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 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 TECU=10¹⁶·m^-2.

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 Positioning System satellites. TEC is strongly affected by solar activity.

Formulation

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.