Is the International Atomic Time TAI a coordinate time or a proper time?

The International Atomic Time TAI is a physically realized time scale which is ultimately used for comparisons between observations and dynamical theories. Its definition should tell unambiguously what an ideal TAI should be. For terrestrial applications, TAI has been defined as a geocentric coordinate time. In Solar System Dynamics, a barycentric coordinate time is needed. In general, it is not possible to convert a coordinate time into another coordinate time. But a specific clock synchronized on TAI in the terrestrial system can be considered as reading a 'modified', proper time [TAI]_i, which can be converted into a barycentric coordinate time. In this conversion appears a small location dependent term. By this process all the clocks of the TAI system give an unique barycentric time with the same metrological properties as TAI.