Most regions of Southern California avoided significant damage this week from Tropical Storm Hilary, but authorities continued their rescue and cleanup efforts on Tuesday in several mountain and desert communities where homes were flooded and fast-moving mudslides had washed away sections of roadway and stranded residents.

In one desperate situation, crews were searching for a 75-year-old woman who has been missing for nearly two days in the mountains of the San Bernardino National Forest.

Christie Rockwood, who lived in a trailer home in a tiny community known as Seven Oaks, had not been heard from since Sunday evening, when she spoke to a friend by phone, according to her daughter Tracey Monteverde.

“I’m trying to hold out hope, but it’s really hard,” Ms. Monteverde, 56, said. “I just can’t imagine her being out there with no food and water, probably injured.”

Remote communities dot the San Bernardino Mountains, sought out for their idyllic setting and inexpensive housing about 90 miles east of Los Angeles. But the rustic surroundings can work against those living there, who often find themselves under the threat of fire or mud, or even snow. Thirteen people died in the San Bernardino Mountains in March after they were trapped by several feet of snow following intense storms.

Ms. Rockwood, a retired accountant for a Riverside County school district, had owned her trailer for several decades, using it as a weekend vacation spot until she moved in full time about 10 years ago, her daughter said. A local fixture known for her good-natured disposition, she often hosted people around the fire pit on her deck, playing cards and horseshoes late into the night. She was in good health, although her right knee troubled her. By Tuesday, residents reported no sign of Ms. Rockwood’s trailer.

The tropical storm had prompted the Santa Ana River to overflow, sending rocks and debris into Seven Oaks, a canyon that remains under an evacuation order, according to the San Bernardino County Sheriff’s Department. After a bridge was wiped out, about 30 residents were stranded on a riverbank, cut off from access to a main road. They were ordered to shelter in place on Sunday.

“Boulders the size of a car were rolling down, taking trees and snapping them like toothpicks,” said Randy Foster, a Seven Oaks resident who was rescued by helicopter on Tuesday.

Several people who remained in Seven Oaks on Tuesday said they were unaware that the community was required to evacuate before the storm arrived. They said that authorities typically delivered evacuation orders to them in person because they were so remote, but that this time around that had not happened.

Officials with the San Bernardino County Fire Department said rescue teams determined on Monday that it was too hazardous to try to cross the rushing water that had cut off the community and they instead hoisted a woman with a lower leg injury into a hovering helicopter. Others declined to be rescued, wanting to wait until the waters receded.

On Tuesday, crews hiked in and cleared a path to create a landing zone for a helicopter that, by late afternoon, had lifted out nearly two dozen people in multiple trips. Some firefighters carried residents’ dogs, scrambling onto fallen trees as they forded the rushing river.

The most populous regions of Southern California closer to the coast — Los Angeles, Orange County and San Diego — suffered few serious problems from Tropical Storm Hilary beyond downed power lines, fallen trees and minor street flooding. State and local officials generally expressed relief this week that they had avoided a catastrophe after having feared the worst. There had been no reports of deaths related to the storm as of Tuesday afternoon.

About 70 miles southeast, in the Coachella Valley desert region, residents were struggling with a much different effect from the storm. In Cathedral City, home to about 50,000 people, mud choked the thoroughfares. Those who attempted to traverse the knee-high sludge found themselves sinking and becoming stuck. A blistering sun and temperatures that nearly reached triple digits only added to their frustration.

Dozens of cars and trucks that had once floated down driveways into streets were mired in a thick river of brown. Homeowners who had made every attempt to keep water from surging inside were now left to shovel out the muck. Outside one house, a telling scene: a boat that had been swept up onto the lawn.

Japan will begin releasing treated radioactive wastewater from the ruined Fukushima Daiichi nuclear plant into the ocean this week, its government said on Tuesday, setting aside regional and domestic objections as it moves to eventually discharge over a million tons of the water into the sea.

Prime Minister Fumio Kishida made the announcement after a meeting of his cabinet, saying the release would begin on Thursday if weather and ocean conditions allowed.

The International Atomic Energy Agency said in July that the government’s plan met the agency’s safety standards, and it has said that releasing the treated water is not likely to pose a serious health threat to humans.

But some scientists have raised questions about whether the Japanese government and the company that operated the plant, Tokyo Electric Power, have been sufficiently forthcoming about what radioactive material may remain in the holding tanks.

The Chinese government has strongly opposed the plan, and Chinese internet users responded angrily to the news on Tuesday, calling for boycotts of Japanese goods and posting racist comments. A large segment of the South Korean public also objects to the discharge, as do fishing groups and others in Japan.

Mr. Kishida visited the wrecked nuclear plant on Sunday and met with leaders of the Japanese fishery industry in Tokyo on Monday, vowing to ensure that fishermen can continue to make a living after the release.

Masanobu Sakamoto, head of the National Federation of Fisheries Cooperative Associations, said that while many of his group’s members had come to accept the government’s assurances on the safety of the discharge, it remained opposed because of the potential effects on fishermen’s livelihoods.

Since an earthquake and tsunami triggered a triple meltdown in Fukushima in 2011, the question of what to do with the accumulating tons of water used to cool nuclear fuel rods has been one of the biggest challenges facing both the government and Tokyo Electric.

For Japan, it is as much a political problem as it is an engineering or environmental one. Despite the determination by the international agency that it was safe to release the water, opponents at home and in neighboring countries have questioned both the government and the agency’s motives. When Japan’s cabinet approved the treated-water plan in 2021, it described the controlled ocean release as the best available disposal option.

