Detecting Instantaneous Tidal Signals in Ocean Models Utilizing Streaming Band-Pass Filters

Through the implementation of a streaming filter, output of numerical ocean simulations can be band-pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi-diurnal and diurnal tides. Utilizing the filters, the frequency-dependent internal wave drag is applied to the semi-diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de-tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting.