UTC time scales and leap second support.

1. UTC time calculation

The world's standard time scale is Universal Coordinated Time (UTC). UTC is directly based on International Atomic Time (TAI) (ts-taistd/time/instant/ts-tai: timescale) and uses standard SI seconds. The UTC time scale differs from TAI in that UTC stays within 1 second of UT1; the time scale based on the rotation of the Earth. To keep UTC close to UT1 about every 1.5 year a leap second is added to the day (appearing as a 60th second in the last minute of the day, e.g. 23:59:60h).

In order to calculate SI second durations between time instants, we need to know when a leap second is inserted. For example, there was a leap second inserted on 2017-01-01Z, so:

time(2017,1,1,0,0,0) - time(2016,12,31,23,0,0)
time(2017,1,1,0,0,0) - time(2016,12,31,23,0,0)

equals 3601 SI seconds to account for the extra leap second. We also need to know the inserted leap seconds to convert UTC time to TAI which forms the basis of many other time scales (see std/time/astro).

The occurrence of leap seconds cannot be reliably predicted though and the IERS usually announces leap seconds about half a year in advance. The IERS leap second table contains a list of all currently announced leap seconds. As such, any future duration calculation in UTC is essentially non-deterministic since it may be off by a number of (as yet unannounced) leap seconds. This means in practice:

• You cannot reliably tell how many SI seconds in the future a certain UTC time occurs (since there may be leap seconds inserted in the future). If you need to store a future date, then store it as an ISO calendar date, like 2020-01-01T12:00:00Z, not as a time stamp.

• Do not use Unix time stamps as those may be ambiguous (see unix-instant); this library already defaults to time stamps as SI seconds since epochstd/time/instant/epoch: instant which are monotonic and unambiguous. If no interaction with the user is needed, consider using TAI time and calendar instead.

1.1. Effect types and future leap seconds

Since UTC time calculations depend on a leap second table (leaps-tablestd/time/utc/leaps-table: V), the UTC time scale can only be created from such table (ts-utc-createstd/time/utc/ts-utc-create: (leaps : leaps-table) -> timescale). For most precise UTC time, you can use ts-utc-load to automatically download and cache the latest IERS leap second information. This can be somewhat cumbersome though as this is a function with an iostd/core/io: E effect.

International Time (TI) (or Temps International) is a proposed time scale that matches exactly UTC up to some date but with no further leap seconds added after that – which makes time calculations robust and deterministic with regard to future dates. For this reason, this library defaults to using TI instead of UTC. The TI time scale (ts-tistd/time/utc/ts-ti: timescale) is defined to exactly match UTC before the compiler release date (currently 2019) but ignores any future leap seconds.

1.2. UTC between 1961 and 1972

UTC only got integral leap seconds after 1972-01-01Z. Before 1972, the UTC time was broadcast using a combination of fixed time steps (i.e. mini leap seconds) and an offset from the atomic clock frequency. By adjusting the frequency, UTC time was effectively running at a linearly adjusted rate relative to TAI. We call this adjustment drift. For example, between 1963-11-01Z and 1964-01-01Z the frequency offset was -130×10^-10 which means UTC was running ahead of TAI by 0.0011232 seconds per day. The drift was then defined as:

 (TAI-UTC) = 1.9458580 + 0.0011232×Δ(1962-01-01)

where the function Δ(date) returns the number of days since date. Therefore, the difference started as 2.6972788s (as there were 669 days between 1962-01-01 and 1963-11-01) and increased linearly up to 2.7657940s on 1964-01-01Z. For dates between 1961-01-01Z and 1972-01-01Z the library calculates the UTC time based on the historical USNO drift data (see Table 1).

Here are some interesting time steps that occurred in this time frame:

• There was a negative time step of -0.1s inserted on 1968-02-01Z:

  instant(1968,1,31,23,59,59,0.9).time(cal=cal-tai) == "1968-02-01T00:00:06.185682Z TAI"
  instant(1968,2,1).time(cal=cal-tai) == "1968-02-01T00:00:06.185682Z TAI"
  instant(1968,1,31,23,59,59,0.9).time(cal=cal-tai) == "1968-02-01T00:00:06.185682Z TAI"
  instant(1968,2,1).time(cal=cal-tai) == "1968-02-01T00:00:06.185682Z TAI"
  

  The only other negative time step was inserted on 1961-08-01Z with a duration of -0.05s.

• On the transition to modern UTC at 1972-01-01Z there is a mini leap second of 0.107758s. (because the final drift just before 1971-01-01 is 9.892242s)

  instant(1972,1,1,0,0,9,0.99999999,cal=cal-tai).time.show(6) == "1971-12-31T23:59:60.107758Z"
  instant(1972,1,1,0,0,10,cal=cal-tai).time.show == "1972-01-01T00:00:00Z"
  instant(1972,1,1,0,0,9,0.99999999,cal=cal-tai).time.show(6) == "1971-12-31T23:59:60.107758Z"
  instant(1972,1,1,0,0,10,cal=cal-tai).time.show == "1972-01-01T00:00:00Z"
  

UTC was only established in 1960 (Arias and Guinot [1]), and the TAI instant 1961-01-01 00:00:01.422818Z TAI was set to be UTC instant 1961-01-01Z exactly.

1.3. UTC before 1961

The TAI timescale was established with a 1958-01-01Z epoch, where the difference (UT2 - TAI) was set to be approximately zero¹. In the time frame 1958 up to 1961 the relation between TAI and UTC is not formally defined.

We can however use the time steps and frequency adjustments as broadcast by the NIST WWV radio station (see Explanatory Supplement to the Astronomical Almanac [2, pages 86–87]). Historically there were 18 20ms time steps from 1958. The frequency offset in the year 1958 is not clear, and is described in the Supplement as “.. an offset of about -100×10^-10 during 1958”. We fixed the offset at -85×10^-10 in order to have a zero difference from TAI at exactly 1958-01-01Z.

In the library, this makes UTC coincide with TAI up to 1958-01-01, interpolated with ‘drift’ up to 1972-01-01, and using integral leap-seconds after that.

Interestingly, in the time before 1961, most leap steps occurred at 19:00h instead of at the last second of the day, for example, on 1959-01-28 there was a 0.02s leap step:

instant(1959,1,28,19,0,0,0.50,cal=cal-tai).time.show == "1959-01-28T18:59:60.007866Z"
instant(1959,1,28,19,0,0,0.52,cal=cal-tai).time.show == "1959-01-28T19:00:00.007866Z"
instant(1959,1,28,19,0,0,0.50,cal=cal-tai).time.show == "1959-01-28T18:59:60.007866Z"
instant(1959,1,28,19,0,0,0.52,cal=cal-tai).time.show == "1959-01-28T19:00:00.007866Z"

showing the seconds at 60 just before 19:00h.

1.4. All historical leap second adjustments

Table 1 shows all leap second time steps from 1958 up to 2017. This table is calculated and uses historical data for time steps before 1972.

– Daan Leijen, 2016.

References

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