INNOVATION
GPS and Leap Seconds Time to Change?
Dennis D. McCarthy, U.S. Naval Observatory William J. Klepczynski, Innovative Solutions International
Since ancient times, we have used the Just as leap years keep our calendar approxi- seconds. While resetting the GLONASS Earth’s rotation to regulate our daily mately synchronized with the Earth’s orbit clocks, the system is unavailable for naviga- activities. By noticing the approximate about the Sun, leap seconds keep precise tion service because the clocks are not syn- position of the sun in the sky, we knew clocks in synchronization with the rotating chronized. If worldwide reliance on satellite how much time was left for the day’s Earth, the traditional “clock” that humans navigation for air transportation increases in hunting or farming, or when we should have used to determine time. Coordinated the future, depending on a system that may stop work to eat or pray. First Universal Time (UTC), created by adjusting not be operational during some critical areas sundials, water clocks, and then International Atomic Time (TAI) by the of flight could be a difficulty. Recognizing mechanical clocks were invented to tell appropriate number of leap seconds, is the this problem, GLONASS developers plan to time more precisely by essentially uniform time scale that is the basis of most significantly reduce the outage time with the interpolating from noon to noon. civil timekeeping in the world. The concept next generation of satellites. As mechanical clocks became of a leap second was introduced to ensure Navigation is not the only service affected increasingly accurate, we discovered that UTC would not differ by more than 0.9 by leap seconds. Spread-spectrum systems that the Earth does not rotate “like second from UT1, the time determined by the also rely on time synchronization for effec- clockwork,” but actually has a slightly rotation of the Earth — a choice made pri- tive communications. When sychronization nonconstant rotation rate. In addition marily to meet the requirements for celestial is lost, so too is coherent communication. to periodic and irregular variations navigation. Thus, while a leap second is being intro- caused by atmospheric winds and the To determine longitude and latitude using duced, and until sychronization is estab- interaction between the Earth’s core a sextant and observations of stars, one needs lished, communications can be disrupted and the mantle, the tidal interaction to know UT1 at the instant of the observa- between some systems. of the Earth and the Moon causes a tions. An error of one second in time could In view of these emerging problems, user secular slowing down of the Earth’s translate into an error of about 500 meters in dissatisfaction with leap seconds is beginning rotation. So rather than use the position. Celestial navigation was one of the to surface, and concern is growing that users variable time scale based on the major navigation techniques used throughout will construct time scales independent of Earth’s rotation, we now use time the world in 1972, when the first leap second UTC that they perceive are more suited to scales based on extraordinarily was introduced. With the recent proliferation their individual requirements. This would precise atomic time, the basis for all of satellite navigation, however, it is appro- lead to an increased number of nonstandard the world’s civil time systems — priate to reconsider this historical position, as time scales. Coordinated Universal Time (UTC). the leap second may in fact be detrimental to Although we have accurate estimates of However, because of the desire some systems, possibly creating life-threat- the deceleration of the Earth’s rotation, sig- to keep UTC more or less in ening situations. nificant variations prevent the prediction of synchronization with the Earth’s Modern commercial transportation sys- leap seconds beyond a few months in rotation as an aid in determining tems now almost entirely depend on satellite advance. This inability to predict leap sec- navigation fixes using astronomical navigation systems. In the future, commer- onds, coupled with the growing urgency for a observations, leap seconds are added cial aviation is expected to rely on various uniform time scale without discontinuities, to UTC — currently about every 18 augmentation systems to improve satellite makes it appropriate to re-examine the leap months. navigation accuracy, reliability, integrity, second’s role. Later in this article, we will In contrast, the time scale used to and availability beyond current capabil- outline several possible scenarios for dealing regulate the Global Positioning System ities. The introduction of a leap second with leap seconds in the future, but first, let’s — GPS Time — is a “pure” atomic does not affect GPS operations because its review how the present system came to be. time scale without leap seconds. In time system is GPS Time, which is not this month’s column, Drs. Dennis adjusted to account for leap seconds. But A BRIEF HISTORY McCarthy and William Klepczynski GPS does provide UTC by transmitting the Historically, humans used astronomical phe- suggest that the practice of adding leap necessary data in its navigation message, nomena to keep time. The passage of the Sun seconds to UTC be done away with or permitting a receiver to compute UTC from across a north–south (meridian) line deter- at least modified, as more and more GPS Time. mined noon. Until 1960, the average solar navigators adopt Global Navigation By contrast, GLONASS uses UTC as its day was used as the basis for timekeeping, hours with the second defined as 1/86,400 of the 3 ם Satellite Systems as their primary time reference (actually UTC means of positioning. which is Moscow Time), and so its satellite mean solar day. Under this system, the length clocks must be reset to account for any leap of the second depended on the Earth’s rate of
