LSF Tides
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Least Squares Fit for ROMS Tides
A ROMS state variable, , can be represented in terms of its time mean, , plus a set of -tidal harmonics of frequency, .
The unknown tidal amplitude , and and unknown state coefficients are evaluated by minimizing the least-squares error function defined by:
In discrete space:
Minimization subject to the additional constraints , , result in a linear set of equations:
in matrix form ( harmonics). Note: all instances of are actually where is the number of time-steps in the time-averaging window.