Now, a group of scientists have extended this field of research to a global scale. In a new study, published Monday in the journal Proceedings of the National Academy of Sciences, they’ve analyzed the influence of global warming on extreme climate events, such as record-breaking temperatures or rainfall, all over the world. And they’ve found that climate change has had a substantial effect.

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The study suggests that anthropogenic global warming, as it has advanced, has had a significant hand in the temperatures seen during the hottest month and on the hottest day on record throughout much of the world. It finds that climate change substantially increased the likelihood of these record warm events occurring in the first place, and also made them more severe than they otherwise would have been, in more than 80 percent of the observed world.

“This suggests that the world isn’t yet at a place where every single record-setting hot event has a human fingerprint, but we are getting close to that point,” said Noah Diffenbaugh, a climate scientist at Stanford University and lead author of the new paper. “Greater than 80 percent of those record hot events is a substantial fraction.”

The study also finds that climate change had increased the probability and severity of the driest year on record — that is, the year that experienced the least amount of precipitation — in 57 percent of the observed areas of the world. And it found that the for wettest five-day period in each of these areas, or the five-day period with the most amount of precipitation on record, warming had increased the chance of its occurring in 41 percent of the observed areas of the world.

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Some of the strongest effects of climate change on these extremes were seen in the tropics, a stark reminder that “a lot of the burden for climate change falls on regions that have emitted only a tiny fraction of the CO2 that caused the shifts,” said Gabriele Hegerl, a climate scientist at the University of Edinburgh and co-leader of a World Climate Research Programme project focusing on weather and climate extremes, in an emailed comment to The Washington Post. (Hegerl was not involved with the new study.)

Finally, the study suggests that global warming contributed substantially to a record low in Arctic sea ice extent in 2012, as well.

“There’s been an explosion of research into possible connections between global warming and individual extreme climate events,” Diffenbaugh told The Post. Just at the end of last year, for instance, a special report in the Bulletin of the American Meteorological Society described a number of extreme events from 2015, including cyclones, heat waves and wildfires, that probably were influenced by climate change.

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Much of this type of research has been in the form of case studies on individual events, Diffenbaugh noted. But in the new paper, he and his colleagues analyzed a variety of climate extremes all across the world using different approaches designed to investigate the influence of global warming.

One approach, for instance, involves simply looking at the observational record to see whether historical climate trends have influenced the probability or severity of certain types of events over time, Diffenbaugh noted. Another approach involves using models to compare scenarios that include human-caused climate change with scenarios in which the climate remains static to see if the occurrence of extreme events is different between them.

The new paper includes several variations of these types of approaches, including both historical observations and model-based strategies. The researchers applied these techniques to four categories of extreme events, which were “unprecedented in the historical record,” Diffenbaugh said. These included the hottest month, the hottest day, the driest year and the wettest five-day period on record. Data on these extremes is not uniformly available around the world, but the researchers analyzed the areas for which information was available.

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The researchers looked at historical trends in temperature and precipitation, as well as comparisons between different model scenarios — with and without the influence of human-caused climate change — to draw conclusions about how global warming has affected long-term climate patterns, and how these trends have affected the likelihood or magnitude of an extreme event.

The researchers later applied the same framework to the Arctic sea ice record to quantify the influence of global warming on the 2012 record-low extent. And, according to Diffenbaugh, the framework can also be applied to certain specific physical conditions — atmospheric patterns, for instance — that help make an extreme event, like a storm or a heat wave, possible in the first place.

For example, he said, the team examined data on the water vapor content present in the atmosphere during a period of intense flooding in Colorado in 2013 and found that its condition was “clearly more likely with global warming than without global warming.”

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In the future, this strategy could become an important way to improve projections of certain types of extreme weather events under different climate scenarios, by analyzing the likelihood of specific conditions and patterns that could combine to give rise to different weather outcomes.

Overall, the researchers’ approach is a “step forward” from the types of individual case studies that have been done in the past, according to climate scientist Adam Sobel, director of Columbia University’s Initiative on Extreme Weather and Climate, who was not involved with the new research. The strategy “allows general statements about what fraction of events of the given types selected have a statistically significant anthropogenic influence subject to the assumptions,” he said in an email to The Post.

He added that the findings linking extreme temperature events to global warming in so many places are not exactly surprising. What’s more interesting, he said, are the physical processes that have made these extreme possible in the first place — that is, the idea that the temperature signal here is found to be due not just to simple global warming, but to “changes in the frequency of atmospheric patterns,” he said.

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This reinforces the importance of looking not just at whole events, such as heat waves and floods, but at their complex, underlying physical causes — and to what extent these causes may be affected by climate change.

As it is, the new study focuses only on climate change and extreme events that have already occurred since the pre-industrial era. But Diffenbaugh points out that the same framework could be used to make predictions about the future climate.