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rotation, because its rotation causes the Sun to appear to move across the sky. 80 During the mid-1930s, astronomers con- cluded the Earth did not rotate uniformly, basing their findings on measurements of the 60 most precise clocks then available. We now know that a variety of physical phenomena affect the Earth’s rotational speed. This 40 caused the second to be redefined in 1960 in terms of the Earth’s orbital motion around 20 the Sun. The new second was called the “Ephemeris” second and the time scale 0
derived from this definition was called (seconds) T Ephemeris Time (ET). ⌬ The name called attention to the fact that -20 the definition depended on the position and motion (ephemeris) of the Sun (or Moon) used in the astronomical determination of -40 time. It was originally thought that the new definition would provide a more uniform -60 measure of the second’s length. ET is very 1600 1700 1800 1900 2000 difficult to measure and observe, however, Year requiring a series of accurate astronomical observations stretching over years. In 1967, the second was again redefined, Figure 1. Observations and quadratic fit of the difference between a uniform time this time in terms of the resonance frequency scale and one based on the Earth’s rotation of the cesium atom, which had already been calibrated with respect to ET. By the early we would have to add some time to the face can vary either way. So far, all leap seconds 1960s, cesium frequency standards became of our atomic clock, which is exactly what have been positive. known as reliable, uniform, and accurate we do when we add a leap second to our Astronomical observations show a near- clocks. Defining the second this way pro- clocks. We are bringing the faces of our lab- constant deceleration of the Earth’s rotation vided a uniform standard that easily could be oratory clocks back into agreement with rate caused by the braking action of the tides. measured in a laboratory with greater preci- the time kept by the rotating Earth, so that This deceleration explains why the length of sion and accuracy than any astronomical sunrise will occur at the “correct” time from the astronomical day is approximately two phenomena. year to year. milliseconds longer today than at the begin- Increasing Accuracy. Subsequently, ET was The Move to Cesium. With the introduction of ning of the twentieth century. With the differ- superseded by a set of dynamical time scales the cesium atom–based definition of the sec- ence between UTC and UT1 growing at the defined to meet special relativistic require- ond, it was known that there would be a time rate of two milliseconds per day, or 0.7 sec- ments. At the level of accuracy with which varying discrepancy between a clock running ond per year, currently about one leap second ET could be determined (approximately at a uniform rate and a theoretical one using a per year must be inserted in UTC. 0.001 second), these new time scales are second defined solely by the Earth’s rotation The astronomical observations provide a equivalent to ET and include Terrestrial rate. Beginning in 1961, the Bureau Interna- clear estimate of the magnitude of the decel- Dynamical Time (TDT), Barycentric tional de l’Heure (the forerunner of the Inter- eration of the Earth’s rotation rate. Figure 1 Dynamical Time (TDB), Terrestrial Time national Earth Rotation Service) accounted combines data from as far back as the 1600s (TT), Geocentric Coordinate Time (TCG), for these observed variations by making with data recently acquired using modern and Barycentric Coordinate Time (TCB). small adjustments, on the order of a few mil- space geodetic techniques to show the The advantage of these scales over ET is the liseconds, to our civil time clocks and by difference between astronomical time and incorporation of relativistic effects and a making occasional small adjustments to the uniform time, along with a parabola fit to the defined relationship to atomic time. frequency of the cesium clocks. data. With the advent of more accurate observa- In 1972, the present system of UTC was tional techniques, astronomers and geode- adopted. The second of UTC is the Système INTERNATIONAL ATOMIC TIME sists could measure variations in the Earth’s International (SI) second, the atomic second International Atomic Time (TAI) is the uni- rotation rate by comparing the passage of defined by the resonance frequency of form time scale from which UTC is derived. astronomical objects across the sky with cesium. But the “face of the clock” is set to It is produced at the Bureau International