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metrologia

The leap second: its history and possible future
R. A. Nelson, D. D. McCarthy , S. Malys, J. Levine, B. Guinot, H. F. Fliegel , R. L. Beard and T. R. Bartholome w

Abstract. This paper reviews the theoretica l motivatio n for the leap second in the context of the historica l evolutio n of time measurement . Th e periodic insertio n of a leap second step into th e scale of Coordinate d Universal Time (UTC) necessitates frequent changes in comple x timekeepin g systems an d is currentl y th e subject of discussion in working groups of variou s internationa l scienti c organizations. UTC is an atomi c tim e scale that agrees in rate with Internationa l Atomic Tim e (TAI), but differs by an integral number of seconds, and is the basis of civil time. In contrast, Universal Tim e (UT1) is an astronomical time scale de ned by the Earth's rotation an d is used in celestia l navigation . UTC is presently maintaine d to within 0.9 s of UT1. As the needs of celestia l navigatio n that depend on UT1 can now be met by satellit e systems, such as the Global Positioning System (GPS), option s for revising th e de nition of UTC an d the possible role of leap second s in the future ar e considered .

1. Introduction: why we have leap seconds Approximatel y once a year , a leap second is introduce d into UTC, the world's atomi c tim e scale for civil time , in order to keep it in phase with the rotatio n of the Earth. Leap seconds ensure that, on average , the Sun continue s to be overhead on the Greenwich meridia n at noon to within about 1 s. When the atomi c de nitio n of the Internationa l System of Units (SI) second was introduce d in 1967, it was effectivel y made equivalen t to an astronomica l secon d based on a mean solar day of 86 400 s in abou t 1820. However, over approximatel y the past 1000 years, th e Earth 's rotation has been slowing at an average rate of 1.4 ms per century, so that the day is now abou t 2.5 ms longer than it was in 1820. A differenc e of 2.5 ms per day amounts to about 1 s per
R. A. N elson : S atel li te E ngi neer i n g Researc h C orpor ati on , 770 1 Woodm on t Avenue , S ui te 208 , Bethesda , M D 20814 , U S A. D. D. M cCart hy : U S Nava l Observat ory , 345 0 M assachuset t s Avenue , NW , Washingt on , D. C., 20392 , U S A. S . M alys: Nati ona l Im ager y and M appi n g Agency , Resear c h and Technolog y O f ce AT T R ( MS D- 82) , 460 0 S angam or e R oad , B ethesda , M D 20816 , US A. J. L evine : N ati onal I nsti tut e of S t andar d s and Technology , D epar t men t of Com mer c e M S 847 , 32 5 Br oadway , Boul der , C O 80303 , U S A. B. Gui not : Observat oir e de P ar is, Depar temen t d' Astr onomi e á F ondam ent ale , 61 avenu e de l'Obser vat oir e , F- 7501 4 P ar is, F rance. H. F . F li egel : T he A erospac e C orpor ati on , 235 0 E . E l S egundo B lvd. , E l S egundo , C A 90245 , US A. R. L . Beard : Nava l R esearc h L aborat ory , 455 5 Over loo k Avenue , S W, Code 8150 , Washingt on , D. C., 20375 , U S A. T . R. Bart holom ew : L it ton TA S C, I nc., 13 1 Nat iona l Busines s P ar kway , Annapoli s Juncti on , M D 20701 , US A. M et rol ogi a , 2001, 38 , 509- 529

year and this is the reason for the mor e or less regular insertio n of leap seconds. Superimposed on this ver y slowly increasin g differenc e ar e shorter-term variation s in the length of the day. Periods between leap seconds are not, therefore, constant and, in fact, over the past thirty year s there hav e been several year s in which leap seconds have been omitted . The primar y reason for introducing th e concept of the leap secon d was to meet th e requiremen t of celestia l navigatio n to keep th e difference between solar time and atomi c time small. However, the motivatio n for the leap second has diminished because of th e wide availabilit y of satellit e navigatio n systems, such as GPS, while the operational complexitie s of maintainin g precise timekeepin g systems have made the insertio n of leap second adjustment s increasingl y dif cult and costly. The question currentl y bein g debate d in recentl y created working groups of various internationa l scienti c organization s is whether ther e continues to be a need for th e leap second, with its man y technical inconveniences , or whether it would be better simply to let atomic time run freely and accep t that the world's civil time scale will slowly diverge from the rotation of the Earth ? This articl e gives the histor y and detailed technica l background to the current practic e and outlines various solutions. 2. Measuremen t of tim e 2.1 Clocks Two element s ar e needed to measur e the passage of time : (a) a time "reckoner ", which is a repeatabl e 509


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phenomenon whose motion or change of state is observable and obeys a de nite law, and (b) a time reference , with respect to which the position or state of the time reckoner can be determined . These element s correspond to th e two propertie s of time measurement : interva l an d epoch. Together , the time reckoner and the time reference constitut e a clock . From remote antiquity , the celestia l bodies ­ the Sun, Moon an d stars ­ have been the fundamenta l reckoner s of time. The rising and setting of th e Sun an d th e star s determin e the day and night; th e phases of the Moon determin e the month; and the position s of the Sun and star s along th e horizo n determin e the seasons. Sundials were among the rst instruments used to measur e the tim e of day. The Egyptians divided the day an d night into 12 h each, which varied with the seasons. While th e notio n of 24 equal hours was applied in theoretica l works of Hellenisti c astronomy, the unequal "seasonal hour" was used by the general public [1]. When the rst reliabl e water clock s were constructed , great care was taken to re ect the behaviour of a sundial instead of the apparent motion of the heaven s [2]. It was not until the fourteent h centur y that an hour of unifor m length becam e customar y due to the inventio n of mechanica l clocks. These clocks were signi cant, not only because they were masterpiece s of mechanica l ingenuity , but also because they altere d the public's perceptio n of time [3, 4]. In the er a of telescopi c observations, pendulum clock s served as the standard means of keeping time until th e introductio n of moder n electronics . Quartzcrystal clocks were develope d as an outgrowth of radio technolog y in the 1920s and 1930s [5]. Harold Lyon s [6] at the National Bureau of Standard s in Washington, D.C. (now the National Institute of Standards and Technology, Gaithersburg, Md.) constructe d the rst atomi c clock in 1948 using the microwave absorption line of ammoni a to stabiliz e a quartz oscillator . Louis Essen an d J. V. L. Parry [7] at the National Physical Laborator y in Teddington, UK, constructe d a practical caesium beam atomi c clock in 1955. Commercial caesium frequency standard s appeare d a year later . Norman Ramsey develope d the hydrogen maser at Harvard University in 1960 [8]. Once practica l atomi c clocks becam e operational , the Bureau Internationa l de l' Heure (BIH) an d several nationa l laboratorie s began to establish atomi c time scales [9]. The responsibility for th e maintenanc e of the internationa l standar d is now given to the Bureau Internationa l des Poids et Mesures (BIPM). Some form of atomi c time has been maintaine d continuously since 1955 [10]. 2.2 Time scales Three primar y method s of measurin g time have been in common use for modern application s in astronomy, physics and engineering . These methods hav e evolved 510

