A Machine Learning Parameterization for the Internal Gravity Wave Spectrum

We introduce a stochastic model designed to parametrize the spectral properties of internal tides, using two functions that represent the semidiurnal spectral cusps and the energy continuum between the inertial and the buoyancy frequencies. We estimated model parameters from long-term in-situ mooring temperature data from the Australian Northwest Shelf (NWS) and Timor Sea using the debiased Whittle likelihood in the frequency domain. The interpretable parameters revealed site, depth, and seasonal variations in internal wave properties, including energy and timescales of non-phase-locked internal waves, and the energy roll-off rate of the internal gravity continuum. The median integral timescale, indicative of the extent of the phase modulation, was 3 - 3.7 days. The depth variation for the amplitude of the energy continuum and the semidiurnal spectral cusp exhibited an internal wave mode-1 eigenfunction, particularly at the deeper mooring sites. The greatest amplitudes were observed within the thermocline. We also found that the continuum spectral slope was up to 10% flatter than the Garrett-Munk slope at the NWS moorings compared with the Timor Sea. The spectral slope varied seasonally and decayed more rapidly in summer. Our parameterization can be used to generate time predictions with Gaussian process regression or for stochastic boundary conditions of coastal nonlinear internal wave modeling.