Yeah, it's probably perfed about 5/8 of an inch deep.
My gaps were much smaller (3/8 by 1/2") but I had terrific results using polyurethane caulk. (available @ HD/Lowes)
It is messy so your prep has to be good. Tape off (with masking tape) each side of the joint after you pull the top piece of foam out. Make sure you get the tape stuck down to the vertical edge of the joint as precisely as you can.
Then fill the joint with the caulk. Do this by overfilling it just a little tiny bit then taking a 1" putty knife and start compacting and smoothing the top surface of the caulk. The caulk will bulge back up just a little but that's good....it shrinks some as it dries. This is the hardest part, the stuff is really gooey and you can make a mess if you try to play with it too much. You'll get the hang of it quickly, tho.
Then, simply let it dry FOR 24 HOURS AT LEAST WITH NOBODY TOUCHING IT. The darn stuff is slow to set up.
When it's done, you have a flexible, waterproof (if you do a good job) seal that will last for years.
It comes in several colors.