Alliance for Lighting Information

What Blue Skies Tell Us About Light Pollution

by David M. Keith

The growing concerns about "light pollution" in the night sky - known as skyglow - have led to increased interest in the causes of such pollution. Using radiant energy outdoors - or in rooms with windows - will always contribute to skyglow, because surfaces outdoors are reflective and the same radiant energy we use to see can escape into the sky. However, it is obvious that we can and should make appropriate efforts to control and reduce skyglow. As a starting point we should understand how skyglow occurs, and what lighting designers and society can do to improve the situation.

Skyglow is radiant energy which escapes from lighting near the ground into the atmosphere, where it is redirected back toward the ground. The redirection of radiant energy by the atmosphere is a complicated subject, with many transient elements that are very difficult to model or evaluate. Most are beyond the control of lighting designers and society, but some are not. Using the idea of "all other things being equal", we can make some limited change to one part of the situation and evaluate the relative effect between the differing results. When we do that for skyglow, we learn a very important lesson from the blue sky of the daytime.

The clear sky enjoyed in so many ways during the day is the desired weather condition for astronomers. The clearer the sky the better the viewing.

So if we want to find out what contributes the most skyglow at the time when skyglow is most problematic, we should look at "blue sky" conditions. When we do, we find that redirection of radiant energy by the atmosphere occurs predominately through the phenomenon of Rayleigh scatter. This is what makes the clear sky blue and sunrises and sunsets colored in their specific pattern. The reason Rayleigh scatter produces such vivid colors is that it effects radiant energy differently depending on the associated wavelength. Each photon has a wavelength associated with it, and short wavelength photons (at 460 nanometers) corresponding to blue light are six times more likely to be redirected than long wavelength photons (at 640 nm) corresponding to red light. The equations first derived by Lord Rayleigh in 1871 describe the scattering of radiant energy by particles the size of most of the molecules in the atmosphere. The equations show a relationship between Rayleigh scatter and radiation based on the inverse fourth power of the wavelength of the radiation. All by itself, Rayleigh scatter accounts for the brightness of the blue sky under clear sky conditions, while any additional brightness near the horizon or sources such as the moon has various and different causes.

This additional brightness around the horizon or the moon - and the sun, but don't try to see it yourself - is principally caused by the second most significant form of atmospheric redirection of radiant energy, called Mie scatter. Mie scatter is not dependent on wavelength and so it produces a white brightness in most situations - although it can blend colors at sunrise and sunset too. Mie scatter also produces very little angular redirection of radiant energy, so while it will cause a halo around a source from radiation slightly redirected, it will not contribute significantly to skyglow coming off the ground into the atmosphere above and back down to the ground.

This capacity for redirection is the most significant aspect of Rayleigh scatter. Relative to its initial direction, a photon will most likely be redirected due to Rayleigh scatter forward or backward - and almost as often sideways. In fact the likelihood of redirection backward or forward is the same. This possibility for a high angle of redirection means that radiant energy headed away from the ground can quite probably be turned around back toward the ground by Rayleigh scatter. Such significant redirections from Mie scatter are improbable.

So far we have seen that the redirection of radiant energy is what causes skyglow, and Rayleigh scatter is the predominant cause of that redirection. The next step is to determine whether Rayleigh scatter varies depending on the different aspects of lighting which designers and society can control.

We begin to evaluate Rayleigh scatter by defining a simple metric that incorporates the aspects of radiant energy that matter for Rayleigh scatter - how much radiant energy at each wavelength and the value for that wavelength. We combine them according to Lord Rayleigh's equation, but only using those parts that are relevant. With "all other things being equal", the amount of radiant energy S(w) and its wavelength w are what concern us. Including a factor to scale the number to a useful value, we end up with a metric called Rayleigh Scatter Index (RSI), defined as:

Eq: RSI = F * Summation [ S(w) * (1/w)4 ]

This equation shows how to calculate RSI: for each wavelength the amount of radiant energy at that wavelength is multiplied by the value of the wavelength raised to the negative fourth power, and then a summation is made over the range of 360 to 770 nanometers, which corresponds to the visible portion of the electro-magnetic spectrum. When the factor F is set to 5.0E11, the S(w) is scaled to 1 Watt total radiant power over the spectrum and the wavelengths are in nanometers, the resulting RSI values typically are between zero and ten.

