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Thermosphere

History

Prior to the space age, the only indirect access to the height region above about 100 km altitudes came from ionospheric and geomagnetic research. Electromagnetic waves below the VHF-range (VHF = very high frequencies; 30 - 300 MHz) reflected and attenuated in the ionospheric D-, E-, and F- layers depending on frequency, time of day, geographic location ,and solar activity can be observed on the ground . The geomagnetic activity, likewise observed on the ground, was attributed to upper atmospheric electric currents, known today as currents flowing within the ionospheric dynamo region and the magnetosphere . With the advent of the russian satellite Sputnik in 1957, observations of the Doppler effect of the satellite signal overhead allowed for the first time to determine continuously the orbital decay of the satellite and thus the atmospheric drag from which the variations of the thermospheric density could be derived. Mainly involved in these early measurements were L.G. Jacchia and J.W. Slowey (USA), D.G. King-Hele (Great Britain), and W. Priester and H.K. Pätzold (Germany). They discovered for the first time the large daily variations of the atmospheric density, its reaction on geomagnetically disturbanced conditions, etc.

Today, an armee of satellites measures directly the various components of the atmospheric gas. A full summary of early and present observations can be found in .

It is convenient to separate the atmospheric regions according to the two temperature minima at about 12 km altitude (the tropopause) and at about 80  (the mesopause) (Figure 1). The thermosphere (or the upper atmosphere) is the height region above 80 km, while the region between the tropospause and the mesopause is the middle atmosphere (stratosphere and mesosphere) where absorption of solar UV radiation generates the temperature maximum near 45 km altitude and causes the ozon layer.

Datei:Nomenclature of thermosphere.jpg

Figure 1. Nomenclature of atmospheric regions based on the profiles of electric conductivity (left), temperature (middle), and electron density (right)

The density of the Earth's atmosphere decreases nearly exponentially with altitude. The total mass of the atmosphere is M = ρ_A H  ≃ 10 kg/m² within a columne of 1 square meter above the ground (with ρ_A = 1.29 kg/m³ the atmospheric density on the ground at z = 0 m altitude, and H ≃ 8 km the average atmospheric scale height). 80% of that mass is already concentrated within the troposphere. The mass of the thermosphere above about 80 km is only 0.005 % of the total mass. Therefore, no significant energetic feedback from the thermosphere to the lower atmospheric regions can be expected.

Neutral Gas Constituents

Turbulence causes the air within the lower atmospheric regions below the turbopause at about 110 km to be a mixure of gases that does not change its composition. Its mean molecular weight is M ≈ 29 g/mol with molecular oxygen (O₂) and nitrogen (N₂) as the two dominant constituents. Above the turbopause, however, diffusive separation of the various constituents is significant, so that each constituent follows its own barometric height structure with a scale height inversely proportional to its molecular weight. The lighter constituents atomic oxygen (O), helium (He), and hydrogen (H) successively dominate above about 200 km altitude and vary with geographic location, time, and solar activity. The ratio N₂/O which is a measure of the electron density at the ionospheric F region is highly affected by these variations . These changes follow from the diffusion of the minor constituents through the major gas component during dynamic processes.

Energy Input

Energy Budget

The thermospheric temperature can be determined from density observations as well as from direct satellite measurements. The temperature vs. altitude z in Fig. 1 can be simulated by the so-called Bates profile

(1) {{pad|4em}} T = T_∞ - (T_∞ - T_o) exp{-s (z - z_o)}

with T_∞ the exospheric temperature above about 400 km altitude, T_o = 355 K, and z_o = 120 km reference temperature and height, and s an empirical parameter depending on T_∞ and decreasing with T_∞. That formula is derived from a simple equation of heat conduction. One estimates a total heat input of q_o≃ 0.8 to 1.6 mW/m² above z_o = 120 km altitude. In order to obtain equilibrium conditions, that heat input q_o above z_o is lost to the lower atmospheric regions by heat conduction.

