The Philippines's Typhoon Haiyan and its appalling death toll is a terrible example of the increasing force of extreme weather events. Will it shatter complacency about climate change, and electrify the laborious UN ministerial negotiations that are taking place in Warsaw? Do not bank on it, but do not despair either.

Hurricane Katrina came and went in 2005, and Gallup found that Americans worried about climate change jumped from 51% to 62%. Since then, recession focused people on survival, and climate worries receded. In Maslow's hierarchy, basic needs always trump the far-off threat. With recovery and Hurricane Sandy, American public concern is rising again, and it's now at 58%.

Our own flash floods in the summer of 2007 cost £3.2bn – part of a pattern of rising storm damage – but the impact was soon eclipsed by the Climategate email scandal casting misplaced doubt on the science, and then by the recession. Public opinion has only just begun to turn around again, with YouGov finding a rising 56% believing in man-made climate change.

Ironically, economic recovery is allowing people to raise their sights to the climate threat, and none too soon. The new report from the UN Intergovernmental Panel on Climate Change assesses a 95% chance that climate change is man-made, a high enough risk to spur action in any other field of public policy.

If you were told that your house was virtually certain to burn down, you would think that an insurance premium costing 2% of your income in 2050 – Lord Stern's economic estimate of the cost of sorting carbon emissions – looked like a steal.

But what about the global warming pause much beloved by sceptics? There are always variations due to solar activity and other effects, but a new study by British and Canadian scientists Kevin Cowtan and Robert G Way casts doubt on any pause. It suggests that the global temperature rise of the last 15 years has been greatly underestimated.

The reason is the data gaps in the weather station network, especially in the Arctic. If you fill these data gaps using satellite measurements, the warming trend is more than doubled, and the pause disappears. The trend of the last decade looks exactly the same as the trend since the 1950s.

The problem is simple. If we are to hold the rise in global temperatures to 2C above pre-industrial levels – the point at which global damage becomes potentially catastrophic – we have to stop increasing our carbon emissions by the end of this decade, and then reduce them. This is still possible, despite the backsliding on the Kyoto protocol begun by the Canadians.

The Japanese, never keen on Kyoto, have announced they are reducing their carbon target due to a phasing out of low-carbon nuclear in the wake of the Fukushima disaster. They have been followed by the new rightwing Australian government, dumping the Labor coalition's flagship carbon tax. Both moves are causing understandable bad feeling among developing countries in Warsaw, but they are not yet fatal. Other countries are ramping up: the new German coalition, for instance, is likely to aim for 40% cuts in carbon emissions by 2030.

Targets are important, and so is the international agreement now promised for the Paris annual meeting in 2015, not least because it would kill the myth in so many countries that only they are tackling climate change. Why inconvenience ourselves when China is building new coal power stations by the month?

The reality is that China and the United States are continuing to take action. China's low-carbon zones are working. Its low-carbon nuclear energy programme is enormous: it is building another 30 reactors to add to its 17. Its renewable energy target is 15% of primary energy consumption by 2020, the same as the UK's modest contribution to the overall EU target of 20%.

The US federal government is tightening emission standards for coal generators. California is the world's twelfth-largest economy, and is responsible for vehicle standards that are driving electrification of cars. BMW's electric car range is a clear response to the inroads that the electric Tesla is making in this key market.

Both solar panels and onshore wind can, in the right sunny or windy conditions, be cheaper ways of generating electricity than fossil fuels. Solar panels are a quarter of their cost in 2008. Industry estimates suggests that solar will be cheaper (without subsidy) than other ways of generating electricity almost everywhere by 2020, and onshore wind even earlier.

But both solar and wind are intermittent, so a key is battery storage, which is still too expensive. With cheap batteries in the loft or the substation, home heat and light using low-carbon electricity will be attractive. It will open up a new path for developing countries, leapfrogging the need for costly grids and big power stations. In transport, batteries provide long ranges and quick charging for an upmarket luxury car like the Tesla, but the price will need to tumble to attract the mid-range Mondeo buyer.

The shape of low-carbon technology is increasingly clear. The issue is keeping up the pace of change to avert disaster. That means a global deal in December 2015 to curb emissions by 2020, however lopsided it may be. The US Senate will not find the two-thirds majority to ratify a treaty, but the Obama administration can and should make commitments backed up by domestic legislation.

A solution also means tackling the remaining obstacles to the electric economy, particularly batteries. As the EU, let's offer big money like the Longitude prize to spur research. Let's do joint EU-US research with real urgency, like the wartime Manhattan project to make the nuclear bomb.

We need to capture and store the carbon emitted by fossil fuels, or they must be competed out of existence. There has never been a change in the capitalist economy as potentially disruptive or which is likely to be so hard fought by vested interests. For the sake of the victims of Haiyan, and other disasters still to come, it can and must happen.