The hurricane center said there were no coastal watches or warnings in effect, but swells generated by Rosa were expected to cause risky surf and rip current conditions along portions of southwestern Mexico, the peninsula and southern California.
Rosa still had maximum sustained winds of 85 mph (140 kph) early Sunday and it was centered about 355 miles (570 kilometers) southwest of Punta Eugenia in Mexico.
It was about 585 miles (940 km) southwest of San Felipe Mexico at 2 a.m. The National Hurricane Center said Baja California could get 3 to 6 inches.
The rain could lessen as the storm moves toward Arizona, but it could also bring a small dust storm Sunday evening. It's expected to turn north, weaken over several days and make landfall over northern Baja California.
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There's more rain on the way, but this time it's not from a monsoon storm.
Remnants of the Rosa are expected to hit Arizona on Sunday, bringing heavy rain, high winds and the threat of localized flooding, the National Weather Service said. The storm is expected to become a tropical depression Friday night and degenerate into a low pressure trough by late Saturday.
That kind of rain would be significant for Yuma, which gets only 3½ inches of rain a year on average, Deemer said.
"Coastal areas are expected to received 0.25" to 0.50" of rain Tuesday into Wednesday, said Brandt Maxwell, a weather service forecaster.