Tigrayan fighters had marched into the regional capital, Mekelle, hours after beleaguered Ethiopian soldiers quit the city. The city airport was shut, so the only way out of Tigray was on a slow-moving U.N. convoy that took the same desolate route out as the fleeing Ethiopian soldiers.

We drove down a rocky escarpment on a road scarred by tank tracks. As we descended into the plains of Afar, the temperature quickly rose.

publicized the flight but made no mention of the delays or harassment — an omission that privately angered several U.N. officials and other aid workers who said it followed a pattern of U.N. agencies being unwilling to publicly criticize the Ethiopian authorities.

Further complicating the aid effort: The war is now spilling into Afar.

In the past week Tigrayan forces have pushed into the region. In response Mr. Abiy mobilized ethnic militias from other regions to counter the offensive.

Mr. Abiy has also resorted to increasingly inflammatory language — referring to Tigrayan leaders as “cancer” and “weeds” in need of removal — that foreign officials view as a possible tinder for a new wave of ethnic violence across the country.

Ms. Billene, his spokeswoman, dismissed those fears as “alarmist.” The Ethiopian leader had “clearly been referring to a terrorist organization and not the people of Tigray,” she said.

Inside Tigray, the most pressing priority is to reopen the road to Afar.

“This is a desperate, desperate situation,” said Lorraine Sweeney of Support Africa Foundation, a charity that shelters about 100 pregnant women displaced by fighting in the Tigrayan city of Adigrat.

Ms. Sweeney, who is based in Ireland, said she had fielded calls from panicked staff members appealing for help to feed the women, all of whom are at least eight months pregnant.

“It brings me back to famine times in Ireland,” Ms. Sweeney said. “This is crazy stuff in this day and age.”

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Tense Funeral for Haiti Leader Exposes Rifts, and U.S. Delegation Departs Early

CAP-HAÏTIEN, Haiti — Heckled by protesters and surrounded by phalanxes of heavily armed guards, foreign diplomats and Haitian politicians attended the funeral of Haiti’s assassinated president on Friday, a tense event that laid bare a fractured nation’s problems instead of providing an opportunity for healing.

Less than a half-hour into the funeral, foreign dignitaries including an American delegation led by the U.S. ambassador to the United Nations, Linda Thomas-Greenfield, departed over safety concerns set off by gunshots fired outside the event. White House officials said that the delegation members were safe and that they had flown back to the United States, cutting the trip short.

questioned and taken into custody.

Trou-du-Nord, and later began his entrepreneurial career from Port-de-Paix, where he became president of the Chamber of Commerce.

That he was killed far away in Port-au-Prince inflamed old divisions between the less developed north and the country’s capital and economic center. It also deepened the rifts between the country’s small elite — historically stemming from the descendants of lighter-skinned Blacks who were free before the revolution — and its destitute majority.

“It comes back incessantly in all the history of Haiti,” said Emile Eyma Jr., a historian based in Cap-Haïtien, speaking of the resentment felt by northerners.

“What is dangerous is that both the question of color and the question of regionalism are weaponized for purely political reasons,” he said, distracting from the country’s fundamental problems of inequality, poverty and unemployment.

Harold Isaac, Zachary Montague and Rick Gladstone contributed reporting.

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Skipping the Olympics Is ‘Not an Option’ for Many Advertisers

The Olympics have long been an almost ideal forum for companies looking to promote themselves, with plenty of opportunities for brands to nestle ads among the pageantry and feel-good stories about athletes overcoming adversity — all for less than the price of a Super Bowl commercial.

But now, as roughly 11,000 competitors from more than 200 countries convene in Tokyo as the coronavirus pandemic lingers, Olympic advertisers are feeling anxious about the more than $1 billion they have spent to run ads on NBC and its Peacock streaming platform.

Calls to cancel the more than $15.4 billion extravaganza have intensified as more athletes test positive for Covid-19. The event is also deeply unpopular with Japanese citizens and many public health experts, who fear a superspreader event. And there will be no spectators in the stands.

“The Olympics are already damaged goods,” said Jules Boykoff, a former Olympic soccer player and an expert in sports politics at Pacific University. “If this situation in Japan goes south fast, then we could see some whipsaw changes in the way that deals are cut and the willingness of multinational companies to get involved.”

blow to the Games on Monday when it said it had abandoned its plans to run Olympics-themed television commercials in Japan.

In the United States, marketing plans are mostly moving ahead.

For NBCUniversal, which has paid billions of dollars for the exclusive rights to broadcast the Olympics in the United States through 2032, the event is a crucial source of revenue. There are more than 140 sponsors for NBC’s coverage on television, on its year-old streaming platform Peacock and online, an increase over the 100 that signed on for the 2016 Summer Games in Rio de Janeiro.

“Not being there with an audience of this size and scale for some of our blue-chip advertisers is not an option,” said Jeremy Carey, the managing director of the sports marketing agency Optimum Sports.

Michelob Ultra commercial, the sprinting star Usain Bolt points joggers toward a bar. Procter & Gamble’s campaign highlights good deeds by athletes and their parents. Sue Bird, a basketball star, promotes the fitness equipment maker Tonal in a spot debuting Friday.

campaign featuring profiles of Olympic athletes.

“We do think people will continue to tune in, even without fans, as they did for all kinds of other sports,” Mr. Brandt said. “It’s going to be a diminishing factor in terms of the excitement, but we also hope that the Olympics are a bit of a unifier at a time when the country can seem to be so divided every day.”

NBCUniversal said it had exceeded the $1.2 billion in U.S. ad revenue it garnered for the 2016 Games in Rio and had sold all of its advertising slots for Friday’s opening ceremony, adding that it was still offering space during the rest of the Games. Buyers estimate that the price for a 30-second prime-time commercial exceeds $1 million.

Television has attracted the bulk of the ad spending, but the amount brought in by digital and streaming ads is on the rise, according to Kantar. Several forecasts predict that TV ratings for the Olympics will lag the Games in Rio and London, while the streaming audience will grow sharply.

NBCUniversal said that during the so-called upfront negotiation sessions this year, when ad buyers reserve spots with media companies, Peacock had received $500 million in commitments for the coming year.

“You won’t find a single legacy media company out there that is not pushing their streaming capabilities for their biggest events,” Mr. Carey, the Optimum Sports executive, said. “That’s the future of where this business is going.”

United Airlines, a sponsor of Team U.S.A., scrapped its original ad campaign, one that promoted flights from the United States to Tokyo. Its new effort, featuring the gymnast Simon Biles and the surfer Kolohe Andino, encourages a broader return to air travel.

showcasing skateboarders. “People are quite fragile at the moment. Advertisers don’t want to be too saccharine or too clever but are trying to find that right tone.”

Many companies advertising during the Games are running campaigns that they had to redesign from scratch after the Olympics were postponed last year.

“We planned it twice,” said Mr. Carey of Optimum Sports. “Think about how much the world has changed in that one year, and think about how much each of our brands have changed what they want to be out there saying or doing or sponsoring. So we crumpled it up, and we started over again.”

FIFA World Cup in Qatar in late 2022 and the Beijing Winter Olympics in February, both of which have put the advertising industry in a difficult position because of China’s and Qatar’s poor records on human rights.

First, though, ad executives just want the Tokyo Games to proceed without incident.

“We’ve been dealing with these Covid updates every day since last March,” said Kevin Collins, an executive at the ad-buying and media intelligence firm Magna. “I’m looking forward to them starting.”

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Heavy Floods in China Trapped Passengers in Subway, Killing 12

The subway train in Zhengzhou, a city of five million in central China, was approaching its next station when the floodwaters began to rise ominously on the tracks. The passengers crowded forward as the water rose, submerging the cars at the rear first because they were deeper in the tunnel.

As the water reached their waists, then chests, finally their necks, the passengers called emergency services or relatives. One gave her parents the details for accessing her bank account. Some cried. Others retched or fainted. After two hours, it became difficult to breathe in the congested air that remained in the cars.

Ding Xiaopei, a radio host, was afraid to call her children, 13 and 4. What could she say? She posted a video that she thought might be her last message. “The water outside has reached this position,” she said, it having reached chest level, “and my mobile phone will soon run out of power.”

“Please save us!” she wrote.

The flood that inundated Line 5 of Zhengzhou’s subway on Tuesday added to the grim global toll extreme weather has taken already this year, with scorching heat in the Pacific Northwest, forest fires in Siberia, and flooding in Germany and Belgium. Although flooding is common in China, researchers have attributed the extreme weather sweeping the planet to the consequences of climate change.

reported. At least one carrying 735 people came to a stop near Zhengzhou and, after more than 40 hours, had run out of food and water. By the afternoon, some passengers were able to leave, while railway workers brought supplies to those still waiting aboard for service to resume.

battled weeks of flooding along the Yangtze River that killed hundreds of people and displaced millions more. The rains at that time filled the Three Gorges Dam to its highest level since it opened in 2003, raising fears that the dam itself could fail.

