I have a dutch gutter that drains the storm water away to the gutter
inlet that leads below to the courtyard deck and tie into a 4" pipe
that drains outside.

There are several issues associated with this gutter design. Here is
a picture.

http://i173.photobucket.com/albums/w...r/P1000997.jpg

One of the issues is that the drain inlet leaks below. I know what
the problem is and I just need to install a real dome shaped roof
drain with a clamp that tightens to the deck that allows for some
movement, and I have to reflash around that. Not a problem I can deal
with that.

The other issue is if you look close enough, the previous owner has
installed a drip edge (brown color) over the edge of the gutter, and
have decided to screw them into the edge of the 2x12 below. One screw
every 8 inches or so. My understanding is that there should not be
any exposed screws. I don't know why this was done, but probably was
an attempt to repair something...I don't know. I think I have to rip
out the drip edge and see what is going on there. The drip edge
should have wrapped the gutter on both sides and the membrane go over
that, I believe.

Now the biggest problem is that the gutter itself is not pitched steep
enough to drain water quickly. In some areas of the gutter there are
low spots which caused slight ponding and contributes to leaks. I
took the soffit panel off from below and as best I can tell, the
framing was done this way as illustrated in the picture below:

http://i173.photobucket.com/albums/w...tterconfig.jpg

The concrete tiles run to a point about 16" back of the edge. Then a
membrane lined the gutter. The membrane sits on top of the plywood
which sits on the truss. The vertical edge of the gutter is a piece
of 2x12. Now wedged in between the plywood and the 2x12 face is a
piece of strange shaped lumber. It looks like a piece of 4x4 or even
6x6 custom cut...in the picture above it is the piece shown in red.

My question is, how was this piece made 36 years ago?

My plan is to take out the last row of tiles, and rip out the existing
membrane and drip edge to expose all the way to the plywood and
visually inspect the situation. I expect to find a few spots of
rotted wood that I will need to repair.

Now, how would I redo the gutter to give it a bit more pitch? Using a
standard minimum gutter slope of 1/16" per foot so the longest gutter
run is 30', I can create a high point in the middle and drain down 15'
on each side, which means I will need to have a rise of 0.9375 or say
1". Heck let's make it 2".

Is it possible to create a piece of lumber, same shape as the red
piece in the picture, but tapered the depth so that on one end it's 2"
deeper? Can a lumber yard do this custom shaped tapered wood? If I
can order and fabricate such a piece, then lay a new membrane over the
entire gutter then a new drip edge, I believe that would create the
pitch I need...thoughts?

I have explored the idea of eliminating the dutch gutter altogether
and let water just drain over and install a structural gutter (they
call them super gutter) and the screening framing would attach to
that. However that created another unsolvable challenge.

Sorry for the long post, it's a complicated situation and not easy to
explain.