as th e design and constructio n of clocks have advance d in precisio n and sophistication . The rst is Universal Time (UT), the time scale based on the rotation of the Earth on its axis. Th e second is Ephemeri s Time (ET), the time scale based on the revolution of the Earth in its orbit aroun d th e Sun. The thir d is Atomic Time (AT), the time scale based on the quantum mechanic s of the atom . Each of these measures of tim e has had a variet y of re nement s and modi cation s for particula r applications. The true measur e of the Earth's rotatio n is UT1, which is the form of Universal Tim e correcte d for polar motion and used in celestia l navigation . However, owing to irregularitie s in the Earth's rotation , UT1 is not uniform . UT2 is UT1 corrected for the seasonal variation. Ephemeri s Time (ET) is a theoreticall y uniform time scale de ned by th e Newtonian dynamical laws of motion of the Earth, Moon, and planets. This measure of time has been succeede d by several new time scales that ar e consistent with the general theor y of relativity . The scale of Internationa l Atomic Time (TAI) is maintaine d by the BIPM with contribution s from nationa l timekeepin g institutions. TAI is a practica l realizatio n of a uniform time scale. The basis of civil tim e is Coordinate d Universal Time (UTC), an atomi c tim e scale that corresponds exactl y in rate with TAI but is kept within 0.9 s of UT1 by the occasiona l insertio n or deletio n of a 1 s step. The decision to insert this leap secon d is made by th e International Earth Rotatio n Service (IERS). Since 1972, when UTC was introduced , there hav e been twenty-tw o leap seconds, all of which have been positive. 3. Tim e measured by the rotation of the Eart h 3.1 Universal Time Universal Time (UT1) is the measur e of astronomica l time de ned by the rotation of the Earth on its axis with respect to th e Sun. It is nominall y equivalen t to mean solar tim e referred to the meridian of Greenwich and reckoned from midnight. Th e mean solar day is traditionall y described as th e time interva l between successive transits of the ctitiou s mean Sun over a given meridian . Historically , the unit of time , th e mean solar second, was de ned as 1/86 400 of a mean solar day [11, 12]. The eclipti c is the apparent annual path of the Sun against the background of stars. Th e intersectio n of the eclipti c with the celestial equato r provides a fundamenta l referenc e point called the vernal equinox. In practice , Universal Tim e is determined , not by the meridian transit of the mean Sun, but by the diurnal motion of the vernal equinox in accordanc e with a conventiona l formula specifyin g UT1 in terms of Greenwich Mean Sidereal Time (GMST). Th e
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current de ning relatio n for UT1 with respect to the astronomical referenc e system of the Fifth Fundamental Katalog (FK5) [13] is given in [14]. UT0, a designatio n no longer in common use, is UT1 corrupted by th e torque-free precessional motio n of the Earth's axis of rotatio n with respect to the Earth's surface [15]. This effect , called variatio n of latitude, was predicted by Leonhar d Euler [16] in 1765 as a property of rigid body motio n and was identi ed observationall y by Seth Chandler [17] in 1891. The difference [UT0 ­ UT1] has a maximum value of about 20 ms at mean latitud e [18]. Apparent solar time , as read directl y by a sundial or mor e precisel y determine d by the altitud e of the Sun, is th e local time de ned by the actual diurnal motion of the Sun. However, because of the tilt of the Earth's axis and the elliptica l shape of the Earth's orbit, the tim e interva l between successive passages of the Sun over a given meridian is not constant. The difference between mean and apparent solar time is calle d the equatio n of time . Th e maximu m amoun t by which apparent noon precede s mean noon is about 16.5 min aroun d 3 November , while the maximu m amount by which mean noon precede s apparent noon is abou t 14.5 min around 12 February. Until th e early nineteent h century, apparen t solar time was used as the argument for astronomical ephemerides . However, as clock s improved and their use by ships at sea and by railroad s grew, apparent solar tim e was gradually replaced by mean solar time . 3.2 Siderea l Time Local Sidereal Time (LST) is the measur e of astronomical time de ned by th e rotatio n of the Earth with respect to the stars. LST may be de ned as the right ascension of th e local meridian , which is the angle between the vernal equinox and the local meridia n measured along the celestial equator . In particular , Greenwich sidereal time is th e right ascensio n of the Greenwich meridian . The sidereal day is the time interval between successive transits of the vernal equinox. It represents the Earth's perio d of rotation relativ e to the star s and is approximatel y 86 164.0905 mean solar seconds. Owing to precession of the Earth's axis with respect to the celestia l referenc e system, the sidereal day is about 0.0084 s shorter than the actua l period of rotation in inertia l space. Thus the true rotationa l perio d of the Earth is approximatel y 86 164.0989 mean solar seconds. However, the mean solar day presently exceed s a day of exactl y 8 400 SI seconds by about 2.5 ms. Therefore, the Earth's period of rotation is currentl y about 86 164.1014 SI seconds. Even LST is not a uniform measure of astronomical time . In the early twentiet h century, the inherent accurac y of the Shortt free-pendulum clock s rst
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reveale d th e periodic effect s of nutation . The principal term consists of an eighteen-yea r oscillatio n with an amplitud e of about 1 s. These effect s cannot be neglecte d and it becam e necessar y to introduce the concept of mean sidereal time , which is affecte d only by precession. Greenwich Mean Sidereal Time (GMST) is mean sidereal tim e with respect to the Greenwich meridian , from which Universal Time (UT1) is derived. In the past, UT1 was determine d using a worldwide network of visual transit telescopes , photographic zenit h tubes and impersonal (prismatic ) astrolabes. Three basic technique s are now used to estimat e UT1: (a) Very Lon g Baseline Interferometr y (VLBI) measurement s of selecte d radio point sources, mostly quasars; (b) satellit e laser ranging; and (c) trackin g of GPS satellites . Strictly speaking, because of th e motion of satellite orbital nodes in space, VLBI provides the only rigorous determinatio n of UT1. A revised conventiona l celestial referenc e fram e based on the observed positions of extragalacti c object s is bein g develope d that changes the basis for UT1, removes the need for th e equinox, an d changes the use of precession and nutation . 3.3 Variations in the Earth's rotation Three types of variatio n in the Earth's rotation have been identi ed: a stead y deceleration , random uctuations , and periodic changes [19]. As early as 1695, Sir Edmon d Halley [20] was led to suspect an acceleratio n in the mean motion of the Moon from a study of ancien t eclipse s of the Sun recorded by Claudius Ptolem y and the medieval Arabian astronomer, Muhammed al- Bat tanåÓ . By the å mid-eighteent h century, th e lunar acceleratio n was fully established . In 1754, Immanuel Kant [21] suggested that this acceleratio n might be an apparent phenomenon caused by a steady deceleratio n in the Earth's rotation due to tidal friction . Part of the effect was later attributed to the variatio n in th e solar perturbatio n on the Moon's orbit. As shown by Pierre-Simo n Laplac e and John Couch Adams, the planetar y perturbation s cause the Earth 's orbital eccentricit y to diminish and, as a consequence , the Sun's mean actio n on the Moon also diminishes. In addition , the observed lunar acceleratio n is affecte d by th e recessio n of the Moon from the Earth in order to compensat e the decrease in the Earth's rate of spin by conservatio n of angular momentum . It was not until the twentiet h century that an apparen t acceleratio n of the Sun was also identi ed [22-24]. Recen t studies of eclipse s by F. R. Stephenson and L. V. Morrison [25, 26] suggest that the long- ter m average rate of increase in the length of the day is about 1.7 ms per centur y (­4.5 10­22 rad/s2 ). Although the increase in the length of day seem s miniscule , it has a cumulativ e effect on a time scale based on the Earth's 511


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rotation . In th e past 2000 year s th e Earth actin g as a clock has lost over 3 h. For example , th e calculate d path of the total eclipse of the Sun witnessed in Babylon in 136 B.C. would be in error by 48.8 , corresponding to a time differenc e of 11 700 s, assuming a unifor m rate of rotatio n [27]. Sir Harold Jeffrey s made th e rst quantitativ e estimat e of global tidal friction in 1920 [28, 29]. He found that the energ y dissipatio n in the shallow seas appeared to be of th e correct order of magnitude to account for the apparent lunar and solar accelerations . Th e rate of energy dissipation by tidal friction is now considered to correspond to a rate of increase in the length of day of 2.3 ms per century (­6.1 10­22 rad/s2 ). To account for th e observed deceleration , there must also be a componen t in th e opposite directio n of abou t 0.6 ms per centur y (+1.6 10­22 rad/s2 ), which is possibly associate d with changes in the Earth oblatenes s paramete r caused by post- glacia l rebound [30] or with deep ocean dissipation [31]. Evidenc e for a long- ter m deceleratio n in the Earth's rotation , extendin g over million s of years, also exists in coral fossils that exhibit both daily an d annual growth rings [32]. For example , several corals dating from the middle of the Devonian Period, some 370 millio n year s ago, indicat e that the number of days in the year was between 385 and 410. Th e evidenc e suggests that the rate of deceleratio n was substantiall y the same then as it is now [33]. Besides a stead y decrease, the Earth's rotation is subject to frequent small changes that ar e random and cumulativ e [34, 35]. This variatio n was inferred from studies of statistical irregularitie s in the displacement s of the Moon, Sun, Mercur y an d Venus in proportio n to their mean motions. Random uctuation s were rst observed directl y by atomi c clock s in the mid- 1950s [36]. There is also a periodic seasonal variatio n caused principall y by meteorologica l effects. Th e seasonal variatio n was rst reported in 1936 by A. Scheib e an d U. Adelsberger [37], who performed measurement s of th e Earth's rotation with excellen t quartz- crysta l clock s at the Physikalische- Technisch e Bundesanstalt (Germany). N. Stoyko [38] at the BIH in 1937 found that the length of the day in January exceede d that in July by 2 ms, based on the performance of Shortt pendulu m clocks and by comparison of th e rates of quartz- crysta l clock s at th e nationa l time services. The seasonal variatio n in the length of the day is now known to be of the order of 0.5 ms about the mean [39]. The rotatio n of th e Earth runs slow by about 30 ms in May an d runs fast by a simila r amount in November . By internationa l agreement , an empirical correctio n for the seasonal variatio n has been applie d since 1 Januar y 1956, resultin g in th e time scale UT2. The difference between UT2 an d UT1, as currentl y applied , is given in [40]. UT2 has a peak- to- peak amplitud e of about 60 ms. 512

