The world is warming; consider the facts.

• Author: Rahmstorf, Stefan

This April was the hottest April on record, globally, for at least 130 years, according to the worldwide temperature records maintained by NASA and the U.S. National Oceanic and Atmospheric Administration. The past twelve months was the hottest twelve-month period since measurements began.

That is what the data from weather stations and ships show. But if you prefer satellite data, the picture is similar. Satellite data have this March as the hottest March on record, with April ranking second-hottest; the surface data have it the other way round, with March the second-hottest and April the hottest.

Of course, more important, scientifically, are the long-term trends. For the past thirty years--that's how long the satellite measurements have been taken--the trend is clearly upward and similar in magnitude in all the available data sets.

Should you still have doubts that the planet is heating up, look at the shrinking mountain glaciers around the world, or the declining sea-ice cover on the Arctic Ocean, which in recent summers has been little more than half its size in the 1970s.

What is causing this climatic warming? Physics tells us that if you want to know why something is getting warmer, seek the source of the heat. (That's a consequence of the first law of thermodynamics: energy is always conserved.) We thus have to look at the heat balance of our planet to understand the reason for the warming.

That is surprisingly simple: there is only one source of heat coming in, and that is radiation from the sun (which is largely visible light, or what physicists call short-wave radiation). And there is only one form of heat leaving the planet, and that is radiative heat (which is invisible, or what physicists call long-wave radiation). They are essentially the same physical phenomenon; the difference in wavelength comes only from the sun being much hotter than Earth.

So, could changes in solar radiation explain the warming of the planet? Measurements of incoming solar radiation show that it has not increased in the past fifty years--in fact, the record even shows a small decrease. But the record's predominant feature is the recurrence of solar radiation cycles lasting about eleven years (called Schwabe cycles, after the astronomer who discovered them in 1843).

In the past few years, we've been in the deepest and longest minimum of a Schwabe cycle since satellite measurements began. That's right: while global temperatures are at a record high, the...