HIDRA-D: deep-learning model for dense sea level forecasting using sparse altimetry and tide gauge data

Abstract. This paper introduces HIDRA-D, a novel deep-learning model for basin scale dense (gridded) sea level prediction using sparse satellite altimetry and in situ tide gauge data. Accurate sea level prediction is crucial for coastal risk management, marine operations, and sustainable development. While traditional numerical ocean models are computationally expensive, especially for probabilistic forecasts over many ensemble members, HIDRA-D offers a faster, numerically cheaper, observation-driven alternative. Unlike previous HIDRA models (HIDRA1, HIDRA2 and HIDRA3) that focused on point predictions at tide gauges, HIDRA-D provides dense, two-dimensional, gridded sea level forecasts. The core innovation lies in a new algorithm that effectively leverages sparse and unevenly distributed satellite altimetry data in combination with tide gauge observations, to learn the complex basin-scale dynamics of sea level. HIDRA-D achieves this by integrating a HIDRA3 module for point predictions at tide gauges with a novel Dense decoder module, which generates low-frequency spatial components of the sea level field in the Fourier domain, whose Fourier inverse is an hourly sea level forecast over a 3 d horizon. When comparing 3 d forecasts against satellite absolute dynamic topography (ADT) data in the Adriatic, HIDRA-D achieves a 28.0 % reduction in mean absolute error relative to the NEMO general circulation model. However, while HIDRA-D performs well in open waters, leave-one-out cross-validation at tide gauges indicates limitations in areas with complex bathymetry, such as the Neretva estuary located in a narrow bay, and in regions with sparse satellite ADT data, like the northern Adriatic. Importantly, the model shows robustness to spatially-limited tide gauge coverage, maintaining acceptable performance even when trained using data from distant stations. This suggests its potential for broader applicability in areas with limited in situ observations.