Samar Khatiwala's description of the 'ocean carbon problem' is deceptively simple. A scientist, he says, cannot simply scoop up a water sample and tell how much of the carbon in it came from carbon dioxide released by human activities and what fraction is the naturally dissolved carbon. But he and his colleagues have now found a way to tackle the problem, using not-so-simple maths (see page 346).

The oceans absorb roughly a quarter of the CO2 released into the air from the burning of fossil fuels, making them the most important sink for this greenhouse gas. Previously, scientists tried to back-calculate the amount of anthropogenic carbon in the oceans by subtracting the level of natural carbon from the total dissolved carbon. But that involved assumptions about poorly understood biological and geochemical processes acting on natural carbon — and resulted in much disagreement between calculations.

As a result, Khatiwala, an oceanographer at the Lamont-Doherty Earth Observatory of Columbia University in Palisades, New York, and his colleagues, decided to ignore the natural carbon and measure only the signal of the carbon released by humans.

Because the amount of carbon in the oceans from this source is tiny compared with the amount of natural carbon, they decided to treat it as a conservative tracer — something carried passively through the ocean by circulation. They knew that a differential equation called the advection-diffusion equation describes how certain chemical tracers move around the ocean, and that this equation can be solved using a Green's function, named after the nineteenth-century British mathematician George Green. “If we could treat man-made CO2 as a conservative tracer in its own right, then we could apply all this mathematical machinery to the ocean carbon problem,” says Khatiwala.

To be able to do this, they first had to infer the ocean's Green's function from observations of the distribution of other conservative tracers. The next piece of the puzzle was obtaining measurements of the ocean-surface history of carbon released by human activities. This history turned out to have a simple relationship to the amount of anthropogenic carbon in the atmosphere, data that go back to the start of the industrial period.

With all the pieces in hand, the team reconstructed the amount of anthropogenic carbon in the oceans from 1765 to 2008. The study revealed that the Southern Ocean around Antarctica absorbs a much bigger chunk of emissions than was previously appreciated, about 40% of the total. It also showed that the ocean's uptake rate has increased sharply since the 1950s, when emissions started rising. But this increase slowed between 2000 and 2008, while emission rates rose by a factor of three.

“That means more emissions are remaining in the atmosphere, as a smaller proportion is taken up by the ocean. That was really very surprising,” says Khatiwala. There are competing hypotheses as to why the uptake rate is falling off; Khatiwala says he favours a fairly simple explanation — the limits of ocean chemistry. “As the ocean absorbs more carbon it becomes acidic and can hold less CO2. Plus, ocean uptake is a relatively sluggish process. If emissions grow too rapidly, then the oceans cannot keep up.”