Actually, I started with the idea of using a bladder-fitted tank with the bladder enclosed inside the tank and chargeable from an outside source with air at normal ASME air tank pressures of 120-200PSI but this would require a special construction and would cost more but would be far simpler.
In any case, I figure the device would need to dump (rain) at least one inch of water in less than 5 minutes to be effective, which is why I said it would take at least 63 gallons for a 10 foot by 10 foot floor area.