One of the season's fiercest winter storms battered California with heavy rain and high winds today, triggering coastal flooding and mud slides and touching off two tornadoes, one of which ripped off part of the roof of the Los Angeles Convention Center.

High seas and gale-force winds forced cancellation of a scheduled presidential reception for Queen Elizabeth II in Santa Barbara Harbor and a horseback ride for the royal party at President Reagan's ranch northwest of here in the Santa Ynez mountains.

The queen settled for a reception in an airport hangar and lunch at the ranch, to which she was taken in a four-wheel-drive vehicle on a road crossed by seven swollen streams. Her yacht, the HMS Britannia, remained moored in Long Beach Harbor because of hazardous seas.

In Los Angeles, a tornado shredded the roof and part of the main hall of the convention center, ripped one side off of the building, tore up trees and light standards and knocked over vehicles nearby. Convention center officials, who estimated the damage at $2.5 million, were amazed.

"We're not in tornado country," observed Chuck Woolf, the center's national sales manager. "You expect that in Kansas."

Another twister touched down in Pasadena, 10 miles to the north, but did not cause as much damage as the first, which authorities said damaged or destroyed about 100 buildings in a three-mile swath about 8 a.m. PST. More than 20 tornado-related injuries were reported.

The Los Angeles Police Department confirmed a single case of looting in the tornado area, and patrolled a wide area tonight to prevent further incidents.

By nightfall, Los Angeles officials said, 2.94 inches of rain had been recorded at City Hall, bringing the season total to 20.21 inches, more than 9 inches above normal.

Two earthquakes also struck in southern California within 14 hours today, but little damage was reported. Terry Wallace of the California Institute of Technology's seismological laboratory in Pasadena said the tremors were centered near Inglewood, northeast of Los Angeles International Airport.

Major concern was focused on the continuing storms, which forced thousands of persons out of their homes along the coast and inland rivers today.

The death toll since last weekend rose to nine tonight when a Los Angeles police helicopter struck power lines, killing one officer.

The National Weather Service has forecast rain and high winds this week along the Pacific Coast, which has suffered throughout the winter from a long series of storms that triggered waves, mud slides and flooding.

In northern California, heavy rain caused flooding in the Sacramento River Valley, and officials were concerned that further downpours could intensify the problem.

The greatest damage was along the coast, where many expensive oceanfront homes have been battered by pounding surf and flooding in earlier storms. Some of California's best beaches were suffering heavily from erosion.

In Santa Barbara, the reception for Queen Elizabeth II took place in an airport hangar, where a 160-foot red carpet was hastily laid and a crowd dominated by schoolchildren was rounded up for the welcome.

Travel was so difficult on mountain roads that it took the president's nine-car motorcade 30 minutes to negotiate the tortuous 6 1/2 miles from Reagan's mountaintop ranch to the interstate highway at Refugio State Beach for the drive to Santa Barbara Airport.