Time Scales, UTC, and Leap Seconds

(Based on Chapter 2, Section 2.1 of Time and Frequency Users Manual, edited by George Kamas and Sandra L. Howe, NBS Special Publication 559, November 1979. Edited and updated by J. Vig, May 1997.)

Time Scales

A time scale is simply a system of assigning dates to events (e.g., counting pendulum swings). The apparent motion of the sun in the sky is the basis for one type of time scale, called astronomical time. Today, we also have atomic time, where an atomic oscillator is the “pendulum”. To see how the various time scales came about, let’s take a brief look at the evolution of time scales.

Solar Time

To review what has happened to timekeeping and the name given to the resulting time of day, consider a time system that uses the sun and the sundial. The sun is the flywheel and has a period of 24 hours. The sundial can indicate the fractions of cycles (time of day). As complete days elapse, calendars can be used to count the days and divide them into weeks and years. But our newly formed clock is not uniform in its timekeeping because the earth’s orbit around the sun is not circular. It slows down and speeds up depending on its distance from the sun. The early astronomers and mathematicians understood these laws of motion and were able to correct the “apparent solar time” to obtain a more uniform time called “mean solar time”. This correction is called the Equation of Time and is often found engraved on sundials. Universal Time (UT0) is equal to mean solar time if you make the correction at the Greenwich meridian in England. UT0 is the first in a series of designations for time that has evolved through the past years.

If you use the apparent motion of a star that is farther away than our own sun, the fact that the earth is not in perfect circular orbit becomes unimportant. This is the basis for “sidereal time” which is similar to mean solar time since both are based on the earth’s spinning on its axis. The rate is different by one day per year since the earth circles the sun in a year.

As better clocks were developed, astronomers began to notice a discrepancy in Universal Time measured at different locations. The discrepancy was eventually identified as being caused by a wobble in the earth’s axis. The amount of wobble is about 15 meters. By careful measurements made at various observatories throughout the world, this wobble was corrected for and a new time designation called UT1 was born. In our search for uniformity, we have now taken care of the non-circular orbit (UT0) and the axis wobble of the earth (UT1).

As science and technology improved pendulum and quartz crystal clocks, it was discovered that UT1 had periodic fluctuations whose origin was unknown. Due to the availability of excellent clocks, these fluctuations could be and were removed, resulting in an even more uniform time scale, UT2.

To review, UT1 is the true navigator’s time scale related to the earth’s angular position. UT2 is a smooth time and does not reveal the real variations in the earth’s position. When the world’s timekeepers went to UT2, they bypassed the navigators’ real needs. A little later we shall describe the present-day system which in effect remedies the dilemma.

Up until now we have been talking about the Universal Time family. Let us now examine the other members of the time family. The first of these is “ephemeris time”. An ephemeris is simply a table that predicts the positions of the sun, moon, and planets. It was soon noticed that these predicted positions on the table did not agree with the observed positions. An analysis of the difficulty showed that in fact the rotational rate of the earth was not a constant, and this was later confirmed with crystal and atomic clocks. In response to this problem, the astronomers created what is called “ephemeris time”. It is determined by the orbit of the earth about the sun, not by the rotation of the earth on its axis.

Atomic Time

Another kind of time that can be generated and used is atomic time. Whereas the Universal Time scale is obtained by counting cycles of the earth’s rotation from some agreed-upon starting point, an atomic time scale can be obtained by counting cycles of a signal locked to some atomic resonance.

In the late 1940’s, the National Bureau of Standards announced the first atomic clock. Shortly thereafter several national laboratories, including the International Time Bureau (BIH, in France), started atomic time scales.

In 1971 the General Conference of Weights and Measures officially recognized the Atomic Time Scale and endorsed the BIH (now BIPM) time scale as the International Atomic Time Scale, TAI. Since the first of January 1972, most countries in the world have distributed the Atomic Time Scale. In 1997 TAI was generated from data from about 230 atomic clocks kept by 65 laboratories around the world. Timing centers from about 30 countries regularly contributed data to BIPM.

Today, the time of day can be obtained to a very high order of accuracy because, unlike a coarse sundial, an atomic clock can accurately measure small fractions of a second. Furthermore, atomic clocks give us essentially constant units of time – it is a uniform timekeeper. Uniformity is important in technology, e.g., in the general problem of synchronization – trying to make two things happen or start at the same time.

Let’s review for a moment the several time scales we have discussed. First, the universal time family is dependent on the earth’s spin on its axis. Second, ephemeris time depends on the orbital motion of the earth about the sun. And finally, atomic time, which is very uniform and precise, depends on a fundamental property of atoms.

Because of the slow orbital motion of the earth, about one cycle per year, measurement uncertainties limit the accuracy of Ephemeris Time to about 0.05 second in a 9-year period. Universal Time can be determined to a few thousandths of a second, i.e., to several milliseconds, within one day. Atomic Time is accuracy to a few billionths of a second (nanoseconds) can be obtained in a minute or less. From these numbers, it is easy to see why scientists prefer a time scale derived from an atomic clock.

