Keep in mind that the smaller the panel area the longer your pump will need to be run ($$) in order to get heat gain into the pool. You are likely to save more money with more panels even taking into account the extra cost of the panels.
As for the pipe heat loss, I put together a SS based upon the methodology outlined in this paper:
Heat transfer model of above and underground insulated piping systems
Note that the paper shows that the dominate heat loss mechanism for an underground pipe is conduction which makes sense because the dirt is in contact with the pipe so there is no radiation loss and no convection loss because soil does not circulate.
There are five scenarios in the
spreadsheet:
Scenario 1: Soil saturated with water - Very unlikely in CA during the summer since we get very little rain if any.
Scenario 2: Most likely scenario with dry soil. Shows a 0.15 degree temperature loss from end to end in the pipe which would be nearly impossible to measure. Keep in mind that this is with a 9.2 GPM flow rate (due to panel size) which is very slow. The faster the flow rate, the lower the temperature difference in the pipe.
Scenario 3: Adds insulation. Cuts the heat loss in half but it is still only about 1% heat gain so probably not worth the effort or cost. This assumes the Home Depot 3/8" foam pipe insulation (R-1.8).
Scenario 4: Same as 2 but with double the panel area. This decreases the impact of the pipe heat loss because the panel is producing twice as much heat plus you only need to run the pump half as long to get the same heat gain so less total heat is lost in the pipe.
Scenario 5: Same as 4 but with double the panel area again.
The most interesting aspect of this analysis was that 3' of dry dirt has an R-12 value which isn't too bad. Depending on the dirt composition, it can be better or worse than this.
You can download the spreadsheet by going to File > Download as...
Let me know if you have any questions.