app28
Leap Seconds
and
Leap Years
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com
Introduction
Why Have Leap Seconds ?
Leap seconds keep the atomic clock based International Time Scale, UTC (Universal Time Coordinated), in
agreement with earth time based on the rate of rotation of the earth as determined by astronomical
observations, to within 0.9 of a second. Leap seconds keep the two time scales in agreement and compensate
for the decreasing rotational rate of the earth, which is slowly decreasing by approximately 1.4 milliseconds per
century. This decrease in the Earth’s rotational rate is due to effects such as tidal braking. Atomic clock based
time scales are much more stable than the daily rotational rate of the earth, therefore to keep the two
synchronized, leap seconds are added (or subtracted, although because the rate of rotation is decreasing, in
practice leap seconds are only added to compensate).
Whether or not a leap second is added is determined by the International Earth Rotation and Reference
Systems Service. The last leap second was added on June 30, 2012.
The organization responsible for measuring the relationship between UTC (Coordinated Universal Time) and
the rate of Earth’s rotation (the International Earth Rotation and Reference Systems Service - IERS), decides
whether or not a leap second should be added to UTC to keep UTC in line with IERS.
If required, leap seconds can be added either on June 30, or December 31 of the year in which the leap
second is to be applied. IERS determines which date is more appropriate. The table below shows when leap
seconds have been added, since their introduction in 1972.
June
December
December
December
June
December
June
June
30, 2012
31, 2008
31, 2005
31, 1998
30, 1997
31, 1995
30, 1994
30, 1993
June
December
December
December
June
June
June
June
30, 1992
31, 1990
31, 1989
31, 1987
30, 1985
30, 1983
30, 1982
30, 1981
December
December
December
December
December
December
December
December
31, 1979
31, 1978
31, 1977
31, 1976
31, 1975
31, 1974
31, 1973
31, 1972
In 2012 a leap second was added on June 30. Adding a leap second increases the length of the last minute of
the last UTC day in the year to 61 seconds. The sequence of dates of the UTC second markers was:
Normal Transition
2012 June 29 23h 59m 58s
2012 June 29 23h 59m 59s
2012 June 30 0h 0m 0s
Leap Second Transition
2012 June 30 23h 59m 59s
2012 June 30 23h 59m 60s <<<
2012 July 1 0h 0m 0s
Normal Transition
2012 July 1 23h 59m 58s
2012 July 1 23h 59m 59s
2012 June 2 0h 0m 0s
For clarity the transitions on the day before and day after have also been shown.
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com
Also, an interesting point to note is that although leap seconds are added, a clock with the leap second added
versus a clock without the leap second added will be 1 second behind, slightly counter intuitive. See below:
Clock With Leap Second Added
2012 June 29 23h 59m 58s
2012 June 29 23h 59m 59s
2012 June 29 23h 59m 60s << leap second added
2012 June 30 0h 0m 0s
2012 June 30 0h 0m 1s
2012 June 30 0h 0m 2s
2012 June 30 0h 0m 3s
Clock without Leap second added
2012 June 29 23h 59m 58s
2012 June 29 23h 59m 59s
2012 June 30 0h 0m 0s
2012 June 30 0h 0m 1s
2012 June 30 0h 0m 2s
2012 June 30 0h 0m 3s
2012 June 30 0h 0m 4s
Leap Seconds and NTP.
NTP (Network Time Protocol) is always referenced directly to UTC. UTC commenced at 00:00 hours on
January 1, 1972. At that time it was determined to set the NTP second to a value of 2,272,060,800.0 which
meant that extrapolating back, the NTP second epoch (i.e. started at 0) at 00:00 hours on January 1, 1900.
The NTP packet includes a 2 bit LI, or leap second indicator ( see App_23_part1_NTP) with possible
indications as follows:
LI Value Meaning
------------------------------------------------------00
0
no warning
01
1
last minute has 61 seconds
10
2
last minute has 59 seconds
11
3
alarm condition (clock not synchronized)
Typically the value of 2 ( binary 10) is never used as the earth is always slowing down, meaning leap seconds
if needed are only ever added in.