des laboratory clocks. They established that be within 0.9 second of astronomical time, Poids et Mesures (BIPM), where clock data the Earth’s rotation rate is slowing down UT1. When the difference between UT1 and are gathered from timing laboratories around with respect to a uniform atomic time scale. UTC approaches a point when it will exceed the world. Approximately 200 clocks in 50 Thus, if we were to observe a recurring 0.9 second, a leap second is introduced to laboratories are used to form TAI. This infor- astronomical event, we would see it occur- bring UTC back into closer agreement with mation is combined to provide a time scale ring earlier each day. To bring our clock back UT1. The leap second can be positive or neg- without a relationship to the Earth’s rota- into agreement with the astronomical event, ative, because the rate of rotation of the Earth tional speed. No leap second adjustments are www.gpsworld.com GPS WORLD November 1999 51 INNOVATION
OPTIONS FOR UTC years. This projection is based on the deceler- 35 Even with the possible ation rate shown earlier. increased use of TAI, the Of course, if we continue the current prac- 30 leap second problem can- tice, there will be no change for GPS. The 25 not be dismissed. GPS GPS navigation message (see “The GPS users, for example, will Navigation Message” sidebar) includes the 20 still need to relate GPS number of leap seconds a GPS receiver 15 Time to civil time. And should subtract from its determination of with UTC as the basis for GPS Time to obtain UTC. Eight bits in the 10 civil time, the practice of navigation message are used to convey this TAI–UTC (seconds) 5 inserting leap seconds will information, accommodating 1,023 leap sec- continue as a regular duty onds. With the Earth’s current deceleration 0 of maintaining the civil rate, a leap-second “rollover” wouldn’t occur Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan 60 64 68 72 76 80 84 88 92 96 00 time scale. The require- for about a thousand years. Figure 4 graphi- Year ment for the current prac- cally portrays the current relationship tice to maintain UTC and between GPS Time and the other time sys- Figure 2. Since 1972, the difference between Interna- the tolerance adopted for tems. tional Atomic Time (TAI) and UTC is an integer number of the difference between Discontinue Leap Seconds. Discontinuing the seconds — currently 32. Prior to 1972, UTC was UT1 and UTC must be use of leap seconds would eliminate the adjusted in smaller steps and its rate was also varied. reviewed to understand if problems discussed at the beginning of this the current procedure is article. The concerns associated with a grow- still required for general ing difference between UT1 and UTC would made to TAI. UTC is currently derived from usage. Only when the needs of modern pre- remain, however, and grow to be more of a TAI (see Figure 2), however, using the cise time users are well understood will it be potential problem. The difference between expression possible to carefully evaluate any options for UT1 and UTC would near one minute in the continued maintenance of UTC. Outlined 2050, if no further leap seconds were inserted UTC = TAI – (10 + number of leap seconds). below are some options for handling leap in UTC. On the other hand, it is likely that the seconds in the future. difference, although large and growing, At first glance, TAI would appear to be the Continue Current Procedure. If current proce- would be well known to users by means of ideal time scale for those who consider the dures continue into the twenty-first century, electronic dissemination through navigation UTC leap seconds a nuisance. One problem we can expect to insert more than one leap and timing systems. It is unlikely that the with TAI, however, is the fact that it is not second per year, on average. By 2050, we growing difference between clock time and easily accessible from the national timekeep- will have to add approximately 1.5 leap sec- levels of daylight would be noticeable to a ing laboratories. Although some timing labo- onds each year. The current emerging prob- significant percentage of the population for ratories may maintain an approximation lems and the resulting dissatisfaction with the foreseeable future. Figure 5 shows the close to TAI, it is generally not accessible to leap seconds will only continue to grow. One historical (labeled actual) and the projected the average precise time user, except through advantage of the status quo, however, is there difference between UT1 and UTC if the leap the local realization of UTC. This is because would be no need to re-educate users of time. second were to be abandoned, again assum- UTC is the basis for civil time around the The possibility also exists that those users ing the constant deceleration of the Earth’s world. Should the demand for TAI increase, will adapt to an increased number of one-sec- rotation rate given earlier. By the end of the timekeeping laboratories may need to con- ond discontinuities in time. Figure 3 shows twenty-first century, we see that UTC would sider making this time scale more accessible graphically the projected number of leap sec- be expected to differ from UT1 by more than to the user. onds that might be added in the coming two minutes.
