On 10 May 2013, the concentration of climate-warming carbon dioxide in the atmosphere passed the milestone level of 400 parts per million for the first time in human history. The last time so much greenhouse gas was in the air was several million years ago, when the Arctic was ice-free, savannah spread across the Sahara desert and sea level was up to 40 metres higher than today.

The milestone moment was a sobering reminder that the emission of globe-warming gases is continuing unabated, despite ever more certainty that the burning of fossil fuels and deforestation is on track to end the millennia of relatively stable climate during which human civilisation has flourished.

In September, a landmark report on climate change science from the Intergovernmental Panel on Climate Change (IPCC) concluded it was "unequivocal" that global warming was the result of human actions. Its authors said that, without "substantial and sustained" emissions reductions, the 2C limit set by the world's governments would be breached, resulting in heatwaves, droughts and more extreme weather. Ban Ki-moon, the UN secretary general, urged world leaders to pay heed to the "world's authority on climate change" and forge a new global deal on cutting emissions. "The heat is on. Now we must act," he said.

Ban Ki-moon, the UN secretary general, addresses the United Nation's Intergovernmental Panel on Climate Change via video link. 'The heat is on. Now we must act,' he said. Photograph: Jonathan Nackstrand/AFP/Getty Images

John Kerry, the US secretary of state, said: "This is yet another wake-up call: those who deny the science or choose excuses over action are playing with fire."

The IPCC report, compiled by hundreds of the world's climate experts, was the first for five years and also stated that sea levels are expected to rise a further 26-82cm by 2100, though a significant number of scientists think this is an underestimate. The IPCC also warned of the increasing acidification of the oceans as it absorbs CO2, with an October report finding the seas are becoming more acidic at the fastest rate in 300 million years and a mass extinction of species may already be almost inevitable.

The so-called "pause" in climate change – a slowing of the global air temperature rise over the last 15 years – was dismissed by IPCC co-chair Thomas Stocker, who said climate trends "should not be calculated for periods of less than 30 years." Other scientists noted that excess heat has continued to be trapped by greenhouse gases and that just 1% of it heats the atmosphere, compared to 93% that warms the oceans. Another much-discussed issue – how sensitive the climate is to increases in atmospheric CO2 – turned out to make little difference to the temperature rises projected by the IPCC.

Excess heat has continued to be trapped by greenhouse gases and 93% warms the oceans. Photograph: Joe Raedle/Getty Images

The most controversial part of the IPCC report was its first statement on how much more CO2 humans can pour into the atmosphere without triggering dangerous levels of climate change – and the conclusion that more than half of that "carbon budget" has been used up.

"There's a finite amount of carbon you can burn if you don't want to go over 2C," said Stocker. "That implies if there is more than that [in fossil fuel reserves], that you leave some of that carbon in the ground."

The climate economist Lord Stern and others had warned in April of the risks of a "carbon bubble", because two-thirds of the fossil fuel reserves underpinning the value of oil, gas and coal companies will have to remain underground to keep warming under 2C. "The financial crisis has shown what happens when risks accumulate unnoticed," said Stern, who added that the risk was "very big indeed" and that almost all investors and regulators were failing to address it.

The consensus of climate scientists on the cause of global warming had been emphasised in May, when a study of thousands of research papers published between 1991 and 2011 showed 97% endorsed human-caused global warming.

The annual meeting of the UN's climate body, the UNFCCC, took place in November in coal-friendly Poland. Photograph: Jenny Bates

This consensus on the science was not matched by consensus on a political deal to tackle climate change. The annual meeting of the UN's climate body, the UNFCCC, took place in November in coal-friendly Poland, and concluded by sending nations away to "do their homework" ahead of a deadline for a global deal in 2015. The critical question: which nations should cut their emissions and by how much?

Australia attracted criticism after its new government, led by Tony Abbott – who has called climate change "crap" – failed to send a minister to the UN climate talks but set about dumping the country's nascent carbon tax. Meanwhile, Australia's spring was the warmest on record.

Anti-carbon tax protesters in Australia. Photograph: Torsten Blackwood/AFP/Getty Images

However, the big two global emitters – China and the US together cause 40% of emissions – provided brighter news when agreeing in July to expand their joint efforts against climate change, a move seen as raising the prospects for an eventual global climate deal. The agreement covered cleaner vehicles, carbon capture technologies, energy efficiency and smart grids.

2013 also saw China establish carbon trading schemes in Beijing, Shanghai and Shenzhen, which may help address appalling air pollution problems. Such schemes, where permits to pollute are traded are seen by many as the cheapest way of cutting emissions but the world's biggest scheme – the EU's – saw only modest progress in addressing the glut of permits that is holding the carbon price at rock-bottom levels.

In the UK, the coalition fought over green policies, with the prime minister, David Cameron, reported as saying he wanted to get rid of all the "green crap" – the environmental levies charged on energy bills. In contrast, the deputy prime minister, Nick Clegg, said: "We will do everything we can to strengthen the role of the low-carbon sector in the new economy." In December, the government's official advisers on climate change told ministers there was no evidence supporting the weakening of emissions targets in a review demanded by the chancellor, George Osborne.

(L-R) Britain's opposition Labour party leader, Ed Miliband, deputy prime minister, Nick Clegg, and prime minister, David Cameron. Photograph: Toby Melville/Reuters

Perhaps the most unusual place that scepticism about climate change turned up was in the Twitter feed of one of the UK's largest rail companies, First Capital Connect. When a passenger questioned why the company was using outdoor heaters on mild October day, one of its social media team lost his cool, tweeting back that the science underpinning climate change had been "shattered" by reports and the climate had always changed naturally. The "deeply sorry" company deleted the offending tweet.