4. Tim e measured by the orbital motions of the celestia l bodies The need for more uniform measures of astronomica l time resulted in the de nition of tim e scales determine d from the motions of th e celestia l bodies in the solar system. Originally based on Newtonian mechanics , they have been re ned to take into account the effect s of general relativity . In addition , the unit of time, previously within the exclusive domain of astronomy, was incorporate d into the creatio n of th e SI. In 1948, at the request of the International Union of Pure and Applied Physics (IUPAP), the 9th General Conference on Weights and Measures (CGPM) resolved to adop t for internationa l use a practical system of units covering all branches of metrology. A limite d set of base units, includin g the second, was selecte d by the 10th CGPM in 1954 and a representativ e list of derived units was compile d by the Internationa l Committe e for Weights and Measures (CIPM) in 1956. The SI was of ciall y establishe d by the 11th CGPM in 1960 [41]. 4.1 Ephemeris Tim e Because th e variation s in th e Earth's rotation are complex , the CIPM referred the study of a new de nition of the secon d to the Internationa l Astronomical Union (IAU) in 1948. At the suggestion of G. M. Clemenc e [42], the Conference on the Fundamental Constants of Astronomy held in Paris in 1950 recommended to the IAU that, instead of the period of rotatio n of the Earth on its axis, the new standard of time ought to be based on th e perio d of revolution of the Earth around the Sun, as represente d by Newcomb's Tables of the Sun published in 1895. The measur e of astronomica l tim e de ned in this way was given th e name Ephemeris Time (ET) . The working de nition of Ephemeris Tim e was through Newcomb's formula for the geometri c mean longitude of the Sun for an epoch of Januar y 0, 1900, 12h UT [43], L = 279 41 48 .04 + 129 602 768 .13 T + 1 .089 T2 , where is the tim e reckoned in Julian centurie s of 36 525 days. The linea r coef cient determine s the unit of time , while th e constan t determine s the epoch. Th e IAU adopted this proposal in 1952 at its 8th General Assembly in Rom e [44]. Initially , the period of revolution of the Earth was understood to be th e sidereal year . However, it was subsequently pointed out by AndreáDanjo n that the tropical year is more fundamental than th e sidereal year, as the length of th e tropical year (equinox to equinox ) is derived directl y from Newcomb's formula, whereas the length of th e sidereal year ( xed star to xed star) depends on the adopted value of th e precession [45]. From the value of th e linear coef cient in Newcomb's formula, th e tropica l year of 1900 contain s
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[(360 60 60)/129 602 768.13] 36 525 86 400 = 31 556 925.9747 s. Therefore, at the recommendatio n of th e CIPM, th e 10th CGPM in 1954 proposed the followin g de nition of the second : "The second is the fractio n 1/31 556 925.975 of the length of the tropical year for 1900.0." But although the IAU approved this de nition at its General Assembly in 1955, Danjon commented that the fractio n ought to hav e a slightly mor e precise value to bring about exact numerica l agreemen t with Newcomb's formula [46]. Consequently, th e CIPM in 1956, under the authority given by the 10th CGPM in 1954, de ned the second of ephemeri s time to be "th e fractio n 1/31 556 925.974 7 of the tropica l year for 1900 January 0 at 12 hours ephemeri s time ". This de nition was rati ed by th e 11th CGPM in 1960 [47]. Referenc e to the year 1900 does not imply that this is the epoch of a mean solar day of 86 400 s. Rather, it is th e epoch of the tropical year of 31 556 925.974 7 s. Although ET was de ned in terms of the longitude of the Sun, in practic e it was realize d indirectl y by compariso n of observations of lunar positions with lunar ephemerides. Thus, a set of secondar y time scales (denoted by ET0, ET 1 an d ET2) were de ned that differed because of subsequent improvement s to the conventional ephemerides [48]. In 1958, the IAU General Assembly adopted a resolutio n that de ned the epoch of Ephemeri s Time to coincid e with Newcomb's formula as follows [49]: "Ephemeri s Time (ET) , or Temps des Ephemerides áá (TE), is reckoned from the instant, near th e beginning of the calenda r year A.D. 1900, when the geometri c mean longitude of the Sun was 279 41 48 .04, at which instant the measure of Ephemeris Time was 1900 January 0d 12h precisely." Th e resolutio n also include d the de nition of the second given by the CIPM in 1956. In a separate resolution, the epoch for Universal Time was chosen as 1900 Januar y 0d 12h UT based on the Fourth Fundamental Katalog (FK4) [50]. However, the equinox of Newcomb's Sun, the lunar theory, and the FK4 did not agree precisel y an d they were moving with respect to one another. Thus the actua l instant in time correspondin g to the epoch of ET was approximatel y 4 s late r than the epoch of UT [51]. Ephemeri s Time (ET) is a dynamical time determine d by the theor y of celestial mechanic s and is theoreticall y uniform [52]. ET may be characterize d as the independen t variabl e that brings the observed position s of the celestia l bodies into accord with their calculate d positions constructe d from the Newtonian law s of motion. Therefore, in effect, it is de ned by these law s [53].
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4.2 Relativisti c tim e scales In 1960, ET replace d UT1 as the independen t variabl e of astronomica l ephemerides . However, ET did not include relativisti c effects and did not distinguish between proper time and coordinat e time . Accordingly, at the 16th General Assembly in Grenoble in 1976, the IAU de ned time-lik e argument s that distinguish coordinat e system s with origins at the centr e of the Earth and the centr e of the solar system, respectively , and are consistent with the general theor y of relativit y [54]. In 1979, these time scales receive d the names Terrestrial Dynamica l Time (TDT) and Barycentri c Dynamical Time (TDB) [55]. TDT replaced ET in 1984 as the tabula r argument of the fundamenta l geocentri c ephemerides. TDT has an origin of 1 Januar y 1977 0 h TAI, with a unit interval equal to the SI second , an d maintain s continuit y with ET. At this epoch, a rate correctio n of ­10 10­13 was applied to TAI to bring the unit of TAI more closely into accor d with the SI second [56]. In 1991 the IAU rename d TDT simply Terrestria l Time (TT) . A practical realizatio n of TT is [57] [TT] = [TAI ] + 32.184 s. The constant offset represents the differenc e between ET and UT1 at th e de ning epoch of TAI on 1 Januar y 1958. The relationshi p between TT an d TAI is not strictl y rigorous for two fundamenta l reasons [58]. First, TAI is a statisticall y formed time scale based on contribution s from th e major timin g centres, whereas TT is theoreticall y uniform. Second, a scale of time based on the laws of gravitatio n may not be philosophicall y equivalen t to one based on the quantu m mechanics of th e atom. For ephemeride s referred to th e barycentr e of the solar system , the argumen t is TDB. Through an appropriatel y chosen scaling factor , TDB varies from TT or TDT by only periodic variations , with amplitudes less than 0.002 s. From the deliberation s of the IAU Working Group on Reference Systems formed in 1988, ther e arose nine recommendation s that were containe d in Resolution A4 adopted by the 21st IAU General Assembly in 1991 [59]. The general theory of relativit y was explicitl y introduce d as the theoretica l basis for th e celestia l referenc e frame and th e form of the space-tim e metric to post-Newtonian order was speci ed. Th e IAU also clari ed the de nition of Terrestria l Time (TT) and adopted two additiona l time scales, Geocentri c Coordinate Time (TCG) an d Barycentri c Coordinate Time (TCB) [60]. The "coordinate" time scales TCG and TCB are complementar y to the "dynamical " time scales TT (or TDT) and TDB. They differ in rate from TT and are relate d by four-dimensional space-tim e coordinat e transformation s [61]. These de nitions were 513


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further clari ed by resolutions adopted at the 24th IAU General Assembly held in Manchester in 2000 [62]. 5. International Atomic Tim e Although ET was a uniform time scale, it was not easily realize d or disseminated . Th e rapid developmen t of atomi c clock s permitted yet another de nition of time [63]. 5.1 Experimental atomic time scales Th e rst operationa l caesiu m beam frequency standar d appeared in 1955 at the National Physical Laboratory (NPL, UK) [64]. The Royal Greenwich Observator y (RGO) establishe d a tim e scale, known as Greenwich Atomic (GA), using free- running quartz- crysta l clock s periodicall y calibrate d in term s of this standard . A commercia l caesium frequency standard , the "Atomichron", was develope d in 1956 [65]. The US Naval Observator y (USNO) inaugurate d its A.1 atomi c time scale on 13 Septembe r 1956, initiall y based on a caesium clock at the Naval Research Laboratory (NRL) consisting of an Atomichron caesiu m standard and a quartz- crysta l clock. The frequency of th e crystal was matche d daily to the caesiu m standard, which was not operate d continuously [66]. The National Bureau of Standards (NBS) in Boulder , Colo., also maintaine d an atomi c time scale, NBS- A, startin g 9 October 1957. Th e epochs of A.1 and NBS-A were mad e coinciden t an d set equal to UT2 on 1 January 1958 [67]. The A.1 time scale was introduce d for world use on 1 January 1959. By 1961, A.1 was based on atomi c oscillator s at the USNO, NRL, NBS, USNO Tim e Service Sub- Statio n (Richmond , Florida) , Harvar d University, National Research Council (Ottawa), NPL, Centr e á National d'Etudes des Telecommunication s (Bagneux) , áá an d Observatoire de Neuchatel (Switzerland) [68, 69]. ö Once continuous atomic time becam e establishe d at variou s laboratories , th e BIH began a mean atomi c time scale based on frequency comparison s by mean s of VLF carrier s at 3 kHz to 30 kHz used for long- distance communication s and radio navigatio n [70]. Initiall y it was designate d AM, and then A3, representin g an average of th e three best scales. In 1960, th e BIH began publicatio n of th e difference s between UT2 and various individual atomi c times obtaine d by integratio n of accurat e frequency comparisons. By 1969 th e BIH had rede ned A3 to be an average d atomi c time scale (TA) based on several primar y laborator y standards. In 1971, this scale becam e the scale of International Atomic Tim e (TAI) [71]. 5.2 Atomic de nition of the second In June 1955, Louis Essen and J. V. L. Parry of the NPL measured th e operationa l resonance frequency of the laboratory 's caesium standar d with respect to th e second 514

