A Machine Learning Parametrisation for the Internal Gravity Wave Spectrum

Understanding internal wave is essential, as they exert a profound influence on a multitude of oceanic processes, including mixing and the transfer of energy across a vast range of spatial scales. The phase of internal waves can undergo a rapid alteration during propagation, resulting in the formation of broad spectral peaks. In this study, we introduce a stochastic model designed to parametrise the spectral properties of coastal internal waves. This model employs a Lorentzian function to characterise the broad internal tide peaks and a Matern function for the energy continuum. The efficacy of our model is validated using long-term in-situ mooring temperature data from the Australian Northwest Shelf (NWS) and Timor Sea. By optimising the model parameters using debiased Whittle likelihood in the frequency domain, our approach is able to reproduce the spectrum of internal wave incoherent peaks and the continuum of energy down to the buoyancy frequency. The fitted parameters allow for a comparison of internal wave properties between sites, depths, and seasons. The decorrelation timescale, indicative of the extent of the phase shift, exhibited a median value between 3 and 5 days and demonstrated minimal variation across sites and depths. The depth variation for the energy continuum amplitude and the amplitude of the semidiurnal peak exhibited an internal wave mode-1-like structure, particularly at the deeper mooring sites. The greatest amplitudes were observed within the surface mixed layer and thermocline. The slope parameter of the continuum exhibited a median value slightly less than the content slope in Garret-Munk spectral model and demonstrated seasonal variation, with a more rapid decay of energy in the summer compared to winter. The parameters obtained through our method can be further utilised to construct more realistic internal tide boundary conditions using Gaussian processes, thereby enabling more sophisticated modelling of internal waves in coastal regions.