Numerical wave models predict ocean wave spectra. Some physics involved remains troublesome. For example, the Boltzmann integral must be computed to derive the nonlinear wave-wave interactions (Hasselmann & Hasselmann, 1985). This integral is too expensive to compute in real-time. Consequently, operational wave models use the Discrete Interaction Approximation (DIA) (Hasselmann & Hasselmann, 1985). The DIA is a 40-year-old parameterised diffusion operator, and its flaws are explicitly mentioned as limitations in the literature (Ardag & Resio, 2019).

This project aims to use machine learning to create a surrogate model for the Boltzmann integral. Other works that do this exist (Chen et al., 2026; Ikuyajolu et al., 2026), but our work differs in two ways. Firstly, our model will operate independent of resolution through the choice of our architecture. Secondly, our model will work on observational wave spectra extracted from airborne LiDAR data (Villas Bôas et al., 2022). Principles of physics-informed machine learning will be used to iteratively enhance the model and to make its dynamics more physical.

For about the project contact Mr Merlijn Surtel, Research Fellow at the Department of Mathematics and Statistics at the University of Strathclyde.

For a list of the research areas in which ARCHIE-WeSt users are active please click here.

References

Ardag, D., & Resio, D. T. (2019). Inconsistent spectral evolution in operational wave models due to inaccurate specification of nonlinear interactions. Journal of Physical Oceanography, 49, 705-722. https://doi.org/10.1175/JPO-D-17-0162.1

Chen, J., Adcock, T. A., Liu, Q., Clark, R., & Tang, T. (2026). Machine learning approximations for fast and accurate prediction of nonlinear four‐wave interactions in spectral wave models. Journal of Geophysical Research: Machine Learning and Computation, 3(1), e2025JH000864.

Hasselmann, S., & Hasselmann, K. (1985). Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum. Part I: A new method for efficient computations of the exact nonlinear transfer integral. Journal of Physical Oceanography, 15, 1369-1377. https://hdl.handle.net/21.11116/0000-0008-7C26-3

Ikuyajolu, O. J., Van Roekel, L., Brus, S. R., & Thomas, E. E. (2026). NLML: A deep neural network emulator for the exact nonlinear interactions in a wind wave model. Journal of Geophysical Research: Machine Learning and Computation. https://doi.org/10.1029/2025JH000699

Villas Bôas, A. B., Lenain, L., Cornuelle, B. D., Gille, S. T., & Mazloff, M. R. (2022). A broadband view of the sea surface height wavenumber spectrum. Geophysical Research Letters, 49. https://doi.org/10.1029/2021gl096699