Well, a Half million btu should do the trick
But seriously, since I don't personally know enough about heat pumps to understand the limitation, can you help me, and the OP perhaps, get a grasp on what's not possible here.
I'm serious about it taking less btu to maintain heat -- if the pool were "kept" at 90 in AZ, would the OP, using a cover, really ever need to recover more than 6 degrees in a 24 hour span?
Eg. With gas in dead winter I recover that in 6 hrs, albeit with a 266 btu gas heater.
But lets say the heat pump can for whatever reason only net .3 degrees an hour...that would have him covered on the recovery if the heat pump was simply Thermostatting.
As to the hot tub...maybe not achievable if its an open, integrated spa that's part of the pool. But a stand alone hot tub could easily keep 104 degrees 24/7....I know, because MINE does, all winter long, even in subzero conditions.
So, if its the spa part that makes this not viable and he really wants to stick to electric, skip the spa, buy a stand alone hot tub. But if its the operating temp that's the limitation, then yeah, geothermal loop might be the only way to extract heat on coldest days.
On the other hand, selling back the energy generated would handily cover the gas or propane cost...
I just think if I can manage the exact temps he wants up here in usually-snowy Michigan (mind you, not without an energy budget that some would not entertain) there should be some way to leverage his energy to achieve the same in a state that barely knows how to spell winter
