Total electron content (TEC) is an important descriptive quantity for the

ionosphere The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays ...

of the Earth. TEC is the total number of

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

s integrated between two points, along a tube of one meter squared cross section, i.e., the electron columnar number density. It is often reported in multiples of the so-called ''TEC unit'', defined as TECU10¹⁶el/m². TEC is significant in determining the scintillation and group and phase delays of a

radio wave Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (sho ...

through a medium. Ionospheric TEC is characterized by observing carrier phase delays of received radio signals transmitted from satellites located above the ionosphere, often using

Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite ...

satellites. TEC is strongly affected by solar activity.

Formulation

The TEC is path-dependent. By definition, it can be calculated by integrating along the path ''ds'' through the ionosphere with the location-dependent electron density ''n_e(s)'': : TEC =

\int n_e(s)\,ds

The ''vertical'' TEC (''VTEC'') is determined by integration of the electron density on a perpendicular to the ground standing route, the ''slant'' TEC (''STEC'') is obtained by integrating over any straight path.

Propagation delay

To first order, the ionospheric

radio propagation Radio propagation is the behavior of radio waves as they travel, or are propagated, from one point to another in vacuum, or into various parts of the atmosphere. As a form of electromagnetic radiation, like light waves, radio waves are affect ...

effect is proportional to TEC and inversely proportional to the radio frequency ''f''. The ionospheric phase delay compared to propagation in vacuum reads: :

\tau_p^\mathrm = -\kappa \frac

while the ionospheric group delay has the same magnitude but opposite sign: :

\tau_g^\mathrm = -\tau_p^\mathrm

The ionospheric delay is normally expressed in units of length (meters), assuming a delay duration (in seconds) multiplied by the vacuum speed of light (in m/s). The proportionality constant ''κ'' reads: :

\kappa = q^2 / (8 \pi^2 m_e \epsilon_0) = c^2 r_e / (2\pi)

where ''q'', ''m''_e, r_e are the electron charge,

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...

, and

radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...

, respectively; ''c'' is the vacuum speed of light and ''ϵ''₀ is the

vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

. The value of the constant is approximately ''κ'' ≈ 40.308193 m³·s⁻²; the units can be expressed equivalently as m·m²·Hz² to highlight the cancellation involved in yielding delays τ in meters, given ''f'' in Hz and TEC in m⁻².

References

Ionosphere Satellite navigation {{climate-stub