It is probably the most influential paper on climate science today. But few outside scientific circles even know it exists.
Though just six pages long, its dense, technical writing makes it largely incomprehensible to non-experts. And yet this paper is transforming the climate change debate—prompting the financial world to rethink the value of the world's fossil fuel reserves and giving environmental activists a moral argument for action.
That's because behind its complicated terminology is a simple question that affects every aspect of society and business: How much time do we have before the burning of fossil fuels pushes the climate system past tipping points? In a worst-case scenario, about 11 years at current rates of fossil fuel use, according to the paper.
"Once you hear the numbers, at least for me, there is no more room for wishful thinking, for speculation or for doubt," said Bill McKibben , founder of the activist group 350.org . Last year, McKibben plucked the science from popular obscurity and used it in a Rolling Stone article  and speaking tour to stoke the moral case for carbon controls.
The paper, "Greenhouse-Gas Emission Targets for Limiting Global Warming to 2C ," was published in April 2009 in Nature, the prestigious science journal. It was the work of researchers from Germany, the UK and Switzerland, led by Malte Meinshausen , a climatologist at Germany's Potsdam Institute for Climate Impact .
The study filled a factual void in a simmering debate over climate change. By 2006, the year the scientists began their research, many world governments had endorsed the scientific consensus that global temperature rise should be kept below 2 degrees Celsius in this century. But governments didn't know how far down the path of global warming they had already gone—and how much further they could safely go.
Meinshausen and his team, which included his brother Nicolai, a statistician at the University of Oxford, took up the puzzle. "It seemed the obvious thing to do with so many governments asking the question," Meinshausen said.
The scientists created what is called a global "carbon budget," which details how much carbon countries have emitted in the atmosphere from burning coal, oil and natural gas—and how much more they can "spend" before crossing 2 degrees. They didn't invent the concept—many others had crunched carbon budgets. But none were as rigorous.
The paper's methodology was groundbreaking. It was the first to incorporate hundreds of uncertainties in the climate system into a single climate model—factors that had never been modeled together or that hadn't been given proper weight in previous studies, such as radiative forcing or unknowns in the carbon cycle like how much carbon is stored in the deep ocean. In total, 400 environmental parameters were run under 1,000 different emissions scenarios.
What they found was stark: To have a 50-50 chance of keeping temperature rise below 2 degrees, humans would have to stick to a carbon budget that allowed the release of no more than 1,437 gigatons of carbon dioxide from 2000 to 2050.
To have an 80 percent chance of avoiding that threshold, they would have to follow a stricter budget and emit just 886 gigatons.
The paper found that by 2006, nations had already spent a quarter of that amount, or 234 gigatons. Meaning, the planet's carbon budget would be exhausted by 2024—11 years from now— if emissions levels stayed the same, or even earlier if they continue their upward trend.
From a scientific point of view, burning all of the world's proven fossil fuel reserves isn't an option, the paper suggested. The reserves "vastly exceed the allowable CO2 emission budget for staying below 2C" of warming, it said.
In 2009, the findings were used by the International Energy Agency  (IEA), a policy group that advises 28 countries about their energy policies, to make the case for steep reductions in climate-changing gases. "We are currently eating into these CO2 budgets at a disproportionate rate," the authors wrote in its World Energy Outlook  that year.
Less than four years later, the paper is one the most cited environmental science studies ever. To date, it has garnered 262 citations in scientific articles, according to Web of Science , an online citation index run by media conglomerate Thomson Reuters, putting it in the top 0.1 percent cited environmental papers in recent years, and just missing being among the top 0.01 percent. The paper has racked up more than 600 citations in Google Scholar, a more inclusive citation index that includes mentions in books, professional societies and on university websites.
Christopher King, editorial content manager of Thomson Reuters' ScienceWatch , a site that tracks trends in research, said it "unquestionably ranks among the elite."
In science, that many citations reflects a rare consensus, according to Gavin Schmidt , deputy chief of the NASA Goddard Institute for Space Studies  and a climate modeler. He said that while a few minor details in the paper have raised discussion, the overall results are widely accepted.
After impressing scientists, it wasn't long before the findings rippled through the global financial world.
For years, investors had been hearing of carbon budgets and the 2-degree threshold—and they were growing concerned. As much as 30 percent of the value of some of the world’s stock exchanges is in proven coal, oil and gas reserves, which energy companies are banking on mining and selling one day.
But what if governments buckled to activist pressure and decided to require firms to keep some of those reserves in the ground? What would that do to the market values of powerful energy companies? What would that do to the world's financial systems?
A newly formed group, made up of green-minded investors in London and called the Carbon Tracker Initiative , sought to assess those risks in a scientific way. They used Meinshausen's paper as the basis of their own report, "Unburnable Carbon ," published in 2011.
