If one wishes to experience the full spectrum of the annual cycle of the four seasons, Edmonton is certainly the place to visit. Though it varies every year, you can expect an early start to spring around March, with summer setting the pace in June, autumn settling in with September, followed closely by winter arriving around October at the earliest. Winter, in fact, is the chief minstrel of Edmonton’s seasonal ballad (Figure 1), with Boreas providing for the brittle winds, and dense snowfall that sweep across the city during this season.
Who doesn’t like snow? I myself have never denied an opportunity to jump into or wade my way through a dense pools of snow (just make sure you are wearing the appropriate gear for the occasion), or on some occasions push others into them (my partner, Leina, in particular, could relate to a few “sweet” memories). In fact, it was only after arriving in Edmonton, 19 years old to boot, that I first saw snow in my life. This was back in 2009, and now that 2016 has come to an end, I have rounded off seven years to my predominantly snow-filled life in Edmonton, Alberta, Canada. Despite all of this, if there is one thing that I could never get used to in all these years, it would have to be waking up in the early hours of the day to the bright, and mildly annoying pure, ambient white light emanating from the snow outside my apartment, leading now to the subject of our post, “Why Is Snow So Bright?”
The answer is quite simple. Snow has the highest albedo of any naturally occurring substance on Earth. Albedo is the percentage of reflectance (of light) off the surface of an object. Snow is ~ 90% reflective, which is why it is so damn bright. This begs the question of how a reflective surface may appear brighter than its diffuse illuminant (the sky, in this case). Having done a little bit of back-reading, it is reported,
“Three factors are largely responsible for this visually striking effect: the law of darkening for the cloud cover, the reflectivity of the snow and the average landscape albedo, and the observer’s contrast sensitivity function.”
J.J. Koenderink, and W.A. Richards, Why is snow so bright?, J. Opt. Soc. Am. A, Vol. 9, No. 5, May 1992.
We find that the explanation for the brightness of snow is a mixed physical, and psychophysical phenomenon. While the paper provided by J.J. Koenderink, and W.A. Richards go into great detail on the scientific methods that support these observations, I will provide a summary covering some of the interesting facts found in the paper. The three factors, aforementioned, are examined in a sequential manner, and the necessary conclusions derived accordingly.
The Scattering of Light
We begin with the law of darkening for the cloud cover. This involves intuitive observations we often make about the radiance or illuminance of the sky. The sky is not uniformly illuminated. This is quite noticeable depending on the elevation of our line of sight with respect to the horizon. Two factors are largely responsibly for the darkening that is usually observed from the maximum brightness we find at the zenith (point in the sky directly above us) to the grayish haze that we identify as the horizon:
“The angular distribution of the forward scattering (average differential scattering cross section) and the backreflectance to the clouds off the surface of the Earth.”
Light, or electromagnetic radiation, from the sun is scattered by particles in the atmosphere. This is commonly known as Rayleigh Scattering named after the British physicist Lord Rayleigh (Figure 2), a principle that describes the scattering of light by particles much smaller than the wavelength of the radiation.
These particles can be individual atoms or molecules. The light from the sun is a mixture of all colors of the rainbow. Using a prism one can separate the “white” light from the sun to its different colors forming a spectrum (Figure 3). These colors are distinguished by their different wavelengths. Our vision is limited to what is known as the visible part of the spectrum ranging between red light at wavelengths of 720 nm to violet with a wavelength of 380 nm.
In between, we have orange, yellow, green, blue, and indigo. The retina of the human eye has three different types of color receptors that are most sensitive to red, green, and blue wavelengths providing us the colored vision of our environment. On a clear cloudless day, we observe that the sky is blue. This is because molecules in the air scatter blue light from the sun more than they scatter red light. Meanwhile, at sunset we see the familiar red, and orange haze because the blue light from earlier has been scattered out, and away from our line of sight (Figure 4).
Similarly, forward scattering is a subset of radiation scattering which involves changes in direction of less than 90 degrees. In contrast, the effect of the backreflectance of the surface of the Earth is found to be largely independent of the visual angle of observation as the clouds of an overcast sky are roughly Lambertian. No matter from what angle the observer views a Lambertian surface, the brightness of the surface apparently is the same. Unfinished wood is known to roughly exhibit Lambertian reflectance, while a glossy/coated wooden surface does not. These two factors, forward scattering and backreflectance, contribute to the radiance of the sky, and the observed darkening of the sky from the bright zenith to the grayish horizon.
What about our eyes?
From here onwards, it is smooth sailing. The paper discusses the last two major factors including the reflectivity of snow and the average landscape albedo, and the observer’s contrast sensitivity function. It is found that the albedo of snow typically ranges from 80% to 95% across the spectrum with lower values for higher snow densities. Though snow is not a true Lambertian surface, the approximation is satisfactory. The landscape albedo figures into much of the calculations involved, and we find that it is only in extreme situations that the radiance of the snow is equal to the radiance of the horizon sky. In general, a whiteout (Figure 5), is only possible if the reflectance of the landscape is above 50% which rules out most effective natural landscapes with the exception of snow itself.
Much of what is demonstrated in the paper shows that the contrast effect of snow can cause the sky at the horizon to appear darker than the zenith sky. But, the zenith sky is still found to be brighter than the snow, so why is it that we are not able to recognize this difference, and identify that the sky is indeed brighter than the snow? The answer is once again quite simple. The sky at the horizon is darker than at the zenith owing to the law of darkening described earlier. This results in a gradient over the circular dome above us, but one that is so shallow that the gradient is generally not noticeable to the comparative resolution of our eyes, thus leading us to believe that the snow is in fact brighter than the sky that illuminates it.
- J.J. Koenderink, and W.A. Richards, Why is snow so bright?, J. Opt. Soc. Am. A, Vol. 9, No. 5, May 1992.
- Wikipedia/Online articles: