Characteristic velocity and timescales of non-phase-locked internal tides in a mesoscale eddy field

We present a new parametric autocovariance kernel function for characterizing properties of the mesoscale eddy field and the non-phase-locked internal tide from ocean time series records. We demonstrate that the model captures the important spectral properties, namely the spectral roll-off of the mesoscale continuum and the broad spectral ``cusps" centered around the tidal forcing frequencies. The spectral cusp model has three main parameters that characterize the non-phase-locked internal tide: the amplitude, a decorrelation timescale and a shape parameter that captures the rate at which the cusp rolls away. Estimation of the third shape parameter is novel. We argue that an integral timescale is the most suitable characteristic timescale and show how it relates to the parametric decorrelation timescale. A key innovation of this work is that we estimate the parameters in the frequency domain using the debiased Whittle likelihood. We apply our spectral parameter estimation technique to outputs from idealized and realistic numerical experiments of internal tides propagating through a mesoscale eddy field. We demonstrate that the non-phase-locked internal tide integral timescale was 2--7 d, is influenced by the Rossby number of the mesoscale flow field, which is linked to the eddy timescale, and is relatively constant in space. Furthermore, we demonstrate that the internal tide integral timescale is set by the global properties of the eddy field because internal waves have memory of past interactions. The intended use of our parametric kernel functions are for generating probabilistic predictions of ocean time-series.