The Zonal Tidal Effect on the Variation in the Rotation Rate of the Earth with a Fluid Core Ⅱ.Numerical Calculation and Comparisons

The tidal variation in Earth rotation rate is a periodical response to solar-lunar tide generating potential (TGP), which can be expressed as a function of the non-dimensional parameter k/c_m (kandc_m are effective crust-mantle Love number and effective polar moment of inertia, respectively).Different from theory by Yoder.C.F (1981), some theoretical formulae are given here based on Doodson development of TGP including the variations in Earth rotation rate, LOD and UT1.Finally the zonal tidal effect on the variation in the fluid core Earth rotation rate is calculated according to the formula deduced by Xi Qinwen (1995).Result shows its good consistency with IERS (96).Besides, Xi s formula comprises more tidal waves. The development of TGP has been well deduced with high precision thanks to the excellent work by Xi Qinwen (1995).The formula he gave firstly in 1987, including 1178 tidal waves, was such a theoretically rigorous one that it can identify waves with slim difference in frequency while assuring the accuracy and reliability of their arguments.It was also pointed out that the calculating performance according to his formula suffered mainly from the errors of the ephemeris used and truncation errors, but the former ones can be avoided by choosing an ephemeris with required precision while the latter can also be solved carefully.In his revision published in 1993, the amplitudes of the tidal waves has been kept one more digital along with some other improvements.Including as high as 3070 items, this new version of development of TGP is now being recommended internationally to use in high precision tidal data analysis.Despite its highest precision, we should note that it is not yet at the ngal level. The non-dimensional parameterk/c_m, a factor in the theoretical formula to calculate the tidal variation in the Earth rotation rate, remains a constant when the Earth is treated as the one with a elastic mantle, the equilibrium ocean tide and non-coupling core-mantle.But it should be an complex number and related with the tidal frequency due to non-equilibrium disturbances of ocean tide.Besides, atmosphere and viscous elasticity of the Earth mantle can cause the disturbance of k(effective Love number of rotation rate)individually.Hence the tidal variation in the Earth rotation rate is recalculated using the latest released tidal data and its influences on the involved geophysical processes are analysed. The calculation shows that the results in this paper are well consistent with the ones in IERS (96), which indicates the correctness of the theoretical formula we deduced.It is also shown that the effects from the high frequency parts are relatively small, within the observing precision so far; relatively large effects due to the lower parts, which should be able to be seperated from the observed data, are actually difficult to make because of the influence from some non-tidal factors as well as short time span data.