So I designed my schedule based on reading and trying to approximate what the coral would see "in the wild", and based on my life and how/when I like to view the tanks.
During the summer, the Great Barrier Reef gets a 13-ish hour "day". Sunrise to sunset is 12.5-13.5 hours. I figured that the majority of that time would probably be more "indirect" sunlight, while only a shorter section in the middle of the day would actually be "peak/direct" light.
The 13-ish hours also happens to fit well with my life. I work from home, so I am looking at the tank all through the day. When I created my schedule, I landed at 14 hours total, 8:30am to 10:30pm. BUT! To avoid blasting my coral with TOO MUCH light, I use VERY long ramp times, with only a 4 hour "peak" in the middle of the day where everything is at its max.
My blues start ramping up at 8:30am, and hit their max intensity at 11:00am. Then, my "whites" start ramping up at 11:00am and hit their peak at 1:30pm. All colors are at the max for the day from 1:30pm to 5:30pm, then the whites ramp down until 8:00pm, then the blues ramp down until 10:30pm. 14 hours total schedule, but the first 5 hours and the last 5 hours are ramping, with only 4 hours of max intensity.
I vary the color mix and peak PAR from tank to tank depending on what's in that tank (LPS, SPS, softies, anemones, etc), as I also try to approximate the spectrum at the depths where stuff is collected (more or less white, more or less "UV", etc), but the schedule remains the same. I'm aware that stuff growing deeper in the ocean would likely have a "shorter" day, but, again, I also adapted the schedule to fit my lifestyle and how I view the tank.
I use
@luxdium aftermarket LED pucks, so the color sliders don't line up with the actual LED colors, but my schedule looks like this in the myAI app.
For a shallow water, high light tank (SPS, clams, etc) I've used the same schedule but shortened the ramps from 2.5 hours to 2 hours, so the "peak" increases to 6 hours (from 4) in the middle of the day. There are a million ways you could modify it, but I like the blue period in the morning and evening with whites in the middle of the day, so this is just where I landed.
Like you, I went looking for actual data but didn't find it. I just kind of made an educated guess based on experience and observation and rolled with it. It's been working well for me now for 6+ years.