Approximating the Doppler Shift in Sea-Wave Spectra Observed from an Advancing Floating Platform

• Mathematical formula approximating frequency transformations due to forward speed. • Both-way transformations of spectra between fixed and moving reference frames. • Matrix-based formulation for computationally efficient spectral calculations. • Accurate estimates of the spectra by the approximation method, even at large speeds. • Actionable criteria for selecting the method’s hyperparameters. Accurate estimation of sea-wave spectra from advancing floating platforms is challenged by Doppler-induced frequency distortions, particularly in following-to-quartering sea conditions. This study introduces a novel Doppler Shift Approximation (DSA) method that enables a bijective, analytical mapping between intrinsic and observed frequencies, thereby avoiding the triple-value problem inherent in exact formulations. The DSA is derived as a second-order polynomial with coefficients optimised to minimise frequency mapping errors for any angle of wave encounter and any forward speed. A matrix-based implementation of the DSA is proposed to enable efficient spectral transformations, and the corresponding code is made available as open-source software. Its performance is evaluated through numerical simulations of both multidirectional and unidirectional sea states, considering various wave headings and forward speeds of up to 18 knots. Results demonstrate that the DSA yields accurate spectral estimates, with relative errors in significant wave height and mean wave period generally below 10%. The DSA offers a computationally efficient alternative to exact Doppler shift solutions for general seakeeping computations, and may serve applications related to real-time sea state estimation and onboard decision-support systems particularly well.