1. 1 Time Scales UT0, UT1, EAL, TAI, UTC Ricardo José de Carvalho National Observatory Time Service Division February 06, 2008

2. 2 Introduction A system of assigning dates to events is called a time scale. A method that can be used to dating of events leads to the construction of a time scale, for instance, the apparent motion of the sun in the sky constitutes one of the most known time scale. Note that to date an event using the motion of the sun as a time scale, we must count days, that is, make a calendar from some initially beginning and if we need accuracy we have to measure the fractions of a day (i. e., “time of day”) in hours, minutes, seconds, and may be even fractions of seconds.

3. 3 Characteristics of a Time Scale UNIFORMITY A time scale is uniform if the unit of scale is constant. If the scale is uniform, and the unit of scale agrees with some adopted quantity, such as the SI second, we can measure the length of a time interval by two time scale readings.

4. 4 Characteristics of a Time Scale PERENNITY In principle, the possibility to extend, in the past and in the future, a time scale would be interesting. If a time scale is based on a clock manufacture by man, the duration of any measurement can not obviously exceed the Mean Time Between Failure (MTBF) of clock. The obvious solution is to introduce redundancy in the clock system. One can use several atomic clocks in the time scale, each one linked with the preceding one, in order to extend in the future the time scale. But this time scale can not be used to date what happened before the first clock was put in operation.

5. 5 Characteristics of a Time Scale UNIVERSALITY A time scale, in order to be used for dating events, must be universally accepted, and to satisfy this requirement an international effort is done, in order to bring in some agreement different countries. Moreover, the phenomenon that is used as a base for the time scale must be available everywhere.

6. 6 Characteristics of a Time Scale ACCURACY The accuracy of a time scale may be defined as its ability to make the unit of scale as close as possible to its definition, so the accuracy depend on the kind of physical phenomenon chosen as unit of scale.

7. 7 Characteristics of a Time Scale STABILITY The stability of a time scale may be defined as its ability to maintain the unit of scale constant so the measure of stability consists in the estimation of the dispersion of unit of scale.

8. 8 Definition of Time Scale Time being an immaterial quantity, it has to be referred to a physical phenomenon in order to be measured. We can recognize two different types of time scale: dynamic time scales and integrated time scales.

9. 9 Definition of Time Scale In the dynamic time scales, the primary data results from the observation of a dynamic physical system, described by a mathematical model in which time is a parameter that unambiguosly identifies the configurations of the system. The time mesurement thus becomes a position measurement, and the unit of time is defined as a particular duration, for instance the period of rotation of the Earth around its axis.

10. 10 Definition of Time Scale Dynamic time scale –Identifying a suitable dynamic system whose observation allows the identification of particular events that are used as “label” for the time scale; –After the time measurement unit is defined.

11. 11 Definition of Time Scale For integrated time scales, the primary data is a unit of duration, that is, of time interval, defined from a physical phenomenon. The duration of that phenomenon is adopted as unit of scale. The time scale is constructed by fixing a conventional origin and by accumulating units of scale continuosly. This approach is followed for the atomic time scales, for instance the present worldwide reference time scale, International Atomic Time, TAI, is an integrated time scale.

12. 12 Definition of Time Scale Integrated time scale –Firstly the time unit is defined; –After the time scale is obtained by accumulating time units.

13. 13 Examples of Time Scale Universal Time (Dynamic) –Time based on the angular rotation of the Earth on its axis Ephemeris Time (Dynamic) –Time based on the revolution of the Earth around the Sun Atomic Time (Integrated) –Time based on the hyperfine transition of the cesium 133 atom

14. 14 Universal Time (UT) Time measured by the rotation of the Earth on its axis with respect to the Sun UT = mean solar time reckoned from midnight on the Greenwich meridian Traditional definition of the second used in astronomy Mean solar second = 1/86 400 mean solar day

15. 15 Variations in the Earth’s rotation UT0 The Universal Time, UT, is a dynamic time, derived from the observation of the Earth’s rotation. The units UT were chosen so that on the average, local noon would occur when the sun was on the local meridian. UT0 is equivalent to mean solar time as determined at the Greenwich Meridian so the associated unit of time is the second of mean solar time. In principle UT0 should be an uniform time scale, but when better clocks were developed it was found that UT determinations, made at different locations, presented some discrepancies traced to the migration of poles.

16. 16 Variations in the Earth’s rotation UT is not uniform Variations in the Earth’s rotation (Length of Day) ─Steady deceleration (well established by early 20th century) ─Periodic variations (detected in 1930s) ─Random decade fluctuations (measured in 1950s)

17. 17 Forms of Universal Time (UT) UT1 The effect of this polar motion produces an error in UT0 so it is necessary a correction to be introduced in UT0 in order to take into account the polar motion. This correction, called , can amount to some tens of millisenconds, by definition: UT1 = UT0 + .

