Asadora!

One day in 1959, a young girl named Asa Asada is running through the streets of the Port of Nagoya to find the doctor – her mother's going into labor again. Asa's one of eleven children and definitely not keen on the arrival of another, but when she's kidnapped by a strange man, she realizes that she still loves her large family. But while Asa and the man are in an empty warehouse, the rain outside turns into a typhoon, and when they manage to emerge, the Port of Nagoya is basically gone.

Source: Anime News Network Encyclopedia