I might have to have a word with "Aidos" about the one they found.

[It's probably just the same as their one, but it's worth asking. And perhaps Suijin let something else slip while talking to them that she held back from Hakkai and Sharak.]

A schedule could be too much to hope for though. Unless you catch one immediately after it appears, and can be sure that's what you did, the appearances are a little too close together to predict that. The circle we found could be months or days old, for all we know. The best way to judge the timing would be to compare the different circles and the intensity of the energy remaining around them, if it does change significantly.