Light scattering in the Earth’s atmosphere part 2 – why is the sky blue and how the sky colour change?

When we ask ourselves why the sky is blue we can think about the most important type of light scattering in the Earth’s atmosphere. This is Rayleigh scattering. I was writing about this type of light scattering on some occasions, like watching the solar eclipse through the webcams or wondering about the Martian sky. Today I would like to develop this topic and bring a rough answer for one of the most basic questions from geography or physics: why the sky is blue?

1. THE RAYLEIGH SCATTERING & WHY IS THE SKY BLUE DURING THE DAY
   

Rayleigh scattering is the scattering of light by particles much smaller than the wavelength of the radiation.  Rayleigh scattering works best in a gaseous environment. The particles may be individual atoms or molecules. The intensity of scattered light significantly depends on the scattered light wavelength – increasing with the decrease of wavelength in the majority of cases. Sunlight reaches Earth’s atmosphere and is scattered in all directions by all gases and molecules in the air. We see the blue sky for most of the time because blue is scattered more strongly than other colors in the atmosphere. It happens because Rayleigh scattering is inversely proportional to the fourth power of wavelength so that shorter wavelength violet and blue light will scatter more than longer wavelengths (Pic. 2). Why don’t we see the violet in the sky then? Violet basically is almost gone because of three factors: firstly Sun likewise other stars has its own spectrum of light emission, which is not constant and falls away in the violet. Secondly, the shortest, violet wavelengths are absorbed by oxygen particles in the atmosphere. Thirdly human eye is less sensitive to violet. At the finish of this consideration, I can add up the other factor, which is the presence of other light wavelengths scattered in the atmosphere, that finally makes the output sky color pale blue (a mixture of all the scattered colors, mainly green and blue)(Pic. 1). This output can be explained as a dominant wavelength, which for Rayleigh scattering is about 475nm, which lies solidly in the blue if we take this to mean light with wavelengths between 450 and 490nm (Bohren, 2003). Conversely glancing towards the Sun directly the colors are not scattered away. The longer wavelengths such as red or yellow light are visible directly then, giving the Sun itself a slightly yellowish hue throughout the day and accordingly yellow, orange, and red when near the horizon (Pic. 2, 8).

Pic. 1 Basic mechanism of scattering the light on the molecules in the atmosphere. Incoming sunlight as white light is next scattered mainly on blue wavelengths, with a small presence of green and violet wavelengths (atmo.arizona.edu).

Rayleigh scattering results in the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within the particle causing them to move at the same frequency. The particle, therefore, becomes a small radiating dipole, whose radiation we see as scattered light.

Pic. 2 The visible wavelength scale against the scattering of direct sunlight (wikimedia.org).

The Rayleigh scattering of sunlight in the atmosphere causes diffuse sky radiation. Diffuse sky radiation is solar radiation reaching the Earth’s surface after having been scattered from the direct solar beam by molecules or particulates in the atmosphere (Kondratyev, 1969).

Pic. 2 The direct sunlight is scattered in the Earth’s atmosphere causing diffuse sky radiation, which we can see during a typical sunny day. Sun appears to look bright whereas the sky is blue playing the role of medium, where the direct solar beam is scattered and subsequently reaches the Earth’s surface. When the Sun is overcast by a thick cloud layer and another part of the sky is clear at once then we can experience how scattered solar beam reaches the Earth’s surface from the clear section of the sky.

Pic. 3 The typical color of the clear sky. The sky appears to be darker when closer to the zenith. It is caused by Earth’s atmosphere thickness. Once we are looking up the atmosphere is the thinnest. As our sight goes down the thickness of the Earth’s atmosphere increases up to 38x times near the horizon. Hence lower parts of the sky are always much brighter than the zenith sky.

