By calculating calcium carbonate levels back to the Industrial Revolution, their study has shown that the burning of fossil fuels is raising levels of carbon dioxide, causing a reaction that erodes the reefs.
Calcium carbonate is the foundation of coral reefs, produced by tiny reef-dwelling creatures called coral polyps. However, rising levels of carbon dioxide in the atmosphere are causing the sea to become more acidic as the gas is absorbed by the water.
This tends to dissolve calcium carbonate, making reef formation more difficult. In the next century, levels of carbon dioxide in the atmosphere are expected to reach double the level that they were before the Industrial Revolution, when human beings first began to burn fossil fuels on a big scale. The result may be that live reefs become increasingly fragile, and may stop growing.
Coral reefs support what is thought to be the world's richest eco-system, as well as a $500bn (pounds 300bn) fishing and tourism industry. Global warming has already killed most of the corals in the Indian Ocean, and in areas of the western and eastern Pacific.
"We calculate that the precipitation of calcium carbonate has already decreased 6 to 11 per cent since the Industrial Revolution, and would decrease another 8 to 17 per cent if carbon dioxide levels double their pre-industrial values," said Dr Joan Kleypas of the National Center for Atmospheric Research in Boulder, Colorado, who led the research team.