OSLO, Nov 30 (Reuters) - Climate scientists are tracking an erupting volcano on the Indonesian holiday island of Bali for clues about a possible short-cut to curb global warming by injecting sun-dimming chemicals high above the Earth.

Volcanoes are emerging as natural laboratories to mimic "geo-engineering", the idea that governments could deliberately add a veil of sulphur dioxide high above the planet as an artificial sunshade to curb man-made global warming.

Ash and smoke ejected so far by the Agung volcano, which has been erupting in recent days, has not been big enough or high enough in the atmosphere to cool world temperatures. But scientists say they are studying what would happen if the volcano has a repeat of a far bigger eruption in 1963.

"I've been doing some Bali simulations with the U.K. Met office climate model as 'what ifs', and also some geo-engineering simulations," said Jim Haywood, professor of atmospheric science at the University of Exeter.

He estimated that Agung spewed eight million tonnes of sulphur dioxide into the stratosphere in 1963, about 10-15 kms above the Earth's surface, enough to trim world temperatures for months. That eruption killed more than 1,000 people in Bali.

"Many scientists are keeping an eye on the Agung eruption in Bali," said Alan Robock, a professor of climate science at Rutgers University. "Volcanic eruptions serve as an analogue for the idea of humans creating such a cloud."

Satellite measurements of eruptions have only recently become precise enough to exploit volcanoes as models for geo-engineering.

That was impossible, for instance, when Mount Pinatubo in the Philippines erupted in 1991 and blew about 20 million tonnes of sulphur dioxide into the stratosphere, the second biggest eruption of the 20th century after one in Alaska in 1912.

Mount Pinatubo had a cooling effect on the Earth because the sun-dimming sulphur spread worldwide.

"Since Pinatubo we've got a lot better" at measuring the effects of big eruptions, said Matthew Watson of the University of Bristol. "We're waiting for something to happen on a scale where we can start thinking about what it means for geo-engineering."

He estimated that the Agung volcano has probably ejected only about 10,000 tonnes of sulphur dioxide in the latest eruption, and not as high as the stratosphere.

Governments agree they should focus most on cutting greenhouse gas emissions under the 2015 Paris agreement rather than on science-fiction-like short-cuts to limit temperatures blamed for causing more heatwaves, floods and rising sea levels.

But current policies put the world on track to overshoot the Paris goal of limiting rising temperatures to "well below" two degrees Celsius (3.6 Fahrenheit) above pre-industrial times.

U.S. President Donald Trump, who doubts man-made emissions are the prime cause of warming, also plans to pull out of the Paris deal and promote the U.S. fossil fuel industry. That risks further weakening the Paris plan.