I always assumed that the swale on 13 was to help move water coming down the hillside around the green to the creek without it running across the green. Also I think I remember reading that the green was raised to be higher in case of flooding, or maybe that was only the 12th.
The 12th was raised significantly at some point after Ian's picture -- two or three feet. Just look how shallow the front bunker is here, and how the floor of the old back bunkers were well above the green. [I think they were redesigned, instead of just the green coming up to hide the floor of them.]
I don't think the 13th was raised when the swale was built. The old 13th always had drainage problems, even though the topo map underlying the plan Ian posted above shows that there was a small swale in back historically. When I first visited Augusta in the summer of 1981, there was a guy drilling holes five feet deep in the green, and then backfilling with sand, to try and improve the drainage. Nicklaus's change was for the two purposes of making the hole harder for players who bailed out long left with second shots, and improving the drainage.