Hi billis, so one possible technique is like the following.

Build a more plain dome like this:



Build a cutting surface similar to this (here I drew a polyline on the bottom plane and then a path curve and used sweep):



Then do a boolean:



Then shell, then do a fillet to round off the sharp parts:



I've attached the model here as billis2.3dm

I'm not sure if that model will work for you, or if you need something a bit different but at any rate this is one technique that could possibly be used.

- Michael