Ark by Stephen Baxter

With the discovery of another life-sustaining planet light years away, there is hope for a chosen few to leave the soon-to-be submerged Earth. Holle Groundwater is one of the candidates, having been trained for this purpose since childhood, when the ships Ark One and Ark Three were being built. But as Holle prepares to endure life aboard the Ark, she comes to realize that her attempt at escape may be more dangerous than trying to stay afloat on a drowning planet...