Two kinds of wave modes exit : class 1 waves (sometimes called gravity waves), and class 2 waves (rotational waves). Class 2 waves owe their existence to the Coriolis effect and can only exist for periods larger than 12 hours. Tidal waves can be either internal (travelling waves) with positive eigenvalues (or equivalent depth) which have finite vertical wavelengths and can transport wave energy upward, or external (evanescent waves) with negative eigenvalues and infinitely large vertical wavelengths meaning that their phases remain constant with altitude. These external wave modes cannot transport wave energy, and their amplitudes decrease exponentially with height outside their source regions. Each mode is characterized by four numbers: the zonal wave number n, positive for class 1 waves and negative for class 2 waves (their meridional structures becoming increasingly complex with increasing number n), a meridional wave number m, the eigenvalue, and the period, in our case one solar or lunar day, respectively. The modes are labeled as (m, n). Even numbers of n correspond to waves symmetric with respect to the equator, and odd numbers corresponding to antisymmetric waves. At thermospheric heighs, dissipation of atmospheric waves becomes significant so that at above about 150 km altitude, all wave modes gradually become external waves, and the Hough functions degenerate to spherical harmonicss ; e.g., mode (1, -2) develops to the spherical harmonic P11(θ), mode (2, 2) becomes P22(θ), with θ the co-latitude, etc.Volland, H., "Atmospheric Tidal and Planetary Waves", Kluwer Publ., Dordrecht, 1988 Migrating Solar Tides The fundamental solar diurnal tidal mode which optimally matches the solar heat input configuration and thus is most strongly excited is the (1, -2) - mode. It depends on local time and travels westward with the Sun. It is an external mode of class 2. Its maximum pressure amplitude on the ground is about 60 hPa.Chapman, S., and R.S. Lindzen, "Atmospheric Tides", Kluwer Dordrecht, 1970 Within the thermosphere, however, it becomes the predominant mode  reaching temperature amplitudes at the exosphere of at least 140 K and horizontal winds of the order of 100 m/s and more increasing with geomagnetic activity.Kohl, H. and J.W. King, J. Atm. Terr. Phys., 29,1045, 1967 The largest solar semidiurnal wave is mode (2, 2) with maximum pressure amplitudes near the ground of 120 hPa. It is an internal class 1 wave. Its amplitude increases with altitude. Although its solar excitation is half of that of mode (1, -2), its amplitude on the ground is larger by a factor of two. This indicates the effect of suppression of external waves, in this case by a factor of four. Semidiurnal Lunar Tides The dominant migrating lunar tide is the (2, 2) mode depending on lunar local time. Its maximum pressure amplitude near the ground is 6 Pa, which is far below the meteorological noise. Therefore, it is not simple to detect such  small signal. Because it is an internal waves, its amplitude increases with altitude  reaching values at 100 km height two orders of magnitude larger than on the ground.
Two kinds of wave modes exist : class 1 waves (sometimes called gravity waves), and class 2 waves (rotational waves). Class 2 waves owe their existence to the Coriolis effect and can only exist for periods larger than 12 hours. Tidal waves can be either internal (travelling waves) with positive eigenvalues (or equivalent depth) which have finite vertical wavelengths and can transport wave energy upward, or external (evanescent waves) with negative eigenvalues and infinitely large vertical wavelengths meaning that their phases remain constant with altitude. These external wave modes cannot transport wave energy, and their amplitudes decrease exponentially with height outside their source regions. Each mode is characterized by four numbers: the zonal wave number n, positive for class 1 waves and negative for class 2 waves (their meridional structures becoming increasingly complex with increasing number n), a meridional wave number m, the eigenvalue, and the period, in our case one solar or lunar day, respectively. The modes are labeled as (m, n). Even numbers of n correspond to waves symmetric with respect to the equator, and odd numbers corresponding to antisymmetric waves. At thermospheric heighs, dissipation of atmospheric waves becomes significant so that at above about 150 km altitude, all wave modes gradually become external waves, and the Hough functions degenerate to spherical harmonics ; e.g., mode (1, -2) develops to the spherical harmonic P11(θ), mode (2, 2) becomes P22(θ), with θ the co-latitude, etc.Volland, H., "Atmospheric Tidal and Planetary Waves", Kluwer Publ., Dordrecht, 1988 Migrating Solar Tides The fundamental solar diurnal tidal mode that optimally matches the solar heat input configuration and thus is most strongly excited is the (1, -2) - mode. It depends on local time and travels westward with the Sun. It is an external mode of class 2. Its maximum pressure amplitude on the ground is about 60 hPa.Chapman, S., and R.S. Lindzen, "Atmospheric Tides", Kluwer Dordrecht, 1970 Within the thermosphere, however, it becomes the predominant mode , reaching temperature amplitudes at the exosphere of at least 140 K and horizontal winds of the order of 100 m/s and more increasing with geomagnetic activity.Kohl, H. and J.W. King, J. Atm. Terr. Phys., 29,1045, 1967 The largest solar semidiurnal wave is mode (2, 2) with maximum pressure amplitudes near the ground of 120 hPa. It is an internal class 1 wave. Its amplitude increases with altitude. Although its solar excitation is half of that of mode (1, -2), its amplitude on the ground is larger by a factor of two. This indicates the effect of suppression of external waves, in this case by a factor of four. Semidiurnal Lunar Tides The dominant migrating lunar tide is the (2, 2) mode depending on lunar local time. Its maximum pressure amplitude near the ground is 6 Pa, which is far below the meteorological noise. Therefore, it is not simple to detect such a small signal. Because it is an internal waves, its amplitude increases with altitude , reaching values at 100 km height two orders of magnitude larger than on the ground.
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