2. VARIATION OF SKY COLOUR AND BRIGHTNESS

Skylight is not only pure blue. As per the image above we can see different blue hues across the vault of the sky. The best blues is at the zenith (omitting the situation, when Sun is at the zenith). Near the astronomical zenith, the sky is brighter than overhead but of considerably lower purity (Bohren, 2003). The variation of sky brightness becomes better visible when an observer is located higher above mean sea level (Pic. 4 – 7). This effect is best visible to us when flying at cruising altitude. At 10000 m.a.s.l the sky is inherently the most nonuniform in color for us compared with the view from the ground, especially from sea level in lower latitudes. To better understand this phenomenon we must invoke a multiple scattering, that plays here a major role. A solar beam being scattered in Earth’s atmosphere when entered into the medium has been scattered again on atmosphere molecules affected by the earlier single scattered solar beam. It causes multiple scattering, which tends to wash out the strong wavelength dependence. That’s why during the bright day the blue color of the sky is much less saturated near the horizon than higher up.

Pic. 4 Daylight sky seen from mean sea level. Hunstanton, United Kingdom.

Pic. 5 Daylight sky seen from Grimsel Pass, 2164 m.a.s.l. Bernese Alps, Switzerland.

Pic. 6 Daylight sky seen from Pico del Teide 3718 m.a.s.l. Tenerife, Spain.

Pic. 7 Daylight sky, as is seen from the plane at the cruising altitude of around 10000 m.a.s.l. LO 724 TBS – WAW.

The difference between sky color variations arises out of a few factors:
– altitude – comparing the sea level and aircraft cruising altitude there is a huge difference in atmosphere density. Basically, at the upper troposphere, we have around twice the molecules less than at sea level. Because of this, the sky appears much darker, than we used to see from the ground. This effect can be also noticeable in high mountains when altitude is higher than 2000 m.a.s.l. (Pic. 5, 6).
– latitude & climate – basically tropopause lies higher above lower latitudes. The color sky variation will be slightly less noticeable on the equator than in polar areas.
– waver vapor – will strongly influence the sky color variation, however, in conjunction with the altitude will bring the same effect eventually. Basically in the “free atmosphere,” it will affect sky color variations marginally. I will bring more details in forthcoming articles.

3. POLARIZATION OF THE SKY

The light coming from the Sun is unpolarized, but the light of the sky during the day is polarized, as per the video below:

Looking at the sky through a polarizer, which preferentially blocks the polarization in one direction and allows the perpendicular direction to pass, one sees that light in the sky possesses some amount of polarization.
This amount of polarization is dependent on the daily position of the Sun. While all scattered light is polarized to some extent, light is highly polarized at a scattering angle 90deg from the light source. This light source is mainly Sun, but also a Moon. The degree of polarization first increases with increasing distance from the light source and then decreases away from the light source. Thus the maximum degree of polarization occurs in a circular band 90deg from the light source.
When the Sun is located at the zenith, the band of maximal polarization wraps around the horizon, and light from the sky is polarized horizontally along the horizon. During twilight at either the vernal and autumn equinox, the band of maximal polarization is defined by the north-zenith-south plane or meridian. In particular, the polarization is vertical at the horizon in the north and south, where the meridian meets the horizon (Pic. 8).

Pic. 8 The sky polarization pattern at sunrise or sunset, where the highest polarization occurs at the south-zenith-north line alongside the local meridian (wikimedia.org).

Because the polarization pattern is dependent on the Sun and Moon it changes not only throughout the day but also throughout the year.

4. MORNING, EVENING, AND TWILIGHT SKY

When the Sun is at a lower altitude above the horizon, then it appears to look redder instead of yellowish. The reddening of the Sun increase when closer to the horizon because the light being received directly from it must pass a long way through the atmosphere. When Sun is on the horizon the sunlight must pass through the greatest proportion of the atmosphere and looks the most reddish (Pic. 9).

Pic. 9 The Sun is the most reddish when shining on the horizon. Phuket, Thailand.

It happens like this, because when a solar beam must go through the longest portion of the atmosphere thus the longest wavelengths like red and orange are scattered much more than short wavelengths (like blue). It said to be, that Sun is slightly more reddish during the set than during the rise because of the different levels of aerosol concentration.
The long wavelength scattering refers mainly to this part of the sky, which is the closest to the solar disk. When further from the Sun the sky appears to be bluer (Pic. 10, 11).

