"The press reports last year about the unlikely nature of recent global temperature records raised some very interesting questions, but the scientists quoted hadn't done a rigorous calculation," said Michael Mann, distinguished professor of meteorology and director, Earth System Science Center, Penn State. "As a result, the probabilities reported for observing the recent runs of record temperature by chance alone were far lower than what we suspected the true probabilities are. "

Although the new odds of chance producing recent runs of record temperatures are greater than the odds previously reported in the news -- between 1 in 27 million and 1 in 650 million -- they are still incredibly slim at between 1 in 5 thousand and 1 in 170 thousand. Including the data for 2015, which came in after the study was completed, makes the odds even slimmer.

The reason for the inaccuracy of the previous probability calculations is that the individual yearly temperatures analyzed are not independent of each other.

"Natural climate variability causes temperatures to wax and wane over a period of several years, rather than varying erratically from one year to the next," said Mann.

In calculating the odds, the previous reports did not take into account that the data did not end simply because December 31 occurred, but that trends overlap into previous and subsequent years. This needs to be taken into account to determine the real probabilities of chance causing the warming events.

"We provided a method for doing this based on combining information from state-of-the-art climate model simulations with the observational temperature record, and we used this method to estimate the probabilities correctly," said Mann.

Using a combination of observations and climate model simulations, the researchers examined temperatures from both the Northern Hemisphere and the entire globe for specific groups of years. They examined scenarios for record warm years of 1998, 2005, 2010 and 2014; for nine of the 10 warmest years occurring since 2000; and for 13 of the warmest 15 years occurring since 2000. They chose the last two scenarios because these are the ones previously reported in news accounts.

The reason that Mann's team found the probability of naturally occurring global warming more likely than previously reported, is that the effective size of their statistical sample was considerably smaller than estimates based simply on the number of years available. This "serial correlation" means that the chance likelihood of runs of warm temperature -- nine very warm years over the course of a decade -- is much greater than if temperatures were uncorrelated from one year to the next.

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Odds are overwhelming that record heat due to climate change