It used to be the big debate in climate change circles. Whenever an extreme event occurred — like, say, Hurricane Katrina, or the deadly 2003 European heat wave — the question would immediately arise as to whether it was legitimate to in any way “link” it to climate change. Usually, some errant activist would draw the connection, and climate skeptics would pounce, denouncing the leap and questioning any causal attribution.

Over time, though, scientists have clarified matters. They’ve explained that while global warming doesn’t “cause” any single event, it can make them more likely to occur, not unlike (in the helpful analogy) the loading of dice. Indeed, published papers have shown that a warming climate had indeed increased the odds of a number of individual extreme events, including the 2003 European heat wave, the 2010 Russian heat wave and the 2013 Australian summer heat.

As we move further and further into a jarred climate, meanwhile, the research on attributing extreme events has also advanced. Thus, in a new study in Nature Climate Change, Erich Fischer and Reto Knutti, of the science-focused Swiss university ETH Zurich, perform an analysis not for any individual event but rather for all daily heat and precipitation extremes of a “moderate” magnitude occurring over land in our current climate. And they find, strikingly, that 18 percent of today’s moderate precipitation extremes, and 75 percent of moderate heat extremes, were made more likely to occur by global warming.

“The approach here is reminiscent of medical studies, where it is not possible to attribute a single fatality from lung cancer to smoking,” note the authors. “Instead, a comparison of the lung-cancer-related mortality rate in smokers with the rate in non-smokers may allow attribution of the excess mortality to smoking.”

It’s important to be clear what kind of hot extreme events are being referred to here. The analysis looked at the seemingly oxymoronic occurrence of “moderate extremes,” which means events that have a low but not extremely low probability of occurring. In this case, a “moderate” extreme was defined as an event that would only occur 1 out of 1,000 days in a climate that has not been tweaked by global warming.

“We find that what used to be a one-in-1,000-days event or a one-in-three-years event becomes, for instance, a four-in-three-year or five-in-three-year event,” says lead study author Erich Fischer. Hence the 75 percent figure reported in the study.

“This might seem a surprisingly high fraction but is consistent with our understanding of how an upward shift of the temperature distribution rapidly increases the chances of temperatures in the upper tail of the undisturbed distribution,” explains Peter Stott, a researcher at the U.K.’s Met Office Hadley Centre who himself documented the statistical link between the 2003 European heat wave and climate change, in an accompanying commentary on the paper.

This does not mean that these extreme events are “caused” by climate change; rather, it means they were made more likely to occur in a statistical sense. (The difference is crucial in climate science circles.) And for even more rare events, the likelihood would be even higher, says Fischer. “A general tendency we see is, if we pick even higher thresholds, if you look at 1 in 10,000 days, 1-in-30-year events, which we can do at least for hot extremes, the increase becomes even bigger,” he says.

The study was performed by running climate change models for a long period of time without any global warming, to create a kind of “counterfactual” scenario in which humans had not warmed the Earth. “We use long simulations of the world that would have been without any human influence,” says Fischer. Then researchers compared the occurrence of heat extremes in those models with heat extremes in models that included global warming caused by human activities.

Future warming will shift the odds even further, the new study finds. “The probability of a hot extreme at 2C warming is almost double that at 1.5C and more than five times higher than for present-day,” the authors write. This statistic, they add, illuminates a sharp difference between trying to hold global warming to 1.5 degrees C — as many African nations, small island states, and other countries seek — and 2 degrees C, a target generally more supported by large industrialized countries, such as the U.S. and European nations.

“This result has strong implications for the discussion of different mitigation targets in climate negotiations, where differences between targets are small in terms of global temperatures but large in terms of the probability of extremes,” note Fischer and Knutti. Indeed, it’s different enough that this paper may well be cited by supporters of a 1.5-degree limit in future international climate negotiations — for instance, in Paris at the end of this year.

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