Improved harmonic development of the Earth tide-generating potential

Abstract.

An improved technique is proposed for spectral analysis of an arbitrary function of the Moon/Sun/planet coordinates tabulated over a long period of time. Expansion of the function to Poisson series is made where the amplitudes and arguments of the series’ terms are high-degree time polynomials, as opposed to the classical Fourier analysis where the terms’ amplitudes are constants, and the arguments are linear functions of time. This leads to an improvement in accuracy of the spectral analysis of the functions over long-term intervals. The technique is applied to produce a harmonic development of the Earth tide-generating potential (TGP) which was preliminarily calculated and tabulated over an interval of 2000 years centered at epoch J2000.0. (The latest NASA/JPL long-term ephemeris DE/LE-406 has been used as the source of the Moon, Sun and planet coordinates.) The final development of the TGP, named KSM03, includes some 27 000 terms of amplitudes down to the level of 1×10⁻⁸ m² s⁻². The respective accuracy in calculation of gravity tides at a mid-latitude station is 0.025/0.39 nGal (the root-mean-square/maximum error) when compared with a benchmark gravity tide series numerically computed with the use of the most accurate ephemeris DE-405 at every hour within the interval 1600–2200 (the complete period of time covered by the ephemeris). It exceeds the accuracy of any previously made harmonic development of the TGP in the time domain by a factor of at least 3.