Total electron content

{{Short description|Descriptive quantity of the ionosphere}} thumbnail|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 {{10^|16}}&nbsp;electrons&nbsp;per&nbsp;m².<ref>{{cite book |title=Global Positioning System: Theory and Practice|date=2001|publisher=Springer-Verlag|location=New York|isbn=978-3-211-83534-0|author=B. Hofmann-Wellenhof|author2=H. Lichtenegger|author3=J. Collins|name-list-style=amp}}</ref>{{rp|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.

==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 ''n_e(s)'': :<math>{\rm TEC} = \int n_e(s)\,ds</math>

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:<ref name=iers>{{citation| title= IERS Technical Note No.36| chapter=9| contribution-url=https://iers-conventions.obspm.fr/content/tn36.pdf | title-link=IERS}}</ref>{{rp|eq. (9.41)}} :<math>\tau_p^\mathrm{iono} = -\kappa \frac{\mathrm{TEC}}{f^2} </math> while the ionospheric group delay has the same magnitude but opposite sign: :<math>\tau_g^\mathrm{iono} = -\tau_p^\mathrm{iono}</math>

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:<ref name=iers/>{{rp|eq.(9.21),(9.20),(9.19),(9.14)}}<ref>{{Cite book |last=Hagen |first=Jon B. |url=https://books.google.com/books?id=9X5gy_mDamsC&pg=PA360 |title=Radio-Frequency Electronics: Circuits and Applications |date=2009-06-11 |publisher=Cambridge University Press |isbn=978-0-521-88974-2 |language=en}}</ref> :<math>\kappa = \frac{1}{4\pi\epsilon_0} \frac{q^2}{2\pi m_e} = \frac{c^2 r_e}{2\pi} </math> where ''q'', ''m''_e, ''r''_e are the electron charge, mass, and radius, respectively; ''c'' is the vacuum speed of light and ''ϵ''₀ is the vacuum permittivity. The value of the constant is approximately ''κ'' ≈ 40.308193 m³·s⁻²;<ref>{{cite web |url=https://www.google.com/search?q=(electron%20charge)^2%20/%20(8*pi^2%20*%20electron%20mass%20*%20permittivity%20of%20free%20space) |title=Search results |website=www.google.com}} {{Better source needed|date=August 2022}}</ref><ref>{{cite web |url=https://www.google.com/search?q=(speed%20of%20light)^2%20*%202.8179403267e-15%20m%20/%20(2*pi) |title=Search results |website=www.google.com}} {{Better source needed|date=August 2022}}</ref> 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).<ref>{{cite journal |last1=Hernández‐Pajares |first1=M. |last2=Juan |first2=J. M. |last3=Sanz |first3=J. |last4=Orús |first4=R. |title=Second‐order ionospheric term in GPS: Implementation and impact on geodetic estimates |journal=Journal of Geophysical Research: Solid Earth |date=August 2007 |volume=112 |issue=B8 |doi=10.1029/2006JB004707 |doi-access=free}}</ref>

== 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.<ref>{{Cite journal|title= TID characterized using joint effort of incoherent scatter radar and GPS|journal=Annales Geophysicae|date=2014-12-17 |doi= 10.5194/angeo-32-1511-2014|language=en|last1= van de Kamp|first1= M.|last2= Pokhotelov|first2= D.|last3= Kauristie|first3= K.|volume= 32|issue= 12|pages= 1511–1532|bibcode= 2014AnGeo..32.1511V|doi-access= free}}</ref> These small TEC variations are related to medium-scale traveling ionospheric disturbances (MSTIDs).<ref>{{Cite news|url= https://doi.org/10.1029/2007GL031663 |title= Medium-scale traveling ionospheric disturbances detected with dense and wide TEC maps over North America|journal=Geophysical Research Letters|date=2007-11-22 |doi= 10.1029/2007GL031663|access-date=2023-01-23|language=en|last1= Tsugawa|first1= T.|last2= Otsuka|first2= Y.|last3= Coster|first3= A. J.|last4= Saito|first4= A.|volume= 34|issue= 22}}</ref> These ionospheric disturbances are primarily generated by gravity waves propagating upward from lower atmosphere. <ref>{{Cite journal|title=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|journal=Annales Geophysicae|date=2023-10-18 |doi= 10.5194/angeo-41-409-2023|language=en|last1= Günzkofer|first1= F.|last2= Pokhotelov|first2= D.|last3= Stober|first3=G.|last4=Mann|first4=I.|last5=Vadas|first5=S.L.|last6=Becker|first6=E.|display-authors=etal|volume= 41|issue= 2|pages= 409–428|doi-access= free|hdl=10037/32314|hdl-access=free}}</ref>

==References== {{Reflist}}

Category:Ionosphere Category:Satellite navigation