The Arizona Department of Public Safety said there were more than 80 accidents on Valley freeways Tuesday morning, mostly because of unsafe driving in the rain. But some areas could see between 2 to 3 inches (5 to 7.5 centimeters).
Arizona should see the heaviest rain, the National Hurricane Center said, where up to a half-foot of rain is possible in some areas.
The Civil Defense agency for Mexico's Baja California state said schools were closed Monday in several communities, including the state capital of Mexicali, across the border from Calexico, California; San Felipe, on the northern Sea of Cortez; and south of Ensenada, on the peninsula's Pacific coast.
Flash flooding and heavy rainfall called for several water rescues as Valley fire crews rescued people trapped in their vehicles from floodwaters.
Rosa's maximum sustained winds had decreased to 40 miles per hour as of Monday afternoon, and the storm's center was heading north-northeast at 10 miles per hour.
Knowlton also expected residents to be vigilant and more educated because of flooding earlier this year.
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Parents and surrounding neighbors say when it rains, it really pours in this area and they aren't exactly surprised by the school's flooding.
Trooper Kameron Lee of the Arizona Department of Public Safety said rain "played a factor" in numerous vehicle accidents during the morning Phoenix commute, but there were no reports of serious crashes.
Historically, it's unusual for the US Southwest to get pummeled by a hurricane or tropical storm. Utah Gov. Gary Herbert mobilized about 200 National Guard soldiers Monday to prepare for potential flooding south of Salt Lake City.
Elsewhere, flooding temporarily closed a portion of Interstate 17 near Peoria Avenue during Tuesday's morning commute.
After soaking northwestern Mexico with heavy rains as it neared the Baja California Peninsula and reportedly claiming at least one victim, Tropical Storm Rosa is expected to drench the U.S. Southwest.
The center of Rosa, which was a hurricane until late Sunday, was expected to hit Baja California and Sonora by early Tuesday, bringing 3 to 6 inches of rain, the U.S. National Hurricane Center said.
Rosa's remnants are then expected to move across the desert Southwest, where up to 6 inches of rain is forecast, the center said. 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.