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Total electron content

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Total electron content (TEC) is an important descriptive quantity for the <a href="Ionosphere" title="Ionosphere">ionosphere</a> of the Earth. TEC is the total number of <a href="Electron" title="Electron">electrons</a> integrated between two points, along a tube of one <a href="Meter_squared" class="mw-redirect" title="Meter squared">meter squared</a> <a href="Cross_section_(geometry)" title="Cross section (geometry)">cross section</a>, i.e., the electron <a href="Columnar_number_density" class="mw-redirect" title="Columnar number density">columnar number density</a>. It is often reported in multiples of the TEC unit, or TECU, defined as 1016 electrons per m2.<a href="#cite_note-1">[1]</a>: 100

TEC is significant in determining the <a href="Interplanetary_Scintillation" class="mw-redirect" title="Interplanetary Scintillation">scintillation</a> and <a href="Group_and_phase_delays" class="mw-redirect" title="Group and phase delays">group and phase delays</a> of a <a href="Radio_wave" title="Radio wave">radio wave</a> through a medium. Ionospheric TEC is characterized by observing carrier <a href="Phase_delay" class="mw-redirect" title="Phase delay">phase delays</a> of received radio signals transmitted from satellites located above the ionosphere, often using <a href="Global_Positioning_System" title="Global Positioning System">Global Positioning System</a> satellites. TEC is strongly affected by <a href="Solar_variation" class="mw-redirect" title="Solar variation">solar activity</a>.

<div class="mw-heading mw-heading2"><h2 id="Formulation">Formulation</h2></div>

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):

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<annotation encoding="application/x-tex">{\displaystyle {\rm {TEC}}=\int n_{e}(s)\,ds}</annotation>

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</math><img src="./4c66c8c693bd0ed5ef46c3da79a942e89c306107.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.605ex; height:5.676ex;" alt="{\displaystyle {\rm {TEC}}=\int n_{e}(s)\,ds}" loading="lazy"></dd></dl>

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.

<div class="mw-heading mw-heading2"><h2 id="Propagation_delay">Propagation delay</h2></div>

To first order, the ionospheric <a href="Radio_propagation" title="Radio propagation">radio propagation</a> effect is proportional to TEC and inversely proportional to the radio frequency f. The ionospheric <a href="Phase_delay" class="mw-redirect" title="Phase delay">phase delay</a> compared to propagation in vacuum reads:<a href="#cite_note-iers-2">[2]</a>: eq. (9.41)

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<annotation encoding="application/x-tex">{\displaystyle \tau _{p}^{\mathrm {iono} }=-\kappa {\frac {\mathrm {TEC} }{f^{2}}}}</annotation>

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</math><img src="./4f42b239e86edfc92a76f8cf2f99856a69ee1174.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.526ex; height:6.009ex;" alt="{\displaystyle \tau _{p}^{\mathrm {iono} }=-\kappa {\frac {\mathrm {TEC} }{f^{2}}}}" loading="lazy"></dd></dl>

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

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<annotation encoding="application/x-tex">{\displaystyle \tau _{g}^{\mathrm {iono} }=-\tau _{p}^{\mathrm {iono} }}</annotation>

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</math><img src="./3aa16f6e03badebd295a6a1d07dd51d7be285ba3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.917ex; height:3.176ex;" alt="{\displaystyle \tau _{g}^{\mathrm {iono} }=-\tau _{p}^{\mathrm {iono} }}" loading="lazy"></dd></dl>

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:<a href="#cite_note-iers-2">[2]</a>: eq.(9.21), (9.20), (9.19), (9.14) <a href="#cite_note-3">[3]</a>

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<annotation encoding="application/x-tex">{\displaystyle \kappa ={\frac {1}{4\pi \epsilon _{0}}}{\frac {q^{2}}{2\pi m_{e}}}={\frac {c^{2}r_{e}}{2\pi }}}</annotation>

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</math><img src="./26000029ec6b7c22024c870adf6d4f1bf4c10e1d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.179ex; height:6.176ex;" alt="{\displaystyle \kappa ={\frac {1}{4\pi \epsilon _{0}}}{\frac {q^{2}}{2\pi m_{e}}}={\frac {c^{2}r_{e}}{2\pi }}}" loading="lazy"></dd></dl>

where q, me, re are the <a href="Electron_charge" class="mw-redirect" title="Electron charge">electron charge</a>, <a href="Electron_mass" title="Electron mass">mass</a>, and <a href="Electron_radius" class="mw-redirect" title="Electron radius">radius</a>, respectively; c is the <a href="Vacuum_speed_of_light" class="mw-redirect" title="Vacuum speed of light">vacuum speed of light</a> and ϵ0 is the <a href="Vacuum_permittivity" title="Vacuum permittivity">vacuum permittivity</a>. The value of the constant is approximately κ ≈ 40.308193 m3·s−2;<a href="#cite_note-4">[4]</a><a href="#cite_note-5">[5]</a> 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.

