Use a long thin cable on a motorized spool. Rig up a waterproof reinforced box with sensors that detect speed and direction (mercury switch type deals?... I don't know but I bet there is something). Hook them up to a board with some storage. Drop the box in and start reeling the cable off. If the cable goes slack the thing has probably stopped. Maybe it's hung up. Pull it back a bit and try again. If it keeps stopping in the same place it's probably all the information possible by this method. Retrieve the box, get the speed/direction information, do some distance calculations and graph it. Ideally the box will go all the way to the exit point and you will have a profile showing where the water ends up. But even if it doesn't, you will have a good idea of direction and depth the water is traveling for a certain distance at least. This will at least make better guesses in the future.