A Comparative Evaluation of Harmonic Analysis and Neural Networks for Sea Level Prediction in the Northern South China Sea

Long-term sea level variations in the northern South China Sea (SCS) are known to significantly impact coastal ecosystems and socio-economic activities. To improve sea level prediction accuracy, four models—harmonic analysis and three artificial neural networks (ANNs), namely genetic algorithm-optimized back propagation (GA-BP), radial basis function (RBF), and long short-term memory (LSTM)—are developed and compared using 52 years of observational data (1960–2004). Key evaluation metrics are presented to demonstrate the models’ effectiveness: for harmonic analysis, the root mean square error (RMSE) is reported as 14.73, the mean absolute error (MAE) is 12.61, the mean bias error (MBE) is 0.0, and the coefficient of determination (R 2 ) is 0.84; for GA-BP, the RMSE is measured as 29.1371, the MAE is 24.9411, the MBE is 5.6809, and the R 2 is 0.4003; for the RBF neural network, the RMSE is calculated as 27.1433, the MAE is 22.7533, the MBE is 2.1322, and the R 2 is 0.4690; for LSTM, the RMSE is determined as 23.7929, the MAE is 19.7899, the MBE is 1.3700, and the R 2 is 0.5872. The key findings include the following: (1) A significant sea level rise trend at 1.4 mm/year is observed in the northern SCS. (2) Harmonic analysis is shown to outperform all ANN models in both accuracy and robustness, with sea level variations effectively characterized by four principal and six secondary tidal constituents. (3) Despite their complexity, ANN models (including LSTM) are found to fail in surpassing the predictive capability of the traditional harmonic method. These results highlight the continued effectiveness of harmonic analysis for long-term sea level forecasting, offering critical insights for coastal hazard mitigation and sustainable development planning.