With this definition it is clear that we can not work with lumens when investigating atmospheric scatter, because lumens do not have associated wavelengths but are already summed over the visible spectrum themselves. By definition, lumens have no information about the spectral distribution of the radiant energy that comprises them.

When we calculate the RSI for different light sources we find tremendous differences between them. As we might expect, sunlight - described by a "blackbody radiator" at 6600K - has a great deal of scatter and produces a RSI value of 8.8 for radiant energy straight from the "source". For daylight - the combination of sunlight and skylight modeled by the CIE's D65 illuminant - the RSI value is 7.8 for one radiant watt. When the radiant energy is reflected off typical outdoor surfaces such as trees, grass or roads, the RSI decreases by a bit or sometimes a lot. Radiant energy that has bounced off the ground generally produces less skyglow than that which comes direct from the source. The spectral distribution of the radiation coming off a surface is different from radiation direct from the source, due to the greater absorption at shorter wavelengths than at longer wavelengths, typical for surfaces such as asphalt or concrete.

When we calculate RSI for the CIE's incandescent source Illuminant A, the RSI drops to 3.8 for radiant energy from the source. Similarly, radiant energy from Illuminant A that bounces off the ground has RSI values less than half of those for sunlight - when they bounce off the same surface. This is completely consistent with our understanding of Rayleigh scatter - that photons with shorter wavelengths will scatter more than those with long wavelengths. One radiant watt of sunlight or D65 has a great deal of "blue" in it, especially compared to incandescent sources described by Illuminant A, which will be much more "red". Therefore it is no surprise that the amount of radiant energy redirected by Rayleigh scatter from sunlight or daylight is around twice that of Illuminant A.

So what does this mean for outdoor lighting? When we calculate RSI for examples of the two other most common light sources used in outdoor lighting - metal halide (MH) and high pressure sodium (HPS) - we find another significant difference. The RSI for four examples of MH provided by Philips Lighting are between 7.5 and 8.0, with an average of 7.7. For the four examples of HPS also provided by Philips Lighting, the RSI values are between 4.6 and 4.8, with an average of 4.7.

This shows that on average HPS produces 60% of the skyglow radiation that MH produces, for the same quantity of radiant energy from each source.

However, since lighting is typically measured in lumens, the comparison for "equal radiant energy" may be difficult to use. To help with this, we can scale the amount of radiant energy S(l) so the total for each source over the visible spectrum corresponds to 100 lumens. When we do this scaling, we find that on average it takes 0.26 W of HPS and 0.31 W of MH to make up 100 lumens. The radiant energy for the MH is 121% of that for HPS. The corresponding change in RSI is exactly proportional, so the ratio of 60% for HPS-to-MH based on equal radiant energy becomes 50% for HPS-to-MH based on equal lumens of uplight out of the sources.

For the same number of lumens going direct from the source into a clear sky, HPS will produce around half the skyglow radiation of MH. Assuming that the two sources are illuminating surfaces with the same reflectance to the same levels, HPS will produce around two-thirds the skyglow radiation of MH under clear sky conditions.

Obviously, which source we use does significantly effect the quantity of skyglow.

Furthermore, the radiant energy that is redirected from HPS uplight and from MH uplight are not at all the same. For astronomers adapted to darkness, the appropriate measure of the intensity of skyglow is in scotopic lumens. When we compare the radiant energy redirected from HPS sources by Rayleigh scatter to that from MH, the ratio of scotopic lumens is 35-40% for HPS-to-MH. Therefore from lighting systems producing the same number of lumens and illuminance levels, the brightness of skyglow produced by MH is around three times that produced by HPS for dark adapted viewers of a clear night sky.

So our lesson from out of "the blue sky" is that - for clear sky conditions - metal halide sources produce significantly more skyglow and have a greater impact on dark-adapted astronomers - and stargazers - compared to high pressure sodium sources.

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