Raymond Zhong

Pakistan began receiving abnormally heavy rain in mid-June, and, by late August, drenching downpours were declared a national emergency. The southern part of the Indus River, which traverses the length of the country, became a vast lake.

Villages have become islands, surrounded by putrid water that stretches to the horizon. More than 1,500 people have died. Floodwaters could take months to recede.

The deluges were made worse by global warming caused by greenhouse-gas emissions, scientists said Thursday, drawing upon a fast-growing field of research that gauges the influence of climate change on specific extreme weather events soon after they occur — and while societies are still dealing with their shattering consequences.

As climate scientists’ techniques improve, they can assess, with ever-greater confidence and specificity, how human-induced changes in Earth’s chemistry are affecting the severe weather outside our windows, adding weight and urgency to questions about how nations should adapt.

The floods in Pakistan are the deadliest in a recent string of eye-popping weather extremes across the Northern Hemisphere: relentless droughts in the Horn of Africa, Mexico and China; flash floods in West and Central Africa, Iran and the inland United States; searing heat waves in India, Japan, California, Britain and Europe.

Scientists have warned for decades that some kinds of extreme weather are becoming more frequent and intense as more heat-trapping gases get pumped into the atmosphere. As the planet warms, more water evaporates from the oceans. Hotter air also holds more moisture. So storms like those that come with the South Asian monsoon can pack a bigger punch.

But Pakistan’s monsoon rains have long varied wildly from year to year, which made it hard to pin down precisely how much more severe this season was because of climate change, the authors of the new study said. Still, most of their computer models indicated that human-caused warming had intensified the rainfall to some extent, convincing them that it was a contributing factor.

The country might have experienced disastrously high rainfall this year even without global warming, said the study’s lead author, Friederike Otto, a climate scientist at Imperial College London. “But it’s worse because of climate change,” Dr. Otto said. “And especially in these highly vulnerable regions, small changes matter a lot.”

The study was produced by 26 scientists affiliated with World Weather Attribution, a research initiative that specializes in rapid studies of extreme events. This year, scientists with the group found that the heat that scorched India and Pakistan this spring had been 30 times as likely to occur because of greenhouse emissions. July’s extreme heat in Britain had been at least 10 times as likely, the group found. Next up is a study on this summer’s drought in Europe.

Attribution studies aim to link two distinct but related phenomena: climate and weather.

Climate is what happens to the weather over long periods and on a planetary scale. Direct weather records only go back a century or so in many places, which is why scientists use computer models and concepts from physics and chemistry to build out their understanding of the evolving climate. But the weather has always been variable, even without the influence of human activity. Attribution studies try to separate this natural variability from the larger shifts that fossil-fuel emissions are bringing about.

Attribution research “really helps us understand how weather sits within long-term climate change,” said Daithi A. Stone, a climate scientist with New Zealand’s National Institute of Water and Atmospheric Research.

Nearly two decades ago, Dr. Stone worked on the first study to estimate the fingerprints of climate change on a one-off event — in that case, Europe’s brutal 2003 heat wave, which killed tens of thousands of people. Since then, scientists worldwide have published 431 attribution studies on 504 extreme events, according to an informal tally of English-language research by the climate news site Carbon Brief.

The field is still expanding rapidly, by Carbon Brief’s count: Three-fifths of these studies were published in 2017 or later. A fifth were published this year or last.

“The diversity of tools we have at our disposal to look at it now,” Dr. Stone said, “is beyond what we might have imagined back then.”

To perform an attribution, scientists use mathematical models to analyze both the world as it is and the world as it might have been, had humans not spent decades pumping planet-warming gases into the atmosphere. With computer simulations, they can replay recent history dozens, even hundreds, of times in both worlds to see how often the event, and others like it, occur in each. The differences indicate how much global warming was likely responsible.

Researchers often perform this comparison using scores of climate models to ensure their conclusions are sound. They also check the simulations against records of actual events that have occurred in the past.

To examine this year’s flooding in Pakistan, the authors of the new study looked at two metrics: the maximum 60-day rainfall each year between June and September over the entire Indus River Basin, and the maximum five-day rainfall each year over the badly hit southern provinces of Sindh and Baluchistan.

The researchers found that several of their models did not realistically reproduce patterns in the actual rainfall data for Pakistan. And those that did gave divergent answers for how much more intense and more likely this year’s rainfall had become under present levels of global warming.

The models gave clearer answers when considering a higher level of warming, however. This gave the researchers confidence to say that climate change had probably made this year’s flooding worse, though they refrained from estimating by how much.

Recent improvements in the climate models helped the authors narrow their estimates, Dr. Otto said. “The uncertainty bars are smaller than they would have been five years ago,” she said, referring to the lines in statistical charts that show ranges of possible values. “But monsoon is still something that models really struggle with.”

Pakistan’s highly varied topography, from its southern coast to the high Himalayan peaks in the north, causes its climate to be shaped by many physical drivers, said another author of the study, Fahad Saeed, a climate scientist based in Islamabad, Pakistan, with the research group Climate Analytics.

“The representation of all these processes can get tricky when you’re applying a climate model,” Dr. Saeed said.

Scientists often find storms, droughts and wildfires tougher to attribute to global warming compared with extreme hot or cold spells. Those events involve not just temperatures, but also the circulation of air and complex interactions between land, sea and atmosphere. Even so, new and improved models, plus greater quantities of data, are helping to close the gaps.

“For us as climate scientists, our laboratory is our climate models,” said Andrew Hoell of the National Oceanic and Atmospheric Administration in Boulder, Colo. “And they’ve advanced in ways that have allowed us to do more-robust attribution studies.”

Today, models are continuing to get better at capturing weather and its drivers at progressively smaller scales, Dr. Hoell said. Scientists can start to think not just about drought over a large area, but evaporation in specific watersheds and reservoirs. Not just average rainfall, but individual tornadoes and thunderstorms.

Climate scientists have also begun using artificial intelligence and other computational techniques to scour weather data for new insights, said Dim Coumou, a climate researcher at the Dutch university VU Amsterdam. These methods can help scientists uncover the hidden mechanisms that drive complex weather patterns, leading to better attributions and forecasts of extreme events.

“There is just a lot of data that is getting more accessible for scientists,” Dr. Coumou said.

Weather records show that South Asia’s monsoon is whipsawing more between drier years and wetter ones — unwelcome news for farmers who must increasingly deal with either parched fields or inundated ones.

Anders Levermann, a physicist at the Potsdam Institute for Climate Impact Research in Germany, has proposed one explanation. The South Asian monsoon begins each spring when the land warms and draws in moisture-rich air from the Indian Ocean. When this air hits the mountains and cools, its cargo of vapor condenses into rain and, in the process, releases heat. The heat draws even more air toward the land from the sea, which keeps the monsoon going.

On a warmer planet, there is more moisture in this system, which means the rains are amplified. But if anything blocks this inflow, such as an atmospheric disturbance or heavy air pollution, then its weakening effects on the monsoon might also be amplified, Dr. Levermann said.

“That’s the bad thing about climate change,” he said. “It’s not just an increase in something or a decrease in something. It’s an increase in variability.”

Raymond Zhong is a climate reporter. He joined The Times in 2017 and was part of the team that won the 2021 Pulitzer Prize in public service for coverage of the coronavirus pandemic.

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