"We close this window if we follow another decade of ballooning global greenhouse-gas emissions."
Coral reefs are home to almost a quarter of the world's ocean species, they provide coastal protection and can support tourism and fishing industries for millions of people worldwide.
The rise of global average temperatures, warmer seas and the spread of ocean acidification due to greenhouse gas emissions, however, pose major threats to coral ecosystems.
The scientists from the Potsdam Institute for Climate Impact Research, the University of British Columbia and the universities of Melbourne and Queensland in Australia used climate models to calculate the effects of different emissions levels on 2,160 reefs worldwide.
World carbon dioxide emissions increased by more than 3 per cent last year and global average temperatures have risen by about 0.8 degrees Celsius over the past century.
Coral reefs face serious threats even if global warming is restricted to a 2 degrees Celsius limit, which is widely viewed as a safe threshold to avert the most devastating effects of climate change, such as drought, sea level rise or crop failure.
Warmer sea surface temperatures are likely to trigger more frequent and more intense mass coral bleaching, which is when reefs turn pale, the study said.
Although corals can survive bleaching, if the heat persists they can die. This happened in 1998 when 16 per cent of corals were lost in a single, prolonged period of warmth worldwide.
Ocean acidification can put even more stress on corals.
As more and more carbon dioxide is absorbed from the atmosphere, sea water turns more acidic which can hinder calcification which is crucial for corals' growth.
"Thus, the threshold to protect at least half of the coral reefs worldwide is estimated to be below 1.5 degrees Celsius mean temperature increase," the study said.
A separate report last week said Caribbean corals were under immediate threat and urgent action was needed to limit pollution and aggressive fishing practices.
Average live coral cover on Caribbean reefs has declined to just 8 per cent today compared to more than 50 per cent in the 1970s, according to the report by the International Union for Conservation of Nature.