The exospheric temperature T_∞ is a fair measurement of the solar XUV radiation. Since solar radio emission F at 10.7 cm wavelength is a good indicator of solar activity, on can apply the empirical formula for quiet magnetospheric conditions .

(2) {{pad|4em}} T_∞ ≃ 500 + 3.4 F_o

(with T_∞ in K, F_o in 10^{- 2} W m^-2 Hz^-1 (the Covington index) a value of F averaged over several solar cycles). The Covington index varies typically between 70 and 250 during a solar cycle, and never drops below about 50. Thus, T_∞ varies between about 740 and 1350 K. During very quiet magnetospheric conditions, the still continuously flowing magnetospheric energy input contributes by about 250 K to the residual temperature of 500 K in eq.(2). The rest of 250 K in eq.(2) can be attributed to atmospheric waves generated within the troposphere and dissipated within the lower thermosphere.

Solar XUV Radiation

The solar X-ray and extreme ultraviolet radiation (XUV) at wavelengths < 170 nm is almost completely absorbed within the thermosphere. This radiation causes the various ionospheric layers as well as a temperature increase at these heights (Figure 1). While the solar visible light (380 to 780 nm) is nearly constant with a variability of not more than about 0.1 % of the solar constant , the solar XUV radiation is highly variable in time and space. For instance, X-ray bursts associated with solar flares can dramatically increase their intensity over preflare levels by many orders of magnitude over a time span of tens of minutes. In the extreme ultraviolet, the Lyman α line at 121.6 nm represents an important source of ionization and dissociation at ionospheric D layer heights. . During quiet periods of solar activity, it alone contains more energy than the rest of the spectrum at lower wavelengths. Quasi-periodic changes of the order of 100 % and more with period of 27 days and 11 years belong to the prominent variations of solar XUV radiation. However, irregular fluctuations over all time scales are present all the time . During low solar activity, about one half of the total energy input into the thermosphere is thought to be solar XUV radiation. Evidently, that solar XUV energy input occurs only during daytime conditions, maximizing at the equator during equinox.

Solar Wind

A second source of energy input into the thermosphere is solar wind energy which is transfered to the magnetosphere by mechanisms that are not completely understood. One possible way to transfer energy is via a hydrodynamic dynamo process. Solar wind particles penetrate into the polar regions of the magnetosphere where the geomagnetic field lines are essentially vertically directed. An electric field is generated, directed from dawn to dusk. Along the last closed geomagnetic field lines with their footpoints within the auroral zones, field aligned electric currents can flow into the ionospheric dynamo region where they are closed by electric Pederson and Hall currents. Ohmic losses of the Pedersen currents heat the lower thermosphere (see e.g., Volland-Stern model). In addition, penetration of high energetic particles from the magnetosphere into the auroral regions enhance drastically the electric conductivity, further increasing the electric currents and thus Joule heating. During quiet magnetospheric activity, the magnetosphere contributes perhaps by a quarter to the energy budget of the thermosphere . This is about

250 K of the exospheric temperature in eq.(2). During very large activity, however, this heat input can increase substancially, by a factor of four or more. That solar wind input occurs mainly in the auroral regions during the day as well as during the night. 

Atmospheric Waves

Two kinds of large scale atmospheric waves within the lower atmosphere exist: internal waves with finite vertical wavelengths which can transport wave energy upward and external waves with infinitely large wavelengths which cannot transport wave energy . Atmospheric gravity waves and most of the atmospheric tides generated within the troposphere belong to the internal waves. Their density amplitudes increase exponentially with height, so that at the mesopause these waves become turbulent and their enery is dissipated (similar to breaking of ocean waves at the coast), thus contributing to the heating of the thermosphere by about 250 K in eq.(2). On the other hand, the fundamental diurnal tide labelled (1, -2) which is most efficiently excited by solar irradiance is an external wave and plays only a marginal role within lower and middle atmosphere. However, at thermospheric altitudes, it becomes the predominant wave. It drives the electric Sq-current within the ionospheric dynamo region between about 100 and 200  km height.

