Determining tidal elevations and velocities in a forward global ocean model utilizing streaming band-pass filters

Tidal elevations and velocities can be determined by harmonic analysis performed of time series data, provided that data of reasonable temporal resolution and record length are available. For numerical simulations performed in time domain, however, it is not practical to determine the instantaneous tidal elevations or velocities by means of conventional harmonic analysis. Here, we propose an algorithm for constructing a streaming band-pass filter, which, when coupled into numerical ocean models, can determine the instantaneous tidal elevations and velocities while the model is running. The algorithm is computationally efficient, since it does not require the storage of model output data at any of the previous time steps, or any priori knowledge or approximation in the future time. Moreover, because the algorithm is implemented in the time domain, it has the ability to capture the temporal variation of tidal amplitudes and phases. The potential applications of the algorithm include the de-tiding of model output in nested regional ocean models, and the parameterization of frequency-dependent internal wave drag.