The Effect of Ocean and Earth Tides on the Semi-Diurnal Lunar Air Tide

Abstract

The effects of the earth and ocean tides on the semi-diurnal lunar tide in the atmosphere have been ignored in nearly all studies of this air tide. Elementary arguments show that these boundary effects are not trivial. Using linear theory we calculated the combined effect of the lunar potential, the earth tide, and the ocean tide on a realistic model atmosphere. Love's theory was used to represent the earth tide. Numerical calculations by Bogdanov and Magarik and by Pekeris and Accad were used to represent the ocean tide. Our results indicate that the ocean tide has a significant and probably a dominant effect on the lunar air tide. The ocean tide of Pekeris and Accad yielded results that agreed better with the observations. We calculated the effect of a tide in a “small” or “point” ocean on the atmosphere and found that its effects were global. Hence, differences between the observations and our calculations of the lunar air tide cannot easily be reduced by simple manipulation of the forcing function, the ocean tide, in the immediate vicinity of the places where discrepancies occur. The forcing functions of the problem were represented as Fourier-Houghseries, involving 232 Hough functions. Computations, of the semi-diurnal lunar tidal winds at 98 km are presented and compared with observations. Calculations of tidal winds at the surface suggest that the hitherto unexplained sense of rotation of the observed tidal winds is an effect of the ocean tide.