“You could take a risk, and plan your Olympics, and maybe not get the hot days you expect, but that would be a big risk when there are many billions of dollars at stake,” said Kirk Smith, a researcher at the University of California, Berkeley’s School of Public Health and the lead author of the study. Smith completed it with researchers based at institutions in New Zealand, Cyprus, and the U.S.

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At the center of the study is the scary concept of the “wet-bulb globe temperature,” which Smith acknowledges is a rather unfortunate name. What it refers to is a particular combination of temperature, humidity, wind (or the lack thereof), and heat radiation that, at elevated levels, is simply too much for humans to bear for long outdoors, especially when engaging in physical exertion. The core issue is that if there’s too much humidity, it limits our ability to use evaporation, through sweating, to cool down our bodies.

The wet bulb globe temperature is determined based on several separate measurements, including one taken while covering the bulb of a thermometer with a wet towel, and another taken after inserting it into a dark globe, and can be either lower or higher than the actual temperature. But humans can’t tolerate as high of a wet bulb temperature as an ordinary one. The danger zone is around 25 degrees Celsius, or 77 degrees Fahrenheit, for those engaging in major physical activity.

“It’s tricky to measure and tricky to predict, but it’s come to be understood as the best indicator of heat stress on the body,” said Smith of the metric.

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“At 98 degrees and 100 percent humidity, you can walk slowly outdoors, but if you try to run, you can actually die. It’s a matter of just the basic physics of it,” he continued.

The study therefore goes on to calculate how often an unbearable wet-bulb globe temperature would occur in northern hemisphere cities large enough to host the Summer Olympics by 2085, assuming that a high level of human-induced greenhouse gas emissions continue. (High altitude cities weren’t considered, the scientists write, given the stress on athletes “of high altitude [low air resistance and low oxygen partial pressure] that became apparent at the 1968 Mexico City Olympics.”)

The study assumed that with even a 10 percent chance of these extreme conditions, the Olympics couldn’t be held, since it wouldn’t be acceptable to plan the event, spend a fortune, and then have to cancel a signature outdoor event like the marathon due to weather.

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The result was that if you assume that a 26 degree Celsius (78.8 degree Fahrenheit) wet bulb globe temperature (in the shade) is the limit, then “only eight (1·5%) of 543 cities outside of western Europe would meet the low-risk category” for the Games in the year 2085. If you go farther and push the danger zone up to 28 degrees C (82.4 F), then 33 more cities would be viable.

“Projections out to the early 22nd century, which carry even more uncertainty, suggest the last cities in the northern hemisphere with low-risk summer conditions for the Games will be Belfast, Dublin, Edinburgh, and Glasgow,” the study noted.

The paper joins a growing genre: As early as 2010, climate scientists Stephen Sherwood of the University of New South Wales in Sydney, Australia and Matthew Huber of Purdue University found in the Proceedings of the National Academy of Sciences that “a global-mean warming of roughly 7 °C would create small zones where metabolic heat dissipation would for the first time become impossible, calling into question their suitability for human habitation.”

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Similarly, a paper in Nature Climate Change last year found that for the Persian Gulf region, “by the end of the century certain population centres … are likely to experience temperature levels that are intolerable to humans owing to the consequences of increasing concentrations of anthropogenic greenhouse gases.”

These studies used a somewhat different metric — the wet bulb temperature, rather than the wet bulb globe temperature. The former is a simpler calculation based only on heat and humidity that is not as much focused on how the temperature feels to us as it is on basic thermodynamics. But it can be “used to establish an absolute limit on metabolic heat transfer that is based on physical laws rather than the extrapolation of empirical approximations,” Sherwood writes.

Two researchers contacted to comment on the Olympics study said it seemed reasonable, though they questioned whether there might be ways to adapt or change the event to make it more temperature resilient, at least up to a point.

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“I’m confident that the analysis is solid, and the results make sense,” said Reto Knutti, a climate researcher at ETH Zurich who has also published on the dangers of human heat stress due to climate change, in response to the new paper. But he added that the research didn’t necessarily imply an end to the Olympics under extreme warming, so much as the chance that the Games might have to be very different in the future.

“For the Olympics there are many ways to adapt to the increased risk of heat stress, and there I don’t see why one could not change the format of such an event a bit to reduce the risks for the athletes,” Knutti said by email.

“They made approximate calculations using well established heat stress metrics that are well validated in sports and occupational medicine and military contexts and find that a dramatic reduction in the area in which summer marathons can be run for a variety of models and various thresholds,” added Matthew Huber of Purdue University. “As they point out, heat stress is already a major issue in summer sporting events, and it is reasonable to think that this will only become a larger issue in the future.”

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But Huber also suggested that there is the possibility of “adaptation” to changing conditions, and of athlete “acclimatization,” at least up to a point.

“If we commit to such extravagant warming, the health of elite athletes running marathons will be the least of our worries,” he noted.

Indeed, Smith and Knutti also noted the larger point is not about the Olympics, but rather, about people who work outdoors and who are massively more numerous than elite athletes. These are the individuals who will really suffer the most from an increasing risk of heat stress going forward.

“A canceled marathon in the Olympics is just like a particular flooding in a city: the visible tip of the iceberg that is part of a much bigger problem of climate related impacts hitting billions around the world, and mostly the poor,” said Knutti.

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Smith acknowledged, of course, that the world could get off of a high emissions pathway — the Paris climate agreement is meant to do precisely that — and so lessen the blow in the year 2085. He also added that while 2085 might sound far away, many children today will be alive then.