18. 18 Coordinated Universal Time (UTC) The evolution of UTC has progressed in two phases: ─ The first one was effective during the years 1961 to 1971 and was based on two corrective measures applied as needed and coordinated by the BIH (Bureau International de l’Heure) a)The basis frequency was offset, the offset remaining constant during at least one calendar year; b) step adjustments of ±0,1s were introduced whenever needed to keep the difference UTC – UT2 as small as possible; c)The frequency offsets were made with reference to the atomic frequency then already known but adopted only in 1967.

19. 19 UTC frequency offsets 1961 to 1971 From of E.F. Arias, B. Guinot, and T.J. Quinn, ITU-R SRG Colloquium on the UTC Time Scale (Torino, Italy, May 28 – 29, 2003) 0 -100 1958 1960 1962 1964 1966 1972 International offset Offset referred to the BIH atomic time (1965) -150 -130 -150 -300 (Relative frequency offset in units of 10 - 10)

20. 20 Evolution of UTC time steps 1957 1962 1963 1967 1972 20 ms (29) 50 ms (1) 100 ms (8) 1 s (n) number of time steps From of E.F. Arias, B. Guinot, and T.J. Quinn, ITU-R SRG Colloquium on the UTC Time Scale (Torino, Italy, May 28 – 29, 2003)

21. 21 UTC 1972 The Coordinated Universal Time, UTC, was defined in 1972 and representing a a combination of the time scales TAI and UT1, and is defined by the following system of equations: UTC(t) – TAI(t) = n seconds (n integer) and |UTC(t) – UT1(t)| < 0,9 By definition, UTC has the same metrological properties as TAI, which is an atomic time. In addition, it follows the rotation of the Earth to within 1 second.

22. 22 International Atomic Time (TAI) International Atomic Time, TAI, is an integrated time scale, that has been defined by the 14 th Conférence Générale des Poids et Mesures (CGPM) in 1971 as follows “International Atomic Time (TAI) is the time reference coordinated established by the Bureau International de l`Heure (now by Bureau International des Poids et Mesures) on the basis of the readings of atomic clocks operating in various establishments in accordance with the definition of the second, the unit of time of the International System of Units.” The unit of time is the atomic second, which became the SI second in 1967 and is still in use. Its definition adopted by the 13 th Conférence Générale des Poids et Mesures (CGPM) in 1967, is as follows “The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.“

23. 23 International Atomic Time (TAI) The calculation of TAI is based on clock differences and requiring the use of methods of comparison of distance clocks. The frequency of accuracy of TAI is improved by the frequency measurements of primary frequency standards developed in a few time laboratories reporting data to the BIPM.

24. 24 TAI and UTC Today TAI and UTC is computed at the BIPM every month and it is derived through the following steps: Step 1: a worldwide weighted average of about 300 free-running atomic clocks is computed by an appropriate algorithm named ALGOS that optimize the reliability and the long term stability resulting in time scale named EAL (“Echelle Atomique Livre”); Step 2: TAI is derived from the EAL; Step 3: Frequency measurements of primary frequency standards allow to evaluate the relative derivation between the scale interval of TAI and the SI second;

25. 25 Step 4: Depending of relative derivation value, a correction is applied to the frequency of EAL, this process is known as “steering of TAI” with the steps 1 to 4 “TAI is obtained with the optimized frequency stability of EAL and is accurate in frequency as a consequence of the steering process;” Step 5: The UTC is produced by the addition to TAI an integer number of seconds; Step 6: The result process are the differences [UTC – UTC(k)] published in monthly BIPM Circular T. TAI and UTC Today

26. 26 EAL Algorithm We just recall here the main steps of an ensemble time scale algorithm which is the basis of ALGOS; The basic equation of the free atomic time scale EAL is the weighted average of clock reading, that is: where N is the number of the atomic clocks; - w i the relative weight of the clock H i ; - h i is the reading of clock H i at time t, and - h i ‘ is the prediction of the reading of clock H i.

27. 27 EAL Algorithm The weight attributed to a given clock are proportional to its long-term stability, because the objective is to obtain a weighted average that is more stable in the long term than any of the contributing clock. Weights are determined from the estimation of the variance of monthly frequency values. Weights are subject to a maximum value which has the role to ensure reliability in case a single clock should fail. The definition (1) is nevertheless not appropriate for the practical computation because the experimental data which are available are only the time differences between readings of clocks, that is:

28. 28 EAL Algorithm Suppose that the time difference x i (t) between each clock H i and EAL, at date t, is written as: With the equations (1), (2) and (3) we obtain the system:

29. 29 EAL Algorithm To solve the system (4) it follows that Which is considered the basic time scale equation.

30. 30 Dissemination of TAI and UTC The time scales TAI and UTC are disseminated every month by Circular T (BIPM). Access of UTC is provided in the form of differences [UTC – UTC(k)] making at the same time the local UTC realization traceable to UTC. The values of frequency corrections on TAI and their intervals of validity are regularly reported at Circular T.

31. 31 International Time Links

32. 32 BIPM Time Scale Generating

33. 33 Conclusions Nowadays TAI is the international reference for timing. The international reference time scale, TAI is purely atomic, but coherence with the Earth rotation has been maintained by the production of UTC. The UTC became the basis time scale for civil, legal, and scientific uses.