Nonlinear Interaction of the Lunar Tide M2 and the Diurnal Variation of Electron Density in the Ionosphere

Ground-based observations of time series of ionospheric electron density indicated the existence of spectral components at the periods of the lunar tidal constituents $O_1$ (25.82 hr) and ${\text{MK}}_3$ (8.18 hr). It was unclear whether these variations are excited by $O_1$ and ${\text{MK}}_3$ tides propagating from the surface into the ionosphere or if the variations are due to a nonlinear interaction of the semidiurnal lunar tide $M_2$ with the diurnal variation of ionization ($S_1$). A simulation was performed with the NSF National Center for Atmospheric Research thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM). In the stratosphere at the lower boundary of TIME-GCM, the signal of the atmospheric semidiurnal lunar tide $M_2$ is introduced. The TIME-GCM simulation of January–February 2009 shows that the electron density variation in the equatorial $F_2$ region contains not only a spectral component of the $M_2$ period but also spectral components of the $O_1$ and ${\text{MK}}_3$ periods fulfilling the nonlinear interaction resonance condition for the frequencies of the wave triads ($M_2$ + $S_1$ = ${\text{MK}}_3$) and ($M_2$ − $S_1$ = $O_1$). The nonlinear interaction resonance condition of the zonal wavenumbers of these wave triads is also fulfilled. Moreover, the relevance of nonlinear interaction of $M_2$ and $S_1$ is supported by observations of total electron content (TEC). The amplitude spectrum of the long-term time series of TEC shows that the quasi-diurnal and terdiurnal lunar spectral lines precisely occur at the frequencies of $M_2$ − $S_1$ and $M_2$ + $S_1$.