INVERNESS, Calif. (AP) — An academic couple who got lost during a Valentine’s Day hike in the woods of Northern California was found Saturday by rescuers who spent almost a week looking for them and had given up hopes of finding them alive.

Carol Kiparsky, 77, and Ian Irwin, 72, were found in a densely forested area near Tomales Bay, a narrow inlet about 30 miles north of San Francisco, and were airlifted to a hospital for treatment of hypothermia, Marin County Sheriff’s Sgt. Brenton Schneider said at a news conference.

“This is a miracle,” he said.

They were unprepared for a long hike or the cold weather, when night temperatures dipped into the 30’s, and survived by drinking from a puddle, he said.

At some point, they may have fallen and Kiparsky attempted to find help alone. She tried parts of her scarf to branches in order to get back to her partner, Schneider said.

“They thought this was the end for them.”

Kiparsky and Irwin were last seen Feb. 14 at a vacation cottage near Inverness, a town at the foot of the bay. The couple from Palo Alto never checked out the next day as planned and failed to show up for an appointment on Feb. 16, which sheriff’s officials said was highly out of character for them.

When housekeepers went to the cottage to clean up, they found the couple’s phones and wallets. Their vehicle was parked outside.

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No foul play was suspected.

Sheriff’s officials and a volunteer team combed the woods and waters around Inverness for several days with the help of drones, dive teams and boats equipped with radar and sonar. On Thursday, they shifted the operation to a “recovery mission” when they received four independent alerts from cadaver dogs around Shell Beach, about 2 miles (3.2 kilometers) from the cottage, and felt they had exhausted all possible leads.

“We believe that our extensive search efforts with every resource that has been available to us would have located Carol and Ian if they were responsive or in an area accessible by foot on land,” the sheriff’s office said in a press release.

Irwin is a leading Parkinson’s disease researcher. He was a chemist on the team that originally identified an agent responsible for the outbreak of Parkinsonism among heroin addicts in 1982, according to the newspaper.

Kiparsky is a prominent linguist and author of several books on language, including 1975’s “The Gooficon: A Repair Manual for English.”