Modulation of the lunar semidiurnal tide in GNSS TEC by the variable Earth-Moon distance

Klemens Hocke^*

• Institute of Applied Physics, University of Bern, Bern, Switzerland

The lunar semidiurnal tide M$_2$ is generated in the lower atmosphere and propagates upward to the dynamo region where the tide-induced electric field variations are mapped to the equatorial F region. The worldwide network of GNSS receivers (International GNSS Service) monitors the total electron content (TEC) since 1998 and allows to study the influences of the Moon on the Earth's ionosphere in detail. Time series analysis shows that the M$_2$ amplitude in GNSS TEC is modulated by the period of the anomalistic month (27.55455 days) which is the time interval from one perigee transit of the Moon to the next. The variable Earth-Moon distance or the eccentricity of the Moon orbit is clearly responsible for this modulation. The M$_2$ amplitude in TEC after perigee is larger by a factor of 1.25 than the M$_2$ amplitude in TEC after apogee while equilibrium theory of tides predicts a factor of 1.40 for the perigee-to-apogee ratio of the lunar tide in equilibrium elevation of the ocean surface. Composite analysis with respect to the Moon orbit phase and phase differences of fast Fourier transform spectral components show that the maximal M$_2$ amplitude in TEC occurs about 3.0 days after the perigee transit of the Moon. It is suggested that the lunar tide requires three days for the travel from the lower atmosphere to the dynamo region. Analytical equations of tidal wave theory show that the lunar tidal wave modes (2,2), (2,3), (2,4) require travel times of 2.5 days, 2.2 days, and 2.8 days from 0 km to 105 km altitude, depending on their vertical group velocities (assuming a constant temperature profile of 250 K). The observed lunar tide in TEC and its eccentricity modulation seem to be a valuable tool for the study of the vertical propagation of the lunar tide from the surface to the ionospheric dynamo region.