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 <a href="Biases" class="mw-redirect" title="Biases">biases</a>.<a href="#cite_note-6">[6]</a> These small TEC variations are related to medium-scale traveling ionospheric disturbances (MSTIDs).<a href="#cite_note-7">[7]</a> These <a href="Ionospheric" class="mw-redirect" title="Ionospheric">ionospheric</a> disturbances are primarily generated by <a href="Gravity_waves" class="mw-redirect" title="Gravity waves">gravity waves</a> propagating upward from lower <a href="Atmosphere" title="Atmosphere">atmosphere</a>. <a href="#cite_note-8">[8]</a>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFB._Hofmann-WellenhofH._LichteneggerJ._Collins2001" class="citation book cs1">B. Hofmann-Wellenhof; H. Lichtenegger & J. Collins (2001). Global Positioning System: Theory and Practice. New York: Springer-Verlag. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-211-83534-0</bdi>.</cite>

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<li id="cite_note-iers-2">^ <a href="#cite_ref-iers_2-0">a</a> <a href="#cite_ref-iers_2-1">b</a> <cite class="citation cs2"><a rel="nofollow" class="external text" href="https://iers-conventions.obspm.fr/content/tn36.pdf">"9"</a> (PDF), <a href="IERS" class="mw-redirect" title="IERS">IERS Technical Note No.36</a></cite>

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<li id="cite_note-3"><a href="#cite_ref-3">^</a> <cite id="CITEREFHagen2009" class="citation book cs1">Hagen, Jon B. (2009-06-11). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9X5gy_mDamsC&pg=PA360">Radio-Frequency Electronics: Circuits and Applications</a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-88974-2</bdi>.</cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.google.com/search?q=(electron%20charge)^2%20/%20(8*pi^2%20*%20electron%20mass%20*%20permittivity%20of%20free%20space)">"Search results"</a>. www.google.com.</cite>

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<li id="cite_note-5"><a href="#cite_ref-5">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.google.com/search?q=(speed%20of%20light)^2%20*%202.8179403267e-15%20m%20/%20(2*pi)">"Search results"</a>. www.google.com.</cite>

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<li id="cite_note-6"><a href="#cite_ref-6">^</a> <cite id="CITEREFvan_de_KampPokhotelovKauristie2014" class="citation journal cs1">van de Kamp, M.; Pokhotelov, D.; Kauristie, K. (2014-12-17). <a rel="nofollow" class="external text" href="https://doi.org/10.5194%2Fangeo-32-1511-2014">"TID characterized using joint effort of incoherent scatter radar and GPS"</a>. Annales Geophysicae. 32 (12): 1511–1532. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014AnGeo..32.1511V">2014AnGeo..32.1511V</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5194%2Fangeo-32-1511-2014">10.5194/angeo-32-1511-2014</a>.</cite>

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<li id="cite_note-7"><a href="#cite_ref-7">^</a> <cite id="CITEREFTsugawaOtsukaCosterSaito2007" class="citation news cs1">Tsugawa, T.; Otsuka, Y.; Coster, A. J.; Saito, A. (2007-11-22). <a rel="nofollow" class="external text" href="https://doi.org/10.1029/2007GL031663">"Medium-scale traveling ionospheric disturbances detected with dense and wide TEC maps over North America"</a>. Geophysical Research Letters. Vol. 34, no. 22. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2007GL031663">10.1029/2007GL031663</a>. Retrieved 2023-01-23.</cite>

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<li id="cite_note-8"><a href="#cite_ref-8">^</a> <cite id="CITEREFGünzkoferPokhotelovStoberMann2023" class="citation journal cs1">Günzkofer, F.; Pokhotelov, D.; Stober, G.; Mann, I.; Vadas, S.L.; Becker, E.; et al. (2023-10-18). <a rel="nofollow" class="external text" href="https://doi.org/10.5194%2Fangeo-41-409-2023">"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"</a>. Annales Geophysicae. 41 (2): 409–428. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5194%2Fangeo-41-409-2023">10.5194/angeo-41-409-2023</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10037%2F32314">10037/32314</a>.</cite>

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