Muller's research team carefully examined two chief criticisms by sceptics. One is that weather stations are unreliable; the other is that cities, which create heat islands, were skewing the temperature analysis.
"The sceptics raised valid points and everybody should have been a sceptic two years ago. And now we have confidence that the temperature rise that had previously been reported had been done without bias."
Muller said that he came into the study "with a proper scepticism", something scientists "should always have. I was somewhat bothered by the fact that there was not enough scepticism" before.
There is no reason now to be a sceptic about steadily increasing temperatures, Muller wrote recently in the Wall Street Journal. Muller did not address in his research the cause of global warming. The overwhelming majority of climate scientists say it is man-made from the burning of fossil fuels such as coal and oil.
It makes sense to reduce the carbon dioxide created by fossil fuels, he said. "Greenhouse gases could have a disastrous impact on the world." He contends that threat is not as proven as the Nobel Prize-winning Intergovernmental Panel on Climate Change says it is.
Today, Muller is taking his results - four separate papers that are not yet published or peer-reviewed, but will be, he says - to a conference in Santa Fe, New Mexico.
Shawn Lawrence Otto, author of the book Fool Me Twice that criticises science sceptics, said Muller should expect to be harshly treated by global warming deniers. "Now he's considered a traitor. For the sceptic community, this isn't about data or fact. It's about team sports. He's been traded to the Indians. He's playing for the wrong team now."
Muller's study found that sceptics' concerns about poor weather station quality did not skew the results of his analysis because temperature increases rose similarly in reliable and unreliable weather stations. He also found that while there is an urban heat island effect making cities warmer, rural areas are warming, too.
"After lots of work he found exactly what was already known and accepted in the climate community," said Jerry North, a Texas A&M University atmospheric sciences professor.
Chris Field, a Carnegie Institution scientist, said Muller's study "may help the world's citizens focus less on whether climate change is real and more on smart options for addressing it".
Some of the most noted scientific sceptics are no longer saying the world isn't warming. Instead, they question how much of it is man-made, view it as less a threat and argue it's too expensive to do something about, according to Otto.
Sceptical MIT scientist Richard Lindzen said it was a fact and nothing new that global average temperatures had been rising since 1950, as Muller shows. "It's hard to see how any serious scientist will view it otherwise."
AP