It doesn't take long for Auden to get his feet wet with river imagery in "As I Walked Out One Evening." In fact, he jumps right in with that "brimming river" in line 5 and things stay pretty wet and wild. Let's dip a toe, shall we?
Line 5: The poem starts and ends with a river, so that's a pretty good clue that the image and idea of rivers is significant. Rivers often represent the movement or passage of Time. Seeing as Time is one of the major themes in this one, the fact that we start and end with a river makes perfect sense. Shmoop likes it when things make sense.
Line 11: Rivers can do lots of stuff: run, rush, gurgle, gush, you get the idea. One thing they can't do is jump. Remember who's talking here. This is our lover-speaker. His love has caused him to become, well, delusional (don't judge, we've all been there). If, as we said before, rivers often represent Time, then, symbolically, our lover is describing Time doing something it cannot possibly do. Just like a river can never jump a mountain, Time can never stand still or be defeated. The lover is making claims that he just can't back up. Again, don't judge. Dude's got it bad.
Lines 13-14: This time, the lover is using the ocean as a comparison point for his love. And, once again, our lover describes a body of water doing something that just can't be done. He says that he's going to love her "till the ocean is hung up to dry." Not going to happen. But Shmoop gets it. He's trying to make a point. He loves her a lot. Understood. And it's significant that his descriptions are outlandish. He doesn't say your lips are as red as a rose (possible) or your hair is as golden as summer wheat (could be). Instead, Auden makes the lover's claims completely over-the-top and the outlandishness of his descriptions reflect the futility of trying to defeat Time. You just can't make the impossible possible.
Line 37-40: We've gone from river to ocean to a much smaller, personal body of water, the washbasin. The clock-speaker wants us to "plunge [our] hands in the water" and consider the passing of Time. He wants us to understand the foolishness of the lover-speaker's claim that true love can withstand Time. He wants us to take a good, hard look at our reflections in that basin and consider how they are distorted, changed, by the sloshing water in the basin—remember, moving water equals passing time.
Line 60: Here's our river again in the poem's very last line. A lot has happened in the poem: three speakers, talking clocks, nightmares. But it all comes back to Time and water. Auden really wants us to think about this river. He wants the river to be the final image—the picture that sticks in our mind as we finish reading the poem. Like Time itself, he wants that river sloshing around in our heads even after everything else is finished and gone: "And the deep river ran on."