"Climbed up over ..." vs. "climbed over ..."

I found that climbed up over is used in the following sentence of the 'excerpt' “The Amber Spyglass” in The New York Times.

“Ama and her daemon climbed up over the rock shelves and around the little cataracts, past the whirlpools and through the spectrum-tinted spray, until her hair and her eyelids and his squirrel fur were beaded all over with a million tiny pearls of moisture.”

As climbed up over does not have many hits in Google nGRAM, I am wondering, why should we prefer climbed over? To be clear, what is the grammatical rule that we should consider to choice between climbed up over and climbed over?

See the following nGRAM:

Ama and her daemon climbed up over the rock shelves and around the little cataracts, past the whirlpools and through the spectrum-tinted spray...

says that Ama and her daemon climbed up, and then in nice parallelism tells where they went or what they encountered on the way:

• over the rock shelves
• around the little cataracts
• past the whirlpools
• through the spectrum-tinted spray

Thus, while up over may be slightly pleonastic, it is useful as part of a rhetorical device to better evoke an emotional response in readers.

To climb up something is to ascend along some face or surface of that thing. If I climb up the rocks, my action finishes with me on top of the rocks.

To climb over something is to pass an obstacle by climbing up one side of it and then down the other. If I climb over a fence, my action finishes with me on the other side of the fence, at ground level.

To climb up over something, then, is a combination of the two actions; it involves overcoming an obstacle to my upward progress. In this case, Ama's goal was to scale some object (a mountain, perhaps?) and presumably get to the top of it. Along the way, there were some rock shelves that presented a challenge to her climb, but she was able to successfully pass them and continue upwards.