what size would the panel be/ I live in the caribbean so plenty of sun!
What does the advertisement have to do with your question? Yes; BUT, depending on the pump, you may need several panels and possibly an inverter if it is an AC pump. You will ALSO need at least battery in the circuit to provide a load to the panel.
a minimum of 4000 watts, 5KW may well be extra desirable and you do choose an inverter and batteries and in all hazard a variable frequency force till the pump motor is rated for DC which I doubt. suited answer is touch a close-by electrician to do the artwork.
Do you live in a cold place in the Carribean? If it's anything like Hawaii, a pool heater, solar or otherwise, is unnecessary. As for the electricity to run your pool pump, I think the best course is to run it off the same electricity as your house, not a standalone system. You can then displace some of the electrical usage of your house with grid-tied solar, if it makes financial sense. There's a good chance of this if your electric rates are high. Contact a local solar installer to find out.
You will need several panels and it will be expensive.. That's if you are running your pump for 4 hours each day.. You will really need a battery bank to give you Amps and or Watts.. The motor when starting will need up to 5 amps at once if not more... Too much for a solar panel by it's self and even 4.. maybe five would do it At watt per solar panel.. I am not a genius on this issue but there are base lines..