Millions of words have been written about the new report from the Intergovernmental Panel on Climate Change (IPCC). But for me, two key messages stand out – one for its importance, the other for its lack of importance, relative to the attention that it has received. Since our interactive graph about temperatures in your lifetime has generated so much interest, I thought I'd do a graph to explain each of these two points too.

The thing that doesn't matter (much): revisions of climate sensitivity

Commentators such as Matt Ridley and David Rose who are keen to play down the importance of climate change, plus the editorial team at the Economist, have made a lot of noise about the fact that the new IPCC report contains reduced estimates for the 'sensitivity' of the climate to increased levels of greenhouse gas in the air.

Any evidence that the climate is less sensitive to carbon than we previously thought is good news: it means we can expect less warming from any given carbon concentration, reducing the risk of dangerous impacts. But as my first graph makes clear, the gains are actually rather small. It shows four IPCC emissions scenarios, from the highest (RCP 8.5, which so far reflects business as usual) to the lowest (RCP 3PD, which involves actions well beyond the scope of what is currently seen as politically plausible, with emissions falling steeply almost straight away and humans becoming carbon negative later in the century). For each scenario, the graph allows you to compare future warming based on estimates of the climate's sensitivity from the previous and new IPCC reports. The conclusion: this is really no game changer. On current emissions trends, it means global warming of up to 6C rather than 7C over the next century, relative to preindustrial levels. With low emissions, it's the difference between an upper-end warming of around 3.5C and 3C in the same timeframe – an improvement, yes, but hardly reassuring.

For those wanting to understand the numbers on the graph, the sensitivity of the climate to CO2 is usually described in terms of two factors: the transient climate response (TCR), which is the amount of warming that we can expect by the time that carbon emissions reach double their preindustrial levels; and equilibrium climate sensitivity (ECS), which is the (larger) temperature rise that would ultimately ensue if those doubled CO2 concentrations persisted long enough for the world to settle into a new stable state. Neither TCR nor ECS can be precisely pinned down; instead scientists estimate upper and lower values for each. The new IPCC report revised down the upper estimate of TCR and the lower estimate of ECS. One climate scientist summed up the importance of these changes to me succinctly: "Which one matters? Well, neither of them, if we're honest."

One key thing to understand about TCR and ECS is that a doubling of preindustrial CO2 levels is just a convenient but arbitrary point for scientists to use for their calculations. No-one is saying that doubled CO2 has any relation to what's actually going to happen. Worryingly, the UK's environment minister Owen Paterson appears to have completely misunderstood this. He told journalists recently that we don't need to worry much about climate change because the new IPCC report says we're on track only for warming of 1–2.5C. But those are the figures for the TCR – a variable for climate models, not a forecast. It would be funny, were it not so alarming, that Paterson has got so badly confused.

In reality, we're likely to hit a climate forcing equivalent to double preindustrial CO2 by mid-century even with reasonably ambitious emissions cuts, and even sooner on current trends. At that point we'd need to switch off every remaining fossil fuel-burning vehicle, boiler and power station overnight, in order for Paterson's 1–2.5C to be realistic. Perhaps that's his idea of a climate change mitigation plan?

The thing that does matter: cumulative carbon budgets

The really big news in the new IPCC report is the recognition of something that various scientific papers have made clear over the past few years: that to avoid any given temperature rise, the world needs to set itself an all-time carbon budget. The reason is that carbon accumulates in the air over time, so it's the total amount of carbon emitted since the industrial revolution – cumulatively – that determines the level of warming. My second graph shows this, demonstrating that no matter what emissions scenario the world follows, there's a roughly straight-line relationship between temperature rise and cumulative emissions. It also highlights the obvious but often overlooked point that even when annual emissions are falling, cumulative emissions are still rising.

As the graph shows, for a decent chance of limiting warming to 2C, as the world has agreed to do, the global carbon budget is around a trillion tonnes of carbon (which equates to 3.7 trillion tonnes of CO2), give or take a bit depending on much risk of failure we're prepared to accept. Of that total, more than half has already been used up, leaving a remaining budget of around 450 billion tonnes. As Mike Berners-Lee and I show in our recent book, The Burning Question, that's approximately half the carbon in the remaining fossil fuel reserves that are already commercially viable ("proven" in the jargon), and just a small fraction of all the fossil fuels remaining in the ground, including the obscure and unconventional reserves that companies are spending hundreds of millions of dollars each year trying to bring to commercial viability.

In other words, the IPCC has finally confirmed that to meet the agreed global climate target, the vast majority of the remaining fossil fuel reserves either need to be left in the ground or burned only with some form of carbon capture. We knew this before, of course, but without IPCC recognition, governments have been able to avoid facing up to the implications. Indeed, negotiators at the UN climate talks have failed so far even to discuss the concept of a global carbon budget in any meaningful way, focusing instead on piecemeal national pledges in the blind hope that one day these will add up to a solution. Thanks to the new report, however, virtually every government in the world has been forced to consider and recognise that most of the world's fossil fuel reserves need to be left untouched, either forever or at least until we can capture the carbon. If the likes of Owen Patterson, Matt Ridley and the Economist accept the science of the new report, as they seem to suggest, this stark fact is what they are implicitly acknowledging.

To make the situation even tougher, it's not clear that the things we usually assume will help cut fossil fuel use actually work as expected. As The Burning Question argues, the long term trends suggest that global fossil fuel use and carbon emissions have so far been completely unaffected by huge gains in energy efficiency, cleaner energy sources and slowing population growth. Efficiency gains don't necessarily mean less energy use overall; more clean energy supply doesn't automatically mean less dirty energy supply; and a reduction in population growth doesn't in itself slow emissions growth. To avoid a high chance of shooting far past 2C, therefore, we need to focus on the root problem: the production and unabated burning of fossil fuel.