GPS and Leap Seconds: Time to Change?
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 differ- The advantage of these scales over ET is the liseconds, to our civil time clocks and by ence between astronomical time and uniform incorporation of relativistic effects and a making occasional small adjustments to the time, along with a parabola fit to the data. defined relationship to atomic time. frequency of the cesium clocks. With the advent of more accurate observa- In 1972, the present system of UTC was INTERNATIONAL ATOMIC TIME tional techniques, astronomers and geode- adopted. The second of UTC is the Système International Atomic Time (TAI) is the uni- sists could measure variations in the Earth’s International (SI) second, the atomic second form time scale from which UTC is derived. rotation rate by comparing the passage of defined by the resonance frequency of It is produced at the Bureau International des astronomical objects across the sky with cesium. But the “face of the clock” is set to Poids et Mesures (BIPM), where clock data laboratory clocks. They established that be within 0.9 second of astronomical time, are gathered from timing laboratories around the Earth’s rotation rate is slowing down UT1. When the difference between UT1 and the world. Approximately 200 clocks in 50 with respect to a uniform atomic time scale. UTC approaches a point when it will exceed laboratories are used to form TAI. This infor- Thus, if we were to observe a recurring 0.9 second, a leap second is introduced to mation is combined to provide a time scale astronomical event, we would see it occur- bring UTC back into closer agreement with without a relationship to the Earth’s rota- ring earlier each day. To bring our clock back UT1. The leap second can be positive or neg- tional speed. No leap second adjustments are into agreement with the astronomical event, ative, because the rate of rotation of the Earth made to TAI. UTC is currently derived from www.gpsworld.com GPS WORLD November 1999 51 INNOVATION
TAI (see Figure 2), however, using the inserting leap seconds will continue as a reg- problems and the resulting dissatisfaction expression ular duty of maintaining the civil time scale. with leap seconds will only continue to grow. The requirement for the current practice to One advantage of the status quo, however, is UTC = TAI – (10 + number of leap seconds). maintain UTC and the tolerance adopted for there would be no need to re-educate users of the difference between UT1 and UTC must time. The possibility also exists that those At first glance, TAI would appear to be the be reviewed to understand if the current pro- users will adapt to an increased number of ideal time scale for those who consider the cedure is still required for UTC leap seconds a nuisance. One problem general usage. Only when with TAI, however, is the fact that it is not the needs of modern pre- 35 easily accessible from the national timekeep- cise time users are well ing laboratories. Although some timing labo- understood will it be possi- 30 ratories may maintain an approximation ble to carefully evaluate 25 close to TAI, it is generally not accessible to any options for the contin- the average precise time user, except through ued maintenance of UTC. 20 the local realization of UTC. This is because Outlined below are some 15 UTC is the basis for civil time around the options for handling leap world. Should the demand for TAI increase, seconds in the future. 10 timekeeping laboratories may need to con- Continue Current Procedure. If TAI–UTC (seconds) 5 sider making this time scale more accessible current procedures con- to the user. tinue into the twenty-first 0 Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan Jan century, we can expect to 60 64 68 72 76 80 84 88 92 96 00 OPTIONS FOR UTC insert more than one leap Year Even with the possible increased use of TAI, second per year, on aver- the leap second problem cannot be dismissed. age. By 2050, we will have Figure 2. Since 1972, the difference between Interna- GPS users, for example, will still need to to add approximately 1.5 tional Atomic Time (TAI) and UTC is an integer number of relate GPS Time to civil time. And with UTC leap seconds each year. seconds — currently 32. Prior to 1972, UTC was as the basis for civil time, the practice of The current emerging adjusted in smaller steps and its rate was also varied.
