A phenomena is a special encounter which occurs randomly and cyclic in all areas of Unova and has 4 appearances: Rustling Grass, Rippling Water, Flying Shadow and Dust Clouds. There are exclusive species to phenomena, encounters have a >50% chance to have at least one 31 IV, and it may drop Mysterious Gems or Fossils.¹
EDIT: Please see the second answer for updated calculation.
Original post with presumably incorrect assumptions:
It is believed only a single phenomena at a time spawns for t = 15min for the whole server², and afterwards it "jumps" to another location³. There are n = 177 known phenomena locations⁴.
So we can conclude, that for a single location there is a chance of per hour for a phenomena to appear.
Q.E.D.
¹ https://forums.pokemmo.eu/index.php?/topic/76118-changelog-27022018/
² http://boards.4channel.org/vp/thread/38677228/pokemmo-general-v-06-pmmog-tripfag-edition#p38688626
³ http://boards.4channel.org/vp/thread/38677228/pokemmo-general-v-06-pmmog-tripfag-edition#p38688523
⁴ https://forums.pokemmo.eu/index.php?/topic/77087-phenomenon-locations-guide/