This is a simple solution on the GM 8.1L engine. What is happening is that your "tuba" air intake is ingesting water which is soaking your paper air cleaner element and causing the engine to miss.
The solution is to cut off the top of the air intake tuba, turn it 180 degrees, so that it faces the rear, and using duct tape, reattach the intake air horn. I used two pieces of aluminum to screw in to the bottom of the tuba and then screwed the top on before I taped the joint. My cost was really nothing more than some time. I put another 50,000 miles in some very hard rain the the problem was solved.