Most of these parameters cannot change much in the long run. However, they are subject to periodic or quasi-periodic oscillations in a wide range of time scales, and with often considerable amplitude.
(Quasi-)periodic oscillations are due to waves. The shortest periods correspond to sound waves, and their spectral extension beyond the low-frequency limit of human hearing (about 20 Hz) is called "infra-sound". Since the speed of sound depends on temperature, but not on pressure, it can be used for measuring temperature, even at very great altitudes.
For longer periods (and therefore, wavelengths), the bouyancy force of the larger volumes of higher (or lower) density (enclosed between two consecutive zeros of the wave) comes into play. It competes with the pressure difference to try to reestablish the unperturbed state.
Therefore, the waves behave differently from normal sound: Oscillations are not simply longitudinal, but acquire a component of motion in the vertical direction, and even their propagation direction changes, since they "feel" gravity. They are called gravity waves (more precisely, acoustic-gravity waves). The expression is inherited from longer-period water surface waves that do not depend on surface tension (like capillary waves), but on the weight of water (not to be confounded with cosmic "gravitational waves"!).
Beyond a transition period due to atmospheric stability characteristics depending on the vertical temperature profile (the so-called Brunt-Väisälä period; about 5 min near the mesopause), gravity waves change their behaviour and become "internal gravity waves", or simply "gravity waves". Their periods range from about 5 min to several hours.
For waves with large horizontal wavelengths, the Coriolis force due to the Earth's rotation modifies the horizontal wave motion. Also, the finiteness and spherical symmetry of the atmosphere impose limitations on horizontal scale and wave propagation characteristics. Eigenmodes of this finite waveguide with one-day period (and their harmonics) are called diurnal (and semidiurnal, terdiurnal) tidal waves, or thermal (solar) tides, because they are excited by the daily variations in solar heating. Since the maximum solar heat input is at (or near) ground level, tidal waves essentially propagate upwards.
All upward-propagating waves tend to grow considerably in amplitude because of the exponential density decay with height, and the conservation of wave energy. This growth only stops when dissipation wins over, or waves break (like ocean waves break on the shore).
Waves with periods greater than one day are subject to the same kind of planetary-scale eigenmodes as the tides. They are generically called planetary waves. Their excitation is not simply related to solar heating (the term used in meteorology is "forcing"), but to the interaction of zonal circulation, planetary rotation, and orography. The different land-sea and mountain range patterns explain the differences in planetary wave activity between the Northern and Southern Hemispheres.
The seasonal variation of solar input modulates the global circulation pattern in complex ways. The corresponding variation of "background winds" affects the conditions for the generation, vertical propagation, and breaking of the different wave types, and so exerts an influence on the seasonal "climatology" of wave activity. On the other hand, waves themselves also affect the "background" wind, and this influence can become so strong as to be dominant, at certain altitudes: Global circulation patterns inextricably depend on the upward transport of wave momentum and its eventual deposition into the mean flow.
This general view of atmospheric variability as a superposition of different kinds of wave motions is, however, a rather coarse simplification. Not so much because of anharmonicity: Linear approximations for gravity waves work quite well, and wave-wave interactions can be accounted for by introducing small nonlinear terms that give rise to wave mixing. A more serious practical problem is nonstationarity: Long wave trains are rare and short wave packets that last no more than a few (or even single) wave periods are observed most of the time. Even the semidiurnal tide can (and often does) change its amplitude dramatically, from day to day. This is completely incompatible with a weakly nonlinear wave-wave modulation scheme, but would require very strong nonlinearity or non-sinusoidal modulating wave shapes.
Therefore, time series spectral analysis must be applied with caution, is of limited value, and the interpretation of its results is not straightforward. It is astonishing how many useful results have been obtained by these techniques, in spite of their theoretical (and practical) limitations! Note that spectral analysis techniques invariably assume that the superposition principle for different spectral components holds, that is, that the sum of sinusoidal solutions is also a solution, which implies that nonlinear effects are absent, or small enough to be ignored.
Some of the most spectacular dynamical events do not fit into a linear scenario. Abrupt jumps of airglow brightness that travel over the sky and are called "wall events" are an example. There are often wiggles parallel and adjacent to the "wall" that show variations of amplitude and wavelength that can be explained by soliton theory. Solitons (or "solitary waves") are special solutions of certain nonlinear wave equations. They maintain their shape and amplitude as they propagate, as if dispersion and attenuation did not exist. Their nonlinear characteristics would show most dramatically when different solitons overlap, so that this would permit the most striking demonstration of nonlinearity. The resulting perturbation is totally different from the sum of the individual perturbations - the (linear) superposition principle does not even hold, approximately!
Such waves have been observed in the troposphere as single (positive, or negative) atmospheric pressure deviations at ground level. Also traveling ionospheric disturbances in the thermosphere have often been identified with solitons. Wall events were the first good soliton candidates detected in the mesopause region, frequently observed with all-sky airglow imagers. For other phenomena like day-to-day airglow "bursts" (some of which have been recognized after traveling nearly 3000 km), the soliton interpretation is presently still hard to prove. However, with growing observational evidence and a growing interest in these phenomena, it is reasonable to expect that much will be learned about prominent dynamical activity that is not part of the conventional list of dynamical features.