harmonic_analysis module reference
Major revision (August, 2025)
Detailed Description
This module is now independent of MOM_tidal_forcing, providing more flexibility for performing harmonic analyses on tidal constituents not available in MOM_tidal_forcing (e.g., MK3, M4), with the following conditions: 1) For tidal constituents not available in MOM_tidal_forcing, the frequencies and equilibrium phases (if used) must be specified manually in MOM_input. 2) If any tidal constituents not available in MOM_tidal_forcing are used, the nodal modulation cannot be added. Or, if nodal modulation is added, then harmonic analysis can only be performed on major tidal constituents.
Original version (April, 2024)
This module computes the harmonic constants which can be used to reconstruct the tidal elevation (or other fields) through SSH = F * x, where F is an nt-by-2*nc matrix (nt is the number of time steps and nc is the number of tidal constituents) containing the cosine/sine functions for each frequency evaluated at each time step, and x is a 2*nc-by-1 vector containing the constant coefficients of the sine/cosine for each constituent (i.e., the harmonic constants). At each grid point, the harmonic constants are computed using least squares,
(F' * F) * x = F' * SSH_in, => FtF * x = FtSSH,
where the prime denotes matrix transpose, and SSH_in is the sea surface height (or other fields) determined by the model. The dot products (F’ * F) and (F’ * SSH_in) are computed by accumulating the sums as the model is running and stored in the arrays FtF and FtSSH, respectively. The FtF matrix is inverted as needed before computing and writing out the harmonic constants.
Ed Zaron and William Xu ( chengzhu.xu@oregonstate.edu )