Process-based modelling of nonharmonic internal tides using adjoint, statistical, and stochastic approaches – Part 2: Adjoint frequency response analysis, stochastic models, and synthesis

Abstract. Internal tides are known to contain a substantial component that cannot be explained by (deterministic) harmonic analysis, and the remaining nonharmonic component is considered to be caused by random oceanic variability. For nonharmonic internal tides originating from distributed sources, the superposition of many waves with different degrees of randomness unfortunately makes process investigation difficult. This paper develops a new framework for process-based modelling of nonharmonic internal tides by combining adjoint, statistical, and stochastic approaches and uses its implementation to investigate important processes and parameters controlling nonharmonic internal-tide variance. A combination of adjoint sensitivity modelling and the frequency response analysis from Fourier theory is used to calculate distributed deterministic sources of internal tides observed at a fixed location, which enables assignment of different degrees of randomness to waves from different sources. The wave phases are randomized by the statistical model from Part 1 using horizontally varying phase statistics calculated by stochastic models. Essential inputs of the model suite are barotropic tidal currents, background stratification, and the variance and spatial correlation of internal-tide phase speed. An example application to nonharmonic vertical-mode-one semidiurnal internal tides on the Australian North West Shelf shows that (i) phase-speed variability primarily makes internal tides nonharmonic through phase modulation, and (ii) important controlling parameters include the variance and correlation length of phase speed, as well as anisotropy of the horizontal correlation of phase modulation. The model suite also provides a map of nonharmonic internal-tide sources, which is convenient for identifying important remote sources, such as the Lombok Strait in Indonesia. The proposed modelling framework and model suite provide a new tool for process-based studies of nonharmonic internal tides from distributed sources.