If a leap second is to be applied, the NTP leap indicator will be set and the information passed to the client
within the NTP packet. It is the responsibility of the client to correctly apply the leap second at the right time.
The NTP timescale is suspended during the application of a leap second, i.e. the NTP second will read the
same value for two consecutive UTC seconds, see below for the transition on June 30, 2012;
Date
June 30, 2012
June 30, 2012
June 30, 2012
July 1, 2012
Time
23:59:58
23:59:59
23:59:60
00:00:00
NTP Second
3550089598
3550089599
3550089599 <<<< NTP time suspended
3550089600
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com
Although in concept, the addition of a leap second is relatively simple, the implementation of automatically
adding a leap second to a clock is quite complex. The starting point is to be able to flag whether or not a leap
second should be added.
For the many clocks based on received signals from the GPS (Global Positioning Satellite) system (also the
WWVB radio transmission), this is relatively straightforward as there is a special indicator set aside within the
transmitted message to show whether or not a leap second is to be added at the next cycle, either June 30, or
December 31. In GPS this indicator may be set up to six months, or in WWVB up to one month, before the
application of a leap second, once it has been determined that a leap second is to be applied.
For clocks based on receiving "time code" signals there is also an indicator set aside within the time code
message to show whether or not a leap second is pending (bit number 60 of the control codes, 1=pending leap
second, set up to 59 seconds prior ) plus another bit (bit number 61) to show whether the leap second is to be
added or deleted (0 = add, 1=delete) at the next leap second cycle.
For those interested in the sequencing of the automatic application of the leap second, a partial flow chart is
shown in Appendix A.
Finally, for clocks operating completely independently to add a leap second at the right time it is necessary to
manually set a leap second indicator. In practice few (if any) have this capability.
Further information on leap seconds can be obtained at the NIST web site at:
http://www.nist.gov/pml/div688/grp50/timescaledata.cfm
What About Leap Years ?
Leap years are years with 366 days, instead of the usual 365. Leap years are necessary because the
actual length of a year is 365.242 days, not 365 days, as commonly stated. Basically, leap years
occur every 4 years, and years that are evenly divisible by 4 (2004, for example) have 366 days. This
extra day is added to the calendar on February 29th.
However, there is one exception to the leap year rule involving century years, like the year 1900.
Since the year is slightly less than 365.25 days long, adding an extra day every 4 years results in
about 3 extra days being added over a period of 400 years. For this reason, only 1 out of every 4
century years is considered as a leap year. Century years are only considered as leap years if they
are evenly divisible by 400. Therefore, 1700, 1800, 1900 were not leap years, and 2100 will not be a
leap year. But 1600 and 2000 were leap years, because those year numbers are evenly divisible by
400.
For additional information about our year, please see:
http:/www.webexhibits.org/calendars/
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com
Appendix A - Automatic Application Of Leap Seconds
Update Time - run
once per second
Reset lse
armed
No
is a leap second
pending ?
are we in month
1 or 7 ?
No
No
No
Yes
is hour = 23 ?
(UTC)
is minute = 59 ?
(UTC)
is day Dec 31
OR June 30 ?
Set lse
armed
Go to bump time
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com
Reset leap
second pending
Bump Time - called
from Update Time
No
is second >
59 + lse ?
is lse armed ?
No
Flag NTP for
update
subtract (60+last_lse)
from seconds
add 1 to minute
No
is minute > 59 ?
minute = 0
add 1 to Hour
Adjust day, month, year etc.
Precise Time and Frequency, Inc.
50L Audubon Road, Wakefield, MA 01880, USA
Tel: +1 781 245 9090 Fax: +1 781 245 9099 www.ptfinc.com