Sea level forecasting using deep recurrent neural networks with high-resolution hydrodynamic model

Abstract

Changes in climate, along with increasing marine activities in coastal and offshore regions, highlight the need for effective sea level forecasting methods. In recent years, forecasting techniques, especially those utilizing machine learning/deep learning methods (ML/DL), have shown promising capabilities. However, sea level forecasting is often limited in accuracy and spatiotemporal coverage, primarily due to the challenges posed by available observational data, which complicates the assessment of existing ML/DL techniques in complex and dynamic regions like the Baltic Sea. This study addresses these challenges by utilizing a high-resolution spatiotemporal framework that integrates high-resolution hydrodynamic and marine geoid models available to Baltic countries, enabling further capabilities to be explored in terms of sea level accuracy and validation. Specifically, it examines short-term sea level forecasting in the eastern Baltic Sea and the potential of utilizing two recurrent neural network-based models such as the Long Short-Term Memory Networks (LSTMs), and the Gated Recurrent Unit (GRU) along with high-resolution input data sources. These models were specifically chosen, due to their expected capabilities with time series data and their ability to learn both short and long-term connections of the input datasets.

To achieve this, a multivariate multistep-ahead (3, 6, 9, 12, and 24 h) forecasting framework was developed. The DL models' input components are high-resolution sea level data obtained from a bias-corrected hydrodynamic model, wind speed, surface pressure, and sea surface temperature. Results for various time steps (from 3 h to 24 h ahead), during the test period, revealed that the two DL models generally showed similar performance, with slightly superior results with the GRU model. For instance, GRU and LSTM showed an averaged root mean square error (RMSE) of 4.96 cm and 5.3 cm and a coefficient of determination (R²) of 0.93 and 0.92, respectively. Investigations of the time series forecasting performance at selected locations, also demonstrated the superiority of the GRU model, for all time steps, with Willmott's index (WI) values generally above 0.9 and high reliability as reflected in Prediction Interval Coverage Probability (PICP) values mostly exceeding 90 %. The results, however, weren't always perfect; both the GRU and LSTM models encountered limitations with forecasting the sea level maxima. Further examination of the spatial discrepancies also reveals some problematic areas in the eastern Gulf of Finland. This may have been influenced by the exclusion of some input components such as river discharge, salinity and meridional winds, further enhanced by complex hydrodynamics, extreme sea level variations, strong local currents, resonance-induced seiches and seasonal ice cover. In addition, an external validation of the GRU results was performed using along-track satellite altimetry from Sentinel 3A and 3B missions. For most of the satellite tracks, the discrepancy was better than 5 cm, proving the capabilities of the model generalization capabilities. These findings hold significant implications for advancing our comprehension of oceanic dynamics, enhancing maritime safety, and benefiting a wide range of applications that are dependent on accurate sea level forecasting.