ClarkVision.com
| Home | Galleries | Articles | Reviews | Best Gear | Science | New | About | Contact |
Colors of the Daytime Blue Sky
by Roger N. Clark
| Home | Galleries | Articles | Reviews | Best Gear | Science | New | About | Contact |
by Roger N. Clark
The color of the daytime blue sky is interesting because in certain cases it is challenging to show the true color with photography or with display monitors available today. Sunlight illuminates the air molecules and larger particles, called aerosols, in the atmosphere. The smaller particles scatter bluer light more efficiently, called Rayleigh scattering. As particle size increases, the efficiency of scattering long wavelengths (e.g. green, yellow, red) increases, which results in a less saturated blue. In the clearest atmosphere, where only light from air molecules is scattered, the light is said to be Rayleigh scattered and scattering efficiency increases as the inverse of the wavelength to the 4th power. This means, for example, that blue light (wavelength of 0.45 microns, 450 nm) would be brighter by 3.17 times compared to red light (wavelength 0.6 microns, 600 nm). Technical: (0.60 / 0.45)4. The scattering from larger particles is called Mie scattering. An example of larger particle Mie scattering is a white cloud. Smaller particles than the water drops in white clouds are sometimes seen in smoke from a fire: the smoke plume will look bluish at some angles.
Rayleigh scattering conditions are rare because there are often enough aerosols in the atmosphere to add proportionally more longer wavelength light (green, yellow, red) to the sky brightness to dilute (unsaturate) the blue. I live in a pretty clean environment at 6,000 feet elevation in Colorado, USA. I have a spectrometer and can measure the spectrum of the sky to determine the amount of Rayleigh versus larger particle (Mie) scattering. I have found that over several months of observation in Colorado before writing this article, that pure Rayleigh scattering blue sky is rare, occurring only a few times per month. I also have a long professional history of measuring sky conditions for my work in terrestrial remote sensing in calibrating sensor data since the late 1980s.
At sea level near the ocean, ocean spray often adds Mie scattering, making the sky a light blue. On March 17, 2018, I was hiking a beach in Hawaii and made the images in Figure 1. On this day, aerosol scattering from ocean spray and smoke from Kilauea volcano added Mie scattering making the sky a light blue (Figure 1). The haze near the bottom of the figure in front of the Mauna Loa volcano illustrates the aerosol scattering. Even at the zenith, the sky, while bluer, is not a deep rich blue. This is due to the haze scattering all colors of light. In the afternoon I made a trip to the 9,000 foot level of Mauna Kea and made an image of the zenith sky (Figure 2). Again, the the sky was not a deep rich blue. That was because the sky still had haze present from the volcano, making the sky a lighter blue.
Figure 1. Light blue sky on this day in Hawaii was
due to a combination of blue Rayleigh
scattering and whiter Mie scattering from the haze particles.
The volcano in the distance is Mauna Loa, with the summit
about 36.5 miles (58.7 km) away.
Figure 2. The zenith blue sky on the same day as in Figure 1 but at 9,000 feet
elevation on Mauna Kea. The sky was not a deep rich blue because of scattering
from haze particles from the erupting Kilauea volcano.
On March 23, 2018, I experienced a brief period in the late afternoon when the sky turned a deep, rich blue (Figures 3, 4). The Rayleigh condition was confirmed with a spectrometer. A GretagMacbeth Color Checker test chart was set up near normal illumination to sunlight (Figure 3). A steerable mirror was set up to reflect the Rayleigh-blue sky into the same field of view as the color chart. The mirror was in shade to avoid scattering of sunlight off the mirror. The mirror was positioned so that the sky and a blue color on the chart was next to each color for comparison. The mirror was moved to best make the comparison for each blue color. The images in Figure 3 illustrate different processing of the images. The closest match in the images is the blue square at the top, next to the white square. The color chart was also compared in sunlight and under daylight-balanced LED light. In both cases, the out-of camera jpeg gave a closer match on my color calibrated monitors than any of the photoshop output, which are slightly duller. Perceptually, the blue sky matched the blue square at the top of the color chart best, as well as in all processing cases in Figure 3 (at least on my 4 monitors on 3 computers), The closest perceptual color of the live sky view and live sunlit illuminated chart to the 4 different images in Figure 3 was the out-of-camera jpeg.
Figure 3. GretagMacbeth Color Checker images compared with deep-blue Colorado
sky dominated by Rayleigh scattering. Perceptually, the blue patch in the
top row best matched the perceived color in the mirror. The out-of-camera
jpeg image (A) came closest to th perceived colors in the chart, and
in the sky. The region of sky with a larger field of view is shown in
Figure 4. Images from a Canon 7D2.
Here is the raw file if you want to work with raw data (22 MBytes)
Figure 4. The region of blue sky analyzed in Figure 3, and the
values in Table 1 are from the area above the red arrow.
