I always thought one of the biggest draws of wet racing was that it's unpredictable, this would eliminate that entirely since the teams would know exactly when and how much water they would be dealing with.
So play up to the unpredictability: rather than set a designated time when circuits will be flooded, make it completely random. Have a computer randomly decide the following:
1) The probability that the circuit will be flooded. Just because the circuit can be flooded, it doesnt mean it has to be. And entire weekend could go by without a hint of rain, real or artificial. Most importantly, this information would be kept from the teams. If they dont know the likelihood of the circuit being flooded, it adds an extra element of uncertainty.
2) The time when the circuit will be flooded. Rather than limiting it to the race, this could apply to the entire weekend. So it might rain in FP1 and be completely dry for the rest of the weekend. Or the circuit could be flooded before the parade lap, in the final ten minutes or at any time during the weekend. It could even be flooded overnight so that the circuit is mostly dry at the beginning of the next day.
3) The degree to which the circuit will be flooded. The sprinkler system could be programmed to simulate anything from a light shower to a heavy downpour. Again, keep this from the teams to add the element of the unknown.
4) The percentage of the track to be flooded. Just because you can flood the track, it doesnt mean you have to. And on some of the longer circuits like Spa, you can get sections of the circuit that are wet while others are completely dry.
So, combine these four completely random variables, and you could end up with a situation in Silverstone where the Wellington Straight, Brooklands, Luffied and Woodcote are flooded with a medium downpour at the end of Q1. Or at Monza, with heavy rain flooding the circuit at 3am on Sunday morning, so that the circuit is largely damp for the race. Or light rain just enough to make teams consider swapping to intermediate tyres for the last five laps of Valencia. I think that making the element of artificial flooding completely random is the only way the system could work and be accepted by teams and fans.
The most important part, however, is to test the concept out. I believe Paul Ricard can be flooded so that teams can do wet-weather testing even in the middle of the Mediterranean summer. So, rather than go to Bahrain in August, organise a special running of the French Grand Prix at Paul Ricard and test out the idea of a randomly-flooded circuit. If it works, then we can consider expanding on the idea and applying it to various circuits around the world. If not, then no harm, no foul. And we get the return of the French Grand Prix to compensate.