‘Wrong sign paradox’ finally resolved?

A group of colleagues has all but solved one of the greatest remaining puzzles in climate science. But the story is not one of scientific triumph – rather, it is so embarrassing that we had controversial discussions in our group whether to break this to a wider public at all.

The puzzle is known amongst climatologists as the “wrong sign paradox” – our regular readers will probably have heard about it. Put simply, it is about the fact that a whole number of things in climate science would fit very nicely together, if only the sign were reversed. If only plus were minus.

Perhaps the best-known example is how we could explain global warming with variations in solar activity: the hottest year on record (2010) happens to coincide with the deepest solar minimum since satellite measurements of solar luminosity began in the 1970s (Fig. 1). This can’t just be coincidence. But the sign is wrong: physical theory stubbornly insists that temperature should be highest when the sun shines the brightest, not the other way round. The “wrong sign paradox” here is reinforced by the fact that the overall trend in solar luminosity is gently downward over the past 30 years – just those 30 years when we see the well-known strong global warming.

Fig. 1: Global temperature (blue, GISS) and solar luminosity (orange), both as 12-months running means.

Another prominent example is the Pacific Decadal Oscillation (PDO). Basic physical considerations would suggest that the global temperature is warm when the PDO-Index is high, i.e. when sea surface temperatures in the North Pacific are high. A theory that would beautifully fit the data – if only the sign were reversed (Fig. 2)!

Fig. 2. PDO-Index vs. global temperature, with linear trends (dashed) since 1900 and over the last 30 years.

And just to round this off with a third example (there are more of course – perhaps our readers can provide some others): cosmic rays. A very beautiful theory holds that cosmic rays help cloud formation: lots of cosmic rays means lots of cloud and hence cool global temperature. Now cosmic rays have been measured since the 1950s, and they reached their all-time maximum in 2010 (Fig. 3). Bingo: the warmest year on record! But no: a high cosmic ray count should cause cold temperatures, not hot ones.

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