"On a multi-story house, some section of the upper gutters do not have
a
direct connection to the ground level storm drain, but instead dump its

water onto the lower level roof, which eventually reach another gutter
that
drains to the storm drain.

Why do I need this type of gutter? Without it, the water would run off
the
upper roof and drop down to the lower roof anyway. "

I have a roof section where there is no gutter on the upper story. It
overhangs the garage roof and it works fine. The garage roof is even
relatively low pitch and in 17 years, no problem. One thing that you
would think might happen would be more erosion of the shingles near
where the water lands, but I see no evidence of that.

Having said that, in my case, I am probably going to put in a gutter
there. That's because the upper roof is about 7 feet longer than the
garage roof, which means in that last 7 foot section water drops all
the way to the ground. To keep that water away from the house would
require either a short gutter which would look stupid, or else one that
runs the length of the upper roof.

So, that leads to another realted question. In my case, there is no
way to get the water from the upper gutter down to the ground. It
would have to use a leader taking it down to the garage roof. So now
I'd have that water exiting all in one spot on the garage roof. Is
that OK? Any problem with erosion of the shingles?