of UT2 as (9 192 631 830 ± 10) Hz by compariso n with the adopted frequency of a quartz standard , which was calibrate d from astronomical measurement s performed at the RGO [72]. Over the following three years, in cooperatio n with Willia m Markowitz and R. G. Hall at the USNO, they determine d its value in terms of the second of Ephemeri s Time . Photographs of the Moon and surrounding stars were taken by the USNO dualrate Moon camer a over the period 1955.50 to 1958.2 5 to determin e the Ephemeri s Time from the position of th e Moon at a known UT2. Th e UT2 scale, based on observation s made with photographic zenit h tubes (PZTs) at th e USNO, was calibrate d with the caesium beam atomi c clock in Teddingto n via simultaneou s observations of the interval s between time pulses broadcast by radio station s WWV (then in Greenbelt , Md.) and GBR (Rugby, UK). The measured caesiu m frequency was 9 192 631 770 Hz with a probable error of ± 20 Hz [73]. The principa l uncertaint y arose from the astronomica l measurement s themselves . Only seven year s after the de nition of the ephemeri s second as an SI unit in 1960, the 13th CGPM in October 1967 adopted the atomi c secon d as the fundamenta l unit of time in the Internationa l System of Units. The second was de ned as [74] "the duration of 9 192 631 770 periods of the radiatio n corresponding to the transitio n between the two hyper ne level s of the ground state of th e caesiu m 133 atom". The second of atomic time is in principle equivalen t to th e secon d of Ephemeri s Time . However, this decision did not consider a recommendatio n of Commissions 4 (Ephemerides ) and 31 (Time ) of the IAU in 1967 in Prague, which requested the CGPM to recognize th e ephemeri s second as a par t of the IAU system of astronomical constants, thus causin g objection s from some astronomer s [75]. 5.3 Establishment of TAI A prevalen t opinion amon g astronomer s in the mid1960s had been that the atomi c standards could provide the unit of time , but not the continuous scale of time that they needed [76]. But, on the contrary, the BIH was convince d that an atomi c standar d was the best referenc e for time an d devoted its resources to the establishmen t of a practical internationa l scale of atomi c time [77]. In 1967, IAU Commissions 4 and 31 [78] recommende d that the BIH compute an internationa l scale of atomi c time, comprisin g independen t time scales of the major national time services based on experienc e gained from the experimenta l scale A3. It also suggested that this scale be published in the form of correction s to th e contributin g time scales with respect to the internationa l scale. Similar recommendation s followed from th e Internationa l Union of Radio Science
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(URSI) in 1969 and the International Radio Consultative Committe e (CCIR) in 1970. The Comite Consultati f pour la Deánition de la á Second e (CCDS) of the CIPM recommende d guideline s for the establishmen t of International Atomic Tim e (TAI) in 1970. The CCDS stated [79]: "Internationa l Atomic Time (TAI) is th e time referenc e coordinat e establishe d by the Bureau Internationa l de l'Heure on th e basis of readings of atomi c clock s operatin g in various establishment s in accordance with the de nition of the second, the unit of tim e of the Internationa l System of Units." In conformity with the recommendation s of IAU Commission s 4 and 31 in 1967, the CCDS [80] de ned the origin so that TAI would be in approximat e agreemen t with UT2 on 1 Januar y 1958, 0 h UT2. The 14th CGPM approved th e establishmen t of TAI in 1971. Yet an importan t task remained . To de ne th e scale of atomi c time completely , one must de ne where in the universe the SI secon d is to be realized . In recognitio n of the framewor k of general relativity , the de nitio n was completed in 1980 by the statemen t [81]: "TAI is a coordinat e tim e scale de ned in a geocentri c reference frame with the SI second as realize d on the rotatin g geoid as the scale unit." Thus relativisti c correction s ar e required for the primary laborator y realization s of the SI secon d used in the calibratio n of TAI to compensat e the frequency shifts between their individual location s and a point xed on the surface of the rotatin g geoid. TAI, when formall y adopted in 1971, was an extensio n of the BIH atomi c time scale that had been continuous back to 1955. In 1988, responsibility for maintainin g TAI was transferred from th e BIH to the BIPM. A distributio n of approximatel y two hundred clock s maintaine d in fty laboratories contribute to TAI using an optimize d weighting algorithm . 6. Coordinated Universal Tim e Ther e were two communities of users. Some, such as astronomers, geodesists an d navigators, wanted a broadcast tim e connecte d with the angle of the Earth's rotatio n in space. Others, such as physicists and engineer s at tim e and frequency laboratories , wanted it to be perfectl y unifor m to agree with th e best clocks. Attempt s to meet the needs of both communities led to the creatio n of Coordinated Universal Time (UTC). 6.1 Original UTC system Originally, radio time signals controlle d from the Royal Greenwich Observator y were kept closely in phase with the Earth's rotation using direct astronomical observations, resultin g in a nominal tim e interva l of
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a second that could vary slightly from day to day. Beginnin g in 1944, the tim e signals were generated by quartz- crysta l clocks at a uniform rate, with step correction s introduced when necessar y to maintai n agreemen t with astronomical time. When an atomi c standard becam e availabl e at the NPL in 1955, the MSF time and frequency broadcast service of the UK based its signal on the provisional frequency of 9 192 631 830 Hz for caesium . In 1958, the NPL adopted the frequency 9 192 631 770 Hz, but announced that the MSF service would hav e an annual rate offset of a stated amount, in additio n to step corrections , to keep th e disseminate d tim e signals close to the scale of UT2 [82]. Following the creatio n of their atomi c time scales in the perio d 1956- 57, the USNO and th e NBS each maintaine d two systems of atomi c clock time. Th e USNO system of uniform time , A.1, was related to Ephemeri s Time, while the USNO Master Clock was adjusted daily to UT2 from PZT observations. Similarly , the NBS time scale NBS-A had a uniform rate synchronized with A.1, while NBS-UA was derived by applyin g rate offsets and small steps to follow UT2 and was disseminated by radio station WWV . A summary of the correction s utilized by WWV is given in [83]. At rst, time signals broadcast from variou s countrie s were so loosely controlle d that a listene r monitoring several station s could hear th e pulses arriving at different times. To reduce the disparities, the World Administrativ e Radio Conference (Geneva) in 1959 requested the CCIR to study the question of establishin g and operatin g a worldwide standar d frequency and time signal service. The nautica l almanac s of th e UK an d the USA were combine d in 1957, beginning with th e editions for 1960. In August 1959 it was also agreed to coordinat e their time and frequency transmissions. Coordinatio n began 1 January 1960. Th e participatin g observatorie s and laboratorie s were the USNO, RGO, NBS, NRL and NPL. Gradually other countries joined the system, which was entrusted to the BIH in 1961. In Januar y 1965, the BIH decided to attach UTC to its atomi c time A3 (which becam e TAI) by a mathematica l relationship [84]. This was th e origin of th e link between TAI and UTC. The nam e "Coordinate d Universal Time (UTC)" was approved by a resolution of IAU Commission s 4 and 31 at the 13th General Assembly in 1967 [85]. 6.2 Revised UTC system Detail s of th e UTC system were formalize d by CCIR Study Group 7 in Geneva in 1962 and were adopted by th e CCIR in its Recommendatio n 374 [86] of 1963. The frequency offset was announced by th e BIH, after consultatio n with the observatories concerned , to match as nearly as practica l the rotationa l speed of the Earth and remaine d constant for each year, while steps of 100 ms were inserted periodicall y at the beginning of 515


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the month, on dates determine d by the BIH, to maintai n the tim e signals to within abou t 0.1 s of UT2. As UTC included rate offsets to reduce the need for step adjustments , the broadcast time signals indicate d neither th e SI secon d nor the mean solar second, but rather variabl e interval s to stay in step with UT2, from which the SI secon d could be obtaine d by applying a known correction . Attempts to follo w these uctuation s necessitated revisions in comple x equipmen t on a frequent basis and risked temporar y interruption s of service. At an interi m session in Monte Carlo during March 1965, Study Group 7 suggested that experimenta l broadcasts and studies should be mad e to investigat e how to provide both the epoch of Universal Time an d the internationa l unit of tim e interva l in the sam e emission [87]. The revised CCIR Recommendatio n 374-1 [88] of 1966 allowed for the limite d and provisional use of an experimenta l "Stepped Atomic Time (SAT) ", in which th e broadcast time rate was the atomi c time rate, with no carrier deviation , but in which frequent step adjustment s of 200 ms were applied to matc h UT2 to within 0.1 s. Th e existenc e of two paralle l systems, UTC and SAT, was regarded as a phase in th e evolutio n an d adoptio n of a single, practical and internationall y acceptabl e system [89]. 6.3 Present UTC system At the 15th General Assembly of the URSI in Munich in 1966, Commission 1 expressed the opinion that all proposed methods of operatin g standard time and frequency services contained defect s and that these services must inevitabl y develop toward s a system of unifor m atomi c time an d constant frequency . For those requiring astronomical time , some form of correctio n would be necessar y [90, 91]. In 1967, at a meetin g held in Brussels under the auspices of th e URSI to consider frequency coordinatio n in Europe, it was unanimously agreed that both rate offsets and step adjustment s should be discontinued . It was suggested that th e deviation s of UTC from UT2 would have no signi cance for civil purposes, but could be disseminate d to navigator s in tables or in the transmission s themselve s [92]. Dissatisfactio n with the existing form of UTC and the need to study the implication s of the new de nitio n of the second adopted in 1967 prompted discussions by the CIPM and th e CCIR. Following a recommendatio n of the CCDS, the CIPM formed a preparator y commission for th e internationa l coordinatio n of time scales. The concep t of th e leap second, analogous to the leap day in the calendar , was proposed independentl y by G. M. R. Winkle r [93] an d Louis Essen [94] at a meetin g of the commission held at the BIPM in May 1968 [95, 96]. It was proposed that intege r steps of seconds replace the step s of 100 ms or 200 ms then being used because they were too frequen t and too small. Consideratio n of possible modi cation s to UTC 516

was also given by CCIR Study Group 7 in Boulder in August 1968 [97]. The view was expressed that the best system would be one with 1 s step s without rate offsets, so that equipmen t generatin g a pulse train would not requir e a change in frequency. To meet the needs of navigators, it was suggested that coded informatio n might be incorporate d in the emissio n to indicat e the differenc e between UTC and UT2 to higher resolution. An Interim Working Party, IWP 7/1, was formed to investigat e requirements , submit proposals, an d x a date for th e introductio n of the new system . The option s under consideratio n at this time were summarize d as follows [98]: "Discardin g the suggestio n (for practica l reason s and to avoid confusions) of two time scales, one approachin g UT (the presen t UTC) an d the other without offsets and adjustments, only three alternative s remain : (a) step adjustmen t of 0.1 s or 0.2 s to maintai n the UTC suf cientl y near to UT2 to permit to ignor e the differenc e in most of th e applications ; (b) complet e disuse of UTC system, replacin g it with a coordinate d uniform time scale without offsets and steps and therefor e not approachin g UT; (c) step adjustmen t of 1 s exactly." Speci c proposals were made by Study Group 7 in Genev a in October 1969, which were approved by the CCIR XIIth Plenar y Assembly in New Delhi in Januar y 1970. In its Recommendatio n 460 [99], th e CCIR stated that (a) carrie r frequencie s and time interval s should be maintaine d constant and should correspond to the de nition of the SI second ; (b) step adjustments , when necessary, should be exactl y 1 s to maintai n approximat e agreemen t with Universal Time (UT); and (c) standard signals should contai n informatio n on the differenc e between UTC and UT. Th e CCIR also decide d to begin th e new UTC system on 1 Januar y 1972. At the IAU's 14th General Assembly in Brighton , UK, in August 1970, the chairma n of CCIR IWP 7/1, H. M. Smith, sought the view s of Commission s 4 (Ephemerides ) and 31 (Time) . Th e appropriat e metho d of providing both precise Earth orientatio n to navigator s and uniform time to time an d frequency laboratorie s was discussed. As th e navigato r requires knowledg e of UT1 rather than UT2, it was recommende d that radio time signals should disseminat e differences in the form of [UT1 ­ UTC]. Several astronomers emphasized that visual observers in astronomical and relate d elds requir e UT1 to a precision of 0.1 s, as this is about the limi t of human time discrimination . In addition , the almanac s were designed to permit a determinatio n of positio n to 0.1 minute of arc, an d for this a comparabl e precision in time of 0.25 s was required. At Brighton , Commission 31 adopted recommendation s simila r to those of the CCIR. Also, the IAU General Assembly resolved that adequat e means should be provided to ensure that the difference [UT1 ­ UTC] would be
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availabl e befor e permittin g UTC to depar t from UT1 by mor e than abou t 0.1 s [100]. Detailed instructions for the implementatio n of CCIR Recommendatio n 460 were drafted at a further meetin g of Study Group 7 that was held in Februar y 1971 [101]. The de ning epoch of 1 Januar y 1972, 0 h 0 m 0 s UTC was set 10 s behind TAI, which was the approximate accumulate d differenc e between TAI and UT1 since th e inceptio n of TAI in 1958, an d a unique fractio n of a second adjustmen t was applied so that UTC would differ from TAI by an integra l number of seconds. The recommende d maximu m departure of UTC from UT1 was 0.7 s. Th e ter m "leap second" was introduce d for the stepped second. An additiona l correctio n DUT1 was introduced , having integra l multiple s of 0.1 s, to be embodie d in the time signals such that, when added to UTC, they would yield a bette r approximatio n to UT1. For example, this second level of correctio n was achieve d by NBS radio stations WWV and WWV H by using double ticks or pulses after th e star t of each minute in its UTC broadcasts [102]. The recommendation s of the IAU were formalize d by resolutions of Commissions 4 and 31 at the 15th General Assembly in Sydney in 1973 and, after further discussion, th e nam e UTC was retained [103]. UTC was recommended as th e basis of standar d time in all countries, the time in common (civil ) use as disseminate d by radio signals. Th e limit of [UT1 ­ UTC] was set at ±0.950 s, as this is the maximu m differenc e that can be accommodate d by the code format. Th e maximu m deviatio n of UT1 from [UTC + DUT1] was set at ±0.100 s. In 1974, the CCIR increase d th e tolerance for [UT1 ­ UTC] from 0.7 s to 0.9 s. The present UTC system is de ned by ITU- R (formerly CCIR) Recommendatio n ITU- R TF.460- 5 [104]: "UTC is the tim e scale maintaine d by th e BIPM, with assistance from the IERS, which form s th e basis of a coordinated disseminatio n of standar d frequencie s and time signals. It correspond s exactl y in rate with TAI but differ s from it by an integra l number of seconds. Th e UTC scale is adjusted by the insertio n or deletio n of seconds (positive or negativ e leap seconds) to ensure approximat e agreemen t with UT1." Th e interva l between time signals of UTC is thus exactl y equal to the SI second. A history of rate offsets an d step adjustment s in UTC is given in [105]. 7. The lea p second 7.1 Rate of increase in length of day Because th e Earth's rotatio n is graduall y slowing down, and in additio n has both random and periodic uctuations , it is not a uniform measur e of time . The
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time differenc e T [ET ­ UT1] [TT ­ UT1] represents th e differenc e between the uniform scale of Ephemeri s Time or Terrestria l Time an d the variabl e scale of Universal Time. Values of T are summarize d in [106]. Befor e 1955, the values ar e given by T [ET ­ UT1] based on observation s of the Moon. After 1955, values ar e given by T [TT ­ UT1] [TAI + 32.184 s ­ UT1] from measurement s by atomi c clocks as published by the BIH and th e BIPM. Accordin g to Stephenson and Morrison [107], over the past 2700 year s can be represented by a parabola of approximatel y the form T = (31 s/cy 2 ) (T ­ 1820)2 /(100)2 ­ 20 s, where T is expressed in seconds and T is the year. Figure 1 plots this equatio n togethe r with observations since 1620. The curve has a minimu m at the year 1820 and passes through 0 at the year 1900. Actual values of T based on astronomical data may differ somewhat from this smoothed t. For example , th e value of T is 32.184 s at 1958.0, the origin of TAI. However, no single parabola can satisfactoril y represent all moder n and historica l data. The derivativ e of T is L
day

