Here's a capsule summary of the big UN climate talks this year:

1) The good news: Every country is submitting a detailed pledge to curb greenhouse gas emissions.

2) The bad: Those pledges, added together, aren't nearly enough to keep us below 2°C of global warming. Short of drastic changes, we're in for some serious shit.

Point 2 can be tricky to conceptualize, since it involves so many moving parts. For more detail, I'd recommend this new paper in Environmental Research Letters by Glen Peters, Robbie Andrew, Susan Solomon, and Pierre Friedlingstein. It's the clearest presentation I've seen of how far off course the world is from its stated 2°C climate goal. And it illustrates why the United States, Europe, China, and even India would have to drastically rethink their climate policies to stay below that target.

The US, Europe, and China will use up the world's carbon budget by 2030

The science here is pretty straightforward: If we want decent odds of avoiding more than 2°C (or 3.6°F) of global warming — which has long been the stated goal — then there's only so much more carbon dioxide we can put into the atmosphere. The world's annual CO2 emissions will need to shrink to zero to stay within this "carbon budget."

In their paper, Peters and his co-authors sketch out a plausible carbon budget if we want a 66 percent chance of staying below 2°C. (Because there's some uncertainty around climate sensitivity, this is couched in terms of probabilities.) Roughly speaking, the world has just 765 gigatons of CO2 left to emit. We currently emit about 35 gigatons per year and don't (yet) have large-scale carbon removal technology.

The authors then compared this carbon budget (the dark line) with what the United States, the European Union, and China* are currently promising to do on emissions between now and 2030:

There's a big problem here: If the United States, EU, and China all followed through on their current emissions pledges, they'd consume practically the world's entire carbon budget by 2030 — leaving only scraps for the rest of the world (the part shaded in gray).

That's untenable. The "rest of the world" is where most of humanity lives — 5 billion people. It includes India, which is still very poor, has per capita emissions that are just one-fourth of Europe's and China's, and will inevitably need to burn more fossil fuels to grow. It also includes Africa, which still has 620 million people without electricity. No one thinks it'd be fair for these developing countries to cut even more deeply than the United States and Europe.

So that leaves a few options. Humanity could emit more CO2 than this budget allows — though at the risk of higher levels of global warming, with all the problems, risks, and potential horrors that entails. If, say, we emitted another 1,535 gigatons of CO2, double the budget above, then our odds of staying below 2°C drop to 50-50. A much bigger gamble.

Alternatively, the US, EU, and China could tighten their belts and cut their emissions even more deeply than they're currently promising, to make space for other, poorer countries. But how would they do that? And is that even realistic?

To stay below 2°C, the US, EU, China, and India would have to cut much, much more

In their paper, Peters and his colleagues explore what a "fair" climate agreement that still keeps global warming below 2°C might look like. Because fairness is an ethical term, not a scientific one, there are all sorts of ways to define it.

One possibility is that emission cuts would be divided equally among countries. The United States and Europe and China and India and Zimbabwe would all make proportionally similar sacrifices to stay below 2°C. When the dust settled, the average American would still emit more than the average Indian, but they'd each have made similar percentage cuts. The authors call this the "inertia" approach.

Another option would be to divvy up cuts so that every country has roughly the same level of per capita emissions. In this scenario, India's emissions are allowed to grow, while the US and Europe have to cut much more deeply. The authors call this the "equity" approach.

We could debate which one is truly fairer all day. But one key point here is that, under either scenario, the United States, Europe, and China would all have to cut a lot more deeply than they're currently promising.

Here's a look at current US climate pledges (the gold line) compared with the much deeper cuts required under either an "inertia" or "equity" approach to staying below 2°C:

Here's the EU's current pledges (in blue) compared with what'd be required to stay below 2°C:

And heres's China. Note that there's some uncertainty over how high, exactly, China's emissions are expected peak in 2030, but no matter what assumptions you use, they're expected to peak much higher (the orange lines) than what would be required under "inertia" or "equity" approaches to stay below 2°C:

We're not even close.

