Unless you can re-do the downspouts so you don't have one so close to the window, I doubt you can do much other than earplugs or learning to love the sound!

Google is your friend. Try "insulating noisy downspout". You are not alone.

Here's one article.

Here is a link that might be useful: tips

Hearing the noise means it's doing it's job and not clogged. Take solice in that fact and find comfort in the noise. It will not bother you as much and you may adjust to it and not even notice it anymore.

Here you go:

Here is a link that might be useful: Rainhandler