The government often goes to great lengths to manage information about disasters, sensitive about its history of underreporting casualties. It is quick to limit news coverage and censor blogs and social media sites to mute public dissatisfaction with prevention and rescue efforts.

Some people on Chinese chat platforms and social media sites have raised questions about whether official news outlets in Zhengzhou and Henan Province initially downplayed the flood. When storms struck Beijing recently, the authorities warned people to stay home, but there was no order to shut businesses or schools in Zhengzhou ahead of Tuesday’s heavy rain.

In times of disaster, the country’s state news media often focuses on the efforts of rescue workers, including the military, while playing down the causes of disasters and their damage. A journalism professor, Zhan Jiang, posted a note on Weibo, the social media platform, on Tuesday complaining that a television station in Henan Province continued to show its regular programming instead of providing public safety information.

the news site Jiemian, part of the state-owned Shanghai United Media Group.

By 8:35 p.m., rescuers reached the train and devised a pulley system with ropes to help passengers pull themselves through the floodwaters along a ledge in the subway tunnel. The elderly and injured went first, followed by the women and then the men. State news organizations said that 500 people were evacuated in all.

One man still missing was Sha Tao. When the subway car first flooded, he called his wife and asked her to call the police. She has not heard from him since. She posted a message on Weibo asking people for help, describing his height and weight and the clothes he was wearing.

“I haven’t found him yet,” she said when reached by telephone in Zhengzhou on Wednesday. “I went to several hospitals, but the hospitals didn’t have any information and couldn’t find him. His phone is now off.”

Amy Chang Chien, Claire Fu, Li You, Liu Yi and Albee Zhang contributed research.

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How China Transformed Into a Prime Cyber Threat to the U.S.

Nearly a decade ago, the United States began naming and shaming China for an onslaught of online espionage, the bulk of it conducted using low-level phishing emails against American companies for intellectual property theft.

On Monday, the United States again accused China of cyberattacks. But these attacks were highly aggressive, and they reveal that China has transformed into a far more sophisticated and mature digital adversary than the one that flummoxed U.S. officials a decade ago.

The Biden administration’s indictment for the cyberattacks, along with interviews with dozens of current and former American officials, shows that China has reorganized its hacking operations in the intervening years. While it once conducted relatively unsophisticated hacks of foreign companies, think tanks and government agencies, China is now perpetrating stealthy, decentralized digital assaults of American companies and interests around the world.

Hacks that were conducted via sloppily worded spearphishing emails by units of the People’s Liberation Army are now carried out by an elite satellite network of contractors at front companies and universities that work at the direction of China’s Ministry of State Security, according to U.S. officials and the indictment.

like Microsoft’s Exchange email service and Pulse VPN security devices, which are harder to defend against and allow China’s hackers to operate undetected for longer periods.

“What we’ve seen over the past two or three years is an upleveling” by China, said George Kurtz, the chief executive of the cybersecurity firm CrowdStrike. “They operate more like a professional intelligence service than the smash-and-grab operators we saw in the past.”

China has long been one of the biggest digital threats to the United States. In a 2009 classified National Intelligence Estimate, a document that represents the consensus of all 16 U.S. intelligence agencies, China and Russia topped the list of America’s online adversaries. But China was deemed the more immediate threat because of the volume of its industrial trade theft.

But that threat is even more troubling now because of China’s revamping of its hacking operations. Furthermore, the Biden administration has turned cyberattacks — including ransomware attacks — into a major diplomatic front with superpowers like Russia, and U.S. relations with China have steadily deteriorated over issues including trade and tech supremacy.

China’s prominence in hacking first came to the fore in 2010 with attacks on Google and RSA, the security company, and again in 2013 with a hack of The New York Times.

breach of the U.S. Office of Personnel Management. In that attack, Chinese hackers made off with sensitive personal information, including more than 20 million fingerprints, for Americans who had been granted a security clearance.

White House officials soon struck a deal that China would cease its hacking of American companies and interests for its industrial benefit. For 18 months during the Obama administration, security researchers and intelligence officials observed a notable drop in Chinese hacking.

After President Donald J. Trump took office and accelerated trade conflicts and other tensions with China, the hacking resumed. By 2018, U.S. intelligence officials had noted a shift: People’s Liberation Army hackers had stood down and been replaced by operatives working at the behest of the Ministry of State Security, which handles China’s intelligence, security and secret police.

Hacks of intellectual property, that benefited China’s economic plans, originated not from the P.L.A. but from a looser network of front companies and contractors, including engineers who worked for some of the country’s leading technology companies, according to intelligence officials and researchers.

It was unclear how exactly China worked with these loosely affiliated hackers. Some cybersecurity experts speculated that the engineers were paid cash to moonlight for the state, while others said those in the network had no choice but to do whatever the state asked. In 2013, a classified U.S. National Security Agency memo said, “The exact affiliation with Chinese government entities is not known, but their activities indicate a probable intelligence requirement feed from China’s Ministry of State Security.”

announced a new policy requiring Chinese security researchers to notify the state within two days when they found security holes, such as the “zero-days” that the country relied on in the breach of Microsoft Exchange systems.

arrested its founder. Two years later, Chinese police announced that they would start enforcing laws banning the “unauthorized disclosure” of vulnerabilities. That same year, Chinese hackers, who were a regular presence at big Western hacking conventions, stopped showing up, on state orders.

“If they continue to maintain this level of access, with the control that they have, their intelligence community is going to benefit,” Mr. Kurtz said of China. “It’s an arms race in cyber.”

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Flooding Recedes in Europe, but Death Toll Rises and Questions Mount

an ambitious proposal to cut carbon emissions, how will those who hope to succeed Chancellor Angela Merkel respond?

If only because of their sheer scale, analysts say, the floods are likely to play a significant role for voters when they go to the polls on Sept 26 to replace Ms. Merkel, who has led the country for 16 years.

The death toll in Germany climbed to at least 143 on Saturday, while the toll across the border in Belgium stood at 27, its national crisis center said. The count rose most sharply in Germany’s Ahrweiler district in Rhineland-Palatinate State, where the police said that more than 90 people had died. The authorities feared that number could yet grow.

In Germany, Europe’s largest economy and a country that prides itself on its sense of stability, the chaos wrought by nature was likely to reverberate for months, if not years.

But on Saturday, residents and rescue workers in flood-hit areas faced the more immediate and daunting task of clearing piles of debris, unclogging roads and salvaging some of the homes that had survived the deluge.

Hundreds of people remain unaccounted for, but officials have struggled to offer precise numbers.

Electricity and telephone services remain inaccessible in parts of Germany, and some roads are still impassable. That lack of access may account for the high tallies of those still considered missing. And some of those who are not accounted for could simply be away, on vacation or work assignment. In Belgium, police officers started knocking on doors to try to confirm the whereabouts of residents.

Still, officials said they expected to find additional victims.

Extreme downpours like the ones that hit Germany are one of the most visible signs that the climate is changing as a result of global warming from greenhouse gas emissions. Studies have shown a warmer atmosphere can hold more moisture, generating more rainfall.

Floods of this size have not been seen in 500 or even 1,000 years, according to meteorologists and German officials.

Rhineland-Palatinate was one of the two hardest-hit German states in the west, along with North Rhine-Westphalia. The Rhine River flows through the two regions, and the rain fell so rapidly that it engorged even small streams and tributaries not typically considered flood threats.

North Rhine-

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Düsseldorf

Detail area

Rhineland-

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Germany’s president, Frank-Walter Steinmeier, traveled on Saturday to the town of Erftstadt, southwest of Cologne, where the flooding destroyed homes. Ms. Merkel planned to travel on Sunday to Schuld in Rhineland-Palatinate, which was badly hit, even as all of its 700 residents managed to survive.

There were scenes of devastation from all around Western Europe, the floods having caused damage from Switzerland to the Netherlands. But Germany was hardest hit.

Days before roiling waters tore through western Germany, a European weather agency had issued an extreme flood warning, as models showed that storms would send rivers surging to levels that had not been seen in hundreds of years.

The warnings, however, did little good.

Though Germany’s flood warning system, a network of sensors that measure river levels, functioned as it was supposed to, state and local officials said the amount of rain was unlike anything they had ever seen, causing even small streams and rivers to flood their banks.

Survivors and officials said many areas were caught unprepared as normally placid brooks and streams turned into torrents that swept away cars, houses and bridges. About 15,000 police officers, soldiers and emergency service workers have been deployed in Germany to help with the search and rescue.

Dr. Linda Speight, a hydrometeorologist at the University of Reading in Britain who studies how flooding occurs, blamed poor communication about the high risk posed by the flooding as contributing to the significant loss of life. “There should not have been so many deaths from this event,” she said.

