Rajabi-Kiasari et al. (2026) Forecasting sea level maxima using Machine learning with explainability and extreme value analysis

Identification

• Journal: International Journal of Applied Earth Observation and Geoinformation
• Year: 2026
• Date: 2026-01-06
• Authors: Saeed Rajabi-Kiasari, Delpeche-Ellmann Nicole, Artu Ellmann, Tarmo Soomere
• DOI: 10.1016/j.jag.2025.105064

Research Groups

• Department of Civil Engineering and Architecture, School of Engineering, Tallinn University of Technology, Estonia
• Department of Cybernetics, School of Science, Tallinn University of Technology, Estonia

Short Summary

This study develops a two-fold framework combining machine learning (ML)/deep learning (DL) for short-term daily sea level maxima (SLM) forecasting and extreme value theory (EVT) for long-term extreme sea level analysis in the Baltic Sea. The framework demonstrates that hybrid neural networks (CNN-GRU, MLP) achieve the best short-term forecasting performance (RMSE 7–15 cm), accurately capturing most peaks up to 150 cm, while EVT provides long-term risk assessment for rarer extremes.

Objective

• Characterize sea level maxima (extremes) by magnitude, frequency, and duration.
• Identify the most effective ML/DL models for short-term one-day-ahead forecasting.
• Compare models for peaks/storm event detection.
• Determine the key contributors via Explainable ML.
• Estimate return levels and periods of extreme sea levels for long-term prediction (<100 years).

Study Configuration

• Spatial Scale: Baltic Sea, focusing on six tide gauge stations: Narva-Jõesuu (Gulf of Finland), Ristna (north-eastern Baltic proper), Oulu (Bothnian Bay), Greifswald (south-western Baltic), Władysławowo (southern Baltic Sea), and Kungsholmsfort (southern Baltic proper).
• Temporal Scale: Data collected from 1971 to 2022 (52 years). Short-term forecasting is one-day-ahead. Long-term extreme value analysis estimates return periods up to 100 years.

Methodology and Data

• Models used:
  • Machine Learning (ML): Random Forest (RF), Extreme Gradient Boosting (XGB), Multilayer Perceptron (MLP).
  • Deep Learning (DL): CNN-LSTM, CNN-GRU (hybrid models).
  • Extreme Value Theory (EVT): Block maxima method with Generalized Extreme Value (GEV) distribution.
  • Optimization: Bayesian optimization (BO) for hyperparameter tuning.
  • Explainability: SHapley Additive exPlanations (SHAP).
• Data sources:
  • Hourly relative sea level data from six tide gauge stations (1971–2022), converted to Baltic Sea Chart Datum (BSCD2000). Sources: envir.ee (Estonia), ilmatieteenlaitos.fi (Finland), smhi.se (Sweden), wsv.bund.de (Germany), imgw.pl (Poland).
  • Meteorological variables (wind components, surface pressure, evaporation, precipitation, river runoff) from ERA5 re-analysis dataset.
  • Baltic Sea Index (BSI) from ERA5.
  • Significant Wave Height (SWH) data from SWAN wave model (1971–2005) and WAM wave model (2006–2022).

Main Results

• The CNN-GRU model consistently outperformed other approaches, achieving test Root Mean Square Error (RMSE) values ranging from 7 cm (Kungsholmsfort) to 14.9 cm (Oulu), and R-squared (R2) values from 0.61 (Greifswald) to 0.86 (Ristna).
• The Multilayer Perceptron (MLP) model also performed strongly, particularly at Oulu (RMSE 14.5 cm, R2 0.78) and Władysławowo (RMSE 8 cm, R2 0.85).
• Tree-based models (Random Forest and Extreme Gradient Boosting) frequently exhibited overfitting.
• All models accurately captured most sea level maxima (SLM) events up to 150 cm, but consistently underestimated rarer extreme peaks exceeding 150 cm.
• Explainability analysis (SHAP) of the CNN-GRU model revealed that the previous day’s SLM (prefilling) was the most influential feature across all stations (~40% importance).
• Regional variations in meteorological drivers were observed: eastern stations (Narva, Ristna) were primarily influenced by local pressure and wind, while western and northern stations (Oulu, Kungsholmsfort, Greifswald) were more affected by large-scale atmospheric forcing represented by the Baltic Sea Index (BSI), pressure, and wind.
• Extreme Value Theory (EVT) analysis indicated that winter extremes of approximately 150 cm correspond to return periods of about 5 years at Narva and 7 years at Oulu.

Contributions

• First study to integrate Bayesian Optimization with hybrid CNN-LSTM and CNN-GRU models for sea level forecasting.
• Developed a transparent and explainable framework for daily SLM forecasting using SHAP analysis.
• Demonstrated an improved effective forecasting range for SLM from approximately 100 cm to 150 cm compared to previous regional studies.
• Provided a robust and interpretable framework for extreme sea level prediction by integrating ML/DL-based short-term forecasting with EVT for long-term risk assessment.
• Conducted comprehensive exploratory data analysis, feature selection, model optimization, and evaluation using multiple statistical metrics, including storm event detection.

Funding

• Estonian Research Council grants PRG1129 and PRG1785 DYNAREF.

Citation

@article{RajabiKiasari2026Forecasting,
  author = {Rajabi-Kiasari, Saeed and Nicole, Delpeche-Ellmann and Ellmann, Artu and Soomere, Tarmo},
  title = {Forecasting sea level maxima using Machine learning with explainability and extreme value analysis},
  journal = {International Journal of Applied Earth Observation and Geoinformation},
  year = {2026},
  doi = {10.1016/j.jag.2025.105064},
  url = {https://doi.org/10.1016/j.jag.2025.105064}
}