He was going up over the high bridge.
In the above sentence I thought up might means "to the place where somebody/ something is, not 'towards a higher position' " and over might means "from one side to another side".
Then the sentence would mean:
it was a high bridge, and he was going from one side to the other.
But the matter is that "up" seems to be redundant in this case, because it has the same meaning with "over".
What does the above sentence mean?