Pic. 10 The reddish sky appears to be seen close to the solar disk only. The intensity of reddiness depends on the degree of aerosol concentration. The sky is bluer with increasing distance from the Sun. Czorsztyn, Poland.

Pic. 11 Twilight sky in solar direction remains reddish near the horizon and more blue with increasing distance from the horizon towards the zenith. Odrzykoń, Poland.

This is because of two basic reasons. Firstly when further from the Sun you see at least a bit of upper atmosphere (Pic. 12). Being around 10-20 km above the ground the solar beams have a shorter way to encounter the atmosphere, hence scattering shorter wavelengths is more significant. Secondly, the ozone layer absorbs ultraviolet light (invisible to the human eye very short wavelengths with frequency from 10 to 400 nm) and as a result keeps the sky blue for the entire twilight (Pic 12).

Pic. 12 The pattern of solar beam scattering in Earth’s atmosphere throughout the day: A – during the sunrise, B – at the noon, C – around sunset. Blue line – upper troposphere, faint blue – upper Earth’s atmosphere. An observer located in B point sees only short wavelengths coming through, and the solar disk appears to look yellowish then; Observers located both in points A and C see the reddish Sun because the light beam passes longer way through the atmosphere (pattern 3). When taking into account patterns 2 and 1 at the moment of sunrise or sunset we can understand, that solar beam passes through a thinner part of the atmosphere reaching only the upper troposphere (pattern 2) or only the upper atmosphere (pattern 1). For pattern, the 2^nd sky will appear yellow and reddish during the sunset, for pattern1 sky remains still blue because the short wavelength is not absorbed in upper atmosphere conditions. Thus Sun from the aircraft’s cruising altitude looks more orange and yellow, at the moment of sunset (Pattern 2^nd) and is still yellowish in the upper atmosphere (Pattern 1^st).

The third factor lies in scattering the small particles. When closer to the reddish Sun we have more front scattering so this section of the sky appears reddish than the opposite one when backscattering occurs. The 3^rd factor is more important in hazy conditions.

Even in near-Rayleigh conditions, a zenith sky color during the sunrise/sunset looks slightly different (Pic. 13). Whereas it’s a deep blue during the day when evening approaches some greenish and reddish tint appears to be visible on a still dark blue background (Pic. 13). It is effective for both aerosols concentration, which makes sky hue different according to Mie scattering (more in the next article) and general red wavelengths involvement, especially in the lower part of the atmosphere (Pic. 12).

Pic. 13 The zenith sky color difference throughout the day: left – deep blue as seen throughout the day, right – deep blue mixed with greenish and a little bit of reddish tint, as we can see during the morning or evening time.

The reddish effect is visible sometimes in the opposite part of the sky during the sunset. The purple sky is to be seen alongside the twilight wedge at a particular moment just after sunset or before sunrise. This is a secondary response of the long wavelengths that comes from the troposphere (this is caused by back-scattering sunlight bouncing off dust particles suspended high in the atmosphere) and it depends on the atmospheric conditions.

Pic. 14 The twilight wedge (Belt of Venus) simplified pattern depends on the Sun’s altitude below the horizon, where: A – upper atmosphere, O – ozonosphere, B – solar beam. The absorption of short wavelengths has been omitted. The image shows the difference in the Belt of Venus’s appearance throughout the civil twilight for sunset or sunrise (S), the Sun’s position around 1-2 degrees below the horizon (-1), 4 degrees below the horizon (-4) and at the civil twilight border (-6).

