From Arizona to Utah, some residents filled sandbags in anticipation of heavy rainfall forecasts and potential flooding.
Rain totals range from 1 to 3 inches, according to NWS.
As Rosa trudges northeast, the storm will dump 2 to 4 inches of rain on much of Arizona and up to 6 inches in the mountains.
Rogers warned that even a short outburst of rain could still cause flooding in some areas.
Tropical Storm Rosa is hovering over the Pacific Ocean now, looking set to bring bring rain, strong winds, and unsafe surf to southern California in the coming days.
Flash flooding began and lasted most of the day throughout areas of the Valley near washes and drains.
"Rain is also pushing up into Arizona just south of Phoenix and will most likely move into metro Phoenix in the next few hours", Guy said.
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Utah Gov. Gary Herbert mobilized about 200 National Guard soldiers Monday to prepare for potential flooding in areas where recent wildfires left burn scars that could increase runoff.
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FLAGSTAFF -The National Weather Service has put out a flash flood watch in portions of Northern Arizona, including Yavapai County. This could bring "life-threatening flash flooding" and "dangerous debris flows and landslides", the hurricane center said.
National Weather Service meteorologists in Phoenix said central and northern Arizona stood to get hit with the heaviest amounts of precipitation.
Tropical Storm Rosa soaked northwestern Mexico with heavy rains as it neared the Baja California Peninsula late Monday, reportedly claiming at least one victim, and was projected to extend into a drenching of the U.S. Southwest.
Meteorologist Jaret Rogers says Phoenix received more than 2 inches (5 centimeters) of rain, making it the city's second wettest October day on record. Isolated areas in Arizona could receive 6 inches before the storm disperses. But some areas could see between 2 to 3 inches (5 to 7.5 centimeters).
Flash floods are caused by heavy rain. "It doesn't mean something's imminent".
Rosa's maximum sustained winds had decreased to 40 mph (65 kph) as of Monday night, and the storm's center was about 75 miles (125 kilometers) north of Punta Eugenia in Mexico.
Federal authorities declared a state of emergency for Ensenada and Mexicali.
Mexican media outlets reported that a woman was swept away by floodwaters and drowned in the city of Caborca, Sonora, on the Sea of Cortez. It's expected to become a hurricane later Monday and a major hurricane by early Wednesday.