(0.0017 s/d/cy ) (T ­ 1820)/100,

Figure 1. Observations and parabolic t of T versus time since 162 0 ( after Stephenson and Morrison [26]).

Figure 2. Chang e in the length of day with respect to a reference day of 86 400 s versus time (after Stephenson and Morrison [26]).

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Figure 3. Chang e in the length of day since 162 0 (after Stephenson and Mor rison [25]).

which represents th e change in the length of day (LOD) in SI seconds relativ e to the standar d referenc e day of exactl y 86 400 SI seconds. This equatio n is plotted in Figure 2. Accordin g to this long- ter m trend , the rate of increase in the length of the day is about 1.7 ms per century. Figure 3 illustrates observation s of changes in the length of day during the er a of telescopi c observations, from 1620 onwards. Over this modern period, the LOD has been increasin g at about 1.4 ms per centur y [108]. That is, today is approximatel y 1.4 ms longer than a day a centur y ago . Other studies imply slightly different values [109, 110]. The actua l valu e of the LOD will depart from any long- ter m tren d due to short- term uctuation s of between ­3 ms and +4 ms on a time scale of decades. Th e epoch at which th e mean solar day was exactl y 86 400 SI seconds was approximatel y 1820. This is also the approximat e mean epoch of the observations analysed by Newcomb, rangin g in date from 1750 to 1892, that resulted in the de nition of the secon d of Ephemeri s Time from which the SI second was derived [111]. 7.2 Motivatio n for the leap second UTC is kept within 0.9 s of UT1 by th e occasional insertion of a leap second adjustment. When the present UTC system was established in 1972, the time difference T [TT ­ UT1] = [TAI + 32.184 s ­ UT1] was equal to 42.23 s. Thus the difference between TAI an d UT1 in 1972 was approximatel y 10 s. To maintai n continuit y with UT1, UTC was initiall y set behind TAI by this amount. As of 1 Januar y 2001, 22 positiv e leap seconds hav e been added. Thus UTC is presently behind TAI by 32 s. Figure 4 illustrate s the relationship s between TAI, UTC and UT1. The 1 s increment s ar e indication s of the accumulate d differenc e in time between a uniform time an d a time measured by the Earth's rotation . By analogy, if a watch that loses 2 s per day were synchronized with a perfect clock at th e beginnin g of a certai n day, then after one day the watch would be in error by 2 s. At th e end of a month , the watch would be in erro r by roughly 1 min. It would then be convenien t to reset the watch by inserting 1 min of time. 518

Figure 4. Difference between TAI and UT 1 since 195 5 (from Quinn [70]).

Figure 5. Diff erence between TAI and UT C due to leap seconds since 1972 .

Similarly , the insertio n of leap seconds is due to th e fact that th e present length of the mean solar day is about 2.5 ms longer than a day of precisel y 86 400 SI seconds, as a consequence of the long- ter m trend, so that th e Earth's rotatio n runs slow with respect to atomic time. The SI secon d is equivalen t to the second of Ephemeri s Time, which in tur n is equal to the mean solar secon d of th e early nineteent h century. The length of the day was exactl y 86 400 SI seconds in abou t 1820. Befor e then, th e mean solar day was less than 86 400 s an d since then it has been greate r than 86 400 s. At the rate of about 1.4 ms per centur y over the past 180 years, the length of th e day has increase d by roughly 2.5 ms, so that today the length of the day is abou t 86 400.002 5 SI seconds. Th e differenc e of 2.5 ms per day accumulate s to nearly 1 s over an entir e year. It is this accumulate d differenc e that is compensated by the occasiona l insertion of a leap second to make the length of the year 1 s longer. A chang e in the frequency of occurrenc e of leap seconds is an indicatio n of the slowing down or acceleratio n of th e Earth's rotation. A least- squares t of th e differenc e [TAI ­ UTC] since 1972, shown in Figure 5, implie s a nearly linear
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increase with a slope of (2.10 ± 0.05) ms per day . This value represents the average excess in the length of day during the past three decade s and is in approximat e agreemen t with the valu e compute d on the basis of the long-term trend. Recent global weather conditions have contribute d to a short- ter m change in the length of day . Decad e uctuation s due to the interactio n between the Earth's cor e an d mantl e and global ocean circulatio n may also contribute. Thus at present, th e day is actuall y closer to 86 400 SI second s and leap seconds have not been required. However, this conditio n cannot persist an d the long-term trend will be eventuall y restored. The motivatio n for the leap second , therefore , is due to th e fact that the secon d as presently de ned is "too short" to keep in step with th e Earth. However, had the secon d been de ned to be exactl y equal to a mean solar secon d at the origin of TAI in 1958, the discrepancy would not hav e been removed; the agreemen t between the SI second and the mean solar secon d would have only been temporar y an d their difference would simply have becom e graduall y more apparent over the next century. 7.3 Operational dif culties of preserving the leap second Modern commercia l transpor t systems depend almost entirel y on satellit e navigatio n systems. Future systems ar e likel y to rely on these systems and their augmentatio n systems to improve navigatio n accuracy , reliability , integrit y an d availabilit y beyon d current capabilities . Increasin g worldwide relianc e on satellit e navigatio n for air transpor t is likel y to demand systems free of an y unpredictabl e changes in epoch. Many telecommunication s systems rely on precise time synchronization . For example , spread-spectru m communication s ar e not possible without a coherent time reference . Thus, during the introductio n of a leap second, communication s can be lost until synchronizatio n is re- established . However, only systems that depend speci call y on time are affected by the introductio n of leap seconds; system s depending on frequency have littl e or no sensitivit y to epoch. Another important consideratio n is the growing use of computers. In today's world of highspeed intercompute r communication s that time stam p messages at th e sub-second level , 1 s can be a signi cant length of time . In addition , clock s normally coun t from 59 s to 0 s of the next minute. Leap seconds requir e a coun t sequence of 59 s, 60 s, and then 0 s of the next minute. Many computer systems have a problem introducing the second labelled "60". A simila r concer n is that when dating events using the Julian Day (JD) or Modi ed Julian Day (MJD) includin g fraction s of a day , a positiv e leap secon d would create a situatio n where two events 1 s apar t can receiv e identical dates when those dates are expressed with a numerica l precision equivalen t to 1 s.
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In global synchronizatio n operation s involving multipl e locations , one frequentl y deals with differing hardwar e and software systems based on different standard s and operatin g practices . Th e possible introductio n of one or two 61 s minutes per year into continuou s site processes would directl y affect synchronizatio n if the leap seconds were not treate d identicall y at the same instant at all cooperatin g sites. The real- world operatio n of timin g systems is confronted by equipmen t upgrades and personnel changes. Th e possible effect s of maintenanc e procedures and human factor s in accommodatin g leap secon d steps should be given consideratio n in assessing the reliabilit y of such systems. Stand-alone data- gatherin g systems, isolated by speci c specialize d technica l applications , are now extremel y rare. Modern data systems rely on continuous, highly accurat e time . The possibility of disruption s to continuou s service would have a majo r impac t on their interactiv e operation . In some cases, the need to avoid disruption s has led to consideration s of using nontraditiona l timekeepin g systems, such as GPS Time or a time scale maintaine d by an individual government contractor , as a means of servin g this purpose. Continuin g use of a non-uniform tim e scale including leap second s in th e face of these consideration s could lead to th e proliferatio n of independen t uniform time s adopted to be convenien t for particula r objectives . If that happens, UTC would receiv e less acceptanc e as an internationa l standard. 7.4 Operational dif culties of eliminatin g the leap second Many astronomer s and satellit e ground- statio n operator s would prefer that leap seconds should not be eliminated . There is a signi cant amoun t of operational software at astronomica l observatories and satellit e ground stations that assumes implicitl y that DUT1 will always be a small number less than 1 s. This assumption would no longer be true if leap seconds were eliminated . Fixing, testing and documentin g all the computer codes could be an enormous task. The current transmission formats for radio and telephon e broadcasts of time signals depend on the fact that DUT1 is less than 1 s. It may be dif cult to change these formats due to the prevalenc e of legacy hardware. In commercia l industry, there ar e certai n clocks that receiv e radio broadcast tim e signals to automaticall y display accurat e time . These and similar devices might be affecte d adversely by a chang e in the broadcast format. 8. Satellit e navigation systems Historically , the rational e behind the de nitio n of UTC was for its applicatio n to celestial navigatio n while providing a precise standar d for time and frequency. 519


