The announcement of the 2014 temperature record was accompanied by a startling statistic. News media reported that the odds of this spate of record-breaking years happening due to natural variations only — that is, not as the result of human-caused climate change — came to as low as one in 650 million.

Now, a new paper out Monday in the journal Nature Scientific Reports conducts what the authors have described as a more rigorous calculation, concluding that the odds of this series of record-breakers — ending with 2014 — were not quite as low as reported. Even so, the calculations still make it clear that the string of record temperatures was highly unlikely to have occurred by chance alone, supporting the idea that human-caused climate change is the culprit.

“Individual record years and the observed runs of record-setting temperatures were extremely unlikely to have occurred in the absence of human-caused climate change,” the authors write.

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Led by Michael Mann, professor of atmospheric science and director of the Earth System Science Center at Pennsylvania State University, the researchers used a climate model, along with observed temperature data, to produce simulations of what temperature distributions should look like under the influence of anthropogenic climate change versus purely by chance. They paid particular attention to the recent run of record years, in which nine of the 10 warmest (and, in fact, 13 of the 15 warmest, as the authors point out) had occurred since the year 2000.

The researchers calculated the odds for these record-breaking runs occurring in both the Northern Hemisphere alone and worldwide. For the Northern Hemisphere, the simulations suggested a chance of about one in 170,000 that the run of 13 out of the past 15 record breakers would have occurred since the year 2000 without the influence of anthropogenic climate change. And the odds of nine out of the past 10 record breakers occurring in the past decade due only to chance were one in 5,000. Globally, the odds of these record runs were a bit more likely — but still slim.

The authors also examined the odds of individual years producing records, as opposed to strings of years together — for instance, the odds of 2014, alone, becoming the warmest year on record at the time. They noted in the paper, “We find it even less likely that natural variability might have produced the observed specific individual yearly temperature records.” This is because for an individual year to break a temperature record, it must reach a specific heat threshold all on its own, one that tops all the other heat records in individual years before it.

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The researchers found odds of one in a million or less that 2014’s record would have occurred without human influence — both in the Northern Hemisphere alone and globally. “That conclusion also holds for the other record years 1998, 2005, and 2010,” the authors added in the paper.

On the other hand, the analysis also looked at the odds of these same records having been produced by human-caused climate change. The researchers found an 83 percent chance that the run of nine-out-of-10 record years, globally, was produced by anthropogenic global warming. And the likelihood of the 2014 record occurring globally was found to be about 40 percent.

So while the odds are not quite as low as those reported in the press back at the close of 2014, they still point unequivocally to the overbearing influence of human-caused climate change in recent years.

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The key to producing accurate calculations, the authors pointed out in the paper, is to remember that each individual year in a “record run” is linked to the others: “The years are not independent of one another,” they write. Rather than each individual record occurring of its own accord, the factors that influence temperature trends tend to overlap and blur from one year to the next.

The calculations can be taken as further evidence that human-caused climate change continues to exert an overwhelming influence on the Earth and is responsible for a long-term warming pattern that is only expected to continue in the future. The most recent news of 2015’s record-breaking status is just another confirmation.

“In summary, our results suggest that the recent record temperature years are are roughly 600 to 130,000 times more likely to have occurred under conditions of anthropogenic [climate change] than in its absence,” the authors wrote in the paper. “Our findings thus underscore the profound impact that anthropogenic forcing has already had on temperature extremes.”

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