Alberto, the first named tropical storm of the Atlantic hurricane season, has dissipated after being downgraded to a tropical depression, the National Hurricane Center in Miami announced Thursday evening, but not before the storm dumped heavy rain and caused major flooding in parts of Mexico and Texas.

At least four deaths have been blamed on the storm, which made landfall over Mexico earlier Thursday. Although the storm had dissipated as of 5 p.m. ET Thursday, Alberto was still bringing torrential rains and flash flooding to northeastern Mexico, the hurricane center reported. 

Another 5 to 10 inches of rain is possible in some parts of northeastern Mexico, with higher terrain in the Mexican states of Coahuila, Nuevo Leon and Tamaulipas seeing up to 20 inches of rain.   

Across southern Texas, rain would continue to diminish Thursday night, the hurricane center forecasted, seeing totals of one inch or less. All tropical storm warnings associated with Alberto have been discontinued. 

Alberto was centered about 260 miles west of Tampico, Mexico, and 380 miles southwest of Brownsville, Texas, Thursday evening. It had maximum sustained winds of 30 miles per hour, down from earlier Thursday when the maximum sustained winds were 50 miles per hour. The storm is moving west at about 24 miles per hour. 

Immediately after it moved ashore in Tampico, there was initial disappointment at the meager amount of rain that fell. Showers had been sporadic through the early morning with the sun even breaking through at times.

"We had hoped that it would come because water is so needed here, but at far as I can tell it went somewhere else," said Tampico resident Marta Alicia Hernández.

But inland heavy rain was causing damage in the neighboring states of Nuevo Leon and Veracruz.

There, civil protection authorities reported four deaths linked to Alberto's rains. They said one man died in the La Silla river in the city of Monterrey, the state capital, and that two minors died from electric shocks in the municipality of Allende. Local media reported that the minors were riding a bicycle in the rain.

A fourth man in the community of El Carmen, Nuevo Leon, was electrocuted when he tried to repair wires in the rain, civil protection said.