But the good news, Mayor Karen Bass said, is that as of Tuesday afternoon there have been no storm-related fatalities reported in the city.
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"That again is due to Angelenos heeding our warning," Bass said. "We cannot let up. Even when the rain stops, the ground may continue to shift."
Los Angeles Fire Department Chief said the city has seen 475 reports of mudslides and 390 fallen trees during the atmospheric river storm which began Sunday. Firefighters have extinguished a dozen structure fires and successfully made multiple water rescues.
Other city departments, she said, cleared 919 spots where the stormwater system became clogged. The city has received more than 440 reports of new potholes, which crews will work to address. The city Department of Water and Power restored electricity to more than 59,000 customers.
Crowley said the city's non-emergency services fielded more than 4,500 calls since the storm began for issues such as clogged drains and potholes.
"We will rebuild," Crowley said. "We will recover and we will emerge stronger."
Bass noted that the rain is continuing, though perhaps not as powerfully as its first two days. That means that hillsides which are already saturated may slide more and additional problems will continue to crop up.
Studio City homes hit by mudslides
Among the many neighborhoods hit by mudslides was Studio City, where at least two homes were heavily damaged. Even as the rain begins to subside, the concerns remain because of how saturated the hillsides have become.
Studio City homes damaged in mudslide as relentless rain continues
"Still concerned," said LAFD Capt. Erik Scott. "We had a storm before this one that saturated the earth. The earth is a sponge - it can only take up so much water."
At least two homes were yellow-tagged in the Beverly Crest neighborhood as well. Residents were being urged to try to avoid nonessential travel and be prepared for more flows of debris and mud.
More rain on the way
Most of Southern California remained under flood watches, and the weather service warned people to remain on high alert, as swollen and fast-moving creeks and rivers increase the risks of drowning and the need for swift-water rescues.
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"This has truly been a historic storm for Los Angeles," Ariel Cohen, a meteorologist at the National Weather Service's Los Angeles-area bureau told reporters, noting that the city just recorded its third-wettest two-day stretch since recordkeeping began in the 1870s.
The storm has dumped more than half of the city's seasonal rainfall in just two days.
Multiple residents, including children, displaced after debris flow damages homes in Beverly Crest
Officials expressed relief that the storm hadn't killed anyone or caused a major catastrophe in Los Angeles so far despite its size and intensity, though three people were killed in Northern California after the storm came ashore over the weekend with strong winds that toppled trees.
Bass thanked residents for heeding calls to stay off L.A.'s roads, and she urged people to continue doing so as the rain continues.
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"Los Angeles can handle very big challenges. And if we stick together, we will come out so far ahead," she said.
The slow-moving storm that blew into the city over on Sunday and then parked itself could still produce fierce downpours of up to an inch of rain in an hour, the National Weather Service said. That could be particularly precarious since the soil is already saturated after back-to-back atmospheric rivers walloped California in less than a week.
The Associated Press contributed to this report.