Water vs. Oxygen

So the air here is thinner...

and it's giving me headaches. And everyone just says drink more water.

Now I get that water helps prevent dehydration... and dehydration causes headaches. But how does lack of oxygen cause dehydration? I know, I'm a nerd...

According wikipedia.org (I know, highly reputable) the dehydration is due to high rate of vapor loss...

I'm slowly getting used to the altitude though... the headaches are less and less each day. But I'm still exhausted...