A Machine Learning Parameterization for the Internal Gravity Wave Spectrum

Abstract We introduce a stochastic model designed to parametrize the spectral properties of internal waves, using two functions that represent the semidiurnal spectral tidal 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 characteristic timescales of non‐phase‐locked internal waves, and the energy transfer rate of the internal gravity continuum. The characteristic timescale of the internal tide, a measure of the phase modulation of the internal tide, had a median value of 3–3.7 days. The amplitude of the energy continuum and the semidiurnal spectral cusp showed depth variability likely due to stratification, while timescale and slope remained nearly depth‐independent. We also found that the continuum spectral slope was relatively flatter than the canonical Garrett‐Munk value at the NWS moorings. The spectral slope varied seasonally and was steeper 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.