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Celestial navigatio n using stellar observations requires knowledge of UT1 at the time of the observations. When it was introduced , UTC was still the most readil y availabl e worldwide system for independen t determinatio n of position . But as the formation of UTC progressed, the abilit y to track satellite s on a worldwide basis and th e growing global communicatio n an d positioning capabilitie s they could provide becam e major considerations . Today, with GPS [112] and GLONASS [113], complemente d by LORAN an d other radionavigatio n systems, celestia l positio n determinatio n is not as common . These systems an d the augmentatio n systems they have fostered have been incorporated into virtuall y ever y facet of international , telecommunication , militar y an d commercia l technology . With extremel y high accurac y and global coverage, satellit e navigatio n systems have collectivel y become a new public utilit y known by the general designatio n of Global Navigation Satellit e System (GNSS). 8.1 GPS Th e Global Positioning System (GPS) is a satellit e navigatio n system develope d by the US Departmen t of Defense. The programm e evolved from earlier systems an d was formally chartere d in 1973 [114]. Th e GPS comprises a nominal constellatio n of twentyfour satellite s with an orbital radiu s of 26 560 km, corresponding to a period of revolutio n of 12 sidereal hours (11 h 58 min) . There are six orbital planes inclined at 55 with four satellite s per plane. The constellatio n geometr y ensures that between four and eleve n satellite s are simultaneousl y visible at all times from an y point on the Earth. Block I developmenta l prototyp e satellite s were launche d between 1978 an d 1985, while Block II productio n satellite s were launched beginning in 1989. The system was declare d fully operational in 1995. The current GPS constellatio n consists of twenty-eigh t Block II/IIA/IIR satellites . Each satellit e carrie s multipl e caesium and rubidium atomi c clocks. The fundamental clock frequency is 10.2 3 MHz. Th e satellite and global trackin g network atomic clocks ar e used to generat e the continuous system time known as GPS Time , which is speci ed to be within 1 m s of UTC as maintaine d by USNO, except leap seconds are not inserted. The algorith m de ning th e relationshi p between GPS Tim e an d UTC thus includes a correctio n for leap seconds. Th e origin of GPS Time is midnight of 5/6 Januar y 1980, with the consequence that TAI is ahead of GPS Time by 19 s, a constant value. As of 1 January 2001, GPS Tim e is ahead of UTC by 13 s. With appropriat e correction s for signal propagation, relativity , an d other effects, GPS provides a referenc e for time with a precision of 10 ns or better . The GPS satellite s transmit signals at two carrie r frequencies in L- band: the L1 componen t with a centr e 520

frequency of 1575.42 MHz and the L2 component with a centr e frequency of 1227.60 MHz. The precision P code (or the encrypte d Y code used in place of the P code) is a spread- spectrum , pseudo-random noise (PRN) code with a bit rate ("chip rate") of 10.23 MHz. The P(Y) code has a period of 38.058 weeks, but it is truncated into one- week segments to distinguish individual satellites . The coarse/acquisitio n C/A code is a PRN code with a bit rate of 1.02 3 MHz that repeat s itself every 1 ms [115, 116]. GPS provides two level s of service. The Precise Positioning Service, intende d for authorize d users, employ s th e P(Y) code, which is transmitte d on both the L1 and L2 frequencies . Th e Standard Positionin g Service, intende d for civil users, employs the C/A code, which is transmitte d on only the L1 frequency. Th e C/A code is also used for satellit e acquisitio n by all users. The determinatio n of position may be characterize d as the process of triangulatio n using pseudo- rang e measurement s from four or mor e satellites . Th e militar y P(Y) cod e receive r has a 95 % horizontal position accuracy of abou t 5 m. Until recently , the civil C/A code was intentionall y degraded by a techniqu e calle d Selectiv e Availabilit y (SA), which introduce d position error s of 50 m to 100 m by dithering the satellite clock data. This techniqu e also restricted tim e transfer to about 300 ns in real time. However, on 2 May 2000, under a US presidentia l directive , the SA featur e of the C/A code was set to zero. Consequently , th e civil GPS accuracy is now about 10 m to 30 m in position and 10 ns to 30 ns in time. Differential correctio n systems, where they ar e available , can permit position determinatio n to an accurac y of less than a metre . A variet y of GPS modernizatio n initiative s are under way. With th e additio n of a new L2 civil (L2C) signal on GPS Block IIR- M satellite s in 2003, the civil 95 % horizontal positio n accuracy will become about 5 m to 10 m. Also, in 2000 th e World Radiocommunicatio n Conference (Istanbul) approved a thir d civil frequency, known as L5, to be centred at 1176.45 MHz in the Aeronautical Radio Navigatio n Services (ARNS) band . This thir d frequency, to be availabl e on GPS Block IIF satellite s in 2005, would permit th e creatio n of two beat frequencie s that would yield sub-metr e positionin g accurac y in real tim e [117]. A new generatio n of GPS with enhance d capabilities , GPS III, is to be implemente d beginnin g in 2010. The orbit determinatio n process for GPS, like virtuall y all other Earth- orbitin g satellites , requires precise knowledge of [UT1 ­ UTC]. Th e commo n procedur e involves integratio n of the equation s of motion in an Earth- Centre d Inertial (ECI) reference frame. The trackin g stations, however , are located in the Earth- Centre d Earth-Fixed (ECEF) referenc e frame of th e rotating Earth. Th e usual choice of th e inertial coordinat e system is the J2000.0 referenc e frame based on the FK5 star catalogue, while th e physical model of the Earth is the World Geodetic System 1984 (WGS 84)
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[118, 119]. Th e data from the trackin g stations ar e typicall y time-tagge d with a particula r realizatio n of UTC. Moreover, th e Earth's gravitationa l eld is also rotatin g with th e Earth and the perturbing gravitationa l forces must be transformed , via four rotation matrices , from the ECE F frame into the ECI frame as part of the orbit determinatio n process. The matrices account for the Earth 's polar motion , variabl e rotation, nutatio n and precession. Near real-tim e orbit determinatio n must use prediction s of [UT1 ­ UTC]. Today, these prediction s ar e expressed in the form of a polynomial model that is updated weekly [120]. As GPS Time does not include leap seconds, the introductio n of a leap secon d into UTC does not affect GPS users. The GPS operationa l contro l segment, however , must carefull y account for th e leap second step in [UT1 ­ UTC]. Prior to a leap second event, two sets of "Earth Orientatio n Parameters " are provided to the GPS control segment. One set is used up to the time a leap second is inserted and a second set, which contain s the new 1 s step in [UT1 ­ UTC], is used after the leap second is inserted. 8.2 GLONASS Th e Russian Global Navigatio n Satellit e System (GLONASS) has many feature s in common with GPS [121, 122]. The nominal constellatio n consists of twenty- four satellite s in three planes incline d at 64.8 . The orbital radius is 25 510 km and th e perio d is 8/17 sidereal day (11 h 15 min) . The rst satellit e was launched in 1982. The system was fully deployed in early 1996 but currentl y ther e are only nin e operationa l satellites . However, there is a commitmen t to restore the complet e twenty- four satellit e constellatio n by 2004. In contrast to GPS, the GLONASS satellite s all transmit the same codes and ar e distinguished by individual L-ban d carrie r frequencies . Thus, while GPS uses the spread-spectru m techniqu e of Code Division Multiple Access (CDMA), GLONASS uses Frequency Divisio n Multiple Access (FDMA). The GLONASS design uses Moscow Time , [UTC + 3 h], as its time reference instead of its own internal time. Thus, users of this system are directl y affected by leap seconds. During the process of resettin g the tim e to accoun t for a leap second, the system is unavailabl e for navigatio n service because the clock s are not synchronized. 8.3 Utilizatio n of satellit e systems Current CGPM, ITU- R an d IAU recommendation s address th e use of satellite s for space services, frequencies , and time transfer. The growing utilizatio n of satellit e systems and their interna l time scales may graduall y become the primar y source of time for many practica l applications . Laboratorie s separated by several thousand kilometre s can routinely perfor m time comparisons using GPS common- vie w technique s with
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a precision of a few nanoseconds. GLONASS can provide continenta l tim e transfer with somewhat less precision . Another techniqu e coming into wider use is Two-Way Satellit e Tim e Transfer (TWSTT ) using geostationar y communication s satellites. This techniqu e utilizes the wideban d communication s capabilit y to transmit bidirectional , spread- spectrum ranging codes that permit time comparisons at the sub- nanosecond level. In comparison, the DUT1 code availabl e in terrestria l radio signals that disseminat e UTC has a resolution of 0.1 s. The correspondin g position error on the equator is about 50 m. A 1 s resolution between UT1 and UTC corresponds to a positio n erro r using celestial measurement s of 0.5 km. As a result, satellite systems are superseding UTC radio signals as a means of time determinatio n for navigation . 9. International agreements on tim e No single internationa l agency by itself could assume complet e responsibility for the de nition and rules for th e disseminatio n of time . Many internationa l scienti c organizations , listed below , have combined their efforts in the development , realizatio n and disseminatio n of Internationa l Atomic Time (TAI) and Coordinated Universal Tim e (UTC). Their work has established th e link between th e traditional astronomica l determinatio n of time and that based on fundamenta l atomi c phenomena . This essential cooperatio n was required to support the necessar y scienti c foundation . (1) The General Conference on Weights an d Measures (Confeá rence Gen erale des Poids et Mesures, áá CGPM), which has responsibility for the International System of Units (Systeme Internationa l à d'Unites, SI), was established by th e Convention á of the Metr e (Convention du Metre) , signed in à Paris by representative s of seventeen countries in 1875 and amende d in 1921. The Convention now has fty-one signatories. Under the terms of th e Convention, the Bureau International des Poids et Mesures (BIPM) operates under the supervision of the International Committe e for Weights and Measures (ComiteáInternationa l des Poids et Mesures, CIPM), which itself comes under the authority of the CGPM [123, 124]. During the period when TAI and UTC were developed , the CIPM received guidance from the Comite Consultati f pour la De nitio n de la Second e á á (CCDS), set up in 1956. This committe e was rename d the Consultativ e Committe e for Time and Frequency (Comite Consultati f du Temp s á et des Frequences, CCTF) in 1997. The BIPM á organize s th e time links used for computin g and disseminatin g TAI and UTC. It issues a monthly Circular T that contain s the informatio n needed to obtain these time scales at the best level of accuracy. 521