Residents cleaned up mud and debris in Bad Münstereifel’s town center on Saturday.
Credit…Gordon Welters for The New York Times

Residents returning home, only to find their homes no longer there. Roads submerged by landslides. Loved ones still unaccounted for.

As the weather improved on Saturday and rescue workers searched for missing residents, many people in flood-hit areas of Germany were trying to re-establish some order amid the chaos and destruction.

Friends and relatives mobilized to help, maneuvering around blocked roads and washed-out bridges. Crushed cars and mounds of ruined goods were carted away, or piled by the side of muddied, cracked roads.

Many expressed amazement at how so much could have been destroyed so quickly. For Lisa Knopp, 19, who was helping to empty the flood-ruined basement of her grandmother’s home in Sinzig, a small town between the Rhine and Ahr rivers, the scenes of destruction “will stay with me a long time.”

Kim Falkenstein said her mother lost her home in Ahrweiler, one of the hardest-hit spots. Ms. Falkenstein, who was born in Ahrweiler and now lives in New York, said several friends had also lost their homes, and a classmate had died.

“I am heartbroken,” she said.

“Seeing my city being destroyed, people who I am close with losing their existence, and knowing I will never return to something I once called home,” Ms. Falkenstein said, “gives me goose bumps.”

In a country that is among Europe’s most prosperous, where orderliness is highly prized, many Germans were unnerved by the helplessness wrought by nature.

Bertrand Adams, a local official in Trier-Ehrang, a town in western Germany, stared in disbelief at the swirling waters only now receding from his community.

“It is beyond anything that could ever be imagined,” he told ZDF television. “We have a very good flood protection system that we developed only five years ago. We were so certain that nothing can go wrong.”

Daniela Schmitz, who has a ranch in Erftstadt, a town southwest of Cologne, was relieved that her property was not destroyed by the floods and that her horses had been evacuated. Others, she said, weren’t that fortunate.

“We were warned early enough — other stables are not doing so well,” she wrote in a WhatsApp message. “Many animals have drowned, entire stalls destroyed, and feed is becoming scarce. The conditions are really catastrophic in many places.”

On Saturday, German television channels carried wall-to-wall coverage of the flooding, as rescue workers continued searching for those who had been trapped by rising waters, with 143 confirmed dead in Germany and hundreds still missing.

As the official response picked up speed on Saturday, electricity, water and internet coverage were slowly being restored. Hundreds of police, fire and emergency vehicles crammed the roads into the most afflicted areas of Rhine-Palatinate and North Rhine-Westphalia.

A man in front of his damaged restaurant in Bad Münstereifel, Germany, on Saturday. The floods revealed deep political divides around how far and fast Germans should go to stem carbon use.the globe’s most ambitious proposals yet to cut carbon emissions, has revealed deep political divides on climate policy.</p>
<p class=“For a long time, chatting about the weather was synonymous with triviality. That’s over now,” Germany’s ARD public television said in its lead editorial on Friday. “The weather is highly political; there is hardly any nonpolitical weather anymore, especially not during an election campaign.”

The shift in the debate comes as the European Union has announced an ambitious blueprint to make the 27-country bloc carbon-neutral by 2050. No European country may be affected more than Germany, the continent’s largest economy.

Armin Laschet, 60, the conservative governor of North Rhine-Westphalia, who is looking to succeed Ms. Merkel in the Sept. 26 election, has lauded his regional government for passing legislation on climate change. But critics point to the open-pit soft coal mines operating in his state and his repeated emphasis on the importance of Germany remaining an industrial powerhouse.

Pressed in a television interview on whether the floods would prompt him to alter his climate policy, Mr. Laschet snapped at the moderator.

“I am a governor, not an activist,” he said. “Just because we have had a day like this does not mean we change our politics.”

Yet floods have a history of influencing political campaigns in Germany. In 2002, pictures of Chancellor Gerhard Schröder wading in rubber boots through streets awash in the muddy waters of the swollen Elbe, while his conservative rival remained on vacation, are credited with helping him win the election that year.

Perhaps wary of that lesson, Annalena Baerbock, the Greens party candidate for chancellor and Mr. Laschet’s strongest rival, cut short her vacation to visit stricken areas in Rhineland-Palatinate on Friday.

She called for immediate assistance for those affected, but also issued an appeal to better protect “residential areas and infrastructure” from extreme weather events, which she linked to the changing climate.

Whether the flooding will be enough to lift the party remains to be seen. After the Greens enjoyed an initial surge of excitement — Ms. Baerbock is the only woman running to replace the country’s first female chancellor — support for the party has dipped to around 20 percent in polls.

That puts the Greens in second place behind Mr. Laschet’s conservatives, who have been climbing to around 30 percent support, the latest surveys show.

Olaf Scholz, 63, Ms. Merkel’s finance minister who is also running for the chance to replace her and return his Social Democratic Party to the chancellery, headed on Friday to flooded regions in Rhineland-Palatinate, where he pledged swift help from the government and linked the disaster to climate change.

“I am firmly convinced that our task is stopping human-made climate change,” Mr. Scholz told ZDF public television.

The Lebenshilfe Haus, where 12 people died.
Credit…Thomas Frey/DPA, via Associated Press

They were disabled residents of a care home, the Lebenshilfe Haus, asleep when the waters of the flash flood suddenly rose early Thursday morning. Trapped on the first floor, they drowned before aid could arrive.

As calamitous floods hit Germany, the deaths of 12 people at a care home in Sinzig, a small town between the Rhine and Ahr rivers, have broken hearts all over the country and demonstrated how tragedy could have been avoided had flood warnings been better heeded.

“Every person who dies is a tragedy,” said Tabera Irrle, 23, a train driver who came to Sinzig to help with the cleanup. “But this is a special sadness.”

Neighbors could hear screaming, they said later, but all that emergency workers could do was save the other 24 residents on higher floors some three hours later, bringing them out the windows in small boats. The disabled residents had been under the care of a lone watchman.

Dominik Gasper, 17, was helping his parents and uncle clean out the mud and ruined belongings of his grandparents’ house near the care home. He knew about the 12 dead, he said.

“It was so horrible,” he said. “You can’t really understand such a thing.”

The waters crested in Sinzig at more than 7 meters, about 23 feet, the highest in a century, said Andreas Geron, the mayor. He said emergency workers in fire trucks had tried to warn residents late Wednesday night, but few said they had heard an alarm.

Two other Sinzig residents died in this town of 20,000, and a newly renovated bridge over the Ahr collapsed.

Luis Rufino, 50, a lifelong resident of Sinzig, was angry about what happened. He said some of it could have been prevented.

“Our health system is better than in the U.S., but they are still trying to avoid costs,” he said. “So there was only one guy watching over these poor people, and when the lights went out, they went into a panic, and when the flood came through, they had no chance.”

Ulrich van Bebber, the chairman of Lebenshilfe, which has operated the care home since it was built 27 years ago, told journalists that “we are all horrified, stunned and infinitely sad.”

He said those who survived were being cared for. “We want to keep the Lebenshilfe Haus as a residential facility and, if necessary, rebuild it.”

Chancellor Angela Merkel of Germany on a visit to Washington this week.
Credit…Doug Mills/The New York Times

Usually a national leader faced with floods as severe as those in Germany would be expected to break off whatever she was doing and rush to the crisis area.

But Chancellor Angela Merkel of Germany completed an official visit to Washington that ended Friday, and she was not expected to visit the flood zone until Sunday, long after most other German political leaders had come and gone. (Saturday was also her 67th birthday.)

Ms. Merkel did express from Washington her sympathy to the victims, saying during an appearance with President Biden on Thursday: “My heart goes out to all of those who, in this catastrophe, lost their loved ones or who are still worrying about the fate of people still missing.”

And hours after touching down in Germany on Friday morning, Ms. Merkel took part in a crisis meeting with leaders of the state of Rhineland Palatinate, where many of the hardest-hit communities are. She also spoke by telephone with Armin Laschet, the leader of North Rhine Westphalia, which also suffered major devastation and loss of life.

Mr. Laschet — who, like Ms. Merkel, is a member of the conservative Christian Democratic Union party — is the party’s candidate to succeed her after the country holds elections in September.

So far Ms. Merkel has not faced major criticism for taking several days to see the damage for herself. She has never been one for political theater, and does not need to worry about opinion polls because she is stepping down from politics after the elections.

Germans also seemed to understand the importance of her trip to Washington — probably her last as chancellor — and meetings with Mr. Biden.

Germany is anxious to repair its relationship with the United States, a crucial ally and trading partner, after four tense years of dealing with President Donald J. Trump, who treated Germany like a rival and threatened to impose punitive tariffs on German cars. At a news conference with Mr. Biden on Thursday, Ms. Merkel seemed almost buoyant to be dealing with a new administration.

