SST subseasonal-to-seasonal forecasting: A heterogeneous three-path fusion model with wavelet decomposition.

El Niño-Southern Oscillation (ENSO), the Earth's dominant mode of interannual climate variability, is closely linked to sea surface temperature (SST) variability in the central and eastern equatorial Pacific. Accurate subseasonal-to-seasonal SST forecasting in this region supports ocean monitoring and environmental assessment. We propose WDFormer (Wave Decomposition Former), a daily SST forecasting model built on a "decomposition, multi-path processing, and adaptive fusion" paradigm. The model uses 365 daily SST observations from local 4×4 grids around representative ENSO monitoring stations to predict daily SST values over 7-90-day horizons. WDFormer first applies wavelet decomposition to separate the input sequence into a smoother low-frequency component and a higher-frequency residual. Lightweight MLP-based branches process the original and low-frequency components, while a Transformer-based branch models the residual dynamics. Outputs are integrated through a learnable gating mechanism. Experiments on daily OISST data from five representative ENSO subregions show that WDFormer outperforms several deep learning baselines at most 30-90-day horizons. Comparisons with persistence and daily climatology confirm that persistence dominates at very short lead times, whereas WDFormer provides clearer advantages as the horizon extends. An ONI-based ENSO-phase and El Niño-stage stratified evaluation shows that WDFormer achieves the lowest RMSE under El Niño, La Niña, and Neutral conditions, as well as during El Niño onset/development, mature/peak, and decay/termination stages for the 90-day task. Bootstrap confidence intervals and paired RMSE comparisons further support the robustness of the 90-day results. These results support decomposition-based heterogeneous modeling for daily SST forecasting at 30-90-day horizons and motivate broader extensions to probabilistic and multi-variable forecasting.