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(2) The Internationa l Radio Consultativ e Committe e (CCIR) of the Internationa l Telecommunicatio n Union (ITU) was establishe d in 1927 to coordinat e technica l studies, tests and measurement s in the various eld s of telecommunication s and to establish internationa l standards. Recommendation s for standardizatio n of internationa l broadcast time were drafted at the CCIR Xth Plenar y Assembly in Genev a in 1963 and XIth Plenar y Assembly in Oslo in 1966. Study Group 7 was formed in 1959 to includ e space radiocommunicatio n and frequencie s an d was responsible for the de nitio n of UTC as the standar d for frequency and time dissemination . The ITU Plenipotentiar y Conference of 1992 reorganized the CCIR into the ITU- R (Radiocommunicatio n Sector) . Working Party 7A continues as the responsible body for Standar d Frequency and Time Signals. (3) The Internationa l Astronomical Union (IAU) was established during th e Constitutiv e Assembly of the Internationa l Research Council (IRC) held in Brussels in 1919. The IRC was succeeded by the International Council of Scienti c Unions (ICSU) in 1931 (rename d the International Council for Science in 1998) [125, 126]. Through its Commissions 4 (Ephemerides) , 19 (Rotatio n of the Earth) , and 31 (Time) , the IAU standardize d the de nition s of Universal Time, Ephemeri s Time, and the various relativisti c time scales and determined their relationship s to International Atomic Time . (4) The Internationa l Union of Geodesy an d Geophysics (IUGG) is a membe r of the ICSU and was establishe d by the IRC in 1919. The IUGG is dedicate d to the scienti c study of th e Earth and its environmen t in space and includes the International Association of Geodesy (IAG). (5) The International Union of Radio Science (URSI) is a membe r of th e ICSU and was established by the IRC in 1919 to encourage scienti c studies of radiotelegraph y an d promote internationa l cooperation. Its present charter includes intercompariso n and standardizatio n of the measuring instruments used in scienti c work and scienti c aspects of telecommunications . URSI mad e th e original recommendatio n for the worldwide broadcast of offset atomic time. (6) The Bureau International de l'Heure (BIH) was established at the Paris Observator y in 1919 by th e IRC Constitutive Assembly to coordinat e internationa l radio time signals. Originally, the BIH was under the directio n of IAU Commissio n 31, but in 1956 it becam e a service of th e Federatio n of Astronomical an d Geophysical Data Analysis Services (FAGS) with th e IAU, IUGG and URSI as parent unions. The BIH was requested by the CCIR in 1963 to determin e the proper offsets 522

between UT2 and broadcast atomi c tim e an d to coordinat e th e worldwide standar d frequency and tim e signal service prescribed by the CCIR. Th e BIH transferred this function, as well as the establishmen t of Internationa l Atomic Time , to th e BIPM on 1 January 1988, while its activitie s on the rotation of the Earth were taken over by a new service, th e Internationa l Earth Rotatio n Service. (7) The Internationa l Earth Rotatio n Service (IERS) was establishe d in 1987 by the IAU and the IUGG and began operatio n on 1 January 1988. Its structur e was reorganized commencin g in 2001. The IERS is an internationa l consortiu m of nationa l laboratories and observatorie s that provides operationa l data related to the orientatio n of th e Earth in space. It has the responsibility for decision s regarding changes to UTC based on observation s of the Earth's rotation and determines when leap seconds should be applied . The IERS publishes four bulletins. Bulletin A (daily and semiweekly ) is issued by th e Sub- Bureau for Rapid Service and Predictions at USNO and contain s rapid determination s for Earth Orientatio n Parameters; Bulletin B contain s monthly Earth Orientatio n Parameters . Bulletin C, containin g announcement s of the leap seconds in UTC, and Bulletin D, containin g announcements of the value of DUT1, ar e distributed as required. Merely to enumerat e these agencies an d their commissions, study groups and sub- committee s is to realiz e the complexit y of th e internationa l establishmen t in charge of time , and the dif culty of makin g fundamenta l changes. The present de nition of UTC is the result of far- reachin g compromise s among the communitie s that these agencie s represent. Today 's user communitie s have changed signi cantl y in the few ensuing decades, just as the uses of time have changed. Th e traditiona l radio broadcast of time signals is being overtake n by satellit e signals linked directl y to atomi c standards. Ensembles of atomi c standards in individual laboratories and highspeed computer network s are synchronized to these same standards. The man y and diverse purposes that an internationa l time scale must serve are now part of an internationa l telecommunicatio n and commercia l infrastructur e involving signi cant economi c interest s in which changes represen t a major nancia l investment . This new relationshi p could make change mor e dif cult. If a new or revised internationa l standar d is to represen t all the legitimat e interests, coordinatio n with nontraditiona l agencie s an d groups may be necessary. 10. Lega l tim e An important consideratio n with the curren t de nition of UTC is the legal de nition of time implied within
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the domestic law s of individual countrie s [127]. The purpose of statute s governing legal tim e is to promote commerc e and the public interest . 10.1 Standard Time Th e advent of the railroad s in the secon d quarter of the nineteent h century introduced an er a of high-speed transport and mobility . Efforts to coordinat e schedules culminate d in the adoption of regional zones of Standar d Time and the choice of Greenwich as th e internationa l reference for the prime meridian . Greenwich Mean Time (GMT) has been th e legal time in the UK since 1880. In the USA, the Standar d Time Act of 19 March 1918, as amende d by the Uniform Time Act of 1966, established eight time zones that ar e based on mean solar time and ar e nominall y separated in longitude by interval s of 15 (1 h) with respect to the Greenwich meridian [128, 129]. It also authorized the Interstat e Commerce Commission to modif y th e time zone boundaries. In 1983 this responsibility was transferred to the Departmen t of Transportation. The publicatio n of the British Nautica l Almanac beginnin g with the year 1767 by the Astronomer Royal Nevil Maskelyne, which enable d the determinatio n of longitud e at sea using observation s of the Moon's positio n with respect to the stars, and the contemporaneou s developmen t of th e marine chronomete r by John Harrison, had establishe d Greenwich as the de facto fundamental referenc e for longitude and time for over a century [130, 131]. Th e Greenwich meridia n was formally recommende d as a worldwide standar d referenc e for longitud e and time at th e Internationa l Meridian Conference , held in Washington, D.C., in October 1884 at the invitatio n of the United States Government, as a result of discussions that had taken place at several scienti c conference s over the previous decade. By then nearly three-quarter s of the world's commercia l ships used charts based on the Greenwich meridian . The Conference also recommended th e adoption of a Universal Day, de ned as a mean solar day counted from 0 up to 24 hours, that would begin at midnight at the prime meridia n [132, 133]. The idea of time zones was rst proposed in 1870 by Charles F. Dowd [134], an American colleg e professor, as a method of regulatin g time for the railroads. In Dowd's plan , standard tim e would be used by the railroads, while each city and town would preserve its own local time. A simila r proposal, but one that recommended adjusting local time to railroa d time , was late r successfully promoted by William F. Allen [135], editor of a prominent railroad periodica l an d Secretar y of the American Railway Association. Importan t contribution s were also mad e by Clevelan d Abbe [136] of the US Signal Service and Sandford Flemin g [137] of the Canadia n Paci c Railway. To
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permit a more convenien t locatio n of time zon e boundaries, th e Greenwich meridia n was chosen as the primar y referenc e rather than Washington , D.C. "Standar d Railway Time" was adopted throughout North America at noon on Sunday, 18 November 1883, reducing the number of railroad time s from forty-nin e to ve, and was soon extende d to civil time [138]. The rapid growth of the railroad s create d a demand for time synchronizatio n across large distances and the continuin g expansio n of the networ k of telegrap h wires alon g their rights of way provided the means for achievin g it. Towards the en d of th e nineteent h century, the US Naval Observator y was disseminatin g a daily time signal via the Western Union Telegrap h Company to cities throughout th e East, South and Midwest of the USA [139]. Daylight Saving Tim e was conceive d by Willia m Willett , a successful London builder , in 1907 [140]; it was rst introduce d in Europe and North America during th e First World War as a means of conserving energy [141]. In th e USA, the Standar d Tim e Act of 1918 required th e observance of Daylight Saving Time , which is advance d 1 h ahead of Standar d Time over seven months of the year, in additio n to providing a legal basis for ve tim e zones (extended to eight in 1966 to cover all US territories) . 10.2 Greenwich Mean Time Originally , Greenwich Mean Tim e (GMT) was de ned as mean solar time on the meridia n of Greenwich reckoned from mean noon. In 1919, th e BIH undertook to coordinat e th e emission of radio time signals on the basis of Greenwich Civil Tim e (i.e. GMT plus 12 h), as recommende d by the Internationa l Meridian Conference. The astronomical almanac s kept GMT as the time argument until 1925. Beginnin g in 1925, the British Nautical Almanac and many other nationa l ephemerides reckoned GMT from midnight to coincid e with the civil day, rather than noon as had been the traditiona l astronomical practice . The rede ned GMT was designate d Universal Time (UT) by the IAU in 1928 [142]. However, the ter m GMT persisted in almanac s and navigatio n publication s and the ambiguit y in its intended meanin g was the cause of some confusion [143]. 10.3 Coordinated Universal Time The terms "mean solar time " and "GMT" have come to be recognize d as being synonymous with UTC in ordinar y language . In 1970, Commission 31 of the IAU recommende d that clocks in common use would indicat e minutes, seconds and fraction s of UTC and that the ter m "GMT" would be accepte d as the general equivalen t of UTC in navigatio n an d communication s [144]. The 15th CGPM in 1975 adopted the following resolution [145]: 523


