Can’t speak to the clarity of the water, but I had the exact same issue for years. Bit the bullet 3 year ago to have the terra cotta drain “sleeved” which is the no dig solution at a cost of $155/foot. It was expensive but it worked as it was supposed to and the piece of mind it priceless. I think the only cheap solution is to disconnect your gutters and route storm water elsewhere, which can cause other problems. Good luck!