By Richard Black BBC News environment correspondent

The team says it has found "the smoking gun"

The Earth is absorbing more energy from the Sun than it is giving back into space, according to a new study by climate scientists in the US.

They base their findings on computer models of climate, and on measurements of temperature in the oceans.

The group describes its results as "the smoking gun that we were looking for", removing any doubt that human activities are warming the planet.

The results are published in the journal Science this week.

The study attempts to calculate the Earth's "energy imbalance" - the difference between the amount of energy received at the top of the atmosphere from solar radiation, and the amount that is given back into space.

Rather than measuring the imbalance directly, the researchers draw on data from the oceans, in particular from the growing global flotilla of scientific buoys and floats, now numbered in the thousands, which monitor sea temperature.

Slow changes

"Measuring the imbalance directly is extremely difficult, because you are looking for a very small number on a background of very large numbers," Gavin Schmidt, one of the research team from the US space agency's (Nasa) Goddard Institute for Space Studies in New York, told BBC News.

What we are doing now is we are changing that imbalance at a rate which appears to be unprecedented over at least a thousand years Gavin Schmidt, Nasa

"But we know how much energy is going into the oceans - that has been measured and over the last 10 years confirmed by satellites and in-situ measurements - and from our understanding of atmospheric physics, that has to be equal to the imbalance at the top of the atmosphere."

So data gathered from the oceans is plugged into a computer model representing the Earth's complex climate, including the atmosphere, oceans, winds, currents, greenhouse gases and other "pollutants". What emerges is that at the top of the atmosphere, our planet is absorbing 0.85 watts more energy per metre squared than it is emitting into space.

The reason the extra energy is trapped, the researchers say, is the human-produced greenhouse effect - elevated levels of gases such as carbon dioxide that absorb radiation from the Earth's surface which would otherwise disappear into space.

Animated guide: Climate change

"This is almost unprecedented," said Gavin Schmidt. "The normal state of the atmosphere is that pretty much the same amount of energy that comes in leaves; and only when there are very large changes is that going to change.

"Historically, those changes have happened very slowly; but what we are doing now is we are changing that imbalance at a rate which appears to be unprecedented over at least a thousand years and possibly longer."

However, there is a time-lag between the absorption of energy at the top of the atmosphere and resultant heating of the oceans. The extra energy already trapped, according to the Nasa team, means that a global temperature rise of a further half a degree Celsius is inevitable, even if human production of greenhouse gases could be turned off tomorrow.

Sceptical view

Not everyone agrees with these conclusions. One scientist who disagrees is William Kininmonth, a former head of Australia's National Climate Centre and a member of Australia's delegations at various rounds of United Nations climate treaty negotiations.

"The paper implies that it is possible to estimate quite accurately the global radiation imbalance," he told BBC News; other researchers, he says, have "explained why it is not possible to measure the imbalance with an accuracy better than several watts per metre squared".

I do not believe this research team has made a compelling case to suggest that their computer models are sufficiently realistic William Kininmonth, Australian climate scientist

Like other "climate change sceptics", Dr Kininmonth believes too much reliance is placed on computer models rather than hard data.

"I do not believe this research team has made a compelling case to suggest that their computer models are sufficiently realistic to justify the implications of anthropogenic (human-induced) global warming that they make," he said.

But Damian Wilson, manager of clouds and radiation parameterisation at the UK's Meteorological Office, was more enthusiastic.

"The computer model matches temperature changes at the Earth's surface quite well - but that alone doesn't prove it's right," he said.

"Having a model that also matches ocean heat uptake well suggests that the model is doing a pretty good job. I wouldn't like to say the research proves that 0.85 watts per metre squared is the right figure, but it does give us more confidence that the models are doing a good job of producing a reasonable simulation of the energy imbalance."

Computer climate models have grown much more sophisticated over the years. But there are still problems modelling some atmospheric processes, notably heat convection within clouds.