Perched on an Alaskan barrier island, the village of Kivalina faces imminent destruction because of melting sea ice.

Now, the community’s legal effort — which pins the blame on energy companies for the change in climate — is in danger as well. So, too, is a pair of high-profile climate-change suits that may be taken up by the U.S. Supreme Court, one involving an effort by Connecticut and other states to reduce greenhouse-gas emissions, the other stemming from Hurricane Katrina.