Easy, now, it's just a picture. 
I don't know how it happens - leaves, twigs, nests, logs, beaver dams, etc. can fall through those narrow slits in the cowl and gum up the works. 
We had the advantage of my son's fenders being removed for a complete restoration. Access to the drains was easy. We used needle-nose pliers, a wire with a bent hook on one end, and a compressed air blow-tip to dislodge and remove all the thirty years of accumulated debris.
The bottom surface of the cowl has a 4"-5" hole on the passenger side that allows fresh air to enter into the top of the heater/air conditioning box. There is a thick rubber gasket that is sandwiched between the box and the cowl sheet metal. If you blow air down into your cowl grill, some of the dirt, leaves, twigs, pecans, etc. will drop down into your fresh air duct. The next time you turn on the blower fan, you will get a car full of trash.
If you aren't going to remove your fenders, and you suspect there is a lot of built-up debris, I would suggest trying to lower the air box enough to tape off the fresh air hole in the cowl before blowing it out. You can even reach up through the hole and dig out quite a bit of the trash by hand.
Once you clean out the debris, run water into the cowl grill and check for leaks. Don't forget, there are drains on both sides of the car. Some car models have fresh air vent boxes mounted under the driver side of the dash, so there would be another hole in the cowl floor to consider.
Good luck,
Jerry
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(I didn't think this stuff was supposed to start bothering you when you were 20!)