2 UTC GPS TAI TT SI rate 32.184 s (fixed) (ET 1984.0) 32 s (January 1999) Rate 1 13 s (January 1999)
Variable but ± 0.9 s generally slower rate UT1 lag Number of leap seconds leap of Number s = seconds 0 Figure 4. The differences between GPS Time and International 1990 2000 2010 2020 2030 2040 2050 Year Atomic Time (TAI) and Terrestrial Time (TT) are constant at the level of some tens of nanoseconds while the difference Figure 3. The number of leap seconds expected to be between GPS Time and UTC changes in increments of sec- inserted in UTC per year as a function of time onds, each time a leap second is added to the UTC time scale.
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current (or expected) rotation of the Earth. CONCLUSION
140 While this approach would solve the prob- It is important that potential new procedures 120 lem in a fundamental way, it would require to relate a uniform time scale to the Earth’s 100 Projected a redefinition of all physical units and sys- rotation with respect to the Sun be given seri- 80 tems that depend on time, as it would ous consideration. The continued require- 60 affect all time scales, including GPS Time. ment for leap seconds within the user 40 Also, this solution would only be tempo- community should be evaluated. Plans to
UTC–UT1 (seconds) UTC–UT1 20 rary, because the current problems would provide a worldwide standard for time that Actual 0 likely resurface in another hundred years meets the needs of future timing users should 1980 2000 2020 2040 2060 2080 2100 or so. be formulated now. Failure to provide well Year Periodic Insertion of Leap Seconds. Yet another thought-out plans is likely to lead to a chaotic Figure 5. The difference between UT1 and solution would introduce a discontinuity to increase in the number of nonstandard time UTC that would be expected if leap sec- UTC after a specified time interval, to scales, resulting in confusion and a disservice onds were to be discontinued reduce the accumulated difference in time to users. between UTC and UT1 to an acceptable All of the suggestions listed above are limit. While the date of the insertion of possible to implement. However, the redefin- Abandoning leap seconds would give us leap seconds would be predictable, the num- ition of the second appears to be the most an almost constant relationship between GPS ber of leap seconds would not. This would awkward to attempt. Continuing the current Time and UTC. No further updates to the remove the problem with predictability, but procedure and ignoring the coordination of leap-second parameters in the navigation the presumably larger discontinuities are uniform time with the Earth’s rotation alto- message would be required. As long as no likely to still cause concern. gether are equally problematic possibilities. confusion would ensue, either GPS Time or This solution would not cause problems This leaves periodic insertion of leap seconds UTC could be redefined to remove the for GPS. The GPS Master Control Station and the relaxation of the tolerance between integer number of seconds between them, would simply have to check about a week or UT1 and UTC as the most likely candidates leaving us, effectively, with just one time so before “Leap Second Day” whether a for consideration. These options appear equal scale. change to the navigation message leap-sec- in feasibility with the most serious difficulty Change the Tolerance for UT1–UTC. One compro- ond parameters was required and, if yes, being the establishment of an acceptable mise between the extremes of discontinuing upload the new number of leap seconds to the magnitude for a time step in view of current leap seconds and maintaining the status quo satellites. customs and coding protocols. ■ is to increase the tolerance for the difference between UT1 and UTC. The current limit of 0.9 second could be increased to some acceptable limit, with the advantage that it The GPS Navigation Message could be accomplished relatively easily and Words six through 10 of page 18 of subframe four of the GPS broadcast navigation quickly. However, the disadvantages to this message contain the values of Coordinated Universal Time (UTC) parameters that approach are threefold: the larger discontinu- permit a GPS receiver to determine UTC corresponding