Here is the raw file if you want to work with raw data (23 MBytes)
Table 1
Image white patch RGB
R G B
Figure 3A Out-of-camera jpeg, camera sRGB 247 247 239
Figure 3B CS6 ACR Adobe RGB 243 243 238
Figure 3C CS6 ACR WB1 Adobe RGB 243 243 241
Figure 3D CS6 ACR WB1 sRGB 243 243 241
Image blue patch 13 RGB G/B R/G
Figure 3A Out-of-camera jpeg, camera sRGB 50.7 88.0 178.4 0.493 0.576
Figure 3B CS6 ACR Adobe RGB 55.9 86.5 163.0 0.531 0.646
Figure 3C CS6 ACR WB1 Adobe RGB 54.9 84.7 168.4 0.503 0.321
Figure 3D CS6 ACR WB1 sRGB 27.7 82.2 169.5 0.485 0.337
Image blue sky patch RGB G/B R/G
Figure 3A Out-of-camera jpeg, camera sRGB 20.4 42.9 79.0 0.543 0.476
Figure 3B CS6 ACR Adobe RGB 34.5 51.3 78.6 0.653 0.673
Figure 3C CS6 ACR WB1 Adobe RGB 34.3 50.9 82.0 0.621 0.674
Figure 3D CS6 ACR WB1 sRGB 15.8 46.1 80.3 0.343 0.574
custom WB1 = make white patch white
NOTE, HOWEVER, that the blue sky in the images in Figures 3, and 4 is NOT the same blue seen visually in the sky. Also, no blue in my color calibrated monitors, and probably neither yours, can correctly represent the real blue of the Rayleigh scattered blue sky. The reason has to do with the spectral distribution of the light. The 3 blue color patches in the Macbeth Color Checker have spectra that are significant different than the spectrum of Rayleigh scattering (Figure 5). The top row blue patch is patch 13, to it's lower right is patch 8 (called Purplish Blue), and to its lower right is patch 3 (called Sky Blue). Note the eye's color sensitivity extends from about 0.38 microns to beyond 0.7 microns.
As one can see, the "sky blue" patch 03 shows high reflectance at green and red, making a very unsaturated blue, similar to skies with significant aerosol scattering, like that in Figure 1. Patch 03 is not representative of Rayleigh scattering blue.
Patch 08, Purplish Blue, does not match clear blue sky because is contains too much red.
Blue path 13 contains too little green compared to Rayleigh scattering, about the right amount of red, and high blue. It comes closest in color to Rayleigh scattering, but does not match perfectly, though gives us an idea of the color of Rayleigh scattering blue.
None of the MacBeth color patches match the Rayleigh blue because they all have a sharp decrease in reflectance at the shortest wavelengths where Rayleigh scattering is most intense. Blue patch 13 comes closest because the peak of the eye's blue spectral response also peaks near the same wavelength, near 0.45 microns. Short of that peak, the influence of shorter wavelengths becomes less, though is still significant. In any event, this demonstrates that Rayleigh scattering blue is a deep blue, close to the blue patch 13, and not similar to the color chart "sky blue" patch 3.
Figure 5. Spectra of Macbeth Color Chart blue patches are
compared to a Rayleigh scattering function. These spectra
are from the same chart as shown in Figure 3.
Are there materials that better illustrate the true color of Rayleigh scattering? It turns out that in my professional work, I and my colleagues have surveyed the spectra of many materials trying to find a better match for some scientific applications in remote sensing of the Earth and Planets. All too common are the use of organic dyes that absorb wavelengths shorter than about 0.45 microns, preventing a true match. I have surveyed hundreds of blue compounds, including paints, plastics, minerals, and inks. There is great commonality, with a peak in reflectance of blue materials around 0.45 microns. I have found that the ink used in the blue in the magazine Sky and Telescope is a little better, with a peak near 0.44 microns. but still well short of Rayleigh scattering in the visible range.
Some colored glass filters provide closer spectral matches. Hoya filters LB140 and LB200 bound the Rayleigh spectrum (Figure 6) and would be good reference materials for comparing to Rayleigh blue. The comparison must be done with full sunlight with the sun at least 10 to 20 degrees above the horizon in a very clear atmosphere and reflected off of a spectrally-white diffuse surface that is white down to at least 0.4 microns. The white reference Spectralon is ideal, and is what I use. Online images that I have found of the LB140 filter show it as a deep blue. Update: I spent a couple hundred dollars buying LB filters, but the filters I received do not have the same filter transmission as those in Figure 6, and are not a close to the Rayleigh function, though they are closer than the Macbeth Color Chart blue patches.
Figure 6. Transmission spectra of Hoya LB140 and LB200 filters are
compared to Rayleigh functions. LB140 is slightly less blue than
Rayleigh scattering, while LB200 is slightly more blue. These two filters
closely bound the Rayleigh color better than any other materials that I
have found. To show the right color, filter sunlight reflected off of
a diffuse white surface (be sure it is white to at least 0.4 microns).
Spectralon is among the whitest compounds known.
Conclusions
The Rayleigh-scattering blue sky is a special case in perception and reproduction. The dominant short wavelengths are not reproduced by current digital cameras, computer monitors, or typical print media. As such the actual color can only be represented by an approximation. Measurement of the spectra of blue sky shows that the Rayleigh-dominant condition is unusual--more often scattering by aerosol particles adds colors of all wavelengths, making a lighter (unsaturated) blue.
Perception experiments shows that "Rayleigh blue" is perceived as a deep blue, with closest match on a GretagMacbeth Color Checker with patch 13, labeled blue, with CIE chromaticity x, y = 0.187, 0.129, but the true Rayleigh blue should have a y-value lower than this. A Schott BG34 filter shws similar spectral response to the Hoya filters.
The best materials I have found so far are color correction filters, with Hoya LB140, LB165, and LB200 close matches. The LB200 should be slightly bluer than Rayleigh scattering and similar to the color of the Pleiades nebulosity. See: The True Color of the Pleiades Nebulosity.
Lord Kelvin on Rayleigh scattering, in The London, Edinburgh and
Dublin Philosophical Magazine and Journal of Science page 300:
"...it will be seen, that the blueness of the sky, even when the most serene azure,
was always much less deep than the true Rayleigh Blue..."
| Home | Galleries | Articles | Reviews | Best Gear | Science | New | About | Contact |
http://www.clarkvision.com/articles/color.of.blue.sky
First Published March 27, 2018.
Last updated June 15, 2018.