SAN FRANCISCO — Bay Area residents, bedeviled by water restrictions and arid farmland after three years of drought, suddenly had to cope with too much water Thursday as the strongest storm in at least five years pushed across Northern California, flooding roads and towns, toppling trees and knocking out power to tens of thousands of homes and businesses.

By early afternoon, the worst of the storm had passed through the Bay Area, but flooding remained a concern.

As water gushed from storm drains, forming small rivers along roads in the small East Bay community of Orinda, Linda Stepanek, in a raincoat and rubber-soled shoes, spent part of the day cleaning up the mess the rain had left behind. Heavy wind blew over chairs and planters on her deck, where a pool of standing water remained Thursday night.

As the drenching rain lashed down all day, she said, she began to worry that huge oak trees towering over her house and her property might fall if their shallow roots became saturated.