Transfer function for adaptive methods of estimating directional spectra using a fully nonlinear wave model and laboratory measurements

Abstract We analyse the spreading distribution of directional wave spectra across different sea states using a 3D fully nonlinear model and measurements from a wave basin. Using the spreading coefficient, we propose a transfer function for adaptive methods such as the Maximum Likelihood Method (MLM), Maximum Entropy Method (MEM), and Wavelet Directional Method (WDM), with the estimated spectra from 2FFT as a baseline. Our numerical analysis reveals that nonlinear effects broaden the directional distribution at peak frequency, particularly in narrow spectra. This broadening becomes more pronounced as wave steepness increases. With the proposed transfer function, we found that MLM tends to overestimate spreading, resulting in spectra that are 14% broader. In contrast, MEM and WDM produced narrower spectra, by 6% and 3% respectively. When analysing the spreading coefficient across relative frequencies, WDM performs best in the range of 0.8 to 1.15 $$f/f_p$$ , while MEM yields superior results at higher relative frequencies, specifically above 1.3 $$f/f_p$$ . We validate the transfer function using laboratory measurements, which effectively capture the behaviour of the adaptive methods within the error limits. Additionally, due to the plane correction transformation, our laboratory analysis using stereo-imaging measurements showed that adaptive methods generally produced a slightly broader spectrum than those based on probe measurements. These findings highlight the importance of carefully selecting methods depending on the desired balance between accuracy and stability in wave spectral analysis.