In Kherson, volunteers, medics and rescue teams have been meeting on higher ground near a landmark city square, which is flooded but is being used as an evacuation point because it is well known. Outside the city, Ukrainians have watched as their own homes and those around them are dismantled by the flooding.

“Everything washes by,” said Natalia Kamenetska, who lives on a bluff overlooking the Dnipro River, around 60 miles downstream from the ruined dam.

Her village, Stanislav, was under Russian occupation until last fall. It has been bombarded repeatedly by Russian forces since then, and evidence of the fighting is all around her. Burned-out tanks and armored vehicles line the road. Just outside the village, the tail of an unexploded S-300 Russian missile rises out of a green lagoon. Another missile is embedded in a field of red poppies and wildflowers.

But it was not an explosion that awoke Ms. Kamenetska on Wednesday. It was her husband, who pointed out the window at a house floating past. By Wednesday afternoon, a dozen houses dislodged by flooding could be seen.