Tidal analysis of an equally or randomly spaced record with small number of data samples

Problems in the analysis of short-period tides from an equally or randomly spaced record with a limited number of data samples have been investigated. In dealing with an equally spaced record, the primary cause of estimation error is the interference between the major short-period tides such as M₂, N₂, K₁ and P₁. A measure of the interference is given by a function which decreases in an oscillatory fashion with observational duration and/or difference of frequencies between paired constituents. The iterative Darwin method (IDM), newly introduced, and the least-squares method (LSM) can reduce the interference effectively to obtain accurate estimates. Another source of error is due to the interference between a major tide and a minor tide such as T₂ andv ₂. To hold an accuracy of 1 cm in amplitude, we must employ a long record of around one year, or we must include the influential minor tides among the major tides a priori. In dealing with randomly spaced data or randomly sampled data from a long record, on the other hand, a major source of error lies in the random noise resulting from the long-period tides such as M_m and S_a. If the number of data samples is greater than 360 and if random noise is within ±10 cm, both IDM and LSM can estimate tidal constants with probable errors of about 1 cm in amplitude and a few degrees in phase.