Editing Thermosphere (section)

==Dynamics==
[[File:Thermospherewaves.jpg|thumb|upright=2.35|Figure 2. Schematic meridian-height cross-section of circulation of (a) symmetric wind component (P<sub>2</sub><sup>0</sup>), (b) of antisymmetric wind component (P<sub>1</sub><sup>0</sup>), and (d) of symmetric diurnal wind component (P<sub>1</sub><sup>1</sup>) at 3 h and 15 h local time. Upper right panel (c) shows the horizontal wind vectors of the diurnal component in the northern hemisphere depending on local time.]]
Within the thermosphere above an altitude of about {{convert|150|km|mi}}, all atmospheric waves successively become external waves, and no significant vertical wave structure is visible. The atmospheric wave modes degenerate to the [[spherical harmonics|spherical functions]] P<sub>n</sub><sup>m</sup> with m a meridional [[wave number]] and n the zonal [[wave number]] (m = 0: zonal mean flow; m = 1: diurnal tides; m = 2: semidiurnal tides; etc.). The thermosphere becomes a damped oscillator system with low-pass filter characteristics. This means that smaller-scale waves (greater numbers of (n,m)) and higher frequencies are suppressed in favor of large-scale waves and lower frequencies. If one considers very quiet magnetospheric disturbances and a constant mean exospheric temperature (averaged over the sphere), the observed temporal and spatial distribution of the exospheric temperature distribution can be described by a sum of spheric functions:<ref>Köhnlein, W., A model of thermospheric temperature and composition, Planet. Space Sci. '''28''', 225, 1980</ref>

(3) {{pad|4em}} <math>T(\varphi, \lambda, t) = T_\infty \{ 1 + \Delta T_2^0 P_2^0(\varphi) + \Delta T_1^0 P_1^0(\varphi) \cos [ \omega_a (t - t_a) ] + \Delta T_1^1 P_1^1(\varphi) \cos (\tau - \tau_d) + \cdots \}</math>

Here, it is φ latitude, λ longitude, and t time, ω<sub>a</sub> the [[angular frequency]] of one year,  ω<sub>d</sub> the angular frequency of one solar day, and τ =  ω<sub>d</sub>t + λ  the local time. t<sub>a</sub> = June 21 is the date of northern summer solstice, and τ<sub>d</sub> = 15:00 is the local time of maximum diurnal temperature.

The first term in (3) on the right is the global mean of the exospheric temperature (of the order of 1000&nbsp; K). The second term [with P<sub>2</sub><sup>0</sup> = 0.5(3 sin<sup>2</sup>(φ)−1)] represents the heat surplus at lower latitudes and a corresponding heat deficit at higher latitudes (Fig. 2a). A thermal wind system develops with the wind toward the poles in the upper level and winds away from the poles in the lower level. The coefficient ΔT<sub>2</sub><sup>0</sup> ≈ 0.004 is small because Joule heating in the aurora regions compensates that heat surplus even during quiet magnetospheric conditions. During disturbed conditions, however, that term becomes dominant, changing sign so that now heat surplus is transported from the poles to the equator. The third term (with P<sub>1</sub><sup>0</sup> = sin φ) represents heat surplus on the summer hemisphere and is responsible for the transport of excess heat from the summer into the winter hemisphere (Fig. 2b). Its relative  amplitude is of the order ΔT<sub>1</sub><sup>0</sup> ≃ 0.13. The fourth term (with P<sub>1</sub><sup>1</sup>(φ) = cos φ) is the dominant diurnal wave (the tidal mode (1,−2)). It is responsible for the transport of excess heat from the daytime hemisphere into the nighttime hemisphere (Fig. 2d). Its relative amplitude is ΔT<sub>1</sub><sup>1</sup>≃ 0.15, thus on the order of 150&nbsp;K. Additional terms (e.g.,  semiannual, semidiurnal terms, and higher-order terms) must be added to eq.(3). However, they are of minor importance. Corresponding sums can be developed for density, pressure, and the various gas constituents.<ref name="Hedin"/><ref>von Zahn, U., et al., ESRO-4 model of global thermospheric composition and temperatures during low solar activity, Geophy. Res. Lett., ''4'', 33, 1977</ref>