Multi-Horizon Significant Wave Height Forecasting with Multiscale Decomposition and Topological Feature Selection

Accurate multi-horizon Significant Wave Height (SWH) forecasting is vital for offshore safety and efficiency. Beyond scheduling maintenance windows, reliable lead-time predictions provide critical early warnings to protect personnel and high-value assets from hazardous high-wave conditions. However, the non-stationary and multi-scale nature of sea states poses challenges for consistent long-term accuracy. To address this challenge, we propose a robust three-stage framework for decomposition, feature selection, and multi-horizon forecasting. Specifically, Optimal Variational Mode Decomposition (OVMD) is adopted to construct multiscale and multi-view representations of nonlinear SWH sequences, while a Triangulated Maximally Filtered Graph (TMFG) constructs a sparse dependency network to select informative and non-redundant predictors from decomposed components and environmental variables. A hybrid prediction model then combines a Temporal Convolutional Network (TCN) for local multi-scale patterns with a Bidirectional Gated Recurrent Unit (BiGRU) for long-range dependencies. Experiments on real-world buoy observations show that the proposed approach improves accuracy and robustness over commonly used statistical and deep-learning baselines across short-, medium-, and long-term horizons. Ablation studies confirm that integrating modal decomposition with sparse feature selection enhances model robustness, offering reliable decision support for offshore window planning and high-wave condition monitoring.