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This in-depth answer mentions that

...TDB is updated every year. As technology improves, these subtle updates change the timing of past events.

This makes me wonder...

  1. Does this updating result in yearly discontinuities in TDB relative to a smoothly-running (non-discontinuous) atomic clock?
  2. If not, does it result in discontinuities in the first derivative of the difference?
  3. Is TDB ever non-monotonic?
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    $\begingroup$ This is not strictly true and a little more complicated. TT is recomputed every year by the BIPM from all of the measurements and clocks that went into forming TAI. Transforming TT, or an updated TT(BIPM20xx) into TDB or TCB is a lot more complicated as it needs a rate change and either a many body intergral, series expansion of time ephemeris; see Fukushima 1995 or Irwin & Fukushima $\endgroup$
    – astrosnapper
    Commented Jul 8, 2019 at 18:37
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    $\begingroup$ The value TT - TDB is available in the file "TTmTDB.de430.19feb2015.bsp": ssd.jpl.nasa.gov/pub/eph/planets/bsp. If TT is non-smooth (I don't know, but astrosnapper says "TT is recomputed every year...") also TDB must be non-smooth, even if it seems strange to me. A graph of TT - TDB is available here: satprobe.altervista.org/tempi.html , find "Terrestrial time and barycentric dynamical time". $\endgroup$
    – Cristiano
    Commented Jan 29, 2021 at 11:52

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