series analysis method that combines nonlinear decomposition technology with a classic linear prediction model. The core concept of this model is that the original series is subjected to signal decomposition and reconstruction through Singular Spectrum Analysis (SSA), effectively separating the trend, periodic, and noise components. Subsequently, an Autoregressive Integrated Moving Average (ARIMA) model is established for the denoised series to perform predictions. This method fully utilizes the advantages of SSA in signal processing and the maturity of ARIMA in linear modeling, providing an effective solution for predicting complex time series. The construction of the SSA-ARIMA model comprises two main stages. First, the original sea-level series is decomposed by SSA into multiple independent components. Based on contribution rate analysis, the components are classified into trend-periodic components and noise components, and the main components are reconstructed into a new series with a significantly improved signal-to-noise ratio. Second, the reconstructed series is tested for stationarity, and differencing is applied if necessary. Following this, the optimal order of the ARIMA model is determined based on the Akaike Information Criterion (AIC), after which parameter estimation and residual diagnostics are performed, ultimately leading to the establishment of a prediction model. This process ensures that the model retains the main characteristics of the series while also meeting the modeling requirements of the ARIMA model. The SSA-ARIMA model possesses distinct advantages: noise can be effectively filtered out through SSA preprocessing, enhancing the robustness of the ARIMA model; simultaneously, an analysis of the internal structure of the series is provided, which aids in understanding its physical mechanisms. However, certain limitations are also associated with this model: the ARIMA component is inherently linear, limiting its ability to capture complex nonlinear features; furthermore, the overall modeling process is relatively complex and involves high computational costs. These characteristics mean that the advantages and disadvantages of SSA-ARIMA must be weighed when it is applied.

The SSA-ARIMA model is established through the following process: First, the detrended and denoised data obtained by SSA are divided, with 80% allocated to the training set and 20% to the test set. The training set is then tested for stationarity using the adftest and kpsstest functions. Since the result indicates non-stationarity, the training set data are subjected to first-order differencing. The differenced data, shown in Figure 11, are then verified for stationarity again, and the output confirms stationarity. Next, the Akaike Information Criterion (AIC) is applied to determine the model orders, resulting in p = 9 and q = 10. Subsequently, a residual test is conducted, with the results presented in Figure 12. From Figure 12, it can be seen that the standardized residual sequence plot presents irregular random fluctuations, with no obvious trend or periodicity observed, indicating that the systematic components in the sequence have been adequately captured by the model. The histogram shows an approximately symmetric bell-shaped distribution of residuals, which aligns with the basic characteristics of a normal distribution and satisfies the fundamental assumptions regarding error terms in the model. In the plots of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), the correlation coefficients for all lag orders fall within the confidence interval, confirming the absence of significant autocorrelation or partial autocorrelation in the residual series. In the Q-Q plot, the sample quantiles of the residuals show a high overall alignment with the theoretical quantiles of the standard normal distribution, further validating the normality of the residuals. The above residual results collectively indicate that the residuals of the prediction model meet the assumptions of randomness, independence, and normality, demonstrating that the model has effectively extracted the meaningful information from the sequence and that the fitting performance meets the expected requirements.

The prediction results of the SSA-ARIMA model are shown in Figure 13. As can be seen from Figure 13, the SSA-ARIMA model is considered capable of effectively characterizing the sea-level time series.

In this study, the SSA-ARIMA results are compared with the SSA-LSTM results, as shown in

Table 6. Comparison of R² and RMSE between the SSA-LSTM and SSA-ARIMA models.

Model	R2	RMSE
SSA-LSTM	0.761	12.003
SSA-ARIMA	0.349	22.326

. From Table 6, the R² of SSA-ARIMA can be observed to be only 0.349, and its RMSE is as high as 22.326, which is considerably worse than the SSA-LSTM model (R² = 0.761, RMSE = 12.003). Although the residual test results of SSA-ARIMA are considered ideal, and its predicted trend is similar to that of SSA-LSTM, both showing a periodic pattern, its prediction accuracy is significantly insufficient. The primary reason for this phenomenon can be attributed to the fact that ARIMA, as a linear model, has difficulty fully capturing the complex nonlinear characteristics present in the South China Sea’s sea-level changes, whereas the LSTM neural network possesses a natural advantage in this aspect.

