HarmonicAnalysis

The equation that defines the water level changes due to tide is:

<math> \widehat{h} = H_0 + \sum_{n} \widehat{f}_n H_n \cos{\left[ a_n \widehat{t} - \left( \kappa_n - \left[ V_0 + \mu \right]_n \right) \right]} </math>

<math> \begin{align} \widehat{h} &=& \mbox{measured water level (1 dimensional array)} \\ H_0 &=& \mbox{average water level} \\ n &=& \mbox{number of tidal constituents analyzed} \\ \widehat{f}_n &=& \mbox{node factor for constituent }n \mbox{ (1 dimensional array)} \\ H_n &=& \mbox{amplitude of constituent }n \\ a_n &=& \mbox{speed of constituent }n \\ \widehat{t} &=& \mbox{time (1 dimensional array)} \\ \kappa_n &=& \mbox{phase angle of constituent }n \\ \left[V_0+\mu\right]_n &=& \mbox{equilibrium argument for constituent }n \\ \end{align} </math>

Typical tidal analysis programs specify the node factor at the center of the analyzed time-series. I think this is something that is true for a 29-day series, but for longer analysis, the node factor at each measurement should be calculated. This is what TAPPY does.