But as global warming heats the surface layer of the ocean it becomes lighter and therefore separated from the cooler depths from which the phytoplankton get many of their nutrients.

This cuts their numbers, not only reducing the food in the oceans but slashing the amount of carbon dioxide they take from the air and therefore accelerating the climate warming process.

"Rising levels of carbon dioxide in the atmosphere are a key part of global warming," said lead researcher Michael Behrenfeld.

"This study shows that as the climate warms, phytoplankton production goes down, but this also means that carbon dioxide uptake by ocean plants will decrease ... making the problem worse," he added.

Despite their tiny size, phytoplankton account for about half of the photosynthesis on Earth -- converting vast quantities of atmospheric carbon dioxide into organic carbon as food for the planet's marine ecosystem.

The study, published in the science journal Nature, comes from a decade-long analysis of the oceans by NASA's SeaWiFS satellite which measured the changing colours of the waters caused by changing levels of phytoplankton.

The higher the concentrations of these tiny plants, the greener the water.

The scientists -- who also came from the University of California/Santa Barbara, Princeton University, Rutgers University and the University of Maine -- found local variations but a global drop in numbers with higher temperatures.

"This clearly showed that overall ocean productivity decreases when the climate warms," Behrenfeld said.

Scientists predict that global temperatures will rise by between two and six degrees Celsius by the end of the century, due mainly to carbon dioxide from burning fossil fuels for power and transport.

But they also fear that beyond two degrees of warming the planet's climate could trip the so-called feedback mechanism with the rising heat releasing even more greenhouse gases than being produced by human activities.

A comprehensive study last month by former World Bank chief economist Nicholas Stern found that acting now to tackle climate change could cost one percent of global economic output -- a figure that rises 20-fold if action is delayed.