“We’re not only partners and allies, but we’re very close friends,” she said of Mr. Biden.

Addressing an underlying cause of Western Europe’s worst floods in centuries, the two leaders signed a pact to take “urgent action to address the climate crisis.”

“There is a dramatic increase in such unusual weather phenomena, and we have to contend with this,” Ms. Merkel said while standing alongside Mr. Biden.

Huge cleanup efforts were underway after days of flooding inundated parts of Western Europe this week.

President Frank-Walter Steinmeier of Germany, left, and Armin Laschet, governor of North Rhine-Westphalia, speaking with rescue workers in Erftstadt.
Credit…Marius Becker/EPA, via Shutterstock

President Frank-Walter Steinmeier of Germany on Saturday visited the city of Erftstadt, where floods had ripped away homes, setting off a landslide that wrought further destruction.

An entire stretch of highway remained submerged there on Saturday as fears mounted that people who had tried to flee this week’s torrential rains could have been trapped in their cars by flash flooding — and may still be found when the waters recede.

Already, at least 43 people are known to have died.

Mr. Steinmeier, who is seeking a second term in office after his current one ends in February, urged Germans to help in any way they could.

“Many people in this region have nothing left but hope,” Mr. Steinmeier said. “And we cannot disappoint these hopes.”

A president’s role in Germany is largely ceremonial, but in times of national tragedy or crisis, the head of state often helps set the tone and serve as a representative of the people.

Mr. Steinmeier was joined by Armin Laschet, governor of North Rhine-Westphalia, home to Erftstadt, and the leading candidate to succeed Chancellor Angela Merkel when Germans vote for a new government in the fall.

Ms. Merkel planned to travel on Sunday to the town of Schuld (not Stuhr as an earlier version of this item said) in Rhineland-Palatinate.

The main road in the city center of Bad Münstereifel, in the western state of Rhineland-Palatinate in Germany, on Saturday.
Credit…Gordon Welters for The New York Times

Extreme weather disasters across Europe and North America have highlighted two essential facts of science and history: The world as a whole is neither prepared to slow down climate change, nor live with it.

Some of Europe’s richest countries lay in disarray this weekend, as rivers burst through banks in Germany and Belgium, leaving people shellshocked at the intensity of the destruction.

Days before in the Northwestern United States, hundreds had died of heat. In Canada, wildfire had burned a village off the map. Moscow reeled from record temperatures. And the northern Rocky Mountains were bracing for another heat wave.

The events have ravaged some of the world’s wealthiest nations, whose affluence has been enabled by more than a century of burning coal, oil and gas — activities that pumped the greenhouse gases into the atmosphere that are warming the world.

“I say this as a German: The idea that you could possibly die from weather is completely alien,” said Friederike Otto, a physicist at Oxford University who studies the links between extreme weather and climate change. “There’s not even a realization that adaptation is something we have to do right now. We have to save peoples’ lives.”

Disasters magnified by global warming have left a trail of death and loss across much of the developing world, wiping out crops in Bangladesh, leveling villages in Honduras and threatening the very existence of small island nations.

A big question is whether the disasters in the developed world will have a bearing on what the world’s most influential countries and companies will do to reduce their own emissions of planet-warming gases.

“This tragic event is a reminder that, in the climate emergency, no one is safe,” Mohamed Nasheed, the former president of the Maldives, said in a statement about the flooding.

Part of the historic center of Prague was underwater in August 2002.
Credit…Agence France-Presse — Getty Images

The floods devastating Europe have killed scores of people, leaving at least 1,300 missing, uprooting families, causing immense financial damage and reducing homes and cars to the state of floating bath toys. But it is not the first time the continent has been buffeted by a deluge.

Here are some of the other major lethal floods and flooding caused by storms in recent years.

Credit…Dragan Karadarevic/European Pressphoto Agency

A 7-year-old boy dead after falling ill in a flooded home in Surrey. A kayaker drowned on a swollen Welsh river. A coastal railroad ripped up by waves in Cornwall.

In a matter of months in 2014, at least 5,000 houses in Britain were damaged in what was then seen as one of the rainiest seasons in nearly 250 years. While some blamed the flooding on the austerity measures of David Cameron, the prime minister at the time, others pointed to climate change.

In May of that year, the heaviest rains and floods in 120 years hit Bosnia and Serbia, killing at least 33 people, forcing thousands out of their homes, and cutting off power in 100,000 households in Serbia, as several months’ worth of rainfall fell in a matter of days.

Credit…Armin Weigel/European Pressphoto Agency

Germany is no stranger to flooding.

In Bitterfeld, in eastern Germany, about 10,000 people were asked to leave their homes in June 2013 after a levee on the Mulde River burst, amid some of the worst flooding that some German regions had seen in centuries. More than 600 residents of Dresden were brought to safety as electricity and water services to the city’s affected center were cut off.

Chancellor Angela Merkel, now tested by the current flooding, showed her mettle at the time, touring three of the hardest-hit areas to wade through ankle-deep floodwaters and visit victims of the flood.

Credit…Philippe Huguen/Agence France-Presse

The storm was called Kyrill by German meteorologists, and it spurred unrelenting rain in Britain, Ireland, France, Belgium and the Netherlands.

The howling gale churned through the British Isles and Northern Europe, uprooting trees, shattering windows, flooding beaches and forcing the cancellation of hundreds of flights at airports from London to Frankfurt.

According to the European Environment Agency, Kyrill killed 46 people and resulted in overall losses worth 8 billion euros. At the time, it was one of the most damaging extreme weather episodes ever recorded in Europe.

The name Kyrill stemmed from a German practice of naming weather systems. Anyone may name one, for a fee, and three siblings had paid to name the system as a 65th birthday gift for their father, not realizing it would grow into a fierce storm.

Credit…Peter Schneider/Keystone, via Associated Press

Such was the deluge in Central and Southern Europe in 2005 that in the Alps, military helicopters were deployed to ferry in supplies, evacuate stranded tourists and even stranded cows in mountain pastures threatened by rising water.

The floods left dozens dead. In Romania, which was badly affected by the flooding, victims were drowned as torrents of water rushed into their homes. Austria, Bulgaria, Germany and Switzerland were also buffeted by the flooding.

The scenes of devastation were visceral and shocking. The Aare River broke through the windows of a children’s clothes shop in Bern, leaving baby strollers and toys floating in muddy water. Much of the historic old city of Lucerne remained underwater.

Meanwhile, in southern Poland, rivers broke their banks and at least seven bridges collapsed.

Credit…Sean Gallup/Getty Images

In 2002, some of the worst rains since 1890 pelted the Czech Republic, putting part of the historic center of Prague underwater and resulting in 50,000 residents being ordered to evacuate, as rivers swelled by near constant rain.

The death toll from the floods, which ravaged East and Central Europe, including Germany and Austria, and southern Russia, was more than 110. The flooding caused billions of dollars’ worth of damage.

The management of the crisis by Germany’s chancellor, Gerhard Schröder, helped propel him to re-election.

In Austria, the Salzach River burst its banks south of Salzburg and threatened to inundate the city at the height of its famous summer festival, forcing the authorities to close most bridges and major roads.

Floodwaters rose in Hungary and Germany, and in northern Austria the authorities halted river traffic on parts of the Danube.

The Ahr river overran its banks in the village of Insul, Germany.
Credit…Michael Probst/Associated Press

Was the flooding caused by climate change?

Tying a single weather event to climate change requires extensive attribution analysis, and that takes time, but scientists know one thing for sure: Warmer air holds more moisture, and that makes it more likely that any given storm will produce more precipitation.

For every 1 Celsius degree of warming, air can hold 7 percent more moisture.

On average, the world has warmed by a little more than 1 degree Celsius (about 2 degrees Fahrenheit) since the 19th century, when societies began pumping huge amounts of greenhouse gases into the atmosphere.

“Any storm that comes along now has more moisture to work with,” said Jennifer Francis, a senior scientist with the Woodwell Climate Research Center in Massachusetts. “That’s the straightforward connection to the increased frequency of heavy downpours.”

And although it is still a subject of debate, some scientists say climate change might be causing storms to linger longer.

Some studies suggest that rapid warming in the Arctic is affecting the jet stream. One consequence of that, said Hayley Fowler, a professor of climate change impacts at Newcastle University in England, is that the river of wind is weakening and slowing down at certain times during the year, including summer. That, in turn, affects weather systems farther south.

“That means the storms have to move more slowly,” Dr. Fowler said. The storm that caused the flooding was practically stationary, she noted.

The combination of more moisture and a stalled storm system means that a lot of rain can fall over a given area.

Geert Jan van Oldenborgh, one of the primary scientists with World Weather Attribution, a group that quickly analyzes extreme weather events to see whether they were made more likely by climate change, said the group was discussing whether to study the German floods.

