Thermosphere

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) ${\displaystyle T=T_{\mathrm{\infty }}-(T_{\mathrm{\infty }}-T_0)e^{-s(z-z_0)}}$

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, one can apply the empirical formula for quiet magnetospheric conditions.

(2) ${\displaystyle T_{\mathrm{\infty }}\simeq 500+3.4F_0}$

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 the 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 some time 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 XUV spectrum. Quasi-periodic changes of the order of 100% or greater, with periods 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 the low solar activity, about half of the total energy input into the thermosphere is thought to be solar XUV radiation. That solar XUV energy input occurs only during daytime conditions, maximizing at the equator during equinox.

Solar wind

The second source of energy input into the thermosphere is solar wind energy which is transferred to the magnetosphere by mechanisms that are not well understood. One possible way to transfer energy is via a hydrodynamic dynamo process. Solar wind particles penetrate 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 Pedersen and Hall currents. Ohmic losses of the Pedersen currents heat the lower thermosphere (see e.g., Magnetospheric electric convection field). Also, 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 the quiet magnetospheric activity, the magnetosphere contributes perhaps by a quarter to the thermosphere's energy budget. This is about 250 K of the exospheric temperature in eq.(2). During the very large activity, however, this heat input can increase substantially, by a factor of four or more. That solar wind input occurs mainly in the auroral regions during both day and 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 that 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 energy 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 labeled (1, −2) which is most efficiently excited by solar irradiance is an external wave and plays only a marginal role within the 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 at lower and middle latitudes. The variability of this heating depends on the meteorological conditions within the troposphere and middle atmosphere, and may not exceed about 50%.

Dynamics

Within the thermosphere above an altitude of about 150 kilometres (93 mi), all atmospheric waves successively become external waves, and no significant vertical wave structure is visible. The atmospheric wave modes degenerate to the spherical functions P_n^m 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:

(3) ${\displaystyle T(\phi ,\lambda ,t)=T_{\mathrm{\infty }}\{1+\mathrm{\Delta }{T}_2^0{P}_2^0(\phi )+\mathrm{\Delta }{T}_1^0{P}_1^0(\phi )\cos [{\omega }_a(t-t_a)]+\mathrm{\Delta }{T}_1^1{P}_1^1(\phi )\cos (\tau -{\tau }_d)+\cdots \}}$

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 date 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 (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 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 (Fig. 2b). 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 daytime hemisphere into the nighttime hemisphere (Fig. 2d). Its relative amplitude is ΔT₁¹≃ 0.15, thus on the order of 150 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.

Thermospheric storms

In contrast 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' duration. The reaction of the thermosphere to a large magnetospheric storm is called a thermospheric storm. Since the heat input into the thermosphere occurs at high latitudes (mainly into the auroral regions), the heat transport is represented by the term P₂⁰ in eq.(3) is reversed. Also, 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 an 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).

Climate change

A contraction of the thermosphere has been observed as a possible result in part due to increased carbon dioxide concentrations, the strongest cooling and contraction occurring in that layer during solar minimum. The most recent contraction in 2008–2009 was the largest such since at least 1967.

Phenomena in the thermosphere

ELVES are a type of upper-atmospheric lightning that occur at the lower boundary of the thermosphere. They often appear at 100 km (62 mi) above the ground over thunderstorms as an expanding and flat dimly red glow around 400 km (250 mi) in diameter that lasts for typically one millisecond. ELVES were first recorded on a Space Shuttle mission off French Guiana on October 7, 1990.

ELVES is a whimsical acronym for "emissions of light and very low frequency perturbations due to electromagnetic pulse sources." This refers to the process by which the light is generated; the excitation of nitrogen molecules due to electron collisions (the electrons possibly having been energized by the electromagnetic pulse caused by a discharge from an underlying thunderstorm).