Toward real-time wave forecasting via data-driven reduced-order modeling with data assimilation

Reliable wave forecasts are a cornerstone of coastal risk management and offshore operations, yet operational products remain expensive to generate at high resolution and can be insufficiently calibrated for decision-making under uncertainty. We present a hybrid forecasting framework that couples data-driven reduced-order modeling with sequential data assimilation to produce flow-dependent, spatially coherent ensembles of significant wave height over the North Sea. The approach learns a nonlinear manifold of sea-state variability with a convolutional autoencoder trained on WAM wave model, then advances the system in a delay-embedded latent space using a control-aware linear dynamical model driven by low-dimensional controls extracted from wind forecasts. Uncertainty is propagated with an ensemble formulation, and buoy observations are assimilated using a deterministic ensemble square-root filter with innovation-based adaptive inflation to maintain reliability during energetic events. The proposed system reproduces the timing and magnitude of storm growth–peak–decay across the buoy network, while preserving physically consistent basin-scale storm footprints in reconstructed fields. Errors are spatially organized and regime dependent, concentrating near storm maxima where wind–wave misalignment, swell influence, and representativeness effects are strongest, but the assimilation layer mitigates drift and reduces persistent offsets without introducing spatial artifacts. Beyond forecasting, we introduce an observability metric derived from the posterior latent covariance and the decoder sensitivity, yielding time-varying maps that identify where additional in-situ measurements would most reduce forecast uncertainty. The introduced method provides a computationally efficient, uncertainty-aware alternative that bridges physics-based spectral modeling and purely data-driven prediction for operational decision support.