The short answer is yes, and at various times this question of lunar tides in the atmosphere occupied such famous scientists as Isaac Newton and Pierre-Simon Laplace, among others. Newton's theory of gravity provided the first correct explanation of ocean tides and their long known correlation with the phases of the moon. Roughly a century later it was also used to predict the existence of atmospheric tides when Laplace developed a quantitative theory based on a tidal equation now bearing his name. Laplace's equation describes the motions of an ocean of uniform depth covering a spherical Earth [see illustration].
At the point on the ocean's surface closest to the moon (point A in the illustration), the lunar gravitational attractive force is strongest and it pulls the ocean toward itself. On the opposite side of Earth (point B), its attractive force is weakest, which allows the ocean to bulge outward again, in this case away from the moon. As the planet rotates from west to east the two bulges tend to stay on the Earth-moon line. (The moon also revolves around Earth in the same direction as Earth's rotation but at a much slower rate.) For an observer stationed on the surface and revolving with it, the bulges would appear as a giant wave, which follows the apparent motion of the moon to the west and has two crests per lunar day.
Real ocean tides are of course complicated by the waters uneven depth and the presence of land. But Laplace's theory is perfectly applicable to the atmosphere if ocean depth in the tidal equation is replaced by a quantity called equivalent depth, characterizing the extent of the atmosphere above the surface. Just as our weight puts pressure on the ground beneath our feet, the weight of the atmosphere above us exerts pressure on the planet's surface and everything located on it (recall that pressure is defined as force per unit surface). This is the usual atmospheric surface pressure that we hear about in weather forecasts. It is clear then that Laplace's theory predicts two pressure maxima per lunar day corresponding to the two ocean bulges [see illustration]. One occurs approximately when the moon is directly overhead, the other half-a-day later. The dominant lunar tide in the atmosphere is therefore semidiurnal (half-daily).
Theory predicts stronger lunar pressure oscillations in the tropics but their amplitude rarely exceeds 100 microbars or 0.01 percent of the average surface pressure. Detection of such a tiny signal masked by much larger pressure variations associated with weather phenomena required the development of special statistical techniques and the accumulation of a long series of regular observations.
Surprisingly, such observations show that the sun also causes semidiurnal tides in the atmosphere, which are more than 20 times stronger, although the solar gravitational forcing is less than half that of the moon. After all, it is the moon that causes the dominant tides in the ocean, not the sun. (The average lunar day is about 51 minutes longer than the solar day because of the moons rotation around Earth and this allows scientists to reliably separate the two tides in long observational records.) Apparently, Laplace had suspected this, suggesting that the strong solar tide was primarily generated by solar heating and not by solar gravity. Scientists finally confirmed this hypothesis in the 1960s when it became possible to develop adequate models of solar atmospheric heating. As with the gravitational pull of a celestial body, the uneven solar heating on Earth's dayside distorts the spherical symmetry of the atmosphere, but in a more complex way. The thermal solar tide therefore consists of several dominant waves, the most prominent being the diurnal and semidiurnal ones.
Pressure variations cause tidal oscillations in other atmospheric characteristics as well. It is common for atmospheric waves to grow in amplitude with height as the air becomes thinner. The lunar tide, however, remains weak compared to the solar tide in the upper atmosphere. Still, at altitudes above roughly 80 kilometers (50 miles) lunar tides have been detected in winds, temperature, airglow emissions and a number of ionospheric parameters. Almost two centuries after atmospheric lunar tides were predicted and first observed, they are still studied. They represent a unique type of atmospheric motion whose forcing mechanism is known with great precision, allowing us to test our numerical models and theoretical predictions.