We've seen plenty of charts over the past few years showing that wind and solar power are growing at astronomical rates — not just in the United States, but around the world. That seems like an encouraging sign for efforts to tackle global warming.

But here's a sobering counterpoint. Roger Pielke, Jr., an environmental studies professor at the University of Colorado, has charted data on the share of carbon-free energy as a fraction of the world's overall consumption.

When you look at things this way, the share of clean energy around the world has actually stagnated over the past 20 years:

It's true that carbon-free sources like wind and solar and hydropower and geothermal have been growing rapidly. But fossil fuels like oil, coal, and natural gas have also been growing rapidly in the past two decades — particularly in China and India. The result is a stalemate of sorts. The world's energy supply isn't any cleaner than it was in the 1990s.

(By the way, fans of nuclear will note that the share of carbon-free energy grew most quickly 1965 and 1999 — a period, Pielke notes, when "nuclear power increas[ed] by a factor of 100 and hydropower by a factor of 6.")

Another way to look at the same phenomenon is to measure the "carbon-intensity" of the world's energy sector — that is, how many tons of carbon dioxide are released into the atmosphere for each unit of energy that's generated. This takes into account improvements in efficiency and the fact that natural gas is a cleaner fossil fuel than coal.

Here, too, there's been a real stagnation over the past few decades. Check out that gray line:

This chart comes from a report this year by the International Energy Agency, which notes that since 1990, the carbon-intensity of the global economy has improved by a mere 1 percent — despite all the concern and all the conferences on climate change.

If that trend continues, the IEA says, global carbon-dioxide emissions will keep rising sharply and climate models suggest the Earth could heat up by as much as 6°C (10.8°F) over the long term. That's what the purple line represents. By the way, the World Bank isn't sure that humanity will be able to adapt to even 4°C of warming. So 6°C isn't exactly ideal.

Now, alternatively, if the world wants to avoid that balmy fate and keep global warming below 2°C, then carbon intensity will have to improve dramatically — far more dramatically than we've seen over the last four decades. That's what the blue line represents.

Is the blue line actually possible? That's the trillion-dollar question. The full IEA report, "Tracking Clean Energy Progress 2013" (pdf) has a slew of ideas on how to clean up the world's energy sector. For instance, global coal use would have to peak before 2020; power plants and factories would have to get a lot more efficient; things like nuclear power and renewables would have to expand at an even faster rate.

For now, though, the world's not on track.