Back-to-back storms are expected to smack the Bay Area this week, but they're not likely to provide much relief from the region's ongoing drought.

Even as the North Bay is poised to receive more than 3 inches of rain over the next few days, and the Sierra up to 2 feet of snow, forecasters said it's not nearly enough to make up for what so far has been one of the driest rainy seasons on record.

"Basically, we would have to double the amount of rainfall for the next four months to be normal. And that's pretty unlikely," said forecaster Steve Anderson with the National Weather Service.

The first wet-weather system arrived Wednesday night with sprinkles in San Francisco. It is expected to hit hardest during the Thursday morning commute and clear later in the day, according to the weather service. A stronger front will follow late Friday and bring rain through much of the weekend.

The Lake Tahoe area is forecast to receive 3 to 6 inches of snow at 6,000 feet Thursday. Another several inches will arrive over the weekend, while points above 8,000 feet probably will receive up to 2 feet of snow, forecasters said.

In the Bay Area, Sonoma and Napa counties will see the brunt of the storms, with flooding, downed trees and power outages likely Saturday and Sunday, according to the weather service.

San Francisco, Oakland and San Jose aren't projected to see much more than a half inch of rain between the two systems, leaving the areas well short of normal rainfall totals.

To date, downtown San Francisco has received just 2.4 inches of rain since last summer, compared with the 14.3 inches it normally sees by this time in the rainy season.

With November through April typically the area's wettest stretch, "We're rapidly running out of time to make up for the dry weather," Anderson said.

Bay Area skies are expected to clear by Monday, and then more sun is in the forecast.

The dry rainy season, which follows two previous years of below-average rainfall, prompted Gov. Jerry Brown to declare a drought emergency and ask California residents to voluntarily reduce water use by 20 percent. At least a dozen water districts across the state, including a handful in the Bay Area, have imposed mandatory cutbacks.

The weather has also taken a toll on the winter-sports industry.

"More people, it seems, are taking trips to Colorado or Utah or Vancouver, where there's snow," said John Glover, general manager of Helm of Sun Valley, a ski and snowboard shop in San Jose. "But the local people for the Sierra aren't coming in (to our store) as much."