Editing International Atomic Time (section)

== Operation ==
TAI is a [[weighted average]] of the time kept by over 450 [[atomic clock]]s in over 80 national laboratories worldwide.<ref name="Time n.d.">{{cite book
|title = BIPM Annual Report on Time Activities
|url = https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|lang=en
|page = 9
|publisher = International Bureau of Weights and Measures
|volume = 15
|date = 2020
|isbn = 978-92-822-2280-5
|issn = 1994-9405
|access-date = 16 June 2022
|archive-url=https://web.archive.org/web/20210814134522/https://webtai.bipm.org/ftp/pub/tai/annual-reports/bipm-annual-report/annual_report_2020.pdf
|archive-date=14 August 2021
|url-status=live}}</ref> The majority of the clocks involved are [[caesium clock]]s; the [[International System of Units]] (SI) definition of the [[second]] is based on [[caesium]].{{sfn|McCarthy|Seidelmann|2009|p=207, 214}} The clocks are compared using [[GPS]] signals and [[two-way satellite time and frequency transfer]].<ref>{{citation |title=Explanatory Supplement of BIPM Circular T |publisher=[[International Bureau of Weights and Measures]] |url=https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://webtai.bipm.org/ftp/pub/tai/other-products/notes/explanatory_supplement_v0.6.pdf |archive-date=2022-10-09 |url-status=live |date=12 July 2021 |access-date=16 June 2022}}</ref>  Due to the [[signal averaging]] TAI is an [[order of magnitude]] more stable than its best constituent clock.

The participating institutions each broadcast, in [[real-time data|real time]], a frequency signal with [[timecode]]s, which is their estimate of TAI.  Time codes are usually published in the form of UTC, which differs from TAI by a well-known integer number of seconds.  These time scales are denoted in the form ''UTC(NPL)'' in the UTC form, where ''NPL'' here identifies the [[National Physical Laboratory, UK]]. The TAI form may be denoted ''TAI(NPL)''.  The latter is not to be confused with ''TA(NPL)'', which denotes an independent atomic time scale, not synchronised to TAI or to anything else.

The clocks at different institutions are regularly compared against each other.  The [[International Bureau of Weights and Measures]] (BIPM, France), combines these measurements to retrospectively calculate the weighted average that forms the most stable time scale possible.<ref name="Time n.d."/>  This combined time scale is published monthly in "Circular T",<ref>{{citation |title=Circular T |publisher=[[International Bureau of Weights and Measures]] |url=https://www.bipm.org/en/time-ftp/circular-t |access-date=16 June 2022}}</ref> and is the [[canonical form|canonical]] TAI.  This time scale is expressed in the form of tables of differences UTC − UTC(''k'') (equal to TAI − TAI(''k'')) for each participating institution ''k''.  The same circular also gives tables of TAI − TA(''k''), for the various unsynchronised atomic time scales.

Errors in publication may be corrected by issuing a revision of the faulty Circular T or by errata in a subsequent Circular T.  Aside from this, once published in Circular T, the TAI scale is not revised.  In hindsight, it is possible to discover errors in TAI and to make better estimates of the true proper time scale.  Since the published circulars are definitive, better estimates do not create another version of TAI; it is instead considered to be creating a better realisation of [[Terrestrial Time]] (TT).