ARAHAMA, Miyagi Prefecture—When the tsunami warnings sounded after the massive earthquake that struck Japan on Friday, Masaki Kikuchi sprinted upstairs to grab his sleeping 12-year-old daughter before racing away to escape the rushing waters.

In the backyard tied to a small shed, Mr. Kikuchi left behind two dogs: Towa, a two-year-old Sheltie and Melody, a one-year-old Golden Retriever. Mr. Kikuchi assumed the giant tsunami that flattened his neighbors' homes and whisked away their cars probably killed Towa and Melody too.

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