Time Scales UT0, UT1, EAL, TAI, UTC

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Time ScalesUT0, UT1, EAL, TAI, UTC

• Ricardo José de Carvalho
• National Observatory
• Time Service Division
• February 06, 2008

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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.

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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.

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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.
•  

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Definition of Time Scale

• Integrated time scale
• Firstly the time unit is defined
• After the time scale is obtained by accumulating
  time units.

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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

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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

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Variations in the Earths rotation

• UT0
• The Universal Time, UT, is a dynamic time,
  derived from the observation of the Earths
  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.

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Variations in the Earths rotation

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

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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 ??.

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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 lHeure)
• The basis frequency was offset, the offset
  remaining constant during at least one calendar
  year
• step adjustments of 0,1s were introduced
  whenever needed to keep the difference UTC UT2
  as small as possible
• The frequency offsets were made with reference to
  the atomic frequency then already known but
  adopted only in 1967.

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UTC frequency offsets 1961 to 1971
(Relative frequency offset in units of 10-10)
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)
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Evolution of UTC 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)
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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)
• 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.

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International Atomic Time (TAI)

• International Atomic Time, TAI, is an integrated
  time scale, that has been defined by the 14th
  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 lHeure (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 13th 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.

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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.

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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

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TAI and UTC Today

• 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.

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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
• - wi the relative weight of the clock Hi
• - hi is the reading of clock Hi at time t, and
• - hi is the prediction of the reading of clock
  Hi.

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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

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EAL Algorithm

• Suppose that the time difference xi(t) between
  each clock Hi and EAL, at date t, is written as
• With the equations (1), (2) and (3) we obtain the
  system

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EAL Algorithm

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

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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.

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International Time Links
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BIPM Time Scale Generating
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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.