Process-based modelling of nonharmonic internal tides using adjoint, statistical, and stochastic approaches. Part I: statistical model and analysis of observational data

Abstract. A substantial fraction of internal tides cannot be explained by (deterministic) harmonic analysis. The remaining nonharmonic part is considered to be caused by random oceanic variability, which modulates wave amplitudes and phases. The statistical aspects of this stochastic process have not been analysed in detail, although statistical models for similar situations are available in other fields of physics and engineering. This paper aims to develop a statistical model of the nonharmonic, incoherent (or nonstationary) component of internal tides observed at a fixed location, and to check the model's applicability using observations. The model shows that the envelope-amplitude distribution approaches a universal form given by a generalization of the Rayleigh distribution, when waves with non-uniformly and non-identically distributed amplitudes and phases from many independent sources are superimposed. Mooring observations on the Australian North West Shelf show the applicability of the generalized Rayleigh distribution to nonharmonic vertical-mode-one to mode-four internal tides in the diurnal, semidiurnal, and quarterdiurnal frequency bands, provided that the power spectra show the corresponding tidal peaks clearly. These results demonstrate the importance of viewing nonharmonic internal tides as the superposition of many random waves. The proposed distribution can be used for many purposes in the future, such as investigating the statistical relationship between random internal-tide amplitude and the occurrence of nonlinear internal waves, and assessing the risk of infrequent strong waves for offshore operations. The proposed statistical model also provides the basis of investigating processes and parameters controlling nonharmonic internal-tide variance in Part II.