Coordinated Universal Time (UTC) and The Leap Second

Prior to 1972, most standard frequency radio broadcasts were based on a time scale called Coordinated Universal Time (UTC). It is abbreviated in all languages as UTC. The rate of an UTC clock was controlled by atomic oscillators so it would be as uniform as possible. These atomic oscillators operated at the same frequency for a whole year, but were changed in rate at the beginning of a new year in an attempt to match the forthcoming earth rotational rate, UT2.

However, the earth’s rotational rate could not be accurately predicted, and so UTC would slowly get out of step with earth time. This was a problem for navigators who needed solar time – they had to apply a correction to UTC, but it was difficult to determine the amount of correction.

Experience rapidly showed that it would be an advantage to simplify the UTC system to avoid changing the rate each year. A decision was made to broadcast the nominal values of the frequency standards and to do away with annual changes in rate. Thus, a way was developed to keep UTC in closer agreement with solar time.

The new UTC system came about as a solution to the problem of changing the clock rate (frequency) each year or so. It was adopted in Geneva in 1971 and became effective in 1972. Under the new system, the frequency driving all clocks was left at the atomic rate with zero offset. But by using a zero offset, the clocks would gradually get out of step with the day. The resulting situation was not unique because the year has never been an exact multiple of the day, and so we have leap years. Leap years keep our calendar in step with the seasons.

The same scheme was adopted to keep clocks in step with the sun, and the “leap second” was born. To make adjustments in the clock, a particular minute would contain either 61 or 59 seconds instead of the conventional 60 seconds. You could, therefore, either have a positive or a negative leap second. It was expected and proved true that this would normally occur once a year.

The new UTC plan works like this. By international agreement, UTC is maintained within 9/10 of a second of the navigator’s time scale UT1. The introduction of leap seconds will permit a good clock to keep approximate step with the sun. Since the rotation of the earth is not uniform we cannot exactly predict when leap seconds will be added or deleted, but they usually occur on June 30 or December 31.

For example, a leap second was added on July 1, 1997. Coordinated Universal Time (UTC) was retarded by 1.0s so that the sequence of dates of the UTC markers were:

1997 June 30 23h 59m 59s
1997 June 30 23h 59m 60s
1997 July 01 0h 0m 0s

The difference between UTC and International Atomic Time TAI was:

from 1996 01 Jul, UTC to 1997 01 Jul, UTC: TAI-UTC= +30s
from 1997 01 Jul, UTC until the next leap second: TAI-UTC= +31s

Before the leap second, GPS-UTC = +11 (i.e., GPS is ahead of UTC by eleven seconds).
After the leap second, GPS-UTC = +12s (i.e., GPS will be ahead by twelve seconds).

What does this mean to the user of a time and frequency broadcast? It simply means that the time the user gets will never differ from UT1 by more than 9/10 of a second. Most users, such as radio and television stations and telephone time-of-day services, use UTC so they don’t care how much it differs from UT1. Even most boaters/navigators don’t need to know UT1 to better than 9/10 of a second, so the new UTC also meets their needs.

However, there are a small number of users who do need UT1 time to better than 9/10 of a second. To satisfy this need, most standard time and frequency radio stations include a correction in their broadcasts which can be applied to UTC to obtain UT1.

We should keep in mind that the advantage we gain by using the UTC system prevents us from simply subtracting the dates of two events to get the time difference between them. We must in fact, take into account any leap seconds that were added or deleted. One should be especially cautious if the time interval of interest extends backward into a period where the world time system was not operating on the new UTC time scale (prior to 1972).

Time Zones

All standard time and frequency stations broadcast Coordinated Universal Time, which is referenced to the Greenwich meridian. However, many users want to display local time, which, of course, varies with location on the globe. The railroads are generally credited with unifying the various local times into time zones in the continental U.S. In 1884, an international conference recommended that the meridian of Greenwhich, England be the standard reference meridian for longitude and time. Longitude meridians, each 15°, represent 1-hour time zone differences ± 12 hours east and west of Greenwhich.

If the time is being decoded from a time code (as opposed to a voice time-of-day announcement), a timing receiver’s clock can display time for any of the world time zones, even though it is receiving and decoding UTC.


To review then, we had the situation where the scientist wanted a uniform time scale (UTC) and the navigators required a clock tied to the earth’s position (UT1) which is non-uniform. Therefore, corrections must be made to convert UTC to UT1. With the advent of the Global Positioning System (GPS) and inexpensive computers, this “problem” has become less and less important.

The UTC system was developed as a compromise between a purely uniform time scale for scientific applications and the non-uniform measurement of the earth’s position for navigation and astronomy. We keep the calendar in step with the seasons by using the leap years and our clocks in step with the sun (day and night) by using leap seconds.