Heating, predominately by tidal waves, occurs mainly on the dayside hemisphere at lower and middle latitudes. The variability of this heating depends in general on the meteorological conditions within troposphere and middle atmosphere, and may not exceed about 50 %.

Dynamics

Within the thermosphere above about 150 km height, all atmospheric waves successively become external waves, and no signifiant vertical wave structure is visible. The atmospheric wave modes degenerate to the spherical functions P_n^m with n a meridional wave number and m the zonal wave number (m = 0: zonal mean flow; m = 1: diurnal tides; m = 2: semidiunal tides; etc.). The thermophere 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 supressed 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:

(3)   T(φ,λ,t) = T_∞{1 + ΔT₂⁰ P₂⁰(φ) + ΔT₁⁰ P₁⁰(φ) cos[ω_a(t - t_a)] + ΔT₁¹ P₁¹(φ) cos(τ - τ_d) + . . .}

Datei:Thermwavemode.jpg

Figure 2. Schematic meridian-height cross-section of circulation of (a) symmetric wind component (P₂⁰), (b) of antisymmetric wind component (P₁⁰), and (d) of symmetric diurnal wind component (P₁¹) at 3 h and 15 h local time. Upper right pannel (c) shows the horizontal wind vectors of the diurnal component in the northern hemisphere depending on local time

Here, it is φ latitude, λ longitude, and t time, ω_a the angular frequency of one year, ω_d the angular frequency of one solar day, and τ = ω_dt + λ the local time. t_a = June, 21 is the time of northern summer solstice, and τ_d = 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 K). The second term [with P₂⁰ = 0.5(3 sin²(φ)- 1)] represents the heat surplus at lower latitudes and a corresponding heat deficit at higher latitudes. A thermal wind system develops (Figure 2a) with winds toward the poles in the upper level and wind away from the poles in the lower level. The coefficient ΔT₂⁰ ≈ 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 P₁⁰ = 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. Its relative amplitude is of the order ΔT₁⁰ ≃ 0.13. The fourth term (with P₁¹(φ) = cos φ) is the dominant diurnal wave (the tidal mode (1,-2)). It is responsible for the transport of excess heat from the day time hemisphere into the night time hemisphere (Fig. 2d). Its relative amplitude is ΔT₁¹≃ 0.15, thus of the order of 150 K. Additional terms (e.g., semiannual, semidiurnal terms and higher order terms) must be added to eq.(3). They are, however, of minor importance. Corresponding sums can be developped for density, pressure, and the various gas constituents .

Thermospheric Storms

Contrary to solar XUV radiation, magnetospheric disturbances, indicated on the ground by geomagnetic variations, show an unpredictable impulsive character, from short periodic disturbances of the order of hours to long standing giant storms of several days's duration. The reaction of the thermosphere to a large magnetospheric storm is called thermospheric storm. Since the heat input into the thermosphere occurs at high latitudes (mainly into the auroral regions), the heat transport represented by the term P₂⁰ in eq.(3) is reversed. In addition, due to the impulsive form of the disturbance, higher order terms are generated which, however, possess short decay times and thus quickly disappear. The sum of these modes determines the "travel time" of the disturbance to the lower latitudes, and thus the response time of the thermosphere with respect to the magnetospheric disturbance. Important for the development of a ionospheric storm is the increase of the ratio N₂/O during a thermospheric storm at middle and higher latitude . An increase of N₂ increases the loss process of the ionospheric plasma and causes therefore a decrease of the electron density within the ionospheric F-layer (negative ionospheric storm).

References

[[Category:ionosphere]] [[Category:magnetosphere]] [[Category:electromagnetic wave propagation]] [[Category:atmospheric tides]] [[Category:ionospheric dynamo region]]