A. A roof top cooling / spraying system would be configured like an in ground lawn sprinkler system. Zone controller, spray heads, antisiphon valves, distribution lines and controller wiring.
B. The water would need to be very pure / filtered. Free of minerals, otherwise over time a mineral layer will form on the surface reducing the speed or rate of evaporation cooling.
C. An ample supply of water and at low cost would be necessary.
It would be more expensive initially to use a white coating, but in the long run you save money, i.e. no water usage, maintenance of spray system or potential roof repairs or damage.
Then you could also use roof top mounted standard evaporation coolers, if your looking for a way to cool the interior space.
Before the advent of modern solar coatings, the use of spray systems was common.
I have several clients that use both solar coatings and evaporation coolers to reduce their building or homes heat load.
One reference I thought about was first mentioned in 1973, with a pond on the roof and movable insulation over it. See: https://www.slideshare.net/SushilKumarGupta4/roof-pond. I'll admit my age by saying that I read about it at that time. I am sure that this method is far from the only one that has been explored. Do well in your searching.