A lot of these overviews do not make a clear distinction between operational time scales and paper time scales — I know I found this area confusing when I was learning about time scales! And there’s a further distinction to make between different kinds of paper time scale, atomic or astronomical.
The operational time scales are based fairly directly on observations. These include:
UTC from time labs, e.g. UTC(NPL), UTC(NIST)
the GNSS time scales, GPST, GST
earth orientation time: apparent solar time, sidereal time
Operational time scales are not perfect. That’s kind of obvious for our wobbly planet, but it’s true for atomic time scales too. For example, GNSS signals have parameters that describe how to translate system time to UTC, with both rate and phase adjustments; the fixed integer delta between GPST and TAI is a simplification that’s only true as a low precision approximation.
Atomic paper time scales correlate a load of time measurements and publish retrospective corrections some time after the fact. These include:
global consensus UTC, UTC(BIPM)
TAI, intended to be more stable than UTC(BIPM) and published less frequently
the various TT(year) timescales which are able to fix anomalies in TAI
Astronomical time scales are related to each other via an astronomical ephemeris. These include:
UT1
TCB, TDB, TCG
These time scales are coordinates in systems of equations that describe the motions of the earth, moon, planets, etc. I put UT1 here because mean solar time is related to observations of earth orientation via the equation of time.
I have some corrections to suggest:
The UT1 time scale measures time relative to the stars, reflecting the Earth’s actual rotation.
This should be more careful about the difference between solar time and sidereal time! It’s true that we measure earth rotation by observing the stars (because the sun is too big and hot) but those observations are adjusted to be relative to the sun to produce UT1.
Despite these complexities, UTC simplifies matters by assuming a constant 24-hour day, equivalent to 86,400 seconds.
This sentence is OK in context, but the horrible thing about UTC is it’s the only time scale that doesn’t have a constant 24-hour day! I think it would be better phrased something like “UTC avoids difficulties due to earth’s variable rate of rotation by basing its day on 24 hours of fixed-rate SI seconds, usually 86400 seconds per day.”
Temps Atomique International (TAI) is a time scale based on the average of atomic clocks worldwide, providing a precise standard for the duration of a second. UTC is an offset from TAI designed to keep it within one second of UT1.
OK I’m going to be super pedantic now. Your description is a fine way to model the relationship between the time scales, but it sounds like an operational description — and in reality it works the other way round! The time labs produce their versions of UTC, which are averaged to produce UTC(BIPM). When a leap second is introduced into UTC that changes the offset used to produce TAI from the UTC measurements. This sounds weird and backwards if you don’t have a clear notion of operational vs. paper time scales.
Thanks for the details! Those who understand time scales are few. I’ll snag that opportunity to pick your brain some more because I am looking at time scales from the point of view of astrodynamics where I must relate TDB back to UTC (via TAI).
The difference between paper and operational time scales is new to me, and enlightening.
By that definition, I would say that GPST, and other GNSS time scales, are paper time scales, not operational ones. Their definition related them to another time scale, allowing users to convert almanac information provided in weeks and nanoseconds in the week back to another time scale: hifitime computes these transformations for the user. The system time information in the signal is used for precise localization of the spacecraft which I understand as an offset to GPST due to relativity. Tools like RINEX can ingest the GNSS data directly and compute exact positioning using that offset.
This sentence is OK in context, but the horrible thing about UTC is it’s the only time scale that doesn’t have a constant 24-hour day!
That is 100% correct. I spent so much time talking about leap seconds to coworkers that I can’t believe I wrote this. Will fix!
TAI time keeping is confusing… Wikipedia indicates that TAI is what’s measured, but UTC is what’s published by using the leap second offset. It sounds like they’re making it harder on themselves. What am I misunderstanding here?
Looking forward to discussing this topic some more if you can, it’s rare to come across people with a solid grasp of time scales!
When I say “operational” I mean there are physical clocks running as an ensemble to produce the timescale. Each GNSS timescale has its own independent timing laboratory maintaining its timescale, so GNSS timescales are in a similar category to the UTC(lab) timescales.
