A Bathymetry-Conditioned CNN–BiGRU Framework for Wave Hindcasting with Sliding-Window Evaluation

Accurate long-horizon wave forecasting remains difficult in coastal regions where irregular bathymetry produces localized and nonlinear wave amplification. Existing approaches use physics-based models, ConvLSTM, transformers, and multiscale spatial encoders to learn ocean dynamics. However, increasing encoder complexity does not necessarily improve bathymetry-sensitive prediction. Direct multi-step models can lose spatial coherence, while recursive models can accumulate forecast drift. We propose a bathymetry-conditioned CNN-BiGRU framework with internally corrected recursive inference. The CNN jointly encodes dynamic ocean fields and an aligned bathymetric field. The BiGRU captures temporal dependencies only within the observed historical sequence. At each recursive step, the network predicts three consecutive hourly states. The first state updates the next input window. The remaining states are used to estimate the internal forecast inconsistency. The subsequent deviations between these states determine a correction factor to regulate the propagated prediction. This mechanism uses the model's own multi-step outputs to control recursive instability without future observations or external error feedback. Visual analysis indicates that the framework preserves spatial organization and follows localized amplification during extreme conditions. The experiments used 35,017 hourly CMEMS IBI samples with GEBCO-derived bathymetry. The test sequence contains a maximum crest-to-trough wave height of $17.18$m. Over a $168$-hour horizon, the proposed framework achieves an MAE of $0.1375$m and an RMSE of $0.1821$m. Under the same evaluation protocol, a multi-resolution spatio-temporal baseline obtains an MAE of $0.8503$m and an RMSE of $0.9989$m, demonstrating the effectiveness of the proposed framework for extended-horizon wave forecasting.