Why the sky is blue!
Calling out bad "blue sky" research ...
A bit of trivia ….
My colleagues and I were chuckling about a recent article that somehow wriggled through peer review last month. It purports to prove to that our long-held belief on why the sky is blue is wrong. But the new article is a case of the pot calling the kettle black.
As a reminder - just in case you’ve forgotten 😊 - the current theory, which is backed by innumerable research findings, is as follows. When sunlight hits molecules of air in the atmosphere, it gets scattered and bounces off at different angles and with scattering efficiencies that depend on wavelength. In particular, the efficiency of scattering depends on how big the scattering object is compared with the wavelength of light.
The wavelengths of light that our eyes can see falls within a rather narrow range between about 0.4 microns for blue light up to about 0.7 microns for red light (1 micron is one millionth of a metre). The effective size of air molecules is about 1000 times smaller. For example, a molecule of nitrogen, the most abundant gas in the Earth’s atmosphere, is about 0.0003 microns. For such disparate size ranges, the scattering efficiency increases rapidly towards shorter wavelengths.
The effect is called Rayleigh scattering, named after its discoverer, who reported it over 100 years ago. He found that the scattering efficiency of air increases inversely with wavelength to the power of 4, which means that compared with red light at 0.7 microns, blue light at 0.4 microns is scattered about 9 times more efficiently (i.e., by a factor of (0.4/0.7)^-4). So that’s why the sky looks blue and not red. If you’re not looking directly toward the Sun, the light you see is scattered light, and that scattering is more efficient at the blue end of the spectrum.
You might have noticed that at high altitudes (e.g., climbing mountains, or flying in jet aircraft), the sky above looks darker than usual. That’s because there’s less air above to scatter the light.
Rayleigh scattering is also responsible for the yellowish appearance of the solar disk when it is close to the horizon. It appears yellow (rather than white) because light from the blue end of the spectrum is preferentially scattered out of the direct beam by air molecules.
Under polluted conditions, where the lower atmosphere is laden with much larger aerosol particles - for which the wavelength dependence of scattering is smaller - the sky isn’t quite as blue (I said more about that in an earlier posting). It looks whiter (as it does when reflected from clouds which are composed of large conglomerates of water molecules). The solar disk can sometimes even appear red when aerosols and pollutants gases preferentially scatter and absorb light at the blue end of the spectrum.
It’s all part of a long standing Theory of Radiative Transfer, famously described by Indian scientist, Subrahmanyan Chandrasekhar (1910 -1995).
Anyway the ‘new’ - and I should add ‘bogus’ - theory just reported is that the colour is nothing to do with scattering, but is instead due to the colour of ozone. It’s true that ozone is slightly blue in colour because as well as its strong ultraviolet absorption, it also absorbs red light (in the so-called “Chappuis” absorption bands). But that’s not the main reason why the sky is blue.
There are so many mistakes and misunderstandings in the paper that I can’t be bothered starting. Suffice to say that my colleagues and I are not convinced. We already knew from our own work that Chandrasekhar’s theory is the correct one. The excellent correspondence between our spectral measurements of UV radiation reaching the Earth’s surface and corresponding calculations using his theory prove the point, as we showed nearly 30 years ago.
The old black and white plot below from that paper shows that the measured spectral dependence of the ratio of diffuse to direct radiation (solid line) matches that predicted by theory (dotted line). At shorter and shorter wavelengths, the diffuse fraction get larger and larger. For this high-sun spectrum, the ratio at 300 nm is close to one, five times larger than at 450 nm (pretty much as predicted). Similar agreement between measurement and model is seen for all sun elevation angles considered. The tried and trusted theory works! The slight roll-off at the shortest UV wavelengths is interesting. It occurs because the diffuse beam is attenuated more than the direct beam due to its slightly longer path through the lower atmosphere. That roll-off is seen in both curves, which again shows that our understanding of the situation is correct (noting that other evidence in the paper confirms that the sharp feature in the measurements near 305 nm is just a noise spike - reality striking back).
The sky appears blue because of the increased proportion of diffuse radiation at shortest wavelengths that our eyes can detect, not because ozone absorbs some of the red light.
As one of my colleagues quipped when describing the paper (which was authored by one P.K. Raghuprasad), “if Chandrasekhar was still alive today, he’d be rolling in his grave”.
… which reminds me of the irrelevant old oxymoron: “I’d give my right arm to be ambidextrous”.
PS. My colleague Ben Liley pointed out a typo in the units above (now fixed) and also suggested that I add that the effect of the wavelength dependence of Rayleigh scattering is apparent in the plot at the top of my posts, as copied below. It explains why the spectrum of sunlight at Earth’s surface (shown by black line below) falls away from the extraterrestrial spectrum (shown by the blue line below) as you go from red to blue. The Rayleigh optical depth at 700 nm (red) is 0.037 (i.e., 3.5% attenuation), and at 400 nm (violet) it is 0.36 (i.e, 30% attenuation). Thanks Ben!
Thanks for reading this. Previous posts on the intersection between Ozone, UV, Climate, and Health can be found at my UV & You area at Substack.