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In 1972, the leap-second system was introduced so that the UTC seconds could be set exactly equal to the standard SI second, while still maintaining the UTC time of day and changes of UTC date synchronized with those of UT1.<ref name="USNO"/> By then, the UTC clock was already 10 seconds behind TAI, which had been synchronized with UT1 in 1958, but had been counting true SI seconds since then. After 1972, both clocks have been ticking in SI seconds, so the difference between their displays at any time is 10 seconds plus the total number of leap seconds that have been applied to UTC as of that time; {{as of|2024|lc=on}}, 27 leap seconds have been applied to UTC, so the difference is 10 + 27 = 37 seconds. The most recent leap second was on December 31, 2016.
==Rationale==
{{See also|ΔT (timekeeping)}}▼
[[File:Deviation of day length from SI day.svg|thumb|left|Deviation of day length from SI based day with shorter days resulting from faster planetary rotation.]]▼
Leap seconds are irregularly spaced because the Earth's rotation speed changes irregularly. Indeed, the Earth's rotation is quite unpredictable in the long term, which explains why leap seconds are announced only six months in advance.▼
A [[mathematical model]] of the variations in the length of the solar day was developed by [[F. R. Stephenson]] and L. V. Morrison,<ref name="SM1995" /> based on records of [[eclipse]]s for the period 700 BC to 1623, telescopic observations of [[occultation]]s for the period 1623 until 1967 and atomic clocks thereafter. The model shows a steady increase of the mean solar day by 1.70 ms (±0.05 ms) per century, plus a periodic shift of about 4 ms amplitude and [[period (physics)|period]] of about 1,500 yr.<ref name="SM1995" /> Over the last few centuries, rate of lengthening of the mean solar day has been about 1.4 ms per century, being the sum of the periodic component and the overall rate.<ref>{{cite web |
The main reason for the slowing down of the Earth's rotation is [[tidal friction]], which alone would lengthen the day by 2.3 ms/century.<ref name="SM1995" /> Other contributing factors are the movement of the Earth's [[crust (geology)|crust]] relative to its [[planetary core|core]], changes in [[mantle convection]], and any other events or processes that cause a significant redistribution of mass. These processes change the Earth's [[moment of inertia]], affecting the rate of rotation due to the conservation of [[angular momentum]]. Some of these redistributions increase Earth's rotational speed, shorten the solar day and oppose tidal friction. For example, [[glacial rebound]] shortens the solar day by 0.6 ms/century and the [[2004 Indian Ocean earthquake and tsunami|2004 Indian Ocean earthquake]] is thought to have shortened it by 2.68 microseconds.<ref>{{cite web |last1=Cook-Anderson |first1=Gretchen |last2=Beasley |first2=Dolores |date=10 January 2005 |title=NASA Details Earthquake Effects on the Earth |url=http://www.nasa.gov/home/hqnews/2005/jan/HQ_05011_earthquake.html
It is a mistake, however, to consider leap seconds as indicators of a slowing of Earth's rotation rate; they are indicators of the accumulated difference between atomic time and time measured by Earth rotation.<ref>{{cite web |last1=Chester |first1=Geoff |date=15 June 2015 |title=Wait a second… 2015 will be a little longer |url=https://www.doncio.navy.mil/chips/ArticleDetails.aspx?ID=6471 |access-date=4 March 2021 |website=CHIPS Articles: The Department of the Navy's Information Technology Magazine
In 2021, it was reported that Earth was spinning faster in 2020 and experienced the 28 shortest days since 1960, each of which lasted less than {{val|86399.999}} seconds.<ref>{{cite web |last1=Jones |first1=Graham |last2=Bikos |first2=Konstantin |date=6 January 2021 |orig-date=2020-12-23 |title=Earth is in a hurry in 2020 |url=
==Procedure==
{| class="wikitable" style="float:right; margin-right: 0; margin-left: 1em; text-align: center;"
|+ Announced leap seconds to date<ref>{{cite web|title=TAI−UTC (1972-01-01 – 2024-06-28)|date=4 July 2023|access-date=4 July 2023|url=https://hpiers.obspm.fr/iers/bul/bulc/Leap_Second.dat}}</ref>
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Unlike [[leap day]]s, which begin after 28 February, 23:59:59 local time,{{efn|Only the [[Gregorian calendar]]'s leap days begin after 28 February. The leap days of other calendars begin at different local times in their own years ([[Ethiopian calendar]], [[Iranian calendars]], [[Indian national calendar]], etc.).}} UTC leap seconds occur simultaneously worldwide; for example, the leap second on 31 December 2005, 23:59:60 UTC was 31 December 2005, 18:59:60 (6:59:60 p.m.) in [[U.S. Eastern Standard Time]] and 1 January 2006, 08:59:60 (a.m.) in [[Japan Standard Time]].