The paper timescales do not have their own clocks.
I suppose another important distinction that’s often not made clear is whether a timescale is only retrospective, or to what extent it is meaningful to project it into the future. And that depends on what timescales you are comparing, and the level of precision you require. For example, the atomic timescales are operated such that they remain in sync to the microsecond level, UT1-UTC is in sync within a second (but that limit is being abolished), UTC-TAI is unpredictable (though there’s a good chance it will never change again), etc. Whereas the astronomical timescales are defined as exact transformations of a uniform scale.
I would like a library that models multiple timescales to be very clear when a transformation is exact by definition, or when the operators promise the correspondence is accurate within certain parameters that are subject to physical and measurement variability. Like for example the GPS publishes an operational objective saying how close UTC(GPS) should match UTC(USNO) and how close they match GPST mod 1 second.
I need to make a couple of corrections:
It occurs to me that UT1 definitely used to be an operational timescale, before atomic time took over. I was probably being too cheeky listing it as an astronomical paper clock because it’s more directly based on recent observations than the others.
Also:
TAI, intended to be more stable than UTC(BIPM) and published less frequently
This was wrong, they are published at the same time and they are (since 1972) exactly an integer apart. I should have mentioned EAL instead as the BIPM’s less-stable timescale.
Yes the relationship between TAI and UTC is confusing, and it gets moreso when you consider EAL as well. The details are basically the internal procedures of the ex-BIH parts of the BIPM; it’s probably more useful to talk about the inputs and outputs than the internal processes themselves. Especially since the rubric in Circular T and its explanatory supplement are either unclear or inconsistent about how it works.
As I understand it, the time labs report their cross-check measurements of UTC(lab) every few days. The BIPM produces rapid corrections UTCr each week. Each month they send out Circular T which has the details of UTC(labs), UTC, EAL, TAI, and the GNSS timescales (which are important for two-way satellite time and frequency transfer, used to compare the UTC(lab) timescales).
The point being that UTC(lab) is the official (and often legally required) timescale produced by each lab, and UTC is the primary output of the BIPM for the purpose of metrological traceability. Circular T tells you to calculate TAI by adding an offset to UTC; TAI is used for comparing UTC and EAL, and is the basis for TT.
That’s correct, it’s centered around the reference epoch of the given time scale. For ET and TDB, that epoch is 01 January 2000, but for GPST is 05 January 1980 for example.
This isn’t bad but I have some suggestions.
A lot of these overviews do not make a clear distinction between operational time scales and paper time scales — I know I found this area confusing when I was learning about time scales! And there’s a further distinction to make between different kinds of paper time scale, atomic or astronomical.
The operational time scales are based fairly directly on observations. These include:
Operational time scales are not perfect. That’s kind of obvious for our wobbly planet, but it’s true for atomic time scales too. For example, GNSS signals have parameters that describe how to translate system time to UTC, with both rate and phase adjustments; the fixed integer delta between GPST and TAI is a simplification that’s only true as a low precision approximation.
Atomic paper time scales correlate a load of time measurements and publish retrospective corrections some time after the fact. These include:
Astronomical time scales are related to each other via an astronomical ephemeris. These include:
These time scales are coordinates in systems of equations that describe the motions of the earth, moon, planets, etc. I put UT1 here because mean solar time is related to observations of earth orientation via the equation of time.
I have some corrections to suggest:
This should be more careful about the difference between solar time and sidereal time! It’s true that we measure earth rotation by observing the stars (because the sun is too big and hot) but those observations are adjusted to be relative to the sun to produce UT1.
This sentence is OK in context, but the horrible thing about UTC is it’s the only time scale that doesn’t have a constant 24-hour day! I think it would be better phrased something like “UTC avoids difficulties due to earth’s variable rate of rotation by basing its day on 24 hours of fixed-rate SI seconds, usually 86400 seconds per day.”