to a particular instant of GPS ities might cause more problems to the users, Time. This page is transmitted once during the 12.5-minute-long navigation message. the original problem of unpredictability The parameters include the current number of UTC leap seconds since January remains unresolved, and an acceptable limit 1980, when GPS Time was set equal to UTC, as well as information on the most might be difficult to establish. recent or announced future leap second. The navigation message also transmits the Another consideration is that most current coefficients of a first-order polynomial describing the subsecond relationship radio codes used to broadcast the difference between GPS Time and UTC. Table 1 shows the values of the navigation message between UTC and UT1 (such as those used UTC parameters received on October 2, 1999. They indicate that currently the num- by time signal radio stations WWV and ber of leap seconds to be subtracted from a receiver’s determination of GPS Time is WWVB) could not accommodate the greater 13, and that the most recent leap second was introduced at the end of day 5 number of digits required. This would also be (Thursday) of GPS week 990, which began on December 27, 1998 — in other words, the case if leap seconds were discontinued at midnight (UTC) ending December completely and we still wished to broad- 31, 1998. At the subsecond level, Table 1. GPS UTC parameters cast the difference between UTC and UT1 GPS Time is essentially equal to UTC by radio. as it is steered to follow UTC as Parameter Value Changing the tolerance for UT1–UTC maintained by the U.S. Naval A (seconds) 8.381903172ϫ10–9 would have no effect on GPS. It would sim- Observatory. At the (future) UTC data 0 A (sec/sec) 2.042810365ϫ10–14 ply mean that the leap second parameters reference time of 147,456 seconds of 1 ⌬ would stay constant for longer periods of GPS week 6, this subsecond differ- tLS (seconds) 13 ϫ 5 time and that changes in the number of leap ence was estimated to be approxi- tot (seconds) 1.474560000 10 seconds would be greater than one. mately 8.4 nanoseconds (GPS Time WNt (weeks) 6 Redefine the Second. The most fundamental leading UTC) and increasing over the WNLSF (weeks) 990 solution to the problem would be to redefine short term at the rate of about 0.02 DN (days) 5 the accepted length of the second, making it picosecond per second (about 1.7 ⌬t (seconds) 13 more consistent with the appropriate fraction nanoseconds per day). – R.B.L. LSF of the length of the day as defined by the www.gpsworld.com GPS WORLD November 1999 53 INNOVATION
Dr. Dennis McCarthy is director of the U.S. Naval Observatory (USNO) Directorate of Time FURTHER READING in Washington, D.C. He received a B.S. in For further information about the various astronomy from Case Institute of Technology, time scales and their relationships to Cleveland, Ohio, and M.A. and Ph.D. degrees in GPS, see astronomy from the University of Virginia, Ⅲ Charlottesville. Among other accomplishments, “Time, Clocks, and GPS,” by R.B. he developed USNO’s use of GPS observations Langley in GPS World, Vol. 2, No. 10, for the determination of Earth orientation, and November/December 1991, pp. 38–42. he is a member of the Directing Board of the Ⅲ “A Brief History of Precise Time and International Earth Rotation Service. GPS,” by D.W. Allan, N. Ashby, and C. Hodge in Precise Timing, supplement to Dr. William J. Klepczynski is a contractor for GPS World, December 1998, pp. 6–40. the Federal Aviation Administration, Satellite Ⅲ The Science of Timekeeping, by Navigation Program Office, and provides D.W. Allan, N. Ashby, and C. Hodge, consultation for the Wide Area Augmentation Hewlett-Packard Application Note AN System (WAAS) architecture and systems design. Through his affiliation with Innovative Solutions 1289, Hewlett-Packard Company, Test International, headquartered in Washington, and Measurement Organization, Santa D.C., he also provides expert analysis of the Clara, California, 1997. This publication timing of the WAAS network and WAAS’s is available electronically as a PDF file time-transfer capabilities. Klepczynski holds a by way of the Internet at the following Ph.D. in astronomy from Yale University, was URL:
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