When it is mandated, a positive leap second is inserted between second 23:59:59 of a chosen UTC [[calendar date]] and second 00:00:00 of the following date. The definition of UTC states that the last day of December and June are preferred, with the last day of March or September as second preference, and the last day of any other month as third preference.<ref>{{cite web|url=https://www.itu.int/rec/R-REC-TF.460-6-200202-I/en|title=International Telecommunication Union Radiocommunications sector recommendation TF.460-6: Standard-frequency and time-signal emissions|access-date=9 February 2017|url-status=live|archive-url=https://web.archive.org/web/20161017185018/https://www.itu.int/rec/R-REC-TF.460-6-200202-I/en|archive-date=17 October 2016}}</ref> All leap seconds (as of 2019) have been scheduled for either 30 June or 31 December. The extra second is displayed on UTC clocks as 23:59:60. On clocks that display local time tied to UTC, the leap second may be inserted at the end of some other hour (or half-hour or quarter-hour), depending on the local time zone. A negative leap second would suppress second 23:59:59 of the last day of a chosen month so that second 23:59:58 of that date would be followed immediately by second 00:00:00 of the following date. Since the introduction of leap seconds, the mean solar day has outpaced atomic time only for very brief periods and has not triggered a negative leap second.
Recent changes to the Earth's rotation rate have made it more likely that a negative leap second will be required before the abolition of leap seconds in 2035.<ref>{{Cite web |last=Matsakis |first=Demetrios |date=September 21, 2022 |title=Will we have a negative leap second? |url=https://www.gps.gov/cgsic/meetings/2022/matsakis.pdf |access-date=3 June 2024 |website=gps.gov}}</ref><ref>{{Cite journal |last=Agnew |first=Duncan Carr |date=April 2024 |title=A global timekeeping problem postponed by global warming |url=https://www.nature.com/articles/s41586-024-07170-0 |journal=Nature |language=en |volume=628 |issue=8007 |pages=333–336 |doi=10.1038/s41586-024-07170-0 |pmid=38538793 |bibcode=2024Natur.628..333A |issn=1476-4687}}</ref>
==Future==
▲{{See also|ΔT (timekeeping)}}
▲[[File:Deviation of day length from SI day.svg|thumb|left|Deviation of day length from SI based day with shorter days resulting from faster planetary rotation.]]
▲Leap seconds are irregularly spaced because the Earth's rotation speed changes irregularly. Indeed, the Earth's rotation is quite unpredictable in the long term, which explains why leap seconds are announced only six months in advance.
▲A [[mathematical model]] of the variations in the length of the solar day was developed by [[F. R. Stephenson]] and L. V. Morrison,<ref name=SM1995/> based on records of [[eclipse]]s for the period 700 BC to 1623, telescopic observations of [[occultation]]s for the period 1623 until 1967 and atomic clocks thereafter. The model shows a steady increase of the mean solar day by 1.70 ms (±0.05 ms) per century, plus a periodic shift of about 4 ms amplitude and [[period (physics)|period]] of about 1,500 yr.<ref name=SM1995/> Over the last few centuries, rate of lengthening of the mean solar day has been about 1.4 ms per century, being the sum of the periodic component and the overall rate.<ref>{{cite web|url=http://www.ucolick.org/~sla/leapsecs/dutc.html|title=Extrapolations of the difference (TI – UT1)|work=ucolick.org|date=8 June 2011|author=Steve Allen|access-date=29 February 2016|url-status=live|archive-url=https://web.archive.org/web/20160304193859/http://www.ucolick.org/~sla/leapsecs/dutc.html|archive-date=4 March 2016}}</ref>