The report tackled a question that Meinshausen had answered, but not in any depth: How much CO2 is in the world's fossil fuel reserves?
Using official records from U.S. Securities and Exchange Commission filings, among other documents, Carbon Tracker discovered that the world's top 200 fossil fuel companies have 2,795 gigatons of CO2 trapped in their fossil fuel reserves. And that figure didn't include unconventional sources like tar sands, oil shale and methane hydrates.
They also found that in the first 10 years of this century, humans had burned through one-third of Meinhausen's 886 gigaton budget, leaving just 565 gigatons left to use over the next 40 years. In sum, 80 percent of all fossil fuel reserves would have to remain untouched to prevent uncontrollable warming, the report warned.
"Investors need to be wary that stocks may not hold the same value they once did—and companies need to stop putting more capital into finding more reserves," James Leaton, research director for the Carbon Tracker Initiative, said. "The future won't resemble the past for these industries."
"Unburnable Carbon" was the first, but not the last, study to consider whether energy companies' values were based on assumptions that might never pan out. Last month, global banking giant HSBC released a similar report  using Meinshausen's 50-50 carbon budget scenario. It found that the largest oil and gas companies, including BP, Shell and Statoil, could lose 60 percent of their market values if governments proceed with tough carbon reduction targets and force companies to leave reserves untapped.
McKibben Popularizes the Science
Bill McKibben, a mild-mannered college professor and one of the nation's original climate activists, heard about Meinshausen's findings in 2009. But it wasn't until he read "Unburnable Carbon," and saw just how much coal, oil and gas energy companies have in their reserves, that he decided to make the numbers the cornerstone of a campaign to break Washington's silence on climate change.
First, he repackaged Meinhausen's science and the investors' math into a Rolling Stone article called "Global Warming's Terrifying New Math ." In November, he launched a Do the Math tour  to introduce the public to the numbers.
In a month, McKibben and members of his grassroots organization, 350.org , traveled to 21 cities by biodiesel bus and held rock concert-like events before sold-out audiences to try to make decarbonization of the economy a moral issue.
"It made people understand they are going to have to intervene in a more powerful way," McKibben said of the math.
The Do the Math campaign spurred a resurgence of climate advocacy in America that includes a divestment movement , sponsored by 350.org. Students at 252 universities in North America have asked their schools to divest their endowments of fossil fuel companies, and a few have agreed. Several faith-based organizations are also considering divestment , as are some municipal governments, including the City of Seattle.
The group says its #ForwardOnClimate rally on February 17 at the White House against the Keystone XL oil pipeline could be the biggest climate change rally ever in the United States.
President Obama vowed in his State of the Union speech Tuesday night  "to reduce pollution" and "prepare our communities for the consequences of climate change." But it's unclear what action he might take.
He faces difficult decisions in his second term that could change the national energy landscape for decades and increase global temperatures, including on Keystone XL, Arctic oil drilling and natural gas fracking. McKibben said he is using the science and the math to urge supporters to force Obama to draw a line in the sand on those mega-projects and plans.
What's been surprising, McKibben said, is "the fossil fuel industry and skeptics haven't done the slightest thing to say the math isn't true."
Roger Pielke Jr. , an environmental studies professor at the Center for Science and Technology Policy Research at the University of Colorado Boulder, said any criticism about the campaign "has nothing really to do with the science," but more "about the campaign as an incomplete set of policy arguments."
John Felmy, the chief economist for the American Petroleum Institute , the oil industry's main trade group, agreed.
"Oil, gas and coal are going to be used for the foreseeable future. It's inevitable. Instead of talking about an improbable fossil fuel scenario, we need to have a rational discussion about energy policy ... focusing on things like improving efficiency."
Meinshausen said it's common for non-scientists to misuse or exaggerate scientific results, so there's always concern among researchers when their findings are used for advocacy. But, he said, he and his colleagues have been pleased with how McKibben and 350.org have used the numbers to incite action.
"I wouldn't agree necessarily with every wording [the campaign uses]," Meinshausen said. "But the basic message—that we have a finite carbon budget, that we have much more in the ground than we can afford to burn if we want to avoid dangerous climate change—I think all this is uncontroversial."
Leaton of the Carbon Tracker Initiative said he isn't surprised by the popularity of McKibben's efforts.
"The way the campaign has framed these issues makes it easy for anyone who has ever balanced a budget to understand the problem ... When you run out of money, that's it, you’re out. When we've burned through the carbon budget, that's it, we can't afford for the sake of our planet to use more."
Correction: An earlier version of this article said that Meinshausen's paper didn't account for short-lived gases like methane, and that the omission had raised discussion among scientists. The model does account for short-lived gases, and the discussion has been about whether the emission levels of such gases and their impact on the climate system will change over time.