3.5. Sea-Level Prediction for the South China Sea

The sea-level prediction in this paper is conducted based on the SSA-LSTM model. The hyperparameters of the LSTM model are set as follows: the number of hidden units is 130, the number of training epochs is 130, and the initial learning rate is 0.002. The prediction results of the SSA-LSTM model are shown in Figure 14. As shown in Figure 14, the sea level of the South China Sea exhibits an evolution pattern of “fall-rise-rise-rise-rise”. For the next 20 years, an overall upward trend is projected for the sea level in the South China Sea. The prediction results indicate that from 2015 to 2035, the South China Sea’s sea level is expected to rise at a rate of 0.75 mm/yr, with a cumulative rise of approximately 15 mm.

4. Discussion

4.1. Patterns and Driving Mechanisms of Sea-Level Change in the South China Sea

Sea-level change in the South China Sea is characterized by multi-timescale features. At the interannual scale, sea level exhibits significant periodic fluctuations, which are closely related to the ENSO cycle. Spectral analysis (Figure 5) reveals that the 71-year, 33-year, 18-year, 14-year, and 12-year periodic components are the most prominent, which is highly consistent with the fluctuation patterns observed in the prediction results. When the equatorial Pacific is in a La Niña state, the enhanced Walker circulation causes water from the Western Pacific Warm Pool to overflow into the South China Sea, while storm tracks shift westward, jointly promoting sea-level rise in the South China Sea. During El Niño events, although large waves propagating towards the South China Sea can influence sea level, their combined effect differs from that during La Niña periods. This periodic ocean–atmosphere interaction has been identified as the primary cause of the fluctuation pattern observed in the South China Sea’s sea level. On the decadal to centennial scales, a significant upward trend has been observed in the South China Sea’s sea level. Between 1850 and 2015, the sea level showed a clear overall rise, particularly during 1921–1940, when the rate of rise reached 5.49 mm/yr. This long-term trend can be primarily attributed to ocean thermal expansion and the melting of glaciers and ice sheets caused by global climate change. Under the background of global warming, continuously increasing greenhouse gas concentrations lead to rising seawater temperatures, coupled with the input of meltwater from polar ice sheets into the ocean, collectively driving long-term sea-level rise. Additionally, natural factors such as changes in total solar irradiance are also considered to have exerted some influence.

4.2. Impact Assessment of Sea-Level Rise on Coastal Engineering

The continuous rise in sea level in the South China Sea poses severe challenges to coastal engineering. According to predictions, the sea level is projected to rise at a rate of 0.75 mm/yr between 2015 and 2035. Although this rate is slower than in some historical periods, the cumulative effect cannot be ignored. First, the risk of coastal erosion is significantly increased. According to an estimate based on the Bruun rule, with a relative sea-level rise of 2.5 mm/yr, the coastline could retreat by up to 25 cm annually. Simultaneously, sea-level rise elevates the baseline for storm surges, increasing the probability that coastal structures are exposed to stronger wave and current actions during storms, which poses a serious threat to protective structures like seawalls and revetments designed according to previous standards. Second, coastal infrastructure is faced with multiple threats. Sea-level rise causes a rise in the groundwater table, leading to a decrease in the effective stress and bearing capacity of foundation soils. Taking the Shanghai area as an example, when the groundwater table rise exceeds 1.0 m, the ultimate bearing capacity of the foundation decreases by nearly 10%, while the liquefaction risk of silty sand increases significantly. For facilities such as port terminals, the chance of wave overtopping increases, the inundation range of storage yards expands, and maintenance costs rise substantially. Furthermore, estuarine ecosystems and waterway maintenance face new challenges. Sea-level rise reduces river gradients and sediment transport capacity, leading to a tendency for siltation in estuary areas, forming sandbars that affect navigational capacity. Meanwhile, saltwater intrusion is intensified, affecting coastal groundwater quality and ecosystems.