▲The main reason for the slowing down of the Earth's rotation is [[tidal friction]], which alone would lengthen the day by 2.3 ms/century.<ref name=SM1995/> Other contributing factors are the movement of the Earth's [[crust (geology)|crust]] relative to its [[planetary core|core]], changes in [[mantle convection]], and any other events or processes that cause a significant redistribution of mass. These processes change the Earth's [[moment of inertia]], affecting the rate of rotation due to the conservation of [[angular momentum]]. Some of these redistributions increase Earth's rotational speed, shorten the solar day and oppose tidal friction. For example, [[glacial rebound]] shortens the solar day by 0.6 ms/century and the [[2004 Indian Ocean earthquake and tsunami|2004 Indian Ocean earthquake]] is thought to have shortened it by 2.68 microseconds.<ref>{{cite web|last1=Cook-Anderson |first1=Gretchen |last2=Beasley |first2=Dolores |url=http://www.nasa.gov/home/hqnews/2005/jan/HQ_05011_earthquake.html|title=NASA Details Earthquake Effects on the Earth|publisher=[[National Aeronautics and Space Administration]] (press release).|date=10 January 2005|url-status=live|archive-url=https://web.archive.org/web/20110127163105/http://www.nasa.gov/home/hqnews/2005/jan/HQ_05011_earthquake.html|archive-date=27 January 2011}}</ref>
▲It is a mistake, however, to consider leap seconds as indicators of a slowing of Earth's rotation rate; they are indicators of the accumulated difference between atomic time and time measured by Earth rotation.<ref>{{cite web |last1=Chester |first1=Geoff |title=Wait a second… 2015 will be a little longer |url=https://www.doncio.navy.mil/chips/ArticleDetails.aspx?ID=6471 |website=CHIPS Articles: The Department of the Navy's Information Technology Magazine |date=15 June 2015|access-date=4 March 2021}}</ref> The plot at the top of this section shows that in 1972 the average length of day was approximately {{val|86400.003}} seconds and in 2016 it was approximately {{val|86400.001}} seconds, indicating an overall increase in Earth's rotation rate over that time period. Positive leap seconds were inserted during that time because the annual average length of day remained greater than {{val|86400}} SI seconds, not because of any slowing of Earth's rotation rate.<ref>{{cite web |last1=Plait |first1=Phil |title=Followup: Leap Seconds |url=https://www.discovermagazine.com/the-sciences/followup-leap-seconds |website=Discover Magazine: Bad Astronomy |date=31 December 2008|access-date=5 March 2021}}</ref>
▲In 2021, it was reported that Earth was spinning faster in 2020 and experienced the 28 shortest days since 1960, each of which lasted less than {{val|86399.999}} seconds.<ref>{{cite web |last1=Jones |first1=Graham |last2=Bikos |first2=Konstantin |title=Earth is in a hurry in 2020 |url= https://www.timeanddate.com/time/earth-faster-rotation.html |website=timeanddate.com |date=6 January 2021 |orig-date=2020-12-23|access-date=6 March 2021}}</ref> This caused engineers worldwide to discuss a negative leap second and other possible timekeeping measures, some of which could eliminate leap seconds.<ref>{{cite news |last1=Knapton |first1=Sarah |title=The Earth is spinning faster now than at any time in the past half century |url=https://www.telegraph.co.uk/news/2021/01/04/earth-spinning-faster-now-time-past-half-century/ |archive-url=https://ghostarchive.org/archive/20220112/https://www.telegraph.co.uk/news/2021/01/04/earth-spinning-faster-now-time-past-half-century/ |archive-date=12 January 2022 |url-access=subscription |url-status=live |access-date=11 February 2021 |work=[[The Daily Telegraph]] |date=4 January 2021}}{{cbignore}}</ref> The shortest day ever recorded was 29 June 2022, at 1.59 milliseconds less than 24 hours.<ref name="NHM 270324">{{cite news |url=https://www.nhm.ac.uk/discover/news/2024/march/climate-change-causing-days-get-longer-slowing-down-earth.html |title=Climate change is causing days to get longer by slowing down the Earth |first=James |last=Ashworth |date= 27 March 2024 |publisher=Natural History Museum |___location=London}}</ref> In a 2024 paper published in [[Nature (journal)|''Nature'']], Duncan Agnew of the [[Scripps Institution of Oceanography]] projects that the water from increasing [[ice cap]] melting will migrate to the equator and thus cause the rate of rotation to slow down again.<ref name="NHM 270324" />
{{More citations needed|section|date=December 2023}}
The TAI and UT1 time scales are precisely defined, the former by atomic clocks (and thus independent of Earth's rotation) and the latter by astronomical observations (that measure actual planetary rotation and thus the solar time at the [[IERS Reference Meridian]] at Greenwich. UTC (on which [[civil time]] is usually based) is a compromise, stepping with atomic seconds but periodically reset by a leap second to match UT1.
