This article has a cool note at the end. Apparently the best clocks are getting so accurate that time coordination between them requires knowing the altitude of the clocks to within a few meters because the different gravity fields at different heights causes skew between the clocks.
But that won’t be enough for the expected next generation of even more accurate clocks:
That becomes tricky because gravitational theory dictates that the altitude isn’t measured relative to average sea level, but to the geoid, a hypothetical surface that approximates the shape and size of Earth. The geoid’s size fluctuates in response to, for example, ocean tides and the redistribution of water due to climate changes.
Now that is a freakily accurate clock.