An attention fusion of Fourier-analysis-based transformer and CNN-BiLSTM for coastal inorganic nitrogen concentration forecasts.

Accurate forecasting of coastal inorganic nitrogen is critical for mitigating harmful algal blooms but remains challenging due to prevalent data gaps and skewed concentration distributions. This study proposes AFTB, a novel deep learning architecture that integrates a Fourier-enhanced Transformer with a CNN-BiLSTM network via dedicated attention mechanisms for robust multi-step forecasting. A logarithmic transformation is introduced to address severe right-skewness with a modified loss function balancing error weighting. Extreme-value oversampling strategy also improves the performance. Comprehensive evaluation across nine buoy stations in Guangxi, China demonstrates AFTB's superior accuracy over strong baselines (ChloroFormer, CNN-Transformer, Informer). Crucially, controlled Missing-Completely-at-Random experiments provide direct evidence of its exceptional robustness to training data incompleteness, showing minimal mean performance variance as missingness increases. Analysis of internal attention weights reveals interpretable forecasting patterns and validates the design of the fusion mechanisms. With competitive inference speed, AFTB presents a practical and resilient solution for operational water quality forecasting systems.