The table in
this post shows the situation for my pool. If you don't have solar panels and don't use a cover, then the water temperature in a white plaster pool will be a little warmer than the average day/night temperature. The actual temperature can be higher or lower than this depending on the evaporation rate since the pool water gets heated during the day but it gets cooled by evaporation both day and night so which one wins out depends mostly on wind and humidity.
Figure that a solar bubble-type cover alone will keep heat in the pool (mostly from preventing evaporation and some from reducing conduction) to have its average temperature be 10-15ºF higher than the average day/night air temperature. A fairly large solar system (85% of pool surface area) in conjunction with a cover will heat the pool to 20-25ºF higher than average or sometimes higher (30ºF) if the solar cover is very well insulated.
For our pool, without a cover where we live the water would be at best in the low-to-mid 70's. With a solar cover, it would get to 80-85ºF or maybe a little higher at peak summer so maybe 3 months (Jul, Aug, Sep), but our pool uses a relatively thin mostly opaque electric safety cover so we don't get the full benefit of a bubble-type cover (hence more gas use in Sep). With the solar system, we are able to get to 88ºF without too much use of gas heat for 2 more months (May, Jun). It also reduces the amount of gas heating in other months (Apr, Oct). So roughly speaking where I live, a cover gives us 3 months and
the solar panels give us another 2 months and help reduce gas heating costs in an additional 2 months. With gas supplement, we have an expensive 7 month season from roughly mid-April to mid-November. Most people in our area do more of a 5 month season (May-Sep) while some do a traditional 3+ month season from Memorial Day (end of May) to Labor Day (start of September).
Obviously, the devil is in the details including the target pool water temperature vs. the average day/night air temperature. I've put together a similar chart for you based on
Atlanta, GA temperatures and
solar insolation.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
.52..57..65...73..80..86...89..88..82...73..64..54 ... Avg. High Temp
.34..38..44...52..60..68...71..71..65...54..45..37 ... Avg. Low Temp
.44..48..55...63..71..78...81..80..74...64..55..46 ... Average Temp (slightly more weight to daytime temp)
4.2 4.8 4.8 3.4 . 3.7 4.0 5.3 3.9 . 4.5 3.4 4.1 3.9 ... Average monthly rainfall in inches
3.4 4.2 5.1 6.0 . 6.2 6.3 6.1 5.9 . 5.3 4.9 3.8 3.2 ... kWh/m
2/day from the sun (30-year average for month; panels facing south tilted at 34-15=19 degrees)
So with your higher average day/night temperatures in the summer, you need less supplemental heating and can easily warm your pool with a solar cover for very warm water in the 3 months of Jun, Jul, Aug and probably be OK for low-to-mid 80's in May and Sep.
Solar panels would let you heat the pool without a cover in peak summer (Jun, Jul, Aug) and let you extend the season by a couple of months into May and Sep if you use a cover. It would reduce your gas costs in Mar, Apr and Oct if you still wanted to swim (which you might given your milder temperatures) though it won't save a lot of gas unless your target pool water temperature were lower (below 85ºF). Interestingly, you get more sun in the winter compared to where I live because of your latitude, but you get less sun in the summer because of the rain (which implies cloud cover).