5 Answers

Report your neighbour to the local authority.

Get an umbrella handy,  OK seriously you going to have to go to a higher authority like the police.

Your landlord could find himself in some "hot water" if he doesn't maintain a safe and clean environment.  Contact legal aid, or a consumer support agency.  You have way more rights than the property owner. 

Give your upstairs neighbor a flying lesson.

not sure where your from but there is a tenancy tribunal, or failing that the dept for environmental protection, or the health department, but I would be asking the offending neighbor first to find an alternate method of disposing of the water, like down a sink and then take it from there