Somewhat over a century ago, had the Tiber River risen to its present height, the center of the City would have flooded.
In the centro you can find embedded in the walls of buildings, plaques indicating the height of the water in flood. For example,
Today I received three shots of the river.
I may have in my years in Rome seen the Tiber higher, but not by much!
The Principe Amadeo bridge…
Not the barge jammed under the bridge. The "Angel Bridge".
To give you some perspective, here is a shot of the river with its embankments at lower water. You are looking from a different direction, but at the same bridge.
I remember that one of the very best things about the Tiber in flood is that the rats would leave the embankment and seek out the streets.