Coastal cities across the world are threatened by rising sea levels, but a new study has found that we might be significantly underestimating the risk.

The study, published in the journal Nature, shows that Antarctica’s ice cap is less stable than previously thought and sea levels could rise more rapidly than predicted.

Previous studies had predicted sea level rises of up to a metre this century, however these projections failed to anticipate any significant contribution from Antarctic ice.

Only passive melting of the Antarctic by warmer air and seawater are taken into account. However this new study considers the possibility of more active processes, such as disintegration of ice cliffs.

The researchers ran models that found rising levels of greenhouse gases could trigger an increase in Antarctic melting.

This increase would double the previously expected sea level rise to a two-metre rise by the end of the century.

Worst case scenarios predict a 13-metre rise in sea levels by 2500, solely from Antarctic melt.

However, the model also found that a global commitment to the most ambitious goals set out in the 2015 Paris agreement on climate change would halt this melting, leaving the Antarctic ice sheet largely intact.

“The bad news is that in the business-as-usual, high emissions scenario, we end up with very, very high estimates of the contribution of Antarctica to sea level rise,” said Professor Robert DeConto of the University of Massachusetts Amherst and lead researcher on the study.

If emissions were reduced quickly to zero the rise of sea levels caused by melting Antarctic ice would be cut to almost nothing. However DeConto notes that while this reduction would be good news, “we can’t say we are 100% out of the woods”.

Even with a significant reduction in emissions there is a chance that the damage has been done already, and sea levels might still rise dramatically.

Sea level rises like these would have a devastating effect on low-lying coastal cities, with the possibility of increases per year changing from millimetres to centimetres. “At that point it becomes about retreat, not engineering of defences,” DeConto says.

With the combined effect of sea level rises and fiercer storms caused by climate change, coastal cities such as New York, Mumbai and Guangzhou are at greater risk.

The cost of global flood damage is expected to rise to more than $1 trillion by 2050 unless action is taken, with many cities in less wealthy countries being prone to flood damage.

The World Bank notes that in many of the most vulnerable cities, the poor are most at risk when it comes to floods. “Rapid urbanization has pushed them into the most vulnerable neighbourhoods, often in low-lying areas and along waterways prone to flooding,” DeConto says.