OK I’m going to be super pedantic now. Your description is a fine way to model the relationship between the time scales, but it sounds like an operational description — and in reality it works the other way round! The time labs produce their versions of UTC, which are averaged to produce UTC(BIPM). When a leap second is introduced into UTC that changes the offset used to produce TAI from the UTC measurements. This sounds weird and backwards if you don’t have a clear notion of operational vs. paper time scales.
Thanks for the details! Those who understand time scales are few. I’ll snag that opportunity to pick your brain some more because I am looking at time scales from the point of view of astrodynamics where I must relate TDB back to UTC (via TAI).
The difference between paper and operational time scales is new to me, and enlightening.
By that definition, I would say that GPST, and other GNSS time scales, are paper time scales, not operational ones. Their definition related them to another time scale, allowing users to convert almanac information provided in weeks and nanoseconds in the week back to another time scale: hifitime computes these transformations for the user. The system time information in the signal is used for precise localization of the spacecraft which I understand as an offset to GPST due to relativity. Tools like RINEX can ingest the GNSS data directly and compute exact positioning using that offset.
TAI time keeping is confusing… Wikipedia indicates that TAI is what’s measured, but UTC is what’s published by using the leap second offset. It sounds like they’re making it harder on themselves. What am I misunderstanding here?
Looking forward to discussing this topic some more if you can, it’s rare to come across people with a solid grasp of time scales!
When I say “operational” I mean there are physical clocks running as an ensemble to produce the timescale. Each GNSS timescale has its own independent timing laboratory maintaining its timescale, so GNSS timescales are in a similar category to the UTC(lab) timescales.
The paper timescales do not have their own clocks.
I suppose another important distinction that’s often not made clear is whether a timescale is only retrospective, or to what extent it is meaningful to project it into the future. And that depends on what timescales you are comparing, and the level of precision you require. For example, the atomic timescales are operated such that they remain in sync to the microsecond level, UT1-UTC is in sync within a second (but that limit is being abolished), UTC-TAI is unpredictable (though there’s a good chance it will never change again), etc. Whereas the astronomical timescales are defined as exact transformations of a uniform scale.
I would like a library that models multiple timescales to be very clear when a transformation is exact by definition, or when the operators promise the correspondence is accurate within certain parameters that are subject to physical and measurement variability. Like for example the GPS publishes an operational objective saying how close UTC(GPS) should match UTC(USNO) and how close they match GPST mod 1 second.
I need to make a couple of corrections:
It occurs to me that UT1 definitely used to be an operational timescale, before atomic time took over. I was probably being too cheeky listing it as an astronomical paper clock because it’s more directly based on recent observations than the others.
Also:
This was wrong, they are published at the same time and they are (since 1972) exactly an integer apart. I should have mentioned EAL instead as the BIPM’s less-stable timescale.
Yes the relationship between TAI and UTC is confusing, and it gets moreso when you consider EAL as well. The details are basically the internal procedures of the ex-BIH parts of the BIPM; it’s probably more useful to talk about the inputs and outputs than the internal processes themselves. Especially since the rubric in Circular T and its explanatory supplement are either unclear or inconsistent about how it works.
As I understand it, the time labs report their cross-check measurements of UTC(lab) every few days. The BIPM produces rapid corrections UTCr each week. Each month they send out Circular T which has the details of UTC(labs), UTC, EAL, TAI, and the GNSS timescales (which are important for two-way satellite time and frequency transfer, used to compare the UTC(lab) timescales).
The point being that UTC(lab) is the official (and often legally required) timescale produced by each lab, and UTC is the primary output of the BIPM for the purpose of metrological traceability. Circular T tells you to calculate TAI by adding an offset to UTC; TAI is used for comparing UTC and EAL, and is the basis for TT.
When does this 65,536-year duration begin and end? Is it specifiable, so it might begin and end at any time, present, past, or future?
[Edited: Ah, never mind; it appears to be The Reference Epoch, centered around the first day of January in the year 1900?]
That’s correct, it’s centered around the reference epoch of the given time scale. For ET and TDB, that epoch is 01 January 2000, but for GPST is 05 January 1980 for example.