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. Plain Language Summary: In this work, we developed a computationally efficient algorithm for detecting tidal signals from the instantaneous model output, without needing to harmonically analyze the entire time series of model output. This is achieved through the construction of a streaming filter, which takes the instantaneous model output as the input and returns a time series consisting of tidal motions at its target frequency band as the output, in a process that effectively allows signals within its target frequency band to pass through and blocks signals outside of its target frequency band. Unlike the conventional harmonic analysis, the band‐pass filtering process does not require information from any of the previous or future time steps. The filtering algorithm is implemented and validated in a global ocean model. The filters can be utilized to parameterize frequency‐dependent internal wave drag, as demonstrated in this work, and to remove tidal signals from the model output, which has potential application in regional ocean forecasting systems. Key Points: The streaming band‐pass filter can detect sinusoidal motions at tidal frequencies from the instantaneous model outputThe filtering algorithm is computationally efficient and is capable of capturing the temporal variation of tidal signalsThe filters can be utilized to parameterize frequency‐dependent internal wave drag and to de‐tide model output [ABSTRACT FROM AUTHOR]