4.3. Systemic Measures for Addressing Sea-Level Rise

In the face of the long-term threat of sea-level rise, multi-level and systemic response strategies are required. For mitigation measures, global cooperation on emission reduction should be actively promoted to reduce greenhouse gas emissions and control the rate of global warming at its source. This requires a global effort to support climate agreements, promote the transition to clean energy, and establish low-carbon development models. At the level of adaptation measures, coastal engineering design standards need to be re-evaluated based on sea-level rise projections. This includes raising the crest elevation of seawalls, enhancing the stability of armor layers, and optimizing design water levels for ports and terminals. Concurrently, integrated coastal zone management should be strengthened, enhancing coastal resilience through nature-based solutions such as ecological revetments and wetland restoration. Regarding technological innovation, the construction of sea-level monitoring networks needs to be enhanced, combining satellite remote sensing and in situ observations to improve prediction and early warning capabilities. New coastal protection materials and structural forms should be developed to enhance the durability and adaptability of engineering structures. Meanwhile, research on impact assessments of sea-level rise should be strengthened to provide a scientific basis for engineering planning and design. Finally, integrated coastal zone management mechanisms need to be established and improved, inter-departmental coordination must be strengthened, and responses to sea-level rise should be incorporated into all aspects of territorial spatial planning and coastal zone development and protection. By combining engineering and non-engineering measures, the overall resilience of coastal areas to sea-level rise can be enhanced. In summary, sea-level change in the South China Sea is recognized as a result of the combined effects of natural fluctuations and human activities, and its impact on coastal engineering is long-term and profound. Only through scientific prediction, rational planning, and effective response can the long-term safe and stable operation of coastal engineering be ensured and the sustainable development of coastal areas be promoted.

5. Conclusions

This paper constructs a hybrid model based on SSA and LSTM neural networks for analyzing and predicting sea-level changes in the South China Sea. The main findings and conclusions are as follows:

(1) Superimposed on an overall significant upward trend (e.g., a rising rate of 5.49 mm/yr during 1921–1940), significant periodic fluctuations are identified in sea level. Spectral analysis reveals major cycles of 71, 14, 12, 33, and 18 years, among which the 14-year and 12-year cycles are closely linked to climate modes such as ENSO, reflecting the sensitive response of the South China Sea’s sea level to regional climate systems.

(2) SSA effectively separates trend, periodic, and noise components. The reconstructed series retains 95.89% of the information from the original series, significantly improving data quality. After hyperparameter optimization, the SSA-LSTM model demonstrates good fitting and predictive capability in testing (R² = 0.761 and RMSE = 12.003). Its performance is significantly better than that of the traditional SSA-ARIMA model, validating the effectiveness and advancement of this method in handling nonlinear and non-stationary sea-level time series.

(3) Based on predictions from the optimized SSA-LSTM model, the sea level in the South China Sea is projected to rise at a fluctuating rate of approximately 0.75 mm/yr over the next 20 years, with a cumulative increase of about 15 mm. This trend poses long-term challenges to coastal engineering safety, estuarine ecology, and waterway maintenance, indicating that the cumulative effects of sea-level rise need to be considered in the design and management of coastal protection projects.

This paper has several limitations, and future research can be further developed in the following areas:

(1) Data Aspects

Although coral δ¹⁸O proxy data can reflect regional average sea-level signals well, their spatial representativeness and resolution have certain limitations. Future studies could integrate more high-resolution proxy indicators (such as coral Sr/Ca, tide gauge records, satellite altimetry, and other multi-source data) to enhance the spatiotemporal coverage and reliability of the series.

(2) Mechanistic Interpretability

The current model is primarily data-driven and has limited explanatory power for the specific physical processes behind sea-level changes (such as the contribution weights of climate modes like ENSO and PDO, regional hydrodynamic processes, etc.). Future work could combine climate model outputs and attribution analysis to improve the physical interpretability of the prediction results.

(3) Prediction Uncertainty

This paper does not systematically quantify the impacts of different emission scenarios and internal climate variability on sea-level predictions. Subsequent research should conduct uncertainty assessments within multi-scenario and multi-model frameworks to provide a more comprehensive scientific basis for risk management and adaptation planning.

In summary, research on sea-level changes in the South China Sea needs continuous advancement in data integration, mechanistic interpretation, and uncertainty quantification to improve prediction accuracy and application value, thereby better serving coastal protection and climate adaptation strategies.