Forecasting of Sea Level Extremes using Deep Learning and Extreme Value Analysis

Studies have shown that the forecasting of mean sea level by both physics-based and data-driven models produces reasonable results. The challenge lies in accurate forecasting of sea level maxima. This task includes handling of extreme events which are often influenced by compound factors (e.g. winds, pressure gradients and prefilling of semi-enclosed basins, such as the Baltic Sea), interactions of which should be adequately resolved. Another challenge is that return periods of extreme events are long. Such events thus occur infrequently in the existing data sets. To address these challenges, we explore the options of combinations of data driven approaches, such as machine and Deep Learning (ML/DL) methods, with statistical extreme value theory to forecast short-term (one day ahead) and long term (years and decades) sea level maxima in the Baltic Sea.
We employ water level data from six Baltic Sea tide gauge stations from 1971 to 2022. The quality of short-term forecasting of sea level maxima is examined using both machine learning (Random Forest) and deep learning (Convolutional neural network-gated recurrent unit, CNN-GRU) models. Further data analysis by means of mutual index and background knowledge from previous studies indicates that wind speed (zonal and meridional), surface air pressure, Baltic Sea Index (BSI), and significant wave height are the most influential input features. The models' hyperparameters were estimated using a Bayesian optimization algorithm. For long-term forecasting, extreme value analysis based on block maximum method and location, scale, and shape parameters of a General Extreme Value (GEV) distribution was employed to compute the frequency of extreme values for each season and tide gauge.
We demonstrate that the CNN-GRU model performs the best with RMSE values from 7 to 14.5 cm. The performance of this model for storm events was reasonable, however, high sea level peaks were often underestimated. The highest extremes (>150 cm over the long-term mean) tend to occur in the eastern and northern Baltic Sea during the winter season with a return time period >5–7 years (winter) and >20 years (spring). On most occasions, the ML/DL models were not able to forecast these events adequately. However, the knowledge of their magnitude, return period and seasonality can assist in marine planning of these events which are vital for coastal communities and infrastructures design.