I guess the word up indicates an upward direction.
Yes, it can do, and it does here, as is clear by the fact that we're talking about steps.
However,
up doesn't always mean an 'upward' direction in the vertical sense. It can also have a horizontal sense. Maybe I'm in the street and I walk
up to you. Or maybe you're driving
up the road to the shops. In other words, it can also mean 'forward' as well as 'upward'.
Another thing to note is that
up often carries a very basic sense of 'all the way'. You could say
There was a red carpet leading up to the throne and your reader would understand that the carpet stops only at the foot of the throne. In this context, if you omit
up, this won't be so clear. Every word counts.
My question is, since we're talking about steps, would the meaning still be clear without the addition of up?
Is that what you mean by 'necessary'? That the meaning is still clear? I'm always going to say no to this question because I'm more fixated on meaning than other forum members. It's much better to ask what meaning words bring to an utterance rather than asking whether you can dispense with them. As a writer, you ought to understand this, since you're trying to develop your sensitivity to language. Remember that your sentences are intended to create vivid pictures in your reader's mind. You can learn to control the focus of these images by using 'focus' words. I'll argue that if you omit
up, you make it that much harder for the reader to readily form a picture in her mind. It may be only a fraction harder, but it makes a difference.