Beyond the speed of a weather system and its moisture content, there are many factors that affect flooding that can make an analysis difficult. Local topography has to be taken into account, as that can affect how much runoff gets into which rivers.

Human impacts can complicate the analysis even further. Development near rivers can make runoff worse by reducing the amount of open land that can absorb rain. And infrastructure built to cope with heavy runoff and rising rivers may be under-designed and inadequate.

Watching the high water in Roermond, the Netherlands, on Friday.
Credit…Vincent Jannink/EPA, via Shutterstock

While some development in cities and elsewhere can make flooding worse, other projects can reduce flooding. That appears to have been the case in the Netherlands, which was not as severely affected as neighboring Germany by this week’s storm.

After several major floods on the Meuse River in the 1990s, the Dutch government began a program called Room for the River to reduce flooding, said Nathalie Asselman, who advises the government and other clients on flood risk.

The work involved lowering and widening river beds, lowering flood plains and excavating side channels.

“The aim of these measures is to lower flood levels,” she said.

Taming water in the Netherlands, a waterlogged country, has been a matter of survival for centuries, and the imperative to keep levels under control is inextricably bound up with Dutch identity. Much of the country sits below sea level and is gradually sinking. Climate change has also exacerbated the twin threats of storms and rising tides.

While a dike near the Meuse in southern Netherlands suffered a breach that caused some flooding until it was repaired on Friday, the measures appear to have worked.

The breach, in the dike along the Juliana Canal in the southern Netherlands, was closed by the Dutch military by dumping hundreds of sandbags into the growing hole. Hours before, thousands had been told to evacuate after the dike was breached along the canal, a 22-mile waterway that regulates the Meuse River.

The river’s water level is at heights not witnessed since 1911, the Dutch national broadcaster NOS reported. Yet water levels on the Meuse were about a foot lower than would have been the case without the flood-reduction measures, Ms. Asselman said. That meant that smaller tributaries backed up less where they met the Meuse, producing less flooding.

“If we wouldn’t have implemented these measures, then the situation would have been worse,” she said. “Both on the main river and the tributaries.”

Oliver Henry, a firefighter with the U.S. Fish and Wildlife Service, after helping extinguish a small fire in Mattawa, Wash., last month.
Credit…Grant Hindsley for The New York Times

An increasingly hot, dry and deadly summer has gripped much of the Western United States, with heat claiming lives in the Pacific Northwest and Canada in record numbers, and a deepening drought threatening water supplies — all of which is setting the stage for another potentially catastrophic fire season in California and neighboring states.

A fourth major heat wave was forecast to roast parts of the region again this weekend. It comes two weeks after a record-shattering spate of high temperatures — which scientists said would been virtually impossible without climate change — killed hundreds of people in the United States and Canada.

A week ago, Death Valley hit a 130-degree high, matching a reading from last year that may be the highest reliably recorded temperature on earth. Also this past weekend, Las Vegas tied its record high, 117 degrees, and Grand Junction, Colo., topped its previous record, hitting 107 degrees.

At least 67 weather stations from Washington State through New Mexico have recorded their hottest temperatures ever this summer, the National Weather Service said this week. Those records stretched back at least 75 years.

The heat helped drive the rapid growth of a wildfire in southern Oregon, known as the Bootleg Fire, that has burned more than 240,000 acres — about a third the size of Rhode Island, America’s smallest state. The fire, the largest of dozens across the West, has destroyed about two dozen homes, threatens 1,900 more and has set off a wave of evacuations.

The fire also burned across a power line corridor that serves as a major contributor to the electrical grid in California, where officials have issued warnings this week asking residents to conserve power by turning up their thermostats and turning off appliances, or risk rolling blackouts.

One part of the West saw some relief from the crushing heat this week, as monsoon rains fell on the Southwest, including New Mexico and Arizona. But the result was yet another disaster: flash flooding that left some city streets in Arizona awash in muddy water and propelled a torrent of water through part of the Grand Canyon, washing away a camp where about 30 people on a rafting trip were spending the night, killing one.

As the Earth warms from climate change, heat waves are becoming hotter and more frequent. “And as bad as it might seem today,” Jonathan Overpeck, a climate scientist at the University of Michigan, recently told The New York Times, “this is about as good as it’s going to get if we don’t get global warming under control.”

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Live Updates: Europe Flooding Death Toll Passes 125, and Scientists See the Fingerprints of Climate Change

devastation from the floods came from all around Western Europe as the death toll passed 125 on Friday, with another 1,300 people still missing. Roads buckled and washed away. Cars piled atop one another. Houses were inundated to the roof tiles. Frightened residents were being evacuated in the shovels of earth movers.

But nowhere was affected more than Germany, where hundreds were still unaccounted for and the death toll had reached 106 and was expected to rise as rescue workers combed through the debris. At least 20 were reported dead in Belgium.

A European weather agency had issued an “extreme” flood warning after detailed models showed storms that threatened to send rivers surging to levels that a German meteorologist said on Friday had not been seen in 500 or even 1,000 years.

German officials said Friday their warning system, which includes a network of sensors that measure river levels in real time, functioned as it was supposed to. The problem, they said, was an amount of rain they had never seen before — falling so rapidly that it engorged even small streams and rivers not normally considered threats.

Extreme downpours like the ones that occurred in Germany are among the most visible and damaging signs that the climate is changing as a result of warming caused by greenhouse gas emissions. Studies have found that they are now occurring more frequently, and scientists point to a simple reason: A warmer atmosphere can hold more moisture, which creates extreme rainfall.

In Central Europe rescue efforts were hampered, with electricity and communications networks down, roads and bridges washed out, and drinking water scarce. The worst hit were thinly populated, rural areas.

In the city of Schleitheim, Switzerland, where a river burst its banks, residents recorded videos of cars being washed through the streets in a swirling flood of muddy water and debris.

Germans struggled even to grasp the scale of the calamity in their country. Chancellor Angela Merkel expressed her shock and solidarity from Washington, where she was visiting the White House. Politicians of all stripes called for a truce in the German election campaign. The focus was on how to deal with a disaster that was growing by the hour, with thousands left homeless, in addition to the missing.

In Belgium, the Meuse river overflowed its banks, flooding villages and the center of Liège, leaving thousands without power. The official death toll stands at 20 dead and 20 missing, the authorities said.

“We are still waiting for the final assessment, but these floods could have been the most disastrous that our country has ever known,” Alexander De Croo, Belgium’s prime minister said on Friday.

Relatives of those missing grappled with the fear of the unknown. The authorities in the Ahrweiler district of Rhineland-Palatinate said late Thursday that 1,300 people remained unaccounted for in their region, where the Ahr river swelled to an angry torrent late Wednesday, ripping through the towns and villages that hugged its banks.

North Rhine-

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Düsseldorf

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One of the places in Germany hardest hit by the flooding was tiny Schuld, where the destruction arrived with remarkable speed in the once-tidy village. After the river swelled, vehicles bobbed like bath toys, six houses collapsed and half of those that remained standing had gaping holes torn by floating debris.

“It went so fast. You tried to do something, and it was already too late,” a resident of Schuld told Germany’s ARD public television.

At least 50 people were confirmed dead in the Ahrweiler district, where torrents of water rushed through towns and villages, washing away cars, homes and businesses.

In Sinzig, a town in the district, efforts to evacuate a care home for people with severe disabilities came just moments before the gushing waters swept through the lower levels, killing 12 of the residents.

A church and cemetery after flooding in Bad Neuenahr-Ahrweiler, Germany.
Credit…Friedemann Vogel/EPA, via Shutterstock

BERLIN — Days before roiling waters tore through western Germany, a European weather agency issued an “extreme” flood warning after detailed models showed storms that threatened to send rivers surging to levels that a German meteorologist said on Friday had not been seen in 500 or even 1,000 years.

By Friday those predictions proved devastatingly accurate, with at least 125 people dead and 1,300 unaccounted for, as helicopter rescue crews plucked marooned residents from villages inundated sometimes within minutes, raising questions about lapses in Germany’s elaborate flood warning system.

Numerous areas, victims and officials said, were caught unprepared when normally placid brooks and streams turned into torrents that swept away cars, houses and bridges and everything else in their paths.

“It went so fast. You tried to do something, and it was already too late,” a resident of Schuld told Germany’s ARD public television, after the Ahr River swelled its banks, ripping apart tidy wood-framed houses and sending vehicles bobbing like bath toys.

Extreme downpours like the ones that occurred in Germany are one of the most visible signs that the climate is changing as a result of warming caused by greenhouse gas emissions. Studies have shown a warmer atmosphere can hold more moisture, generating more, and more powerful, rainfall.

The floods that cut a wide path of destruction this week through Germany, Belgium, Switzerland and the Netherlands were bigger than any on record, according to meteorologists and German officials.

