Lead-conditioned direct forecasting of daily air–sea interface variables over the Tropical Pacific ocean with soft physical regularization

Extended-range (10–30-day) forecasting of daily air–sea interface variables over the Tropical Pacific is important for linking medium-range weather prediction with subseasonal-to-seasonal, climate-relevant variability. However, it remains challenging because atmospheric initial-condition information decays quickly, errors grow chaotically, and air–sea coupling introduces additional sources of uncertainty. Most existing data-driven approaches still rely on autoregressive rollouts; as errors accumulate recursively with lead time, forecasts tend to become progressively smoother in space and spectrum, washing out sharp gradients and organized structures that matter for physically consistent surface forcing. Here, we propose a physics-constrained, lead-conditioned deep learning framework for high-resolution (0.25°) daily, multi-variable forecasting at lead times of 1–30 days. Our model uses an adaptive Fourier neural operator (AFNO) backbone and conditions predictions on lead time via feature-wise linear modulation (FiLM), enabling direct multi-lead forecasting within a single network and reducing error growth from recursive rollouts. To improve long-lead structure, we add a soft physical regularization (SPR) term that combines total-variation smoothing with Laplacian-based spectral damping, suppressing spurious high-frequency artifacts while preserving large-scale organization. On ERA5, the method reaches ACC values above 0.91 for SST and 0.83 for T2m at a 30-day lead, and yields consistent gains for near-surface winds (U10/V10), surface pressure (SP), specific humidity (SHUM), downward radiative fluxes (SWR/LWR), and precipitation rate (PR), outperforming strong baselines including a fully retrained ClimaX model. Overall, the results show that pairing lead-conditioned direct forecasting with physically motivated regularization improves long-lead skill while maintaining more realistic spatial structure in daily air–sea interface predictions.