Data-driven and physics-guided hindcasting of measured wave spectra

Abstract

Short-range hindcasts of measured wave spectra are evaluated using a recurrent model initialized by one hourly buoy spectrum and supplied with local wind, fetch and depth. Measurements from three Baltic Sea stations are combined for training in 2017--2020, validation in 2021 and testing in 2022. ERA5 reanalysis supplies winds throughout the twelve-hour prediction interval. The comparison examines supervision of spectral variance, peak frequency and peak amplitude, followed by empirical wind-sea bounds and a local relaxation constraint. Variance and peak-frequency supervision gives the lowest spectral error within the data-driven comparison, whereas additional peak-amplitude supervision gives the lowest wave-height error. In the matched physical comparison, relaxation reduces height RMSE by 5.01\% to \PhPtwoHs{}~cm. Extending this constraint through hours 13--24, without spectral targets at those hours, reduces primary spectral RMSE by 2.31\% to \PhPthreeSpec{}~$\unitE$. Upper-bound constraints increase errors. Wind-condition comparisons show spectral gains from extended relaxation in increasing, decreasing and steady strong winds, with little change in steady weak winds. The results support modest, objective-dependent benefits from local physical guidance. Wave-height scores concern the retained frequency band, and operational forecasting and transfer to independent stations remain to be evaluated.