Very good question that I do not have the answer to but will be very interested in the answers you get.
Here is an old thread that also will not answer your question but may raise some more and might give you some insights you may not thought about.
Aeration turnover rate I think there is still a lot to be understood about aeration.
I will say this. I went to a larger capacity pump with considerable more air output than I had been using. I THINK the increased air flow and turnover rate has improved my water quality. I have had problems in past with cyanobacteria (bluegreen algae) during the dog days of summer when pond water levels are low in the past. My water level is very low this year and with the higher capacity pump (even though I do not run it all the time like I did my previous setup) I have had almost no sign of problems.
I have some different ideas about the best time to run the pump (when running less than 24-7) as you will find out if you read the linked thread. But I have no idea that my idea is correct and since I am in a minority view it is likely wrong. As you can tell from that thread, there are still lots of questions that have ideas but few hard "facts" about aeration. There are soooooo many variables and differences in ponds it is hard to give a "one size fits all" recommendation. Yet there is enough experience that at least we do have some general rules of thumb.
Hoping you get a good answer.
I will say one thing about multiple starts and stops of the pump. It takes more electricity each start cycle of the motor. I don't know if it is enough more to make any significant difference in your electric bill, but a motor does draw significantly more amps on startup than in run mode. 4 times a day???? Maybe no big deal. But if you were starting it 20 times a day I think you would see increased electric bill. My opinion - I'm no electrician.
