Total electron content

Total electron content (or TEC) is an important descriptive quantity for the ionosphere of the Earth. TEC is the total number of electrons present along a path between two points, with units of electrons per square meter, where 10¹⁶ electrons/m² = 1 TEC unit (TECU).

TEC is significant in determining the scintillation and group delay 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 Positioning System satellites. TEC is strongly affected by solar activity.

Derivation

To first order, the observed phase of a radio source is retarded by an amount proportional to TEC and inversely proportional to the radio frequency. This can be written

$\Phi ^{\mathrm {iono} }=-{\frac {k}{\nu }}\cdot \mathrm {TECU}$

where k is a proportionality constant equal to 1.3445x10⁹ cyc·Hz/TECU = 10¹⁶·c·r_e/(2π), where c is the speed of light and r_e is the electron radius. Dividing the above equation by the radio frequency gives the ionospheric phase delay

$\tau _{p}^{\mathrm {iono} }=-{\frac {k}{\nu ^{2}}}\cdot \mathrm {TECU}$

while taking the derivative with respect to frequency gives the ionospheric group delay

$\tau _{g}^{\mathrm {iono} }={\frac {k}{\nu ^{2}}}\cdot \mathrm {TECU}$

Note the ionospheric phase and group delays have the same magnitude, but opposite sign.