People’s Daily, a state media organization owned by the Communist Party in China, has referred to the treated water as Japan’s “nuclear sewage.” And in South Korea, where seafood imports from waters near Fukushima are still banned, an opposition lawmaker warned that “no one can tell or predict for sure what the discharging of radioactive materials into the sea over an extended period of time will bring about.”

In Japan, both Fukushima and national fisheries associations have said they fear that once Tokyo Electric starts releasing the water, both domestic and international customers may be reluctant to eat fish from the region.

Although it has been a dozen years since the worst nuclear crisis since Chernobyl forced tens of thousands of people to flee the area around the ruined Fukushima plant, the cleanup is still in an early phase. The government says the water release is likely to take place over a period of 30 years.

The water is stored in more than 1,000 sky-blue tanks lined up on the site of the plant. Tokyo Electric — or Tepco, as it is known — pumps the water through the destroyed reactors to cool melted fuel that is still too hot and radioactive to remove.

As the water passes through the reactors, it accumulates radioactive nuclides. Tepco is putting the water through a powerful filtration system, in some cases repeatedly, that is designed to remove all the radioactive material except for tritium, a hydrogen isotope. Experts say tritium does not harm human health in small doses, and it is prohibitively expensive to remove in any case.

Other nuclear plants around the world, including in China, South Korea and the United States, use similar processes to treat cooling water, and also release water containing tritium into the oceans after such filtration.

Still, some scientists have questions. According to Tepco’s website, just 30 percent of the approximately 473,000 tons of water in the tanks have been fully treated to the point that only tritium remains.

“The idea is, ‘just trust us,’” said Ken Buesseler, a marine radiochemist at the Woods Hole Oceanographic Institution, who said he wanted to see more detailed analyses of what remains in the tanks, particularly those that have already undergone some treatment.

Dr. Buesseler said that while tritium is “one of the least dangerous” radioactive materials, others, like cesium or cobalt, could be more hazardous if they are released into the ocean.

He said the government had not investigated alternative options such as building more tanks or using the treated water to make cement. “I think they just want the cheapest, fastest solution, which is a pipe in the ocean,” Dr. Buesseler said.

Japan’s Ministry of Economy, Trade and Industry describes water treated in its filtration system as “purified” and has said any water that is released into the ocean will be “treated until it satisfies safety standards for all radioactive materials other than tritium.”

Kazuya Idemitsu, a professor of nuclear engineering at Tohoku University, said he was confident that the international agency would monitor the water release to ensure that only water containing tritium and no other radioactive material will be piped into the sea.

Dr. Idemitsu said that much of the public’s anxiety stemmed from the highly technical nature of the treatment process and the government’s difficulties in communicating the science.

“When it comes to this kind of scientific information, there are a lot of people who don’t understand or don’t know about it,” Dr. Idemitsu said. “And it may take more time to get to that understanding.”

Among fishermen who rely on the ocean waters off Fukushima for their daily catches, what matters is what would-be customers think.

“It’s a life-or-death issue for fishermen,” said Masatsugu Shibata, 67, who took his 40-foot fishing trawler out from a port at Iwaki in Fukushima before dawn on a recent morning and caught about a dozen large flounder. “I will be in trouble if they discharge” the water.

Mr. Shibata, who hopes to pass his fishing operation on to his son and grandson some day, said the fishing business had recovered only about 20 percent of its pre-disaster levels. When the water is released, he said, “there will definitely be reactions, for sure,” adding, “Many people would stop eating fish.”

“Now the government says it’s safe,” he said. “But safety and peace of mind are different.”

The government has already paid a total of 10 trillion yen ($68.4 billion) in compensation to fishermen, farmers and evacuated residents from Fukushima and other affected prefectures since 2011 to help make up for losses that resulted from the disaster.

Some countries have signaled their support for the government’s plan. Last week, before President Biden hosted Mr. Kishida and President Yoon Suk Yeol of South Korea at Camp David, Secretary of State Antony J. Blinken said that the United States was satisfied with Japan’s plan. In July, the European Union lifted all restrictions on fish and agricultural imports from Fukushima. The region had blocked shipments of products since the disaster.

While South Korea still bans seafood imports from waters off Fukushima, Mr. Yoon has endorsed the Japanese government plan amid recent warming relations between the two countries.

At a recent rally in downtown Seoul, protesters suggested that Japan use the treated water in farming or industry instead.

Opposition lawmakers have attacked Mr. Yoon for supporting the plan, with one accusing him of defending Japan “like a parrot.”

“We cannot let a government policy crucial for the people’s life and safety be decided by the president’s personal friendly feeling and intimacy toward Japan,” said Lee Byunghoon, an opposition lawmaker.

The Chinese government has been especially critical of Japan’s plan to release treated water at Fukushima, and has rejected the international agency’s report as insufficient proof that the release poses no undue risks.

On Monday, Wang Wenbin, a spokesman for China’s Ministry of Foreign Affairs, called Japan’s decision “extremely selfish and irresponsible” and accused Tokyo of ignoring doubts about the safety of the contaminated water.

Tensions between China and Japan are running high following the signing late last week of a trilateral security agreement between Japan, South Korea and the United States.

Chinese internet users voiced vehement opposition. “Japan has started a new form of nuclear war. We should reject Japanese products and restaurants,” read one comment under an article about the planned release from Mengma News, a media property operated by the government of Henan Province.

“If Japanese people think it is not a problem, they should just drink the water,” read another comment under an article published by China News, a state media organization.

China itself operates nuclear reactors along its seacoast, using seawater instead of scarce freshwater to cool the steam from reactors.

Keith Bradsher contributed reporting from Beijing, Choe Sang-Hun from Seoul, and David Pierson from Singapore. Olivia Wang contributed research.