This weekend I set up my camera using ML for a timelapse and tried to capture a sunrise. Not directly. I set it up shooting out my window facing south. It was pretty foggy and all in all would have been a good day for it. But even with my first shot being nearly black underexposed, it wasn't long before everything was over exposed with completely blown out sky.
What's the easiest way to handle this? I tried manually just riding it between shots (every 10 minutes or so I'd go bump the shutter speed). But that ended up with obvious jumps. I realize I could go frame by frame in post and balance them but that certainly isn't worth it.
Thinking about it after the fact I think if I set the aperture really high or shutter speed really long then changes to another setting would have a less dramatic effect.
What's the easiest method (or combination of methods) to do this? I want to set the camera at pre-dawn then let it go for a couple hours and go from underexposed to just blowing out in smooth incremental steps.