When the observer sees the sunset (Pic. 14) already can see a rising reddish civil wedge at the antisolar point (Pic. 15). When Sun is 1-2 degrees below the horizon (Pic. 13) the civil wedge is clearly visible as a reddish belt, that appears to be fainter as Sun plunge deeper under the horizon. The reddiness of the Belt of Venus arises out of a long way of scattered light between the sunset at the Ozonosphere layer and the observer. When Sun is around 4 degrees below the horizon (Pic. 14) then the way of single scattered light is shorter to an observer, thus the belt of Venus looks less reddish and includes more orange and yellow hue. Finally at the end/beginning of the civil twilight, when the civil wedge covers the local meridian the way of single scattered light to an observer is the shortest. In this case, the border between sunlit and shaded Earth’s atmosphere is marked only by a blue hue, because again only short wavelengths are secondarily scattered toward the observer. Eventually, at this moment the Belt of Venus merges with the twilight sky.

Pic. 15 Twilight wedge (the Belt of Venus) becomes visible at the beginning of dusk, just after sunset in Stockholm (sheratonstockholm.com). It is easy to spot the reddish belt, which stretches alongside the horizon.

Pic. 16 Twilight wedge (the Belt of Venus) visible above Stockholm when the Sun is around 2 degrees below the horizon. Compared to the previous picture it looks less reddish (sheratonstockholm.com).

Pic. 17, 18 Twilight wedge (the Belt of Venus) above Stockholm, when Sun is around 3 deg below the horizon. Normally it has more orange and yellow hues instead of reddish at the sunset: 16 – normal image, 17 – modified in Photoshop Express (sheratonstockholm.com).

Pic. 19 Twilight wedge (the Belt of Venus) seen above Długie in Poland. You can easily point to a greenish-yellowish line. The color of the Belt of Venus can depend on the aerosol concentration in the lower atmosphere also. Długie, Poland.

Pic. 20, 21 Twilight wedge (the Belt of Venus) seen above Stockholm when Sun was around 4 deg below the horizon. A faint orange hue, making the sky greenish is visible in the emphasized image. Just below an Earth’s shadow is visible as a dark bluish area of sky: 19 – normal image, 20 – modified in Photoshop Express (sheratonstockholm.com).

Pic. 22 When the civil dusk end or civil dawn begins, then the twilight wedge (the Belt of Venus) fades out at around 90 deg from the Sun’s location. Podniebyle, Poland; view towards SSE.

This is caused by long wavelengths scattering in the stratosphere and also the long distance to observe, that this reflected and scattered light has to encounter through the atmosphere. As twilight proceeds, the twilight wedge rises up and the purple sky effect disappears (Pic. 15 – 22). Next, a whole belt of Venus merges in the twilight sky (Pic. 22).

Besides the belt of Venus, we can see the Earth’s shadow (Pic. 20, 21), which looks blue. This is because the upper atmosphere is the only part of the atmosphere that remains sunlit above the eastern horizon after sunset. Thus the sunlight hitting the upper atmosphere is Rayleigh scattered. Similarly in the case of late twilight when nearly the whole sky plunge in the Earth’s shadow the sky remains bluish until total darkness due to Rayleigh secondary scattering when you are looking in an anti-solar direction.

Mariusz Krukar

References:

1. Bohren F. C., 2003, Optics, atmospheric ,(in:) Digital Encyclopedia of Applied Physics
2. Kondratyev K. YA, 1969, 6 diffuse radiation of the atmosphere, (in:) International Geophysics, vol. 12, p. 363 – 410.
3. Thekaekara M.P., Drummond J., 1971, Standard values of the solar constant and its spectral components,(in:) Nature Physical Science, vol. 229, p.6-9
4. West W., 2014, Absorption of electromagnetic radiation, Eastman Kodak Company, New York

Links:

1. Blue sky
2. Why is the sky blue?
3. Why is the sky blue? – scheme
4. Why the sky is blue instead of purple?
5. Why the sky is not purple?
6. Why the sky is never green?
7. Why the sky is not violet?
8. Earth’s shadow and the Belt of Venus
9. Light scaterring – information
10. Atmospheric scattering
11. Scattering of light – graphs
12. Why is Earth’s shadow blue?
13. How does the Belt of Venus work?

Wiki:

1. Polarizability
2. Diffuse_sky_radiation
3. Polarization
4. Rayleigh_sky_model
5. Degree_of_polarization

Read also:

1. What is the colour of the Martian sky?