In the practice of tidal analysis and prediction, the number and kind
of astronomical tidal components that are to be included in a tidal mo
del depend on the length of available tidal record and the desired acc
uracy of prediction. Since tidal frequencies, including shallow water
constituents, are distributed unequally in a few narrow frequency band
s, an inappropriate selection of tidal constituents to be included in
the analysis and prediction may cause the normal equations to become i
ll-conditioned, or even singular, and the prediction to become poor. T
his investigation shows how to construct lumped tidal frequencies whic
h better characterize ocean fides with diminishing length of observati
onal series. Further, a sequential tidal analysis model is proposed an
d an algorithm for its implementation is presented, which can rigorous
ly update a tidal solution when the number of observations increases.
The algorithm also brings in automatically additional tidal constituen
ts without a large amount of computation work; the CPU time for this a
nalysis is only about 4 percent of that for the conventional harmonic
technique. The sequential algorithm for ocean tidal analysis and predi
ction has a potential to be used in tide gauge stations for providing
continuous up-to-date tidal prediction.