Interesting indeed!First of all, ADMIRABLE JOBon the record keeping and charts!
Since there seems to perhaps be a correlation with the rain, I wonder if something is happening in the environment that causes a buildup on the screen enclosure. Then the rain washes it suddenly into the pool at a rate high enough to overwhelm the chlorine level.
Is it possible an increase, change of turbulence or wind direction combined with splattering caused by the rain in the retention pond allows whatever is in it (probably lots of nasties in there) to become airborne.
Interesting mystery...
I had considered there may be something on the screen, but visual check and it looks to be pretty clean. A bit foggy this morning, but here's what it looks like today.

And as it rains almost every day or other day, I don't see how anything could build up. But obviously there is something at work here so not ruling anything out.
The retention pond is 15-20 ft away from the pool enclosure so given that distance I don't think that would be possible. Winds will generally never blow from the pond towards the pool, more typical is a cross wind.
I'll keep on looking for other possibilities. Thanks!