Abstract
<title>Abstract</title> <p>Coastal water level forecasts can use recent atmospheric and residual histories yet still smooth high water peaks over a multiday horizon. We introduce dual timescale residual memory, an explicit response state that converts causal summaries of the recent non-tidal residual into bounded fast and slow amplitudes and carries them through the forecast with ordered exponential decay. The formulation gives the coastal state present at the forecast time a direct and interpretable trajectory under the same observation history used by the recurrent predictor. Using 96 hours of history and deterministic tide, we evaluate 72 hour forecasts at four coastal sites with four recurrent architectures and three independent random initializations. The proposed dual timescale memory reduces overall root mean square error (RMSE) by 1.61% (hierarchical 95% confidence interval, 0.81–2.48%), q95 conditioned RMSE by 5.75% (4.61–6.91%), and q99 conditioned RMSE by 5.91% (4.70–7.14%). The corresponding q95 RMSE falls from 195.8 to 184.6 mm and q99 RMSE from 270.5 to 256.0 mm. A matched comparison of memory forms further shows that ordered dual decay provides larger high water tail reductions than a single exponential through a compact correction head. The fast and slow components, their half lives, and their contributions at each forecast lead provide a clear account of coastal response persistence. Dual timescale residual memory therefore improves extreme water level prediction by preserving the elevated coastal state that general recurrent forecasts tend to smooth.</p>