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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 1990 2000 2010 2020 2030 2040 2050 Figure 4. The differences between GPS Time and International 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.
one-second discontinuities in time. Figure 3 rotation rate given earlier. By the end of the ger number of seconds between them, leav- shows graphically the projected number of twenty-first century, we see that UTC would ing us, effectively, with just one time scale. leap seconds that might be added in the com- be expected to differ from UT1 by more than Change the Tolerance for UT1–UTC. One compro- ing years. This projection is based on the two minutes. mise between the extremes of discontinuing deceleration rate shown earlier. Abandoning leap seconds would give us leap seconds and maintaining the status quo Of course, if we continue the current prac- an almost constant relationship between GPS is to increase the tolerance for the difference tice, there will be no change for GPS. The Time and UTC. No further updates to the between UT1 and UTC. The current limit of GPS navigation message (see “The GPS leap-second parameters in the navigation 0.9 second could be increased to some Navigation Message” sidebar) includes the message would be required. As long as no acceptable limit, with the advantage that it number of leap seconds a GPS receiver confusion would ensue, either GPS Time or could be accomplished relatively easily and should subtract from its determination of UTC could be redefined to remove the inte- quickly. However, the disadvantages to this GPS Time to obtain UTC. Eight bits in the navigation message are used to convey this information, accommodating 1,023 leap sec- The GPS Navigation Message onds. With the Earth’s current deceleration Words six through 10 of page 18 of subframe four of the GPS broadcast navigation rate, a leap-second “rollover” wouldn’t occur message contain the values of Coordinated Universal Time (UTC) parameters that for about a thousand years. Figure 4 graphi- permit a GPS receiver to determine UTC corresponding to a particular instant of GPS cally portrays the current relationship Time. This page is transmitted once during the 12.5-minute-long navigation message. between GPS Time and the other time The parameters include the current number of UTC leap seconds since January systems. 1980, when GPS Time was set equal to UTC, as well as information on the most Discontinue Leap Seconds. Discontinuing the recent or announced future leap second. The navigation message also transmits the use of leap seconds would eliminate the coefficients of a first-order polynomial describing the subsecond relationship problems discussed at the beginning of this between GPS Time and UTC. Table 1 shows the values of the navigation message article. The concerns associated with a grow- UTC parameters received on October 2, 1999. They indicate that currently the num- ing difference between UT1 and UTC would ber of leap seconds to be subtracted from a receiver’s determination of GPS Time is remain, however, and grow to be more of a 13, and that the most recent leap second was introduced at the end of day 5 potential problem. The difference between (Thursday) of GPS week 990, which began on December 27, 1998 — in other words, UT1 and UTC would near one minute in at midnight (UTC) ending December 2050, if no further leap seconds were inserted 31, 1998. At the subsecond level, Table 1. GPS UTC parameters in UTC. On the other hand, it is likely that the GPS Time is essentially equal to UTC difference, although large and growing, as it is steered to follow UTC as Parameter Value would be well known to users by means of maintained by the U.S. Naval A (seconds) 8.381903172ϫ10–9 electronic dissemination through navigation Observatory. At the (future) UTC data 0 A (sec/sec) 2.042810365ϫ10–14 and timing systems. It is unlikely that the reference time of 147,456 seconds of 1 ⌬ growing difference between clock time and GPS week 6, this subsecond differ- tLS (seconds) 13 ϫ 5 levels of daylight would be noticeable to a ence was estimated to be approxi- tot (seconds) 1.474560000 10 significant percentage of the population for mately 8.4 nanoseconds (GPS Time WNt (weeks) 6 the foreseeable future. Figure 5 shows the leading UTC) and increasing over the WNLSF (weeks) 990 historical (labeled actual) and the projected short term at the rate of about 0.02 DN (days) 5 difference between UT1 and UTC if the leap picosecond per second (about 1.7 ⌬t (seconds) 13 second were to be abandoned, again assum- nanoseconds per day). – R.B.L. LSF ing the constant deceleration of the Earth’s