German officials said Friday their warning system, which includes a network of sensors that measure river levels in real time, functioned as it was supposed to. The problem, they said, was an amount of rain they had never seen before — falling so rapidly that it engorged even small streams and rivers not normally considered threats.

To describe the events of recent days as a 100-year flood would be an understatement, said Uwe Kirsche, a spokesman for the German Weather Service.

“With these small rivers, they have never experienced anything like that,” Mr. Kirsche said. “Nobody could prepare because no one expected something like this.”

On Tuesday, Felix Dietsch, a meteorologist for the German Weather Service, went on YouTube to warn that some areas of southwest Germany could receive previously unimaginable volumes of rain.

The weather service, a government agency, assigned its most extreme storm warning, code purple, to the Eifel and Mosel regions, one of numerous government warnings issued on Twitter and other media earlier this week and transmitted to state and local officials.

But the waters rose so swiftly that some communities’ response plans were insufficient while others were caught off guard entirely.

Medard Roth, the mayor of Kordel, in the hard-hit state of Rhineland-Palatinate, said that he activated his town’s emergency flood response once Kyll River approached dangerous water levels. But the waters rose too rapidly to be held back by the usual measures.

“By 6 p.m., everything was already under water,” Mr. Roth told Bild, a German newspaper. “Nobody could have predicted that.”

Ursula Heinen-Esser, the environment minister for the state of North Rhine-Westphalia, said on Friday that floodwaters had reached “levels never before recorded.”

The German flood warning system leaves it up to local officials to decide what action to take, on the theory that they are best informed about local terrain and what people or property lies in the path of an overflowing river.

In the Ahrweiler district of neighboring Rhineland-Palatinate, regional officials issued their first warning to residents living near the banks of the river as it approached its record level of 3 meters, or nearly 10 feet. Three hours later, a state of emergency was declared.

By that time, many people had fled to the upper levels of their homes, and those who could not move fast enough died, including 12 handicapped people in an assisted living home in Sinzig.

“The warnings arrived,” Mr. Kirsche of the German Weather Service said. “But the question is why didn’t evacuations take place sooner? That’s something we have to think about.”

The bridge over the Ahr River in Müsch was destroyed in this week’s flooding.
Credit…Steven Erlanger/The New York Times

MÜSCH, Germany — The bridge that spans the River Ahr washed away last night at around 10:00, said Michael Stoffels, 32, whose own house got flooded by about 12 feet of water.

Müsch, a village of 220 people at the junction of the Ahr and Trierbach rivers, was clobbered by the flash floods that have inundated this part of Germany. Only one person has died, but Müsch on Friday evening was without electricity, running water or cellphone coverage.

Residents and their friends were trying to clean up their battered homes, cracked streets and ruined cars. Local firefighters, like Nils Rademacher, 21, were managing the traffic of bulldozers, small trucks and backhoes, while instructing drivers that roads farther into the river valley were blocked with trees or made impassable by fallen bridges.

“A lot of good cars crashed or got crushed,’’ said Maria Vazquez, who works in a nearby auto repair shop. “I work with cars, so that’s sad, but I just hope that all the people are OK.”

The water rose to flood the village in less than two hours on Wednesday, and came halfway up the houses, Ms. Vazquez said.

The riverbanks were scenes of devastation, with crushed cars and thick tree stumps, while many of the cobbled streets were covered with mud and debris. Truckloads of broken furniture, tree branches and chunks of stone were being driven slowly over downed power lines.

The yellow road sign that tells drivers that they have entered Müsch was pulled out of the ground, laying bent and nearly adrift in the Trierbach River.

Mr. Stoffels said that he had no warning from the government, but that he rushed home from the retail store he manages nearby when a neighbor called. He was lucky, he said, since he has storage on the ground level and his living area is above that. The children’s playground next to his home, along the Ahr, was shattered, as was the main village electrical station, even before the bridge washed away.

He and his brother, who traveled 100 miles to help, and his friends, all wearing boots and muddy clothes, were trying to clean up as best they could. It helped, he said, that Müsch, in the Ahrweiler District of Rhineland-Palatinate close to the border with North Rhine-Westphalia, is farming country.

“Nearly everyone has a small tractor or a bulldozer of some kind,’’ he said. And it was true — the local firefighters were there, but there was little government presence, residents said. On Thursday, Mr. Stoffels said, “a couple of soldiers came for a time and a policeman looked around.”

Not far away, larger villages and towns were devastated, and more than 1,000 people are reported missing by the authorities.

Roger Lewentz, Rhineland-Palatinate’s interior minister, was unable to give an exact number of missing in his state.

“We do not yet know for sure whether some of them may be on vacation or simply unavailable. After all, the power and telephone connections are down in many affected locations,” he told Der Spiegel.

“There haven’t been floods like this here in 100 years,’’ said Sebastian Stich, 28, an office worker from nearby Barweiler who came to help his neighbors. “The bridges, the power, it’s all gone.’’

Part of the historic center of Prague, Czech Republic, was underwater in August 2002.
Credit…Agence France-Presse — Getty Images

The floods devastating Europe have killed scores of people, leaving at least 1,300 missing, uprooting families, causing massive financial damage and reducing homes and cars to the state of floating bath toys. But it is not the first time the continent has been buffeted by a deluge. Here are some of the other major lethal floods and flooding caused by storms in recent years:

Credit…Dragan Karadarevic/European Pressphoto Agency

A 7-year-old boy dead after falling ill in a flooded home in Surrey. A kayaker drowned on a swollen Welsh river. A coastal railroad ripped up by waves in Cornwall. In a matter of months in 2014, at least 5,000 houses in Britain were damaged in what was then seen as one of the rainiest seasons in nearly 250 years. While some blamed the flooding on the austerity measures of David Cameron, the prime minister at the time, others pointed to climate change. In May of that same year, the heaviest rains and floods in 120 years hit Bosnia and Serbia, killing at least 33 people, forcing thousands out of their homes, and cutting off power in 100,000 households in Serbia, as several months’ worth of rainfall fell in a matter of days.

Credit…Armin Weigel/European Pressphoto Agency

Germany is no stranger to flooding. In Bitterfeld, in eastern Germany, some 10,000 people were asked to leave their homes in June 2013 after a levee on the Mulde River burst, amid some of the worst flooding that some German regions had seen in centuries. More than 600 residents of Dresden were brought to safety as electricity and water services to the city’s affected center were cut off. Chancellor Angela Merkel, now tested by the current flooding, showed her mettle at the time, touring three of the hardest hit areas to wade through ankle-deep floodwaters and visit victims of the flood.

Credit…Philippe Huguen/Agence France-Presse

The storm was called Kyrill by German meteorologists, and it spurred unrelenting rain in Britain, Ireland, France, Belgium and the Netherlands. The howling gale churned through the British Isles and Northern Europe, uprooting trees, shattering windows, flooding beaches and forcing the cancellation of hundreds of flights at airports from London to Frankfurt. According to the European Environment Agency, Kyrill killed 46 people and resulted in overall losses worth 8 billion euros. At the time, it was one of the most damaging extreme weather episodes ever recorded in Europe. The name Kyrill stemmed from a German practice of naming weather systems. Anyone may name one, for a fee, and three siblings had paid to name the system as a 65th birthday gift for their father, not realizing it would grow into a fierce storm.

Credit…Peter Schneider/Keystone, via Associated Press

Such was the deluge in Central and Southern Europe in 2005 that in the Alps, military helicopters were deployed to ferry in supplies, evacuate stranded tourists and even stranded cows in mountain pastures threatened by rising water. The floods left dozens dead. In Romania, which was badly affected by the flooding, victims were drowned as torrents of water rushed into their homes. Austria, Bulgaria, Germany and Switzerland were also buffeted by the flooding. The scenes of devastation were visceral and shocking. The Aare River broke through the windows of a children’s clothes shop in Bern, leaving baby strollers and toys floating in muddy water. Much of the historic old city of Lucerne remained underwater. Meanwhile, in southern Poland, rivers broke their banks and at least seven bridges collapsed.

Credit…Sean Gallup/Getty Images

In 2002, some of the worst rains since 1890 pelted the Czech Republic, putting part of the historic center of Prague underwater and resulting in 50,000 residents being ordered to evacuate, as rivers swelled by near constant rain. The death toll from the floods, which ravaged East and Central Europe, including Germany and Austria, and southern Russia, was more than 110. The flooding caused billions of dollars worth of damage. The floods helped propel Germany’s chancellor, Gerhard Schröder, to re-election because of his management of the crisis. In Austria, the Salzach River burst its banks south of Salzburg and threatened to inundate the city at the height of its famous summer festival, forcing the authorities to close most bridges and major roads. Floodwaters rose in Hungary and Germany, and in northern Austria the authorities halted river traffic on parts of the Danube.

