A storm with a weak subtropical moisture tap will spread across the San Francisco Bay Area on Tuesday, delivering up to a half-inch of rain in urban areas, including San Francisco and Oakland. The North Bay mountains could see upward of an inch, and the San Jose area could measure less than a quarter inch.

"It's a warmer system and overall it's weak," said Scott Rowe, a meteorologist with the National Weather Service office in Monterey. "It doesn't have all the ingredients coming together to bring widespread impacts. The main impacts I foresee are the wet roadways during the morning commute and this evening during the commute. We're not expecting any widespread flooding."

Rain started falling in the North Bay after 3 a.m. and is forecast to spread southward into the central Bay Area after sunrise.

Chances for sprinkles will continue through the day, and Rowe expects the possibility for more steady, moderate rainfall during the evening commute around 5 p.m.

The system is expected to dissipate overnight and the rain will mostly be over by daybreak on Wednesday.

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As a high-pressure ridge builds on Wednesday, conditions are expected to be mostly dry through Friday and temperatures will slowly inch up with daytime highs in the high-50s to low-60s in the second half of the work week.

Rain returns to the forecast over the weekend with a system first hitting the North Bay on Saturday and sweeping into the central Bay Area on Sunday.

Amy Graff is a digital editor with SFGATE. Email her weather tips and photos at agraff@sfgate.com.