How to get the UT1 directly? or How to get the UT1-UTC I have a question to consult you. Even though I know the relationship between time scales like UT1, UTC, TAI, and TT, I do not know which one is the key point for the computation. That is, from which parameter I can derive others.
For example, if I wanna compute UT1, I must know UT1-UTC. But how to derive UT1-UTC normally? Actually, I know there is some place to distribute the table for UT1-UTC. But compared to that, I prefer to know how to derive that.
In my opinion, all the key point maybe the TAI. We can derive the TAI-UT1 by astronomical observation and then compute other time scales with the relationship formula. Am I right? I hope for the right and professional answer.
 A: TAI, International Atomic Time, ticks according to the second defined by the International System of Units. TT, Terrestrial Time, is separated from TAI by 32.184 seconds.
The second was once defined by the rotation of the Earth, with 86400 seconds per mean solar day. This concept is the basis for UT1, Universal Time. Atomic Time and Universal Time are rather distinct time scales. The Earth's rotation rate is ever so slowly slowing down.This means that a UT1 second is not equal to a TAI second.
Coordinated Universal Time, UTC, is a hybrid time scale. It has seconds that tick in sync with Atomic Time but also has leap seconds introduced intermittently so as to keep UTC and UT1 within 0.9 seconds of one another.

In my opinion, all the key point maybe the TAI. We can derive the TAI-UT1 by astronomical observation and then compute other time scales with the relationship formula. Am I right?

No, you're not. The very slow slowing down of the Earth's rotation rate due to transfer of angular momentum to the Moon is compounded with changes that occur over multiple time scales, varying from centuries to days long (or even shorter; earthquakes are hypothesized to change the Earth's inertia tensor and hence the rotation rate). Some of these changes are predictable, to some extent; others are not predictable at all.
The unpredictability means that $\Delta T \equiv TT - UT1$ is not predictable. This is why the primary job of a number of observational scientists is to collect data regarding the observed Earth rotation rate and publish it via various means. You can receive these data from the International Earth Rotation and Reference System Service (IERS) via its Bulletins A and B. You can also subscribe to these bulletins via email.

Side note regarding the acronyms:
TAI obviously does not jibe with International Atomic Time. (It does jibe in French.) A time scale that I didn't mention, GMST (Greenwich Mean Sidereal Time), does jibe with its acronym, in English. UTC doesn't jibe with Coordinated Universal Time in any language. The acronyms for these internationally recognized time scales are the same in every language.
IERS also obviously does not jibe with International Earth Rotation and Reference System Service. It did do so, once upon a time (in English), when the organization's name was shorter. The acronym remains IERS, in every language.
A: The fundamental issue is we want to agree on what time it is, but all methods of measuring time have issues. Firstly all measurement methods have limited accuracy, secondly thanks to relativity elapsed time is only really defined in a given reference frame. Thirdly when most people talk about time they don't really care about some scientific definition of time, they care about how many days have passed and what time of day it is but those astronmic phenomina are not entirely stable.
TT is a theoretical scientific ideal, measuring time in the earth's reference frame using SI seconds.
TAI is an attempt to realise that ideal (though for historical reasons it has an offset from TT) by averaging results from a bunch of atomic clocks.
The UT0/1/1R/2 series on the other hand are based around attempts to measure earths orbit astronomically. Rather than a second being a SI second, a day is a rotation of the earth relative to the sun and a second is a fraction of a day. The problem here is that the earths rotation is not entirely stable, so the length of a second varies a bit. The different variants apply various smoothing and corrections to try to make the length of a second more consntat.
Since a SI second is not precisely 1/86400 of an earth day the TT time of day will drift over time from the astronomical time of day. On the other hand for short time intervals atomic time with it's relatively stable seconds is usually considered preferable.
UTC makes a compromise, in the short term it is defined by atomic time, but in the long term it is adjusted to keep it reasonably close to UT1. In the early days both frequency adjustments and irregular time steps were used, but since 1971 UTC seconds have been identical to TAI seconds and time steps have always been exactly 1 second.
Since we have two fundamentally different sources of truth here no formula can precisely predict the future relationship between the astronomical and atomic time scales.
