TIJUANA, Mexico — The skies opened before the border did.

A downpour, a blessing for this rain-starved region of Mexico, was a curse for thousands of migrants parked in a squalid encampment.

Having started lightly overnight, the storm unleashed its full fury Thursday morning, quickly flooding the open-air sports complex near downtown Tijuana where most members of a migrant caravan from Central America have been parked since they started arriving two weeks ago.

Within hours, nothing was left on the spit of dirt many had claimed and inhabited — in a tent, or a lean-to fashioned from plastic, blankets and tarp — except fetid muck. The little they had was reduced to piles of soggy blankets, backpacks and stuffed animals they struggled to protect under plastic sheets.

Up to an inch of rain pounded Tijuana every hour, according to local meteorologists.

Some families sought refuge under a large, overcrowded, open-sided tent. Madeline Julissa, 8, stood clutching a baby doll whose body was drier, and better covered, than her own; the girl wore a summer top and damp pants pushed up to mid-thigh. Her family of three, including her mother and baby sister, had lost their shelter, fashioned from plastic and tarp, to the heavy rainfall.