Ok, sorry, I didn't have much time to spend before to help...
If you have 1000 w/m^2 or 317 btu/ft^2. Now, what is confusing about a btu is that a btu in common language isn't really a btu, it's a btu-h. 1btu for one hour. So 1 square foot of peak sunlight can raise 317 lb (about 37 gallons) of water 1 degree in one hour.
Now, for your particular problem, we need a guestimate of your efficiency. A very good solar collector can have an efficiency of 60-80%: http://www.thermomax.com/effi.htm If you get 25%, consider yourself talented. So now we're at about 10 gallons of water, 1 degree per hour per sq ft.
Now, unless your rig tracks the sun, you'll only collect perhaps 1/3 of the energy you otherwise could, and for about 10 hours a day, in the summer. So, 33 gallons, 1 degree per day per sq foot.
The 1000 w/m^2 is based on not having an atmosphere. Depending on where you live, you'll get an average of around 40-60%. We'll split that and call it 50%. So now we're around 16 gallons, 1 degree per day per square foot.
A pool that's 40'x20'x5' contains about 30,000 gallons of water, so to have any noticeable impact on the temperature (say, enough for a 1 degree per day rise), you'll need around 1,900 square feet of collector.
Now, this ignores the heat loss. I can tell you that the biggest form of heat loss is via evaporation and as a result, the equilibrium temperature of a pool is somewhere around the average dew point at your location. A solar cover helps heat the pool, but it also eliminates evaporation, potentially saving much more energy than the cover actually collects. Ie, if you have a heater, a cover will reduce the usage of the heater, but mostly because it reduces the evaporation rate, not because it collects more heat. This calculation is kinda complicated and has been discussed before:
https://www.physicsforums.com/showthread.php?t=158353&highlight=pool+heat+loss+evaporation
That's enough for now - I'll let you chew on that for a while, and then come back later and work on making sure that previous thread got the calculations correct...