Sometimes you find a real build up of 'crud' under the two plastic panels at the base of the screen. Water that gets between the glass and the edge seal strips should be directed toward drain channels but if too choked then cannot clear it. When I took mine off there was enough earth/silt to start a vegetable patch. Once cleaned and polished the water now flows where it should. If you do remove the plastic panels be careful of the white plastic trim studs which hold them as they buckle easily if you do not line them up correctly for the refit. Also, over the passenger side there is a water deflecting panel which often causes grief, (well covered in other threads). There are varying opinions about using sealant but I just cleaned mine and polished it to a high gloss with Autoglym, (even though you cant see the panel with the scuttle trims back on), as the water then beads off it.
Good luck, hope you solve it soon.