By Jeremy Hance / Mongabay

A recent rise in deadly, debilitating, and expensive heatwaves was caused by climate change, argues a new statistical analysis published in the Proceedings of the National Academy of Sciences (PNAS). Climatologists found that extreme heatwaves have increased by at least 50 times during the last 30 years. The researchers, including James Hansen of NASA, conclude that climate change is the only explanation for such a statistical jump.

“This is not a climate model or a prediction but actual observations of weather events and temperatures that have happened,” Hansen, a prominent scientist and outspoken climate change activist, wrote in an op-ed in the Washington Post. “Our analysis shows that it is no longer enough to say that global warming will increase the likelihood of extreme weather and to repeat the caveat that no individual weather event can be directly linked to climate change. To the contrary, our analysis shows that, for the extreme hot weather of the recent past, there is virtually no explanation other than climate change.”

Between 1981 and 2010, extreme heatwaves covered 10 percent of the world, according to the paper, which is 50 to 100 times greater than the 0.1 percent to 0.2 percent of the Earth’s surface covered by extreme heat from 1951-1980. The analysis not only finds that extreme heatwaves (defined as over three standard deviations above the base period) have expanded due to a warming world, but that moderate heat (over half of a standard deviation) has more than doubled: jumping from 33 percent to 75 percent. Many climatologists refer to this phenomenon as “loading the climate dice.”

“In a normal climate without global warming, two sides of the die would represent cooler-than-normal weather, two sides would be normal weather, and two sides would be warmer-than-normal weather. Rolling the die again and again, or season after season, you would get an equal variation of weather over time,” Hansen explains in his op-ed. But now he says, climate change has shifted the dice: instead of only two sides being warmer than average, it should be four sides with one of those sides representing extreme heat.

“The climate dice are now loaded to a degree that a perceptive person old enough to remember the climate of 1951–1980 should recognize the existence of climate change, especially in summer,” the scientists write in the PNAS paper. Given their findings, the researchers also argue it is safe to say that recent heatwaves—like last year’s drought in Texas and Oklahoma, Russia’s heatwave and wildfires in 2010, and the European heatwave of 2003—were caused by climate change.

“[These events] almost certainly would not have occurred in the absence of global warming with its resulting shift of the anomaly distribution,” the scientists write. “In other words, we can say with high confidence that such extreme anomalies would not have occurred in the absence of global warming.”