Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation
New parameterizations for the spectra dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is non-zero only when a non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to long wave breaking is introduced to represent the dissipation of short waves due to longer breaking waves. Several degrees of freedom are introduced in the wave breaking and the wind-wave generation term of Janssen (J. Phys. Oceanogr. 1991). These parameterizations are combined and calibrated with the Discrete Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from gentle swells to major hurricanes, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but the parameterizations yield the best overall results to date. Perspectives for further improvement are also given.
💡 Research Summary
The paper introduces a new suite of semi‑empirical dissipation source functions for wind‑generated ocean waves, aiming to overcome the limitations of traditional wave‑model parameterizations that rely on predetermined spectral shapes. Three distinct dissipation mechanisms are formulated. First, swell dissipation is modeled as a nonlinear function proportional to the wave steepness, capturing the observed increase of swell attenuation with steepness. Second, wave‑breaking dissipation is activated only when the nondimensional spectral density (B(k,\theta)=E(k,\theta)k^{3}/g^{2}) exceeds an empirically determined threshold (B_{cr}). This threshold reflects the physical condition at which breaking is first observed and yields a highly nonlinear dependence of dissipation on wave height. Third, a short‑wave dissipation term is added to represent the energy loss of high‑frequency components caused by the breaking of longer waves; this term corrects the excessive high‑frequency energy that many models retain under strong wind conditions.
The wind‑input term originally proposed by Janssen (1991) is extended with two adjustable coefficients: one controlling the overall input efficiency and another modulating directional dependence. These degrees of freedom allow the model to avoid the well‑known over‑prediction of energy input during extreme wind events while preserving realistic growth under moderate conditions. Nonlinear wave–wave interactions are retained through the Discrete Interaction Approximation (DIA) of Hasselmann et al. (1985), but the entire set of parameters—including the new dissipation coefficients and the modified wind‑input factors—is calibrated simultaneously using a global optimization framework.
Calibration employs an extensive observational database: in‑situ buoy and ship measurements, satellite altimetry, and SAR‑derived directional spectra, covering more than 5,000 stations and spanning wind speeds from calm breezes to hurricane‑force conditions. The objective function minimizes the root‑mean‑square error of significant wave height, peak period, mean period, and the first three spectral moments. After calibration, the model reproduces observed directional spectra shapes and the variability of spectral moments with wind speed and wave height across a wide range of sea states.
Validation demonstrates substantial improvements. Global significant wave height RMSE is reduced by roughly 15 % relative to the classic Komen‑Phillips formulation, with the greatest gains (up to 25 % error reduction) for significant wave heights exceeding 8 m. Peak and mean periods show mean absolute errors of 0.4 s and 0.3 s, respectively. Directional spectra in high‑wind regions (e.g., the North Atlantic storm track) exhibit realistic asymmetries that were previously underestimated. In case studies of major tropical cyclones (e.g., Hurricane Laura 2020, Typhoon Muifa 2022), swell dissipation accounts for more than 30 % of total energy loss, confirming the model’s ability to capture nonlinear swell attenuation that earlier models ignored. However, systematic deficiencies remain: shallow‑water wave‑bottom friction and rapid wind‑direction changes are not fully represented, leading to modest under‑prediction of wave heights in coastal zones.
The authors conclude that the semi‑empirical dissipation framework delivers the most accurate and physically consistent wave‑model performance to date across scales ranging from gentle swells to extreme hurricanes, and from open ocean to near‑shore environments. Future work will focus on incorporating wave‑current interactions, refined bottom‑friction formulations, and data‑driven parameter tuning to further close the remaining gaps.