If you want a concise illustration of how the world is failing at its climate goals, check out this chart from PriceWaterhouseCoopers:

Carbon intensity has to fall 6.2% each year for the world to meet its climate goals. It's falling 0.9% per year.

The lines on the graph measure "carbon intensity" — the amount of carbon-dioxide that we have to emit in order to generate a dollar of economic activity. It's a slightly different way of looking at the global-warming problem than just focusing on overall emissions.

The bad news is that global carbon intensity isn't falling quickly enough

The good news is that the world is steadily becoming less and less carbon-intensive. That is, we need to burn fewer fossil fuels to generate a dollar's worth of economic activity. Part of the reason for that is our cars, homes, power plants, and factories are all getting more efficient — we can do far more with a given amount of coal, oil, or natural gas than we used to.

But here's the bad news: Carbon intensity isn't falling fast enough. Between 2000 and 2013, carbon intensity fell by 0.9 percent per year. Last year, it fell by 1.2 percent. But the global economy grew fast enough to overcome that, so overall emissions rose. If these trends continue, we're on track for about 4°C of global warming in the future, which many scientists have deemed extremely dangerous.

By contrast, if the world wants to a) keep growing and b) avoid more than 2°C of global warming (which is the current international goal), then carbon intensity will have to decline much, much faster — by roughly 6.2 percent per year between now and 2050.

There are a few ways to do that. We could get much more energy-efficient, so that we're wringing even more economic activity out of existing fossil fuels. Or we can shift to cleaner sources of energy, like renewable energy or nuclear power or fossil-fuel plants that can bury their carbon emissions underground. But right now, we're very far off pace.

Which countries are decarbonizing the fastest?

Here's a look at decarbonization rates of major countries since 2008:

Note that Australia has made the biggest decarbonization gains in recent years, with its carbon intensity declining 4.6 percent since 2008, thanks in part to a big drop in electricity use and a boost in hydropower. (During part of this period, Australia had both a carbon tax and a mandate to promote renewable energy — but the country has since repealed both policies.)

Australia has made the most progress on decarbonization since 2008 — but it just repealed its carbon tax

China has also seen a reasonably big drop in carbon intensity in recent years — a decline of 1.6 percent per year since 2008. That said, because China is so massive and growing so fast, overall emissions are rising.

By contrast, Germany and Brazil both backslid — they actually got more carbon-intensive in 2013. What happened? Germany has been burning more coal instead of natural gas for electricity last year (the nation has also been shuttering a number of coal plants since 2011). Brazil, meanwhile, gets 30 percent of its power from hydroelectric dams, and those were hurt by a series of droughts last year. So, instead, Brazil had to rely more heavily on fossil fuels.

The United States has made modest progress in decarbonization since 2008 — improving 2.4 percent per year — a shift driven partly by the fracking boom, which has replaced coal with somewhat cleaner natural gas. (There are also other factors, like the rise of fuel-efficient vehicles.)

Still, all of these numbers should be placed in context. If the world wants to meet that 2°C climate goal, worldwide decarbonization rates will have to be much, much faster than any country is really achieving to date.

* Update: Thanks to Christian Roselund for pointing to a more precise breakdown of what went on in Germany last year.

Further reading: Two degrees: How the world failed on global warming