Originally Posted by Joe-
It doesn't sound like the water pump, but again it's hard to say, it really sounds like a pulley from your video but again, it's hard to tell since we aren't in front of the car listening in certain areas.
You should still watch your engine temps, I've heard of water pumps failing pretty randomly. But in this case I don't think it's your water pump and
As the pulley spins the faster it spins IE engine rotations it will in a sense "Whine" up to where you don't hear it.
Another thing that comes to mind is the alternator, on my e46 my alternator is making that noise, and has been for the last month and is now showing the battery warning light (I think failing bearing on the alternator is my issue), I've been putting it off since I don't drive the car that often.
Check the Pulleys, Belt, and check the alternator make sure it's throwing the correct voltage, not sure what the correct voltage on e9x is suppose to throw on an e46 was 14v
On a side note I noticed you are also in Greenwich, are you under warranty still? Hope you don't service it with Pace, those guys are really dumb.