I'm not sure what sort of sound water could/would make moving down a window, but here are a few ideas for words that might evoke a solitary/solemn/gloomy mood:

the hush of the rain

Or you could replace "hush" with

(staticky) drone
hum

or other subdued words. If you're looking for an aggressive sort of unhappiness, the wind should always be whipping at the trees or plastering sopping brown leaves against the window or whatever. But I'm not sure if any of that is useful at all, because I'm not sure what sort of gloom you're trying to evoke/what sort of mood your character is in and what sort of things she'd be particularly sensitive to/what sounds would register as the most important/how she'd interpret what she saw. I'm sure you'll find just the right word! Good luck!