Killing black algae while pool is drained.

Hello, I have spots of black algae in some of the rough areas around the walls and on the steps.

I plan to do a drain and refill soon for a few different reason and would also like to attack the algae while it's empty. I plan to drain the pool and then hit the algae with chlorine using a pump up sprayer. I think I'll do this a couple times over a few days and then let it dry out for a coupe weeks.

Does this sound like a good approach to killing it? Or will it just grow back once I fill it back up?

Any suggestions are appreciated.

In ground Plaster pool.

I live in Az so not concerned with the pool floating while empty. It sat empty for 4 months when I first purchased the house with no issues.

I also plan to disassemble the filter and spray the grids with bleach and let them completely dry out as well.

No opinions on this approach to rid my pool of the black algae?

With black algae, the key is to scrape off the waxy surface layer with a wire brush to expose the roots of the algae underneath to high chlorine levels. Technically, you could do this without draining and just maintain a high chlorine level in the pool, but again the key is REGULAR brushing to scrape off the surface layers once or twice a day.