In April 2009, the science journal Nature published a paper entitled Greenhouse-Gas Emission Targets for Limiting Global Warming to 2 C.

Its subject was the end of the modern world.

At the time, it attracted little notice. It was a half-dozen pages long. For laymen, its technical content was impenetrable.

The purpose of the paper — researched and written by a team of European scientists headed by Malte Meinshausen, a climatologist with Germany’s Potsdam Institute for Climate Impact — was to determine just how much time mankind had left before our burning of fossil fuels would cause catastrophic global warming.

The marker for what would be considered “catastrophic” warming was generally agreed to be anything above a rise of two degrees Celsius in global temperature.

“More than 100 countries,” the paper noted, (the actual number was 167 countries) “have adopted a global warming limit of 2°C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages.”

The problem was, no one was exactly sure how much fossil-fuel consumption had already contributed to global warming, or how much fossil fuel mankind could consume without going over the two degrees Celsius marker. Those phenomena needed to be quantified.

Meinshausen’s team did just that. It constructed a rigorous model by incorporating hundreds of factors that had never been grouped together before, and then ran them through a thousand different scenarios.

The team’s conclusion?

Time was perilously short.

It found that if we continued at present levels of fossil fuel consumption (and, in fact, consumption has been rising annually), we have somewhere between an 11- to 15-year window to prevent global temperatures from surpassing the two degree Celsius threshold in this century.

And the longer we waited, the worse the odds got.

To quote from a story on the Meinshausen paper by reporter Katherine Bagley of the non-profit news agency, InsideClimate News:

“To have a 50-50 chance of keeping temperature rise below two 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-per-cent chance of avoiding that threshold, they would have to follow a stricter budget and emit just 886 gigatons.”

To put that in perspective, Meinshausen’s team calculated that the world’s nations had already produced 234 gigatons by 2006.

At our present rate, the paper predicted, the world will surpass that 886-gigaton figure by 2024 — or sooner, if annual consumption rates continue to rise as they have.

Since the Meinshausen paper was published, several other studies have corroborated its findings. The math in them comes to basically the same conclusion.

“Yes, I use Meinshausen’s study,” wrote Prof. Mark Jaccard, environmental economist at Simon Fraser University, in an email. “But I also use about five others that basically say the same thing. The reason they all say the same thing is because the math is trivial — no independent analysts dispute it.