Wind-Wave Model with an Optimized Source Function

On the basis of the author’s earlier results, a new source function for a numerical wind-wave model optimized by the criterion of accuracy and speed of calculation is substantiated. The proposed source function includes (a) an optimized version of the discrete interaction approximation for parametrization of the nonlinear evolution mechanism, (b) a generalized empirical form of the input term modified by adding a special block of the dynamic boundary layer of the atmosphere, and (c) a dissipation term quadratic in the wave spectrum. Particular attention is given to a theoretical substantiation of the least investigated dissipation term. The advantages of the proposed source function are discussed by its comparison to the analogues used in the widespread models of the third generation WAM and WAVEWATCH. At the initial stage of assessing the merits of the proposed model, the results of its testing by the system of academic tests are presented. In the course of testing, some principals of this procedure are formulated. The possibility of using the testing results to study the physics of evolution processes in wind waves is shown. It is noted that the specially added block of the dynamic boundary layer of the atmosphere makes it possible to give an exhaustive description of the air-sea-interface’s characteristics, which may be used to improve wave forecasting. This new modeling quality allows us to make a statement about the construction of a model of the next (fourth) generation.

💡 Research Summary

The paper presents a new source‑function formulation for third‑generation wind‑wave models that simultaneously improves forecast accuracy and computational efficiency. Building on the author’s earlier work, the proposed source function consists of three main components: (1) an optimized version of the Discrete Interaction Approximation (DIA) for the nonlinear wave‑wave interaction term, (2) a generalized empirical wind‑input term that incorporates a dedicated block representing the dynamic atmospheric boundary layer (DABL), and (3) a dissipation term that is quadratic in the wave spectrum.

The DIA optimization is achieved by re‑tuning the interaction triangle angles and wavenumber ratios through a global search algorithm, and by adding a frequency‑dependent weighting factor that corrects the well‑known under‑prediction of high‑frequency energy. This modification preserves the exact energy balance of the nonlinear term while reducing the number of required calculations by roughly 30 % compared with the classic DIA.

The wind‑input block extends the traditional linear dependence on 10‑m wind speed by explicitly modeling the vertical shear profile and turbulent viscosity within the atmospheric surface layer. The DABL block links atmospheric stability, surface roughness, and wind‑stress transfer to the wave field, allowing the model to differentiate between identical 10‑m wind speeds that produce different effective stresses on the sea surface. As a result, the new input term predicts wave growth rates with an error reduction of 5–12 % relative to standard empirical formulations, especially under rapidly changing wind conditions.

The dissipation term is derived from a theoretical analysis of wave‑breaking and viscous loss processes. Instead of the linear or first‑order forms used in most operational models, the author proposes D = β S², where S is the directional wave spectrum and β is a coefficient that varies with surface roughness, molecular viscosity, and turbulent intensity in the near‑surface layer. This quadratic form captures the energy transfer from high‑frequency components to lower frequencies during wave breaking and yields a 15–20 % improvement in reproducing the observed high‑frequency spectral tail.

To evaluate the new source function, the model was implemented within the same numerical framework as the widely used WAM and WAVEWATCH models and subjected to the standard suite of academic tests (steady wind, gusts, fetch‑limited growth, etc.). Performance metrics included root‑mean‑square error (RMSE), correlation coefficient (R), and computational time. The optimized DIA reduced RMSE for high‑frequency energy by 0.12 m² s⁻², the DABL input term increased R by 0.06, and the quadratic dissipation term lowered overall RMSE by 0.09 m. The total runtime decreased to 78 % of the original models, demonstrating a clear advantage in both speed and fidelity.

The discussion emphasizes that each component contributes independently to the overall gain, but their combination yields synergistic benefits: the DABL block provides a physically consistent link between atmospheric forcing and wave response, while the quadratic dissipation term ensures realistic spectral shape throughout the evolution cycle. The authors argue that these advances satisfy the criteria for a “fourth‑generation” wind‑wave model—namely, a framework that integrates accurate physics, efficient numerics, and the capacity to interface directly with atmospheric and oceanic climate models.

Future work outlined in the paper includes extensive validation against global buoy and satellite datasets, extension to non‑stationary sea states involving strong currents or rapidly varying bathymetry, and coupling with coupled atmosphere‑ocean prediction systems. In summary, the study delivers a rigorously justified, computationally efficient source‑function package that markedly improves wave growth, spectral evolution, and dissipation representation, paving the way for the next generation of operational wave forecasting tools.