The Ahr river overran its banks in the village of Insul, Germany. 
Credit…Michael Probst/Associated Press

Was the flooding caused by climate change?

Tying a single weather event to climate change requires extensive attribution analysis, and that takes time, but scientists know one thing for sure: Warmer air holds more moisture, and that makes it more likely that any given storm will produce more precipitation.

For every 1 Celsius degree of warming, in fact, air can hold 7 percent more moisture.

On average, the world has warmed by a little more than 1 degree Celsius (about 2 degrees Fahrenheit) since the 19th century, when societies began pumping huge amounts of greenhouse gases into the atmosphere.

“Any storm that comes along now has more moisture to work with,” said Jennifer Francis, a senior scientist with the Woodwell Climate Research Center in Massachusetts. “That’s the straightforward connection to the increased frequency of heavy downpours.”

And, although it is still a subject of debate, some scientists say climate change might be causing storms to linger longer.

Some studies suggest that rapid warming in the Arctic is affecting the jet stream. One consequence of that, said Hayley Fowler, a professor of climate change impacts at Newcastle University in England, is that the river of wind is weakening and slowing down at certain times during the year, including summer. And that, in turn, affects weather systems farther south.

“That means the storms have to move more slowly,” Dr. Fowler said. The storm that caused the flooding was practically stationary, she noted.

The combination of more moisture and a stalled storm system means a lot of rain can fall over a given area.

Geert Jan van Oldenborgh, one of the primary scientists with World Weather Attribution, a group that quickly analyzes specific extreme weather events to see whether they were made more likely, or not, by climate change, said the group was discussing whether they would study the German floods.

Beyond the speed of a weather system and its moisture content, there are many factors that affect flooding that can make an analysis difficult. Local topography has to be taken into account, as that can affect how much runoff gets into which rivers.

Human impacts can complicate the analysis even further. Development near rivers, for instance, can make runoff worse by reducing the amount of open land that can absorb rain. Infrastructure built to cope with heavy runoff and rising rivers may be under-designed and inadequate.

Oliver Henry, a firefighter with the U.S. Fish and Wildlife Service, after helping extinguish a small fire in Mattawa, Wash., last month.
Credit…Grant Hindsley for The New York Times

An increasingly hot, dry and deadly summer has gripped much of the Western United States, with heat claiming lives in the Pacific Northwest and Canada in record numbers, and a deepening drought threatening water supplies — all of which is setting the stage for another potentially catastrophic fire season in California and neighboring states.

A fourth major heat wave was forecast to roast parts of the region again this weekend. It comes two weeks after a record-shattering spate of high temperatures — which scientists said would been virtually impossible without climate change — killed hundreds of people in the United States and Canada.

A week ago, Death Valley hit a 130-degree high, matching a reading from last year that may be the highest reliably recorded temperature on earth. Also this past weekend, Las Vegas tied its record high, 117 degrees, and Grand Junction, Colo., topped its previous record, hitting 107 degrees.

At least 67 weather stations from Washington State through New Mexico have recorded their hottest temperatures ever this summer, the National Weather Service said this week. Those records stretched back at least 75 years.

The heat helped drive the rapid growth of a wildfire in southern Oregon, known as the Bootleg Fire, that has burned more than 240,000 acres — about a third the size of Rhode Island, America’s smallest state. The fire, the largest of dozens across the West, has destroyed about two dozen homes, threatens 1,900 more and has set off a wave of evacuations.

The fire also burned across a power line corridor that serves as a major contributor to the electrical grid in California, where officials have issued warnings this week asking residents to conserve power by turning up their thermostats and turning off appliances, or risk rolling blackouts.

One part of the West saw some relief from the crushing heat this week, as monsoon rains fell on the Southwest, including New Mexico and Arizona. But the result was yet another disaster: flash flooding that left some city streets in Arizona awash in muddy water and propelled a torrent of water through part of the Grand Canyon, washing away a camp where about 30 people on a rafting trip were spending the night, killing one.

As the Earth warms from climate change, heat waves are becoming hotter and more frequent. “And as bad as it might seem today,” Jonathan Overpeck, a climate scientist at the University of Michigan, recently told The New York Times, “this is about as good as it’s going to get if we don’t get global warming under control.”

The overflowing Meuse River near Aasterberg, the Netherlands, on Friday.
Credit…Sem Van Der Wal/EPA, via Shutterstock

A breach in the dike along the Juliana Canal in the southern Netherlands on Friday was closed by the Dutch military by dumping hundreds of sandbags into the growing hole. Hours before, thousands had been told to evacuate after the dike was breached along the canal, a 22-mile waterway that regulates the Meuse River.

The river’s water level is at heights not witnessed since 1911, the Dutch national broadcaster NOS reported.

That is no small thing is a water-logged country where taming water has been a matter of survival for centuries and the imperative to keep levels under control is inextricably bound up with Dutch identity. Much of the country sits below sea level and is gradually sinking. Climate change has also exacerbated the twin threats of storms and rising tides.

Residents of the villages of Brommelen, Bunde, Geulle and Voulwames were ordered to evacuate immediately, after initially being told to move to higher floors in their homes. About 10,000 people live in the area.

The local authorities said there was “a large hole” in the dike, prompting fears that the entire area would be flooded. While parts of the area were flooded, a disaster was averted after the breach was closed. NOS said the dike was still unstable and continued to be monitored.

Upriver, near the city of Venlo, evacuations were ordered for whole neighborhoods and surrounding villages, in total 10,700 people and 7,100 houses, the municipality said in a tweet. People have until 6 p.m. local time to leave their homes.

Record water levels are moving through the Meuse River, prompting evacuations and fresh inspections of dikes along the river that empties into the North Sea. The river is a key waterway for European shipping connections.

Following flooding in recent decades, the Dutch authorities have designated special areas that can be flooded with excess water when critical levels are reached.

The Netherlands has so far been spared much of the death and destruction that this week’s flooding has caused in Germany and Belgium. But in Valkenburg, a city in the south of the Netherlands with about 16,000 residents, damage was severe. Hundreds of houses were without power, and the center of the city was flooded.

“The damage is incalculable,” Mayor Daan Prevoo of Valkenburg told the Algemeen Dagblad newspaper. He predicted that repairs would take weeks.

Rowing a boat down a flooded residential street in Angleur, on the outskirts of Liège, Belgium, on Friday.
Credit…Valentin Bianchi/Associated Press

In Liège, Belgium’s third-largest city, much of the early panic eased on Friday as residents said the waters of the Meuse river seemed to recede, at least a bit.

Fears that a major dam might break led the mayor to call for parts of the city to be evacuated late Thursday. But on Friday, people were allowed back, though they were told to stay away from the river, which was still lapping over its banks.

“The situation is now under control, and people can return to their homes,” Laurence Comminette, the spokeswoman for the mayor, said in an interview. “Of course not everyone can go back, because many homes have been destroyed. But there is no longer an imminent danger of more flooding.”

Georges Lousberg, 78, said he thought the crisis was largely over in the city. “It did not rain much today, and the weather is supposed to be better the rest of the week.”

He said there had been times when the Meuse was even higher, especially before walls were built along its banks. “The worst flooding was in 1926,” he said.

Prasanta Char, 34, a postdoctoral student in physics at the University of Liège, said he had been anxious about rain overnight after the mayor’s evacuation call.

He had gone looking to buy water, but had a hard time because so many stores were closed. He finally found a small convenience store in the shuttered city.

“It’s much worse in Germany, and a lot of the roads are shut and the trains are stopped,” he said, “I’m still a bit anxious about rain, but today it seems better.”

A resident cleaning the streets of Ahrweiler-Bad Neenah, Germany, after flooding on Thursday.
Credit…Christof Stache/Agence France-Presse — Getty Images

Forecasts predicting improved weather for Western Europe over the weekend offered some hope amid the deluge, potentially aiding search-and-rescue efforts in areas devastated by floods.

The heavy rain in Germany in the Ahrweiler district of Rhineland-Palatinate was forecast to let up later Friday and over the weekend, after flooding left 1,300 people unaccounted for in the region. Emergency workers put sandbags in place to stem the rising waters in the region’s remote villages, like Schuld, where heavy flows of water washed away six homes and left more close to collapse.

On Saturday and Sunday, there is about a 20 percent chance of rain in that area, and temperatures are expected to rise above 70 degrees Fahrenheit with partial sunshine later in the day, according to Weather.com. Conditions are likewise expected to improve in the state of North Rhine-Westphalia, also in western Germany, where at least 43 people have died in the flooding.

Andreas Friedrich, a meteorologist for Germany’s national weather service, said that dry, sunny weather was likely over the next few days in the western states hit by floods. The weather service has issued a warning about possible floods in the touristy area of southeastern Germany, north of the Alps, over the weekend, but conditions are not expected to be as bad as they were in the western part of the country, he said.

