# Total electron content

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**Total electron content** (**TEC**) is an important descriptive quantity for the [ionosphere](/source/Ionosphere) of the Earth. TEC is the total number of [electrons](/source/Electron) integrated between two points, along a tube of one [meter squared](/source/Meter_squared) [cross section](/source/Cross_section_(geometry)), i.e., the electron [columnar number density](/source/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](/source/Interplanetary_Scintillation) and [group and phase delays](/source/Group_and_phase_delays) of a [radio wave](/source/Radio_wave) through a medium. Ionospheric TEC is characterized by observing carrier [phase delays](/source/Phase_delay) of received radio signals transmitted from satellites located above the ionosphere, often using [Global Navigation Satellite System](/source/Satellite_navigation) (GNSS) satellites. TEC is strongly affected by [solar activity](/source/Solar_variation).

## 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)*:

- {\rm 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](/source/Radio_propagation) effect is proportional to TEC and inversely proportional to the radio frequency *f*. The ionospheric [phase delay](/source/Phase_delay) compared to propagation in vacuum reads:[2]: eq. (9.41)

- \tau_p^\mathrm{iono} = -\kappa \frac{\mathrm{TEC}}{f^2}

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

- \tau_g^\mathrm{iono} = -\tau_p^\mathrm{iono}

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]

- \kappa = \frac{1}{4\pi\epsilon_0} \frac{q^2}{2\pi m_e} = \frac{c^2 r_e}{2\pi}

where *q*, *m*e, *r*e are the [electron charge](/source/Electron_charge), [mass](/source/Electron_mass), and [radius](/source/Electron_radius), respectively; *c* is the [vacuum speed of light](/source/Vacuum_speed_of_light) and *ϵ*0 is the [vacuum permittivity](/source/Vacuum_permittivity). The value of the constant is approximately *κ* ≈ 40.308193 m3·s−2;[4][5] 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.

The second-order term produces GNSS positioning errors on the order of millimeters. For its computation, see Hernández‐Pajares *et al.* (2007).[6]

## 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](/source/Biases).[7] These small TEC variations are related to medium-scale [traveling ionospheric disturbances](/source/Traveling_ionospheric_disturbance) (MSTIDs).[8] These [ionospheric](/source/Ionospheric) disturbances are primarily generated by [gravity waves](/source/Gravity_waves) propagating upward from lower [atmosphere](/source/Atmosphere). [9]

## 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.

1. ["9"](https://iers-conventions.obspm.fr/content/tn36.pdf), "IERS Technical Note No.36"

1. Hagen, Jon B. (2009-06-11). [*Radio-Frequency Electronics: Circuits and Applications*](https://books.google.com/books?id=9X5gy_mDamsC&pg=PA360). Cambridge University Press. ISBN 978-0-521-88974-2.

1. ["Search results"](https://www.google.com/search?q=(electron%20charge)^2%20/%20(8*pi^2%20*%20electron%20mass%20*%20permittivity%20of%20free%20space)). *www.google.com* [better source needed]

1. ["Search results"](https://www.google.com/search?q=(speed%20of%20light)^2%20*%202.8179403267e-15%20m%20/%20(2*pi)). *www.google.com* [better source needed]

1. Hernández‐Pajares, M.; Juan, J. M.; Sanz, J.; Orús, R. (August 2007). "Second‐order ionospheric term in GPS: Implementation and impact on geodetic estimates". *Journal of Geophysical Research: Solid Earth*. **112** (B8). [doi:10.1029/2006JB004707](https://doi.org/10.1029/2006JB004707)

1. van de Kamp, M.; Pokhotelov, D.; Kauristie, K. (2014-12-17). "TID characterized using joint effort of incoherent scatter radar and GPS". *Annales Geophysicae*. **32** (12): 1511–1532. [Bibcode:2014AnGeo..32.1511V](https://ui.adsabs.harvard.edu/abs/2014AnGeo..32.1511V). [doi:10.5194/angeo-32-1511-2014](https://doi.org/10.5194/angeo-32-1511-2014)

1. 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"](https://doi.org/10.1029/2007GL031663). *Geophysical Research Letters*. **34** (22). [doi:10.1029/2007GL031663](https://doi.org/10.1029/2007GL031663). Retrieved 2023-01-23.

1. Günzkofer, F.; Pokhotelov, D.; Stober, G.; Mann, I.; Vadas, S.L.; Becker, E. 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". *Annales Geophysicae*. **41** (2): 409–428. [doi:10.5194/angeo-41-409-2023](https://doi.org/10.5194/angeo-41-409-2023). [hdl:10037/32314](https://hdl.handle.net/10037/32314)

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