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The irregularity and unpredictability of UTC leap seconds is problematic for several areas, especially [[computing]] (see [[#Issues created by insertion (or removal) of leap seconds|below]]). With increasing requirements for [[timestamp]] accuracy in systems such as process automation and [[high-frequency trading]],<ref>{{Cite news| title = Time Split to the Nanosecond Is Precisely What Wall Street Wants |newspaper =[[The New York Times]]| access-date = 13 December 2022| url = https://www.nytimes.com/2018/06/29/technology/computer-networks-speed-nasdaq.html |date = 29 June 2018}}</ref> this raises a number of issues. Consequently, the long-standing practice of inserting leap seconds is under review by the relevant international standards body.<ref>{{Cite web |last=Dwyer |first=Colin |date=29 December 2016 |title=With A Leap Second, 2016 Promises To Linger Just A Little Bit Longer |url=https://www.npr.org/sections/thetwo-way/2016/12/29/507422729/with-a-leap-second-2016-promises-to-linger-just-a-little-bit-longer |url-status=live |archive-url=https://web.archive.org/web/20230102214327/https://www.npr.org/sections/thetwo-way/2016/12/29/507422729/with-a-leap-second-2016-promises-to-linger-just-a-little-bit-longer |archive-date=2 January 2023 |access-date=24 February 2023 |website=[[NPR]]}}</ref>
===
{{anchor|Proposal to abolish leap seconds}}
On 5 July 2005, the Head of the Earth Orientation Center of the IERS sent a notice to IERS Bulletins C and D subscribers, soliciting comments on a U.S. proposal before the ITU-R Study Group 7's WP7-A to eliminate leap seconds from the UTC broadcast standard before 2008 (the [[ITU-R]] is responsible for the definition of UTC).{{efn|''[[The Wall Street Journal]]'' noted that the proposal was considered by a U.S. official at the time to be a "private matter internal to the ITU."<ref>{{cite news |url=https://www.wsj.com/articles/SB112258962467199210?mod=home_page_one_us |title=Why the U.S. Wants To End the Link Between Time and Sun |newspaper=The Wall Street Journal |access-date=31 October 2017 |url-status=live |archive-url=https://web.archive.org/web/20171107010404/https://www.wsj.com/articles/SB112258962467199210?mod=home_page_one_us |archive-date=7 November 2017}}</ref>}} It was expected to be considered in November 2005, but the discussion has since been postponed.<ref>{{cite news |url=http://news.bbc.co.uk/2/hi/science/nature/4420084.stm |title=Leap second talks are postponed |work=[[BBC News]] |access-date=31 October 2017 |url-status=live |archive-url=https://web.archive.org/web/20171107031708/http://news.bbc.co.uk/2/hi/science/nature/4420084.stm |archive-date=7 November 2017}}</ref> Under the proposal, leap seconds would be technically replaced by leap hours as an attempt to satisfy the legal requirements of several ITU-R member nations that civil time be astronomically tied to the Sun.
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ITU World Radiocommunication Conference 2023 (WRC-23), which was held in Dubai (United Arab Emirates) from 20 November to 15 December 2023 formally recognized the [https://www.bipm.org/en/cgpm-2022/resolution-4 Resolution 4] of the 27th CGPM (2022) which decides that the maximum value for the difference (UT1-UTC) will be increased in, or before, 2035.<ref>{{cite web |url=https://www.bipm.org/en/-/2023-12-12-wrc-dubai |title=ITU-R and BIPM work together at the World Radiocommunication Conference |website=BIPM}}</ref>
==Problems==
[[File:ChronyControl screenshot.webp|thumb|upright=1.5|Screenshot of [[Chrony]]Control on [[macOS]], showing an insert second announcement by NTP on 30 June 2015.]]
===
To compute the elapsed time in seconds between two given UTC dates requires the consultation of a table of leap seconds, which needs to be updated whenever a new leap second is announced. Since leap seconds are known only 6 months in advance, time intervals for UTC dates further in the future cannot be computed.
