Aerial footage showing the rooftop rescue of a family of five and their two dogs after a mudslide left them trapped them at their home in Santa Barbara has been issued by the US Coast Guard.

A helicopter crew airlifted the couple and their three young children to safety from the roof of their home.

The mother can be seen cradling her newborn baby as they prepare to be winched to the helicopter waiting above.

The family's two dogs were also rescued by the team.

At least 15 people have been killed after the first major storm to hit southern California this winter resulted in flooding and mudslides that destroyed homes and prompted emergency rescues and evacuation orders.

The area, which has recently endured historically intense wildfires, saw up to 10 centimetres (4 inches) of rainfall.