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completely and we still wished to broad- UTC and UT1 to an acceptable limit. While
140 cast the difference between UTC and UT1 the date of the insertion of leap seconds 120 by radio. would be predictable, the number of leap sec- 100 Projected Changing the tolerance for UT1–UTC onds would not. This would remove the prob- 80 would have no effect on GPS. It would sim- lem with predictability, but the presumably 60 ply mean that the leap second parameters larger discontinuities are likely to still cause 40 would stay constant for longer periods of concern. UTC–UT1 (seconds) UTC–UT1 20 Actual time and that changes in the number of leap This solution would not cause problems 0 seconds would be greater than one. for GPS. The GPS Master Control Station 1980 2000 2020 2040 2060 2080 2100 Redefine the Second. Year The most fundamental would simply have to check about a week or solution to the problem would be to redefine so before “Leap Second Day” whether a Figure 5. The difference between UT1 the accepted length of the second, making it change to the navigation message leap-sec- and UTC that would be expected if leap more consistent with the appropriate fraction seconds were to be discontinued of the length of the day as defined by the cur- rent (or expected) rotation of the Earth. approach are threefold: the larger discontinu- While this approach would solve the problem FURTHER READING ities might cause more problems to the users, in a fundamental way, it would require a For further information about the various the original problem of unpredictability redefinition of all physical units and systems time scales and their relationships to remains unresolved, and an acceptable limit that depend on time, as it would affect all GPS, see might be difficult to establish. time scales, including GPS Time. Also, this Ⅲ “Time, Clocks, and GPS,” by R.B. Another consideration is that most current solution would only be temporary, because Langley in GPS World, Vol. 2, No. 10, radio codes used to broadcast the difference the current problems would likely resurface between UTC and UT1 (such as those used in another hundred years or so. November/December 1991, pp. 38–42. Ⅲ by time signal radio stations WWV and Periodic Insertion of Leap Seconds. Yet another “A Brief History of Precise Time and WWVB) could not accommodate the greater solution would introduce a discontinuity to GPS,” by D.W. Allan, N. Ashby, and C. number of digits required. This would also be UTC after a specified time interval, to reduce Hodge in Precise Timing, supplement to the case if leap seconds were discontinued the accumulated difference in time between GPS World, December 1998, pp. 6–40. Ⅲ The Science of Timekeeping, by D.W. Allan, N. Ashby, and C. Hodge, Hewlett-Packard Application Note AN 1289, Hewlett-Packard Company, Test and Measurement Organization, Santa Clara, California, 1997. This publication is available electronically as a PDF file by way of the Internet at the following URL:
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ond parameters was required and, if yes, “Innovation” is a regular column featuring discussions about recent upload the new number of leap seconds to the advances in GPS technology and its applications as well as the satellites. fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering at the CONCLUSION University of New Brunswick, who appreciates receiving your comments as It is important that potential new procedures well as topic suggestions for future columns. To contact him, see the to relate a uniform time scale to the Earth’s “Columnists” section on page four of this issue. rotation with respect to the Sun be given seri- ous consideration. The continued require- ment for leap seconds within the user STATEMENT OF OWNERSHIP, MANAGEMENT, AND CIRCULATION community should be evaluated. Plans to (Required by 39 USC 3685) provide a worldwide standard for time that 1.Publication Title: GPS World Senior Debt Portfolio, c/o Boston Management and meets the needs of future timing users should 