SAN FRANCISCO — A storm expected to be one of the windiest and rainiest in five years pushed across parts of Northern California early Thursday after schools canceled classes and residents stocked up on supplies.

Moderate rain and gusty winds hit the area north of San Francisco, with heavier rain expected in the coming hours across the region, the National Weather Service said.

The storm could also cause debris slides, especially in areas affected by this year’s intense and widespread wildfires. Big waves are expected along the coast, and ski resorts in the northern Sierra Nevada could get more than 2 feet of snow.

More than 4 inches of rain was reported in Sonoma County before dawn, and flood warnings were in effect for points along the Russian and Navarro rivers in Mendocino County and the Eel River in Humboldt County, the weather service said. Some tree damage and roadway flooding was reported.

Some flights arriving at San Francisco International Airport were subject to delays averaging three hours and 40 minutes, the Federal Aviation Administration reported on its website.

As much as 8 inches of rain could fall on coastal mountains over a 24-hour period, the weather service said.

“It’s a short amount of time for that amount of water,” forecaster Diana Henderson said. “We are anticipating some localized flooding. maybe some downed trees and downed power lines. It could have an effect on a wide range of people.”

Meteorologist Charles Bell said gusts of up to 50 mph were hitting some buoys off the coast.

Residents rushed to buy emergency supplies, with some stores running out of water, batteries and flashlights. Some cities announced on their Twitter accounts that they had no sandbags or sand left by Wednesday evening.

The storm is expected to later pound parts of Southern California before a weakening system moves east through Nevada, Idaho, Arizona and New Mexico. Those states could get rain and snow, but nothing like what California is expected to experience, forecasters say.

In San Francisco, where as much as 4 inches of rain was forecast, crews cleared storm drains and removed loose rocks from a hillside to prevent them from crashing down. Residents were advised to sweep up leaves and debris in front of their properties to prevent them from clogging drains.

“We have crews working starting tonight in 12-hour shifts,” said Rachel Gordon, a spokeswoman for San Francisco’s public works agency. “It will be all hands on deck.”

Public schools in several Bay Area cities, including San Francisco, Oakland and Berkeley, and some private schools canceled Thursday classes.