If the masonry foundation does not extend above earth, then
you have serious termite and other insect infestation threat.
Wood floor joists must butt end on the outside wall ABOVE
earth ground. Fix the grading.

In the meantime, a dryer vent rising up that high may
eventually create a potential fire hazard if done in plastic.
That vent is best installed in aluminum - not plastic.

You cannot reduce the 4 inch pipe. In fact, the longer that
pipe, then the large diameter that vent pipe must be.

The vent must be high enough to remain clear of snow. You
may just have to bring the vent up through next floor, then
out through wall there. Then build a wall about that vent
pipe on the higher floor.

Don't screw around with 'good enough' solutions. If earth
is above the top of that foundation, then you also have severe
building integrity problems.

Wally wrote:
My dryer is in my basement laundry room which is below ground. There
is not enough room/space to drill a 4" round opening to (or from) the
outside for a dryer vent. At the very top of the basement wall (which
is made of cinder blocks) there is a 9" header I think you call it.
Even this header wood is mostly below ground level.

There is a window on the wall behind the dryer but the window is just
below ground level. The window leads out to a window well on my patio
which is covered by a steel grate.

One option which I really don't want to do is to take out one of the
two side-by-side pieces of window glass and replace it with plexyglass
with a cut out for the 4" round dryer vent. This would route the hot
air out into the window well but, over time, all of the dryer lint
would coat the inside bricks of the window well. Probably the outside
of the remaining window glass too. There'd be no good way to clean it
if that happened.

Most all drier vent tubes are flexible aluminum or plastic in a 4"
diameter. There is a possibility that if I didn't have to use the 4"
venting pipe/tube I'd be able to drill a small hole in the wood header
near the window. But even if I did, the vent would be just above the
patio slate.

There's got to be a way to vent my dryer to the outside, but my
basement is entirely below ground and there's no path to get outside
other than through the top of the header.
Are there smaller diameter hoses that I could use to dead-end into a
smaller vent cover that could be mounted outside?
Any, and I mean ANY, suggestions are most appreciated.

Thanks,
Walter