The ambient outside air is where a heat pump will be drawing the heat for the pool from. They will typically draw, at start up, about 50 amps of current @ 240 volts. If you don't have this service available currently, a service upgrade by an electrician would be called for. This may be as simple as adding a sub panel or a more involved full and larger panel.

These units typically, on a day with 80 degree day with 80% humidity will be rated at about 125,000 BTUs/Hour and able to inject about 80% of the heat into the water. Lower air temps will reduce the efficiency. Higher temps will increase it some.

Water is heated differently from air in that it is harder to heat and releases it's heat more slowly. In order to keep the heat you spent money injecting into the water, a solar cover is strongly encouraged. These covers keep evaporation down. Heat in a pool is typically lost via this mechanism. The term "solar cover" really is a misnomer. Having a roller for the cover will help it last substantially longer than just pulling it off.

Heating the pool water goes by weight and not volume. One BTU will heat one pound of water one degree F. There are 8 pounds of water for each gallon. This is a constant. Using a heat pump is the most efficient method of warming the water when you power costs are taken in consideration. Bear in mind, a gas fired heater can be as much as 400,000 BTUs and that in California, where power can be a lot more expensive, gas may be a less expensive option. In Florida, power pricing makes heat pumps more cost effective.

Gas fired heaters use either natural gas or propane, not butane.

Roof top solar systems need a Southern exposure with low wind. The pool orientation is moot.

Clay tile is not, IMHO, a good surface to mount to. If and when the panels develop a leak, someone has to go up and plug the rib, placing the tiles at further risk. Add to it that wet tiles are significantly more slippery and the risks just aren't worth it.

Scott

Thanks for such a thorough reply
The pool guy got back to me and said the pool is about 15-18000 gallons

We will likely need to have some electric work done to create a circuit for the pump
but when I mentioned getting one to my husband he was not too excited...

The pool deck was "redone" by past owners and a bad job of stamped concrete has started to flake off and needs to be removed/replaced with something else...
so that is what we might choose to do first

personally I think the pool heater would have the most impact for the money but it will probably be shelved for now...