2.Publication Number: 1048-5104 Research, 24 Federal St., 6th Fl, Boston, MA 02110, be formulated now. Failure to provide well 3.Filing Date: 09/01/99 Contact: Scott H. Page; Van Kampen American 4.Issue Frequency: Monthly Capital, One Parkview Terrace, Oakbrook Terrace, IL thought-out plans is likely to lead to a chaotic 5.Number of Issues Published Annually: 12 60181, Contact: Jeffrey Maillet; Indosuez Capital increase in the number of nonstandard time 6.Annual Subscription Price: $64.00 Funding IIA, 1211 Ave. of the Americas, 7th Fl, New scales, resulting in confusion and a disservice 7. Complete Mailing Address of Known Office of York, NY 10036-8701, Contact: Francoise Berthelot; Publication: 131 West First Street, Duluth, Morgan Stanley/Dean Witter, 1585 Broadway, 10th to users. Minnesota 55802-2065 Fl, New York, NY 10036, Contact: James Morgan; All of the suggestions listed above are Contact Person: Bernice Geisert Telephone: Oxford Strategic Income, 24 Federal St., 6th Fl, (218) 723-9217 Boston, MA 02110, Contact: Juliana Riley/Daniel possible to implement. However, the redefin- 8.Complete Mailing Address of Headquarters or Akaya; Pacific Century Bank N.A., 16030 Ventura ition of the second appears to be the most General Business Office of the Publisher: 7500 Old Blvd., Encino, CA 91436-4487, Contact: Robert awkward to attempt. Continuing the current Oak Boulevard, Cleveland, Ohio 44130-3369 Mann, Vice President. Also, Advanstar 9.Full Names and Complete Mailing Addresses Communications has issued certain notes subject to procedure and ignoring the coordination of of Publisher: John Lacasale, Raritan Plaza III, 101 an indenture (the “bonds”). The trustee under the uniform time with the Earth’s rotation alto- Fieldcrest Ave., Edison, NJ 08837. Editor: Glen indenture, which trustee is the registrar and paying gether are equally problematic possibilities. Gibbons. Managing Editor: Scottie Barnes, 859 agent as of July 1, 1999 is: The Bank of New York, Willamette St., Eugene, OR 97401 Attn: Mary Jane Schmalgel, 101 Barclay St., 21st Fl, This leaves periodic insertion of leap seconds 10.This publication is owned by: Advanstar New York, NY 10286. The registered bondholder as and the relaxation of the tolerance between Communications Inc., 7500 Old Oak Boulevard, of July 1, 1999 is: CEDE & CO., Box #20, Bowling Cleveland, Ohio 44130. The sole shareholder of Green Station, New York, NY 10004. UT1 and UTC as the most likely candidates Advanstar Communications Inc., is: Advanstar, Inc., 12.Does Not Apply for consideration. These options appear equal 545 Boylston Street, Boston, MA 02116. 13.Publication Title: GPS World in feasibility with the most serious difficulty 11.Holders of 1.0% or more of Advanstar Communi- 14.Issue Date for Circulation Data Below: cations Inc. Mortgages or Other Securities as of August 1999 being the establishment of an acceptable July 1999: Advanstar Communications Inc. is the 15.Extent and Nature of Circulation magnitude for a time step in view of current Mortgagor under a Credit Agreement dated May 31, Average Actual customs and coding protocols. ■ 1996, as amended, with various lenders as named No. Copies No. Copies of therein from time to time. The agent for the lenders Each Issue Single Issue During Published is: The Chase Manhattan Bank, Attn: Mitchell Gervis, Preceding Nearest to Dr. Dennis McCarthy is director of the U.S. Administrative Agent, 270 Park Ave., 37th Fl, New 12 Months Filing Date Naval Observatory (USNO) Directorate of Time York, NY 10017. The security holders/lenders as of A. Total Number of Copies 4/99 are as follows: Balanced High Yield Fund I Ltd., (Net Press Run) 43,650 53,154 in Washington, D.C. He received a B.S. in State Street Bank & Trust Co.., 2 International Place, B. Paid and/or Requested Circulation astronomy from Case Institute of Technology, Boston, MA 02110, Contact: William Connolly; Bank of New York, One Wall St., 16th Fl, New York, NY 1. Sales through dealers and Cleveland, Ohio, and M.A. and Ph.D. degrees in 10286, Contact: Benjamin B. Todres; BankBoston, carriers, street vendors and astronomy from the University of Virginia, N.A., 100 Federal St., Boston, MA 02110, Contact: counter sales (Not mailed) none none Charlottesville. Among other accomplishments, Jonathan Sharkey, Julie Jalelian; Dresdner Bank, 75 2. 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