Leap second
A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time, to accommodate the difference between precise time and imprecise observed solar time, which varies due to irregularities and long-term slowdown in the Earth's rotation. The UTC time standard, widely used for international timekeeping and as the reference for civil time in most countries, uses TAI and consequently would run ahead of observed solar time unless it is reset to UT1 as needed. The leap second facility exists to provide this adjustment. The leap second was introduced in 1972. Since then, 27 leap seconds have been added to UTC, with the most recent occurring on December 31, 2016. All have so far been positive leap seconds, adding a second to a UTC day; while a negative leap second is theoretically possible, it has not yet occurred.
Because the Earth's rotational speed varies in response to climatic and geological events, UTC leap seconds are irregularly spaced and not precisely predictable. The decision to insert a leap second is made by the International Earth Rotation and Reference Systems Service, typically about six months in advance, to ensure that the difference between UTC and UT1 does not exceed ±0.9 seconds.
This practice has proven disruptive, particularly in modern digital systems that require continuous and precise timestamping. Since not all systems implement leap-second adjustments uniformly, some computational, networking, and satellite-based systems may encounter anomalies.
History
In about AD 140, Ptolemy, the Alexandrian astronomer, sexagesimally subdivided both the mean solar day and the true solar day to at least six places after the sexagesimal point, and he used simple fractions of both the equinoctial hour and the seasonal hour, none of which resemble the modern second. Muslim scholars, including al-Biruni in 1000, subdivided the mean solar day into 24 equinoctial hours, each of which was subdivided sexagesimally, that is into the units of minute, second, third, fourth and fifth, creating the modern second as of the mean solar day in the process. With this definition, the second was proposed in 1874 as the base unit of time in the CGS system of units. Soon afterwards Simon Newcomb and others discovered that Earth's rotation period varied irregularly, so in 1952, the International Astronomical Union defined the second as a fraction of the sidereal year. In 1955, considering the tropical year to be more fundamental than the sidereal year, the IAU redefined the second as the fraction of the 1900.0 mean tropical year. In 1956, a slightly more precise value of was adopted for the definition of the second by the International Committee for Weights and Measures, and in 1960 by the General Conference on Weights and Measures, becoming a part of the International System of Units.Eventually, this definition too was found to be inadequate for precise time measurements, so in 1967, the SI second was again redefined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom". That value agreed to 1 part in 1010 with the astronomical second then in use. It was also close to of the mean solar day as averaged between years 1750 and 1892.
However, for the past several centuries, the length of the mean solar day has been increasing by about 1.4–1.7 ms per century, depending on the averaging time. By 1961, the mean solar day was already a millisecond or two longer than SI seconds. Therefore, time standards that change the date after precisely SI seconds, such as the International Atomic Time, would become increasingly ahead of time standards tied to the mean solar day, such as Universal Time.
When the Coordinated Universal Time standard was instituted in 1960, based on atomic clocks, it was felt necessary to maintain agreement with UT, which, until then, had been the reference for broadcast time services. From 1960 to 1971, the rate of UTC atomic clocks was offset from a pure atomic time scale by the BIH to remain synchronized with UT2, a practice known as the "rubber second". The rate of UTC was decided at the start of each year, and was offset from the rate of atomic time by −150 parts per 10 for 1960–1962, by −130 parts per 10 for 1962–63, by −150 parts per 10 again for 1964–65, and by −300 parts per 10 for 1966–1971. Alongside the shift in rate, an occasional 0.1 s step was needed. This predominantly frequency-shifted rate of UTC was broadcast by MSF, WWV, and CHU among other time stations. In 1966, the CCIR approved "stepped atomic time", which adjusted atomic time with more frequent 0.2 s adjustments to keep it within 0.1 s of UT2, because it had no rate adjustments. SAT was broadcast by WWVB among other time stations.
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. 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;, 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
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, based on records of eclipses for the period 700 BC to 1623, telescopic observations of occultations 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 per century, plus a periodic shift of about 4 ms amplitude and period of about 1,500 yr. 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.
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. Other contributing factors are the movement of the Earth's crust relative to its 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 is thought to have shortened it by 2.68 microseconds.
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. The plot at the top of this section shows that in 1972 the average length of day was approximately seconds and in 2016 it was approximately 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 SI seconds, not because of any slowing of Earth's rotation rate.
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 seconds. This caused engineers worldwide to discuss a negative leap second and other possible timekeeping measures, some of which could eliminate leap seconds. The shortest day ever recorded was 29 June 2022, at 1.59 milliseconds less than 24 hours. In a 2024 paper published in 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.
Procedure
The scheduling of leap seconds was initially delegated to the Bureau International de l'Heure, but passed to the International Earth Rotation and Reference Systems Service on 1 January 1988. IERS usually decides to apply a leap second whenever the difference between UTC and UT1 approaches 0.6 s, in order to keep the difference between UTC and UT1 from exceeding 0.9 s.The UTC standard allows leap seconds to be applied at the end of any UTC month, with first preference to June and December and second preference to March and September., all of them have been inserted at the end of either 30 June or 31 December. IERS publishes announcements every six months, whether leap seconds are to occur or not, in its "Bulletin C". Such announcements are typically published well in advance of each possible leap second date – usually in early January for 30 June and in early July for 31 December. Some time signal broadcasts give voice announcements of an impending leap second.
Between 1972 and 2020, a leap second has been inserted about every 21 months, on average. However, the spacing is quite irregular and apparently increasing: there were no leap seconds in the six-year interval between 1 January 1999, and 31 December 2004, but there were nine leap seconds in the eight years 1972–1979. Since the introduction of leap seconds, 1972 has been the longest year on record: 366 days, 364 of which were 86,400 seconds long and two of which were 86,401 seconds long, for a total of 31,622,402 seconds.
Unlike leap days, which begin after 28 February, 23:59:59 local time, 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 in U.S. Eastern Standard Time and 1 January 2006, 08:59:60 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. All leap seconds 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, 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.