Cutting emissions enough to hit 2°C would take ... a miracle

What these charts show is that the US, Europe, and China are all currently promising ambitious emission reductions. Yet those promises are all laughably inadequate compared with what would be required to stay below 2°C.

In the United States, the necessary cuts for 2°C would require policies titanically more ambitious than anything the Obama administration has been doing through the Environmental Protection Agency. An "equity" approach would require getting to zero carbon by 2040 — just 25 years. We'd be talking about World War II–style mobilization. Congress would need to get involved, either by enacting carbon pricing or other policies to massively scale up zero-carbon energy. Few politicians are talking about anything like this.

Likewise, China would need emissions to peak sharply around 2020 — 10 years earlier than the government is currently envisioning — and then decline drastically thereafter. That's not easy given all the coal plants that the country has built over the last 10 years, facilities that can be expected to last for decades. Many of those plants would need to be either retired early or retrofitted with technology to scrub their emissions and bury the CO2 underground.

By the way, it's not just these countries. India would also have to make wrenching changes. On Twitter, Peters posted a graph comparing India's projected emissions under current policies (the purple line) with what'd be required under "inertia" or "equity" scenarios for staying below 2°C:

Given that India is currently planning to double coal production by 2020 as it lifts itself out of poverty, this looks incredibly unlikely.

So is 2°C still possible? Maybe with negative emissions.

Lately, a growing chorus of climate observers have been pointing out that without a massive — and increasingly improbable — rethink, the world simply won't meet its goal of staying below 2°C of global warming (I laid out the case here; my colleague David Roberts did so here).

Add this paper to the pile. It concludes that there's a "high risk of exceeding 2°C given current trends."

Now, there are a couple of potential caveats. Perhaps clean energy will advance far more rapidly than expected, making it easier for the United States, Europe, China, India, and everyone else to cut emissions more sharply than anyone's predicting. Or... perhaps the current emission pledges will prove to be mere starting points, and policymakers will significantly ramp up the level of ambition after meeting in Paris in December. That's certainly the overarching hope around the current UN talks — that action will build on action, iteratively.

Still, the charts above suggest there's not really much time remaining for a massive change of course. If the US, EU, China, and India don't make any major alterations to their emission plans between now and 2030, they'll have used up the world's entire 2°C carbon budget. At that point, we either have to hope climate sensitivity is on the very low end of the range that scientists have estimated, or we're busting through the 2°C limit. Better start preparing.

There is one other option, however. If we could devise carbon-removal technologies that can suck carbon dioxide out of the atmosphere, we could conceivably extend our existing "carbon budget." The problem is that we'd have to remove a lot of CO2, some 2 to 10 gigatons per year by mid-century, more than all the world's forests and soils currently take up. Planting trees won't be enough. We'd need to look into things like air capture or biomass with carbon capture and sequestration — and scale them up rapidly. (See this interview with Noah Deich for more on that.)

Is that plausible? No one knows. But as climate scientist Kevin Anderson recently argued in Nature Geoscience, the only way we'll stay below 2°C is if we either a) develop negative-emissions technology, or b) opt for negative economic growth. The math just doesn't work otherwise.

One final coda: as I've noted before, even if the world does crash through the 2°C limit, that would hardly mean it's game over. Because the risks and damages from global warming go up significantly the higher that temperatures rise, even 2.5°C warming is still preferable to 3°C, which is better than 4°C, which is way better than 5°C. There's never going to be a point when it's time to just give up.

* Footnote: China has promised that its emissions would peak by around 2030, but it hasn't specified what level they'll peak. So Peters and his co-authors estimated, based on expected carbon-intensity improvements, that China would emit roughly 11.3 gigatons of CO2 in 2030. But the actual figure could well end up being lower (or higher).

Further reading

-- Two degrees: How the world failed on climate change. Our deep dive into the history of the 2°C target, why we're likely to miss it, and what happens once we do.

-- It's time to look seriously at sucking CO2 out of the atmosphere

-- Also possibly related: Geoengineering is an insane way to deal with climate change. Let's consider it anyway.