The web page becomes almost lifelike if text and buttons on it got shuffled around to reflect the speed of wind blowing outside. Taking it a level further might increase and decrease ambient brightness depending on time of day. Having text completely wiped out to draw attention to a raging thunderstorm in the area might be a good way to call attention to it.
The idea of feeling connected to nature and the real world even while in cyberspace is great. The central theme of David Suzuki's The Sacred Balance , we and nature are the same thing and the fate of one is inextricably linked to the other, could be turned into something that you are forced to remain aware of.
The butterfly effect would no longer be a esoteric scientific theory but an undeniable fact of life reaffirmed by the changing landscape of the online newspaper you are reading to reflect real time the consequences of what is going on in the enviornment around you.