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Adam Danz
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New in r2020a: leap seconds

Adam Danz on 17 Apr 2020 (Edited on 18 Apr 2020)
Latest activity Reply by Adam Danz on 7 May 2021

New to r2020a, leapseconds() creates a table showing all leap seconds recognized by the datetime data type.

>> leapseconds()
ans =
  27×2 timetable
       Date        Type    CumulativeAdjustment
    ___________    ____    ____________________
    30-Jun-1972     +              1 sec       
    31-Dec-1972     +              2 sec       
    31-Dec-1973     +              3 sec       
    31-Dec-1974     +              4 sec       
    31-Dec-1975     +              5 sec       
             << 21 rows removed >>
    31-Dec-2016     +             27 sec   

Leap seconds can covertly sneak into your data and cause errors that are difficult to resolve if the leap seconds go undetected. A leap second was responsible for crashing Reddit , Mozilla, Yelp, LinkedIn and other sites in 2012.

Detect leap seconds present in a vector of years

% Define a vector of years
t = 2005:2008; 
allLeapSeconds = leapseconds(); 
isYearWithLeapSecond = ismember(t,year(allLeapSeconds.Date));
% Show years that contain a leap second
t(isYearWithLeapSecond)
ans =
        2005        2008

Detect leap seconds present in a vector of months

% Define a vector of months 
t = datetime(1972, 1, 1) + calmonths(0:11);
t.Format = 'MMM-yyyy';
allLeapSeconds = leapseconds(); 
[tY,tM] = ymd(t); 
[leapSecY, leapSecM] = ymd(allLeapSeconds.Date); 
isMonthWithLeapSecond = ismember([tY(:),tM(:)], [leapSecY, leapSecM], 'rows');
% Show months that contain a leap second
t(isMonthWithLeapSecond)
ans = 
  1×2 datetime array
   Jun-1972   Dec-1972

List all leap seconds in your lifetime

% Enter your birthday in mm/dd/yyyy hh:mm:ss format
yourBirthday = '01/15/1988 14:30:00'; 
yourTimeRange = timerange(datetime(yourBirthday), datetime('now')); 
allLeapSeconds = leapseconds(); 
lifeLeapSeconds = allLeapSeconds(yourTimeRange,:);
lifeLeapSeconds.YourAge = lifeLeapSeconds.Date - datetime(yourBirthday);
lifeLeapSeconds.YourAge.Format = 'y';
% Show table
fprintf('\n Leap seconds in your lifetime:\n')
disp(lifeLeapSeconds)
Leap seconds in your lifetime:
       Date        Type    CumulativeAdjustment     YourAge  
    ___________    ____    ____________________    __________
    31-Dec-1989     +             15 sec           1.9587 yrs
    31-Dec-1990     +             16 sec            2.958 yrs
                        << 8 rows removed >>
    30-Jun-2012     +             25 sec           24.456 yrs
    30-Jun-2015     +             26 sec           27.454 yrs
    31-Dec-2016     +             27 sec            28.96 yrs

What is a leap second?

A second is defined as the time it takes a cesium-133 atom to oscillate 9,192,631,770 times under controlled conditions. The transition frequency is so precise that it takes 100 million years to gain 1 second of error [1]. If the earth’s rotation were perfectly synchronized to the atomic second, a day would be 86,400 seconds. But the earth’s rate of rotation is affected by climate, winds, atmospheric pressure, and the rate of rotation is gradually decreasing due to tidal friction [2,3]. Several months before the expected difference between the atomic clock-based time (UTC) and universal time (UT1) reaches +/- 0.9 seconds the IERS authorizes the addition (or subtraction) of 1 leap second (see plot below). Since the first leap second in 1972, all leap second adjustments have been made on the last day of June or December and all adjustments have been +1 second which explains the + signs in the type column of the leapseconds() table.

[ Image source ]

How to reference the leap second schedule in your code

Since leap second adjustments are not regularly timed, you can record the official IERS Bulletin C version used at the time of your analysis by accessing the 2nd output to leapseconds().

[T,vers] = leapseconds

What do leap seconds look like in datetime values?

A minute typically has 60 seconds spanning from 0:59. A minute containing a leap second has 61 seconds spanning from 0:60.

December 30, 2016 was a normal day. If we add the usual 86400 seconds to the start of that day, the result is the start of the next day.

d = datetime(2016, 12, 30, 'TimeZone','UTCLeapSeconds') + seconds(86400)
d = 
  datetime
   2016-12-31T00:00:00.000Z

The next day, December 31, 2016, had a leap second. If we add 86400 seconds to the start of that day, the result is not the start of the next day.

d = datetime(2016, 12, 31, 'TimeZone','UTCLeapSeconds') + seconds(86400)
d = 
  datetime
   2016-12-31T23:59:60.000Z

When will the next leap second be?

As of the current date (April 2020) the timing of the next leap second is unknown. Based on the data from the plot above, what's your guess?

References

  1. https://www.timeanddate.com/time/how-do-atomic-clocks-work.html
  2. https://www.nasa.gov/centers/goddard/news/topstory/2003/0210rotation.html
  3. https://en.wikipedia.org/wiki/%CE%94T#Universal_time
 
Adam Danz
Adam Danz on 7 May 2021

Peter Perkins' blog post "What is a leap second, anyway?" is a great read on this topic!

 

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