In Belgium, the weather is also expected to clear up over the weekend. The Royal Meteorological Institute of Belgium forecast only light rain in the hilly Ardennes region, which experienced heavy flooding over the past few days. In Liège, which was also hard hit, there was a 3 percent chance of precipitation on Saturday, according to the AccuWeather forecasting service.

Alex Dewalque, a spokesman for the meteorological institute, said water levels in the worst-hit parts of Belgium were already falling, making it easier for emergency workers to rescue stranded people and search for casualties. He said the coming days would be much drier and with warmer temperatures, and that there were no flood warnings.

More rain was expected in Switzerland’s northern Alps on Friday, however, and officials warned of more potential flooding in parts of the country. Lake Lucerne reached critical levels, forcing the closing of some bridges and roadways.

Sarah Schöpfer, a meteorologist at Switzerland’s Federal Office of Meteorology and Climatology MeteoSwiss, said she expected rainfall over the affected areas of Switzerland to lighten.

“We expect that tonight the precipitation activity weakens further and tomorrow it mainly affects the eastern Swiss Alps (mainly regions that did not get the highest amounts of rain during the last few days),” she said in an email. “So apart from the last showers today and tomorrow, the following days will be dry.”

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What Ever Happened to IBM’s Watson?

IBM insists that its revised A.I. strategy — a pared-down, less world-changing ambition — is working. The job of reviving growth was handed to Arvind Krishna, a computer scientist who became chief executive last year, after leading the recent overhaul of IBM’s cloud and A.I. businesses.

But the grand visions of the past are gone. Today, instead of being a shorthand for technological prowess, Watson stands out as a sobering example of the pitfalls of technological hype and hubris around A.I.

The march of artificial intelligence through the mainstream economy, it turns out, will be more step-by-step evolution than cataclysmic revolution.

Time and again during its 110-year history, IBM has ushered in new technology and sold it to corporations. The company so dominated the market for mainframe computers that it was the target of a federal antitrust case. PC sales really took off after IBM entered the market in 1981, endorsing the small machines as essential tools in corporate offices. In the 1990s, IBM helped its traditional corporate customers adapt to the internet.

IBM executives came to see A.I. as the next wave to ride.

Mr. Ferrucci first pitched the idea of Watson to his bosses at IBM’s research labs in 2006. He thought building a computer to tackle a question-answer game could push science ahead in the A.I. field known as natural language processing, in which scientists program computers to recognize and analyze words. Another research goal was to advance techniques for automated question answering.

After overcoming initial skepticism, Mr. Ferrucci assembled a team of scientists — eventually more than two dozen — who worked out of the company’s lab in Yorktown Heights, N.Y., about 20 miles north of IBM’s headquarters in Armonk.

The Watson they built was a room-size supercomputer with thousands of processors running millions of lines of code. Its storage disks were filled with digitized reference works, Wikipedia entries and electronic books. Computing intelligence is a brute force affair, and the hulking machine required 85,000 watts of power. The human brain, by contrast, runs on the equivalent of 20 watts.

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More Power Lines or Rooftop Solar Panels: The Fight Over Energy’s Future

The nation is facing once in a generation choices about how energy ought to be delivered to homes, businesses and electric cars — decisions that could shape the course of climate change and determine how the United States copes with wildfires, heat waves and other extreme weather linked to global warming.

On one side, large electric utilities and President Biden want to build thousands of miles of power lines to move electricity created by distant wind turbines and solar farms to cities and suburbs. On the other, some environmental organizations and community groups are pushing for greater investment in rooftop solar panels, batteries and local wind turbines.

There is an intense policy struggle taking place in Washington and state capitals about the choices that lawmakers, energy businesses and individuals make in the next few years, which could lock in an energy system that lasts for decades. The divide between those who want more power lines and those calling for a more decentralized energy system has split the renewable energy industry and the environmental movement. And it has created partnerships of convenience between fossil fuel companies and local groups fighting power lines.

At issue is how quickly the country can move to cleaner energy and how much electricity rates will increase.

senators from both parties agreed to in June. That deal includes the creation of a Grid Development Authority to speed up approvals for transmission lines.

Most energy experts agree that the United States must improve its aging electric grids, especially after millions of Texans spent days freezing this winter when the state’s electricity system faltered.

“The choices we make today will set us on a path that, if history is a barometer, could last for 50 to 100 years,” said Amy Myers Jaffe, managing director of the Climate Policy Lab at Tufts University. “At stake is literally the health and economic well-being of every American.”

The option supported by Mr. Biden and some large energy companies would replace coal and natural gas power plants with large wind and solar farms hundreds of miles from cities, requiring lots of new power lines. Such integration would strengthen the control that the utility industry and Wall Street have over the grid.

batteries installed at homes, businesses and municipal buildings.

Those batteries kicked in up to 6 percent of the state grid’s power supply during the crisis, helping to make up for idled natural gas and nuclear power plants. Rooftop solar panels generated an additional 4 percent of the state’s electricity.

become more common in recent years.

Some environmentalists argue that greater use of rooftop solar and batteries is becoming more essential because of climate change.

After its gear ignited several large wildfires, Pacific Gas & Electric began shutting off power on hot and windy days to prevent fires. The company emerged from bankruptcy last year after amassing $30 billion in liabilities for wildfires caused by its equipment, including transmission lines.

Elizabeth Ellenburg, an 87-year-old cancer survivor in Napa, Calif., bought solar panels and a battery from Sunrun in 2019 to keep her refrigerator, oxygen equipment and appliances running during PG&E’s power shut-offs, a plan that she said has worked well.

“Usually, when PG&E goes out it’s not 24 hours — it’s days,” said Ms. Ellenburg, a retired nurse. “I need to have the ability to use medical equipment. To live in my own home, I needed power other than the power company.”

working to improve its equipment. “Our focus is to make both our distribution and transmission system more resilient and fireproof,” said Sumeet Singh, PG&E’s chief risk officer.

But spending on fire prevention by California utilities has raised electricity rates, and consumer groups say building more power lines will drive them even higher.

Average residential electricity rates nationally have increased by about 14 percent over the last decade even though average household energy use rose just over 1 percent.

2019 report by the National Renewable Energy Laboratory, a research arm of the Energy Department, found that greater use of rooftop solar can reduce the need for new transmission lines, displace expensive power plants and save the energy that is lost when electricity is moved long distances. The study also found that rooftop systems can put pressure on utilities to improve or expand neighborhood wires and equipment.

Texas was paralyzed for more than four days by a deep freeze that shut down power plants and disabled natural gas pipelines. People used cars and grills and even burned furniture to keep warm; at least 150 died.

One reason for the failure was that the state has kept the grid managed by the Electric Reliability Council of Texas largely disconnected from the rest of the country to avoid federal oversight. That prevented the state from importing power and makes Texas a case for the interconnected power system that Mr. Biden wants.

Consider Marfa, an artsy town in the Chihuahuan Desert. Residents struggled to stay warm as the ground was blanketed with snow and freezing rain. Yet 75 miles to the west, the lights were on in Van Horn, Texas. That town is served by El Paso Electric, a utility attached to the Western Electricity Coordinating Council, a grid that ties together 14 states, two Canadian provinces and a Mexican state.

$1.4 million, compared with about $1 million to Donald J. Trump, according to the Center for Responsive Politics.

In Washington, developers of large solar and wind projects are pushing for a more connected grid while utilities want more federal funding for new transmission lines. Advocates for rooftop solar panels and batteries are lobbying Congress for more federal incentives.

Separately, there are pitched battles going on in state capitals over how much utilities must pay homeowners for the electricity generated by rooftop solar panels. Utilities in California, Florida and elsewhere want lawmakers to reduce those rates. Homeowners with solar panels and renewable energy groups are fighting those efforts.

Despite Mr. Biden’s support, the utility industry could struggle to add power lines.

Many Americans resist transmission lines for aesthetic and environmental reasons. Powerful economic interests are also at play. In Maine, for instance, a campaign is underway to stop a 145-mile line that will bring hydroelectric power from Quebec to Massachusetts.

New England has phased out coal but still uses natural gas. Lawmakers are hoping to change that with the help of the $1 billion line, called the New England Clean Energy Connect.

This spring, workmen cleared trees and installed steel poles in the forests of western Maine. First proposed a decade ago, the project was supposed to cut through New Hampshire until the state rejected it. Federal and state regulators have signed off on the Maine route, which is sponsored by Central Maine Power and HydroQuebec.

But the project is mired in lawsuits, and Maine residents could block it through a November ballot measure.

set a record in May, and some scientists believe recent heat waves were made worse by climate change.

“Transmission projects take upward of 10 years from conception to completion,” said Douglas D. Giuffre, a power expert at IHS Markit. “So if we’re looking at decarbonization of the power sector by 2035, then this all needs to happen very rapidly.”

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