===Missing
Although [[BIPM]] announces a leap second 6 months in advance, most time distribution systems ([[SNTP]], [[IRIG-B]], [[Precision Time Protocol|PTP]]) announce leap seconds at most 12 hours in advance,{{citation needed|date=October 2019}}<ref>{{Cite tech report |title=A Resilient Architecture for the Realization and Distribution of Coordinated Universal Time to Critical Infrastructure Systems in the United States |url=https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933488 |date=November 2021 |doi=10.6028/NIST.TN.2187|doi-access=free }}</ref> sometimes only in the last minute and some even not at all ([[DNP3]]).{{citation needed|date=October 2019}}
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Not all clocks implement leap seconds in the same manner. Leap seconds in [[Unix time]] are commonly implemented by repeating 23:59:59 or adding the time-stamp 23:59:60. [[Network Time Protocol]] (NTP) freezes time during the leap second,<ref>{{Cite web |date=10 February 2010 |title=NIST Internet Time Service (ITS) |url=https://www.nist.gov/pml/time-and-frequency-division/time-distribution/internet-time-service-its |website=NIST}}</ref> some time servers declare "alarm condition".{{citation needed|date=October 2019}} Other schemes ''smear'' time in the vicinity of a leap second, spreading out the second of change over a longer period. This aims to avoid any negative effects of a substantial (by modern standards) step in time.<ref>{{citation|rfc=7164|author=Kevin Gross|title=RTP and Leap Seconds|date=March 2014}}</ref><ref name=google-smear /> This approach has led to differences between systems, as leap smear is not standardized and several different schemes are used in practice.<ref>{{cite web | website = Bureau International des Poids et Mesures | url = https://www.bipm.org/documents/20126/77823803/INTRODUCTION-DRAFT-RESOLUTION-D.pdf/62f31b32-bfe4-969f-5d29-1dc08cc907bb?version=1.2&t=1669373890355&download=true | title = Draft Resolution D: 'On the use and future development of UTC' | last1 = Dimarcq | first1 = Noël | last2 = Tavella | first2 = Patrizia | date = 17 November 2022 | page = 7}}</ref>
===Textual representation
The textual representation of a leap second is defined by BIPM as "23:59:60". There are programs that are not familiar with this format and may report an error when dealing with such input.
===Binary representation
Most computer operating systems and most time distribution systems represent time with a binary counter indicating the number of seconds elapsed since an arbitrary [[epoch]]; for instance, since {{nowrap|1970-01-01}} 00:00:00 in POSIX machines or since {{nowrap|1900-01-01}} 00:00:00 in NTP. This counter does not count positive leap seconds, and has no indicator that a leap second has been inserted, therefore two seconds in sequence will have the same counter value. Some computer operating systems, in particular Linux, assign to the leap second the counter value of the preceding, 23:59:59 second ({{nowrap|59–59–0}} sequence), while other computers (and the IRIG-B time distribution) assign to the leap second the counter value of the next, 00:00:00 second ({{nowrap|59–0–0}} sequence).{{citation needed|date=October 2019}} Since there is no standard governing this sequence, the timestamp of values sampled at exactly the same time can vary by one second. This may explain flaws in time-critical systems that rely on timestamped values.<ref>{{Cite journal |last1=Benzler |first1=Justus |last2=Clark |first2=Samuel J. |date=30 March 2005 |title=Toward a Unified Timestamp with explicit precision |journal=[[Demographic Research (journal)|Demographic Research]] |volume=12 |issue=6 |pages=107–140 |doi=10.4054/DemRes.2005.12.6 |issn=1435-9871 |pmc=2854819 |pmid=20396403}}</ref>
===Others===
Several models of global navigation satellite receivers have software flaws associated with leap seconds:
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Due to a software error, the UTC time broadcast by the NavStar GPS system was incorrect by about 13 microseconds on 25–26 January 2016.<ref>{{cite news|url=https://elpromatime.com/wp-content/uploads/2022/08/US_AirForce_OfficialPressRelease.pdf |title=Air Force Official Press Release – GPS Ground System Anomaly}}</ref><ref>{{cite news |url=https://tf.nist.gov/general/pdf/2886.pdf |title=The effects of the January 2016 UTC offset anomaly on GPS-controlled clocks monitored at NIST |first1=Jian |last1=Yao |first2=Michael A. |last2=Lombardi |first3=Andrew N. |last3=Novick |first4=Bijunath |last4=Patla |first5=Jeff A. |last5=Sherman |first6=Victor |last6=Zhang}}</ref>
==Workarounds
The most obvious workaround is to use the TAI scale for all operational purposes and convert to UTC for human-readable text. UTC can always be derived from TAI with a suitable table of leap seconds. The [[Society of Motion Picture and Television Engineers]] (SMPTE) video/audio industry standards body selected TAI for deriving timestamps of media.<ref>{{cite web|url=http://www.ieee802.org/1/files/public/docs2013/asbt-briscoe-timing-and-sync-SMPTE-0513.pdf|title=Network-Based Timing and Synchronization|author=Paul Briscoe|date=14 May 2013}}</ref>
IEC/IEEE 60802 (Time sensitive networks) specifies TAI for all operations. Grid automation is planning to switch to TAI for global distribution of events in electrical grids. [[Bluetooth mesh networking]] also uses TAI.<ref>{{Cite web|url=https://www.bluetooth.org/docman/handlers/downloaddoc.ashx?doc_id=429634|title=Mesh Model Bluetooth® Specification|date=13 July 2017|website=Bluetooth Technology Website|format=PDF download|access-date=14 December 2019}} See sections 5.1.1 and A.1.</ref>
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