TAI is also a kind of approximation, since time elapses differently depending on gravitational pull, due to relativistic effects. It is defined as the physical time elapsing on a geodesic, an imaginary surface covering the earth at roughly sea level with equal gravitational pull at all points.<p>In reality, physical time elapses at slightly different “rate” depending on where you’re located on the surface of the earth (or possibly not on the surface of the earth), also due to nonuniformities in the earth’s mantle affecting the gravitational field.<p>TAI is taken as the average between the 400-or-so contributing atomic clocks, adjusted for their relative height above sea level, and possibly other factors, and taking into account the signal propagation time between the clocks.<p>Compared to the time in the reference frame of the sun, for example, (which may be taken as a solar-system wide time-keeping standard) TAI wiggles around that solar time according to earth’s yearly cycle around the sun.<p>Of course, those variations are much smaller than DUT1 (at least close to earth’s reference frame).