Corrected Tables of Tidal Harmonics

Summary A small error in the computations of Cartwright & Tayler has been corrected, resulting in improved tables of the time harmonics of the principal terms in the tide-generating potential. The correction removes certain previously anomalous features, and otherwise affects the amplitudes in their 5th decimal places. Cartwright & Tayler (1971) presented new tables of the time harmonics of the tide-generating potential, computed with modern (IAU 1964) astronomical constants from ephemerides for the Moon and Sun accurate to within radians (2”) in angular co-ordinates and x mean values in parallax. They differed from Doodson’s (1921) well-known tables principally in terms dominated by the solar potentia!, and in a few other terms of less importance. Secular trends in the larger amplitudes, of order 1 part in lo4 per century, mainly due to the trend in obliquity, were also revealed. Recently, one of us (DEC) discovered a coding error in one of his own computer programs used in this work, sufficiently trivial to have escaped notice through many rigorous tests, but important enough seriously to affect the 5th decimals of the tabulated harmonics. (The error occurred not in the basic computation of the 12hourly ephemeris, but in the formulae used to interpolate to 3-hourly series. We are grateful to Dr Mark Wimbush, of Nova University, Florida, for pointing out some anomalous results from a related program which led to the error’s discovery). The error having been corrected, we have completely recomputed the affected tables of Cartwright and Tayler, and present the results herewith. The following Table 1 (a), (b) and (c) replaces the original Table 4(a), (b) and (c), pertaining to the second degree spherical harmonics Pzo, Pzl, Pzz, respectively. The 3rd degree harmonics (original Table 5(a)-(d)), were found to be unaffected to the accuracy given; the major discrepancy from Doodson’s result at line number 1 2 0 0 1 0 in Table 5(b) still stands. The leading harmonics of the radiational potential, (original Table 6), result from an independent calculation.