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"The 15th Conference Generale des Poids et Mesures, á áá considering that th e system called "Coordinate d Universal Time " (UTC) is widely used, that it is broadcast in most radio transmissions of time signals, that this wide diffusion makes availabl e to the users not only frequency standards but also International Atomic Time and an approximatio n to Universal Time (or, if one prefers, mean solar time), notes that this Coordinated Universal Time provides the basis of civil time, th e use of which is legal in most countries, judges that this usage is strongly endorsed." Th e internationa l diplomatic authority for the decisions of the CGPM and its organs is conveyed through the Conventio n of the Metr e of 1875. The CCIR in 1978 an d the World Administrativ e Radio Conference (Geneva) in 1979 recommende d that UTC should be used to designate th e time in all internationa l telecommunicatio n activitie s [146]. The ITU Radio Regulation s de ne UTC as the time scale, based on the SI second , as speci ed in Recommendatio n ITU- R TF.460-5 . The de nition is accompanie d by the following Note [147]: "For most practica l purposes associated with th e Radio Regulations , UTC is equivalen t to mean solar time at the prime meridian (0 longitude) , formerly expressed in GMT." This de nitio n is cited in the Code of Federal Regulations , Titl e 47, that speci es th e rules of th e US Federal Communication s Commission (FCC) [148]. The role that UTC play s in national and internationa l monetar y exchange, telecommunication s an d relate d forms of commerce is not clear . Should the de nition of UTC be revised, th e effect on legal codes may need to be investigated . 11. Future developments 11.1 Options for UTC Ther e exist a variet y of options for the future of UTC. Some of these option s are identi ed and discussed below. (1) Maintain th e status quo. The advantag e of maintainin g the present form of UTC is that established timekeepin g practice s will not requir e modi cation . On the other hand, if leap seconds were continued , the required number and frequency can only increase, as shown in Figure 6. By 2100 there would be a need for nearly two leap seconds per year . Th e current emergin g problem s and th e resultin g dissatisfactio n with leap seconds will only continue to grow. Th e operational impact and associated cost of maintainin g leap second s in 524
Figure 6. Projected increase in leap seconds versus time (after McCar thy and Klepczynski [149]) .

complex timekeepin g systems must be considered in evaluatin g their continue d use in the future. (2) Increase the tolerance between UT1 and UTC. A small incremen t of several leap seconds could be inserted into UTC ever y few year s or, alternatively , a "leap minute " in about fty years. The advantag e of this approach is that it would be relativel y easy to adopt. However, due to the paraboli c rate of departur e between solar time and atomi c time, the tolerance would hav e to be continuall y increase d and eventuall y larger time steps would be required. (3) Periodic insertion of leap seconds. A time step could be inserted into UTC at a well- de ned interval , such as on 29 February ever y four years. The advantag e is that the date would be predictable . However, the number of leap seconds would not be predictabl e and larg e time steps would still be required. (4) Variable adjustments in frequency . This alternativ e is simila r to the original form of UTC that was abandoned. Introducing a variabl e atomi c scale in step with solar time would cause signi cant disruptions to equipmen t and would not disseminat e the unit of time , th e SI second. (5) Rede ne the second . This option would appear to be th e most fundamenta l solution. However, it would be inconsisten t with the usual practic e in metrology , which is to adop t a new de nition of a unit only when its realizatio n under the old de nition becomes the limitin g source of experimenta l uncertaint y an d to maintai n continuit y between the old and new realizations . Changing the de nitio n of th e second to be closer to the current rotationa l second would alte r the valu e of ever y physical measuremen t an d render obsolete ever y instrumen t relate d to time . Moreover , the solution would be only temporar y as the Earth continue s to decelerate .
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(6) Substitute TAI for UTC. TAI is the fundamenta l atomi c tim e scale "in the background" from which other scales of unifor m time ar e derived . TAI is relate d to UTC by the relatio n [TAI] [U T C + AT], where AT is the incremen t to be applie d to UTC to giv e TAI and is equal to the total number of leap seconds plus 10 s. In 2001, the value of AT was +32 s. Th e advantag e of TAI is that it is a continuous, atomic tim e scale without steps. However, TAI is currentl y not easily availabl e to the precise time user and, as TAI is currentl y ahead of UTC by an offset of 32 s, a worldwide adjustmen t of clock s would be required if it were adopted as the scale of civil time . Promotio n of two parallel time scales for civil timekeeping , one with leap second s and one without, would be potentiall y confusing . In addition , as UTC is recognize d as the primar y basis of civil time in resolution s of various internationa l treat y and scienti c organization s and by many conforming nationa l legal codes, a worldwide change in the legal de nitio n of tim e would be required if UTC were replace d by TAI. (7) Discontinue leap seconds in UTC. This option would permit continuit y with the existin g UTC time scale an d would eliminat e th e need for futur e adjustment s to comple x timekeepin g systems. Figure 7 shows th e projected differenc e between UTC without leap seconds an d UT1. If th e current rate of deceleratio n of the Earth's rotation were to persist and no leap second s were added, by 2050 the differenc e between UTC an d UT1 would be about 1 min. By the end of th e twenty- rst century, the expected difference would be about 2.5 min [149]. However, these differences are minor compared with th e differenc e between apparent solar time and mean solar time (up to 16.5 min) , mean solar time an d clock time within a given time zone (nominall y up to 30 min) , or Daylight Saving

Time and Standar d Time (1 h). It is thu s unlikely that the growing differenc e between clock time and level s of daylight would be noticeabl e for the foreseeabl e future. Also, certai n religious custom s depen d on the actua l observation of the Sun or the Moon and do not depend on clock time . Therefore, th e eliminatio n of leap seconds would hav e no practica l effect on the correspondence between civil time an d solar time or on contemporar y social conventions. Th e use of UTC without leap second s would retai n all the advantage s of TAI. Th e transition to a continuous UTC system might be planned for a future date suf cientl y far in advance that changes to existing hardware an d software, where necessary, could be accommodate d within th e normal maintenanc e and replacemen t schedules. 11.2 Requirements of celestia l navigatio n There remain s the need to meet the requirement s of celestia l navigation . Three possible options for addressin g this need if the current UTC system were revised are considered . Additional alternative s may be identi ed as the issue is debated . (1) Alternativ e tim e scale fo r navigation. A new broadcast scale of time, possibly designated "UT1C", might be disseminated by supplementar y coded signals that provide the approximat e differenc e between the newly de ned UTC and UT1, just as DUT1 codes currentl y give the differenc e between the presently de ned UTC and UT1 to th e nearest 0.1 s. However, most tim e code formats would hav e to be modi ed to accommodat e a difference in tim e greate r than 1 s. As a bene cial trade-off, the resolution might be increase d in the process, for exampl e to 0.00 1 s. Th e time difference [UTC ­ UT1C] might also be convenientl y disseminate d in satellit e navigatio n messages, possibly as a commercia l service. (2) Greater emphasis on UT1 predictions. These requirement s might also be met by published predictions of [UT1 ­ UTC]. The IERS/USNO provides daily an d semiweekl y prediction s in Bulletin A , availabl e on the Internet at http://www.iers.org. Th e estimated accuracie s ar e 0.0017 s at 10 days and 0.0039 s at 30 days. For example , the National Imager y and Mapping Agency (NIMA) provides Earth Orientatio n Paramete r Predictio n coef cient s based on IERS/USNO weekly post- t values that ar e used to generat e [UT1 ­ UTC] prediction s for GPS orbit determination . In addition , longter m projection s might be include d in the nautical ephemeride s with less precision. With th e usual yearly schedule of publication , the extrapolatio n should not bring error s exceedin g 1 s (leadin g to a positio n error of 0.5 km at most) . Through both short- term and long-term UT1 predictions , it 525

Figure 7. Projected difference between UTC and UT1 if leap seconds were discontinue d (after McCarthy and Klepczynski [149] ) .
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would be possible to complemen t the informatio n to navigator s by disseminatin g a correctio n to the argument of th e ephemerides , as is done currentl y with DUT1. (3) Greater emphasis on satellit e navigation systems. Due to the availabilit y of th e GPS and GLONASS satellit e navigatio n systems and the possibility of simila r future systems, such as Galileo , the need for coded terrestrial radio tim e signals is less than it once was. Existing internationa l agreement s might be recast to redirec t the focus of those agreement s towards increase d use of moder n satellit e navigational aids. 12. Conclusions Th e transition from solar time to atomi c time , made possible by th e developmen t of atomi c clocks, represents a paradigm shift in th e way tim e itself is perceived that is not unlike the transitio n from the unequal hour to th e equal hour ve hundred year s ago, brought about by the inventio n of mechanica l clocks, or the transitio n from apparent time to mean solar time some two hundred years ag o that was mad e possible by improvement s to pendulum clocks. The most basic issue in the futur e of UTC is th e natur e of the social requiremen t to adjust an extremel y precise, unifor m tim e scale to th e time determined using the variabl e rotatio n of the Earth. Common practice today has alread y compromise d this requiremen t to the point that we ar e conten t with conventional construction s such as mean solar time, zone tim e and Dayligh t Saving Time . We should realiz e that, as a result of the change from apparen t to mean time , th e local mean noon of our clocks can sometime s be about 15 min before or after the apparen t noon of th e Sun; thu s the afternoons in November ar e half an hour shorter than the mornings, while in Februar y the mornings are half an hour shorter than the afternoons. This change was even more fundamenta l than that from local mean time to zone time [150]. All these convention s introduce substantial differences between the commonly accepted time and solar time that ar e order s of magnitude larger than the difference between a unifor m tim e scale and a solar time scale. We anticipat e that this difference will grow by an additiona l 2 min over the next century . Will we be willing to neglect this differenc e in civil time scales? Th e astronomicall y determine d rotation angle will be measured with improving accuracy during that perio d an d will be mad e availabl e to users sooner. Will this be able to satisf y user needs? In each stage of the evolution of timekeeping , ther e has been an incrementa l step away from the Sun as the measur e of time in favour of a mor e uniform, accessible , or convenien t standard . The next stag e in th e evolutio n of UTC may be a de nition of civil tim e in term s of a continuous scale of atomic tim e and a disassociatio n 526

of civil time from solar tim e altogether , accompanie d by the adoption of a representatio n of UT1 for those users who need it. Throughout th e histor y of time measurement , from sundials to atomi c clocks, time scales hav e alway s been established by takin g into account prevailin g technolog y and needs. Since the UTC system of leap seconds was introduce d thirty year s ago, both of these factor s have changed. Therefore, we should perhaps not be to o hesitant in adaptin g to moder n technolog y and moder n needs. References
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120 . 121 . 122 . 123.

124. 125 . 126 . 127 . 128.

129. 130. 131 . 132 . 133 . 134.

135 .

Receive d on 9 July 2001 and in revised form on 5 September 2001.

M et rol ogi a , 2001, 38 , 509- 529

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