Rosa's deluge "may produce life-threatening flash flooding", the hurricane center said.
Hurricane Rosa has affected south western America including California since 30 September; the storm is likely to continue until 2 October. "Those planning to be outdoors next week should keep an eye on the weather forecast and make contingency plans", the NWS said.
There was also flooding reported around Tucson.
That's due in part to wind currents that generally push from east to west-but also because the tropical cyclones that power hurricanes need warm water, usually over 80 degrees, while the typical temperature off SoCal coasts is closer to 75.
The National Weather Service says Phoenix Sky Harbor International Airport has received more than 2 inches (5 centimeters) of ran so far Tuesday. They can turn otherwise calm dry washes, burn scars and urban areas with poor drainage deadly.
According to the National Weather Service, the entire Phoenix area is expected to see between 1 and 2 inches (2.5-5 centimeters) of rain.
"This storm still has a punch, it's still unsafe", David Roth, a meteorologist with the National Weather Service's Weather Prediction Center, told Thomson Reuters.
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Elsewhere in the state, flash flood watches in Phoenix and other areas were set to expire later Wednesday as the storm left the region and headed for Colorado and Utah.
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.
Flash-flood watches remained in effect for parts of those two states.
The Maricopa County Flood Control District reported no immediate reports Tuesday morning of flash flooding in the county that includes most of metro Phoenix.
After soaking northwestern Mexico with heavy rains as it neared the Baja California Peninsula, reportedly claiming at least one victim, Tropical Storm Rosa is expected to drench the U.S. Southwest.
La Plata County officials and the National Weather Service were working together to track the potential flood risk, said Butch Knowlton, director of La Plata County's Office of Emergency Management. Yuma, Arizona, the USA's driest city with only about 3.6 inches of rainfall a year, could see almost that much in the next couple of days.
The U.S. National Hurricane Center said Rosa should move over Baja California and Sonora, weakening and bringing 3 to 6 inches (7.5 to 15 centimeters) of rain, with its remnants expected hitting the southwestern United States on Tuesday. Isolated areas might see even more precipitation.