Our results show that the currently attainable carbon fuel resources are sufficient to eliminate the Antarctic Ice Sheet and that large parts of the ice sheet are threatened at much lower amounts of cumulative emission.
German and US scientists have worked out how to melt almost all the ice in Antarctica, raise sea levels by 58 metres (disregarding other ice sheets , and flood cities that are now home to more than a billion people.
The answer is simple: just burn all the planet's remaining fossil fuel resources, which would pump another 10,000 Gt (billion tonnes) of carbon into the atmosphere in the form of the greenhouse gas, carbon dioxide.
But the release of carbon on such a scale would mean that sea levels could rise by three metres a century - and once the planet's average temperatures had risen beyond 2C, the process might be impossible to stop, according to a study published in the journal Science Advances.
It concludes: "Our results show that the currently attainable carbon fuel resources are sufficient to eliminate the Antarctic Ice Sheet and that large parts of the ice sheet are threatened at much lower amounts of cumulative emission.
"The successive sea-level rise far exceeds all other possible contributions from thermal expansion or ice loss from mountain glaciers or the Greenland Ice Sheet. Thus, if emissions of fossil-fuel carbon result in warming substantially beyond the 2°C target, millennial-scale rates of sea-level rise are likely to be dominated by ice loss from Antarctica.
"With unrestrained future CO2 emissions, the amount of sea-level rise from Antarctica could exceed tens of meters over the next 1000 years and could ultimately lead to the loss of the entire ice sheet."
Much larger loss
"Our findings show that if we do not want to melt Antarctica, we can't keep taking fossil fuel carbon out of the ground and just dumping it into the atmosphere as CO2, like we've been doing", says one of the report's authors, Ken Caldeira, an atmospheric scientist at Stanford University's Carnegie Institution for Science, California .
"Most previous studies have focused on the loss of the West Antarctic ice sheet. Our study demonstrates that burning coal, oil and gas also risks loss of the much larger East Antarctic ice sheet."
The report's lead author, Ricarda Winkelmann, climate system analyst at the Potsdam Institute for Climate Impact Research, says such action would cause global sea level rise on a scale unprecedented in human history.
"This would not happen overnight", she says, "but the mind-boggling point is that our actions today are changing the face of planet Earth as we know it, and will continue to do so for tens of thousands of years to come."
The study, although led by German scientists, started in Professor Caldeira's global ecology lab in the US, and in every sense bears his signature. It takes a big, simple idea, strips away all the difficult short-term questions, and follows it to a logical conclusion.
People working with Caldeira in the last two years have settled a number of such big and 'never before asked' questions - for instance, whether geo-engineering could save the Arctic ice cap (it would not).
Another such question is whether treating the ocean as a renewable energy source by exploiting the difference in temperature between warmers surface waters and colder deep waters - a technology known as ocean thermal energy conversion (OTEC) - would actually accelerate global warming (it would).
The same style of thinking has established that it could take just 45 days for the heat from released carbon dioxide to outpace the initial combustion that released it, and that at current fossil fuel emission rates, all the ocean's coral reefs would be at risk within this century.
The timing is no great surprise: the world's political leaders will gather at the UN climate change conference in Paris in December to decide on an international programme to limit global warming.
But though the question the scientists asked themselves is a simple one, it still involved some complex calculation.
"It is much easier to predict that an ice cube in a warming room is going to melt eventually than it is to say precisely how quickly it will vanish", Dr Winkelmann says.
"Our results show that the currently attainable carbon resources are sufficient to eliminate the Antarctic ice sheet, and that major coastal cities are threatened at much lower amounts of cumulative emissions.
"In a world beyond two degrees, long-term sea level rise would likely be dominated by ice loss from Antarctica."
And the bottom line of the latest research is really quite simple: unrestrained fossil fuel burning could cause extreme sea level rise over the next thousand years - and put crowded mega-cities such as New York, Tokyo, London, Shanghai and Calcutta at serious risk considerably sooner than that.
The paper: 'Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet' is by Ricarda Winkelmann, Anders Levermann, Andy Ridgwell & Ken Caldeira' and is published in Science Advances.
Tim Radford writes for Climate News Network. Additional reporting by The Ecologist.