Total electron content

Short description: Descriptive quantity of the ionosphere

Contour plot of the TEC above the contiguous United States on 24 November 2013 from 21:15 to 21:30 UTC

Total electron content (TEC) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons 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 TEC unit, or TECU, defined as 1016 electrons per m2.[1]: 100

TEC is significant in determining the scintillation and group and phase delays of a radio wave 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 Navigation Satellite System (GNSS) satellites. TEC is strongly affected by solar activity.

## Contents

* 1 Formulation
* 2 Propagation delay
* 3 Typical values
* 4 References

## 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 ne(s):

TEC=∫ne(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 effect is proportional to TEC and inversely proportional to the radio frequency f. The ionospheric phase delay compared to propagation in vacuum reads:[2]: eq. (9.41)

τpiono=−κTECf2

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

τgiono=−τpiono

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:[2]: eq.(9.21), (9.20), (9.19), (9.14) [3]

κ=14πϵ0q22πme=c2re2π

where q, me, re are the electron charge, mass, and radius, respectively; c is the vacuum speed of light and ϵ0 is the vacuum permittivity. The value of the constant is approximately κ ≈ 40.308193 m3·s−2;[4]Cite error: Closing `</ref>` missing for `<ref>` tag

## Typical values

Typical daytime values of TEC are expressed on the scale from 0 to 100 TEC units. However, very small variations of 0.1-0.5 TEC units can be also extracted under the assumption of relatively constant observational biases.[5] These small TEC variations are related to medium-scale traveling ionospheric disturbances (MSTIDs).[6] These ionospheric disturbances are primarily generated by gravity waves propagating upward from lower atmosphere. [7]

## References

1. ↑ B. Hofmann-Wellenhof; H. Lichtenegger; J. Collins (2001). Global Positioning System: Theory and Practice. New York: Springer-Verlag. ISBN 978-3-211-83534-0.
2. ↑ 2.0 2.1 "9", IERS Technical Note No.36, https://iers-conventions.obspm.fr/content/tn36.pdf
3. ↑ Hagen, Jon B. (2009-06-11) (in en). Radio-Frequency Electronics: Circuits and Applications. Cambridge University Press. ISBN 978-0-521-88974-2. https://books.google.com/books?id=9X5gy_mDamsC&pg=PA360.
4. ↑ "Search results". https://www.google.com/search?q=(electron charge)^2 / (8*pi^2 * electron mass * permittivity of free space).
5. ↑ van de Kamp, M.; Pokhotelov, D.; Kauristie, K. (2014-12-17). "TID characterized using joint effort of incoherent scatter radar and GPS" (in en). Annales Geophysicae 32 (12): 1511–1532. doi:10.5194/angeo-32-1511-2014. Bibcode: 2014AnGeo..32.1511V.
6. ↑ Tsugawa, T.; Otsuka, Y.; Coster, A. J.; Saito, A. (2007-11-22). "Medium-scale traveling ionospheric disturbances detected with dense and wide TEC maps over North America" (in en). Geophysical Research Letters 34 (22). doi:10.1029/2007GL031663. https://doi.org/10.1029/2007GL031663.
7. ↑ Günzkofer, F. et al. (2023-10-18). "Inferring neutral winds in the ionospheric transition region from atmospheric-gravity-wave traveling-ionospheric-disturbance (AGW-TID) observations with the EISCAT VHF radar and the Nordic Meteor Radar Cluster" (in en). Annales Geophysicae 41 (2): 409–428. doi:10.5194/angeo-41-409-2023.

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