The Albedo of Snow and Other
Diffusely-Reflecting Surfaces

Introduction

My project came about as a result of some measurements our group took on Feb. 18th to learn about light intensity and photodetectors. We started by measuring the light intensity (irradiance) at various distances from an ordinary light bulb. We observed that the intensity of the light obeyed a power law and decreased by a factor of 1/r² . We then went outside to measure the intensity of sunlight. The blizzard Nemo had blown through a week earlier, so the ground was still mostly covered in snow. It occured to us to measure the light reflected from the bright white snow in addition to the strong direct sunlight, and compare these two readings. We measured the reflected light ratio at a few different heights by a crude technique and found much to our surprise that this ratio was nearly independent of height. (At the next class meeting we "did the math" and convinced ourselves that what we had observed was the expected result.)

I later learned that this ratio of reflected to incident light is called albedo and that albedo is an important concept in environmental science and meteorology. I studied papers and web sites on the topic and got very enthused by it. At later class meetings we took albedo measurements for other outdoor surfaces by an improved technique.

Albedo is closely related to diffuse reflection. I first got interested in diffuse reflection after Dr. Noé had us shine a green laser pointer through two polarizers, then rotate the second polarizer, observing a ninety degree rotation of the polarizer would bring us from extinction to maximum intensity. We then preformed the same experiment with a little variation. This time we shined the laser pointer through only one of the polarizers at the whiteboard and held the second polarizer to our eye. This time when we rotated the second polarizer, we did not observe the same maximum-extinction phenomena as before meaning the light was no longer polarized. Dr. Noé mentioned that this was because the light was diffusely reflected off the blackboard. I went home and read an article on diffuse versus specular reflection on The Physics Classroom. As silly as this may sound, before reading The Physics Classroom article, it had never occurred to me that there was more than one type of reflection. I had observed both specular and diffuse reflection on numerous occasions, but never gave them a second thought. (After spending a semester in the Laser Teaching Center, I realize now how many optics phenomena I saw everyday and never questioned. While I am saddened by the lost time, I am excited for my more inquisitive future.) I was intrigued by the straightforwardness of the concept and on Feb. 18th when Dr Noé challenged each of us to give a short presentation on something optics-related we had discovered in our independent studies, I did a short presentation on diffuse versus specular reflection. As part of this project we also did measurements of diffuse reflection on some synthetic materials (Spectralon and paper towels).

Concepts

The albedo of a surface is the ratio between the overall intensity of light reflected from it to the incident intensity. Albedo varies with the frequency of the radiation and while the concept may seem very straightforward, I discovered that there are a multitude of physical properties that affect the albedo of a surface. The albedo of a surface can also be defined as the diffuse reflectivity of a surface.

In diffuse reflection the incident light is reflected at many angles, rather than at just one angle as in specular (mirror-like) reflection. Diffuse reflection occurs when light is reflected off a rough surface. Diffuse reflection happens because the roughness of the surface means that even though rays of light may come in parallel to one another and follow the same laws of reflection, they meet the surface at different orientations; therefore the light scatters in different directions.

Surfaces for which the reflection is completely diffuse are called Lambertian, after the Swiss scientist Johann Heinrich Lambert (1728 - 1777) who first studied such effects. Notably, Johann Heinrich Lambert was also the first person to use the term albedo. Fresh snow is one example of a nearly Lambertian surface; others include fine powders, foams, and many natural materials and surfaces such as grass, soil and concrete when viewed from an appropriately large distance. The closest approximation to an ideal Lambertian surface is provided by certain synthetic materials optimized for this purpose, such as "Spectralon".

One factor that we have yet to fully understand is what we lovingly refer to as the “cosine factor”. The cosine actor is a phenomena predicted by Lambert’s Law, which states I(θ_s) = I₀ cos⁡ θ_s, where θ_s is the polar angle of the scattered light. Lambert’s Law is an ideal and is not followed exactly is nature, but can be used to approximate the reflection off a very rough surface, Lambertian surface, very well. A list of good Lambertian surface approximations is listed in the previous paragraph.

The importance of albedo

The albedo of snow and other terrestrial surfaces is a key factor in global climate change. The albedo of a surface determines the amount of solar radiation the surface reflects back into space. Fresh snow typically has a high albedo, ninety-five to eighty percent reflection. Snow is also the single largest component of the cryosphere, covering an average of 46 million square kilometers or eleven percent of the Earth’s total surface area annually. Snow’s abundance and high albedo makes it responsible for the majority of solar radiation reflection, which makes it a very important part of the global energy budget. In contrast, surfaces, such as trees, plants, and soil, typically only reflect ten to thirty percent of incident light.

As average global temperatures continue to rise, the interest in and importance of modeling snow albedo has also increased. Understanding albedo is essential in order to predict snowmelt and runoff rates and to understand snowfield growth and decay. Modeling snow albedo is an extremely complex process with a lot of factors affecting the albedo of the snow’s surface. While there exist a number of different ways to model albedo, the following factors are factors that meterologists have generally agreed affect snow albedo: grain size, liquid-water content, the albedo of the underneath surface, and impurities in the snow.

Grain size- The albedo of snow falls as the grain size increases. The drop in albedo occurs because larger grains are more absorptive and more forward scattering. The grain size of snow increases as the snow ages. The largest effect of grain size on albedo is in the infrared, where albedo can fall by a factor of 2+ with a radius change as small as r=50μm to 1000μm. In contrast, the reduction in albedo in the visible light spectrum is never larger than ten to fifteen percent.

Liquid-water content- Snow albedo decreases as the liquid-water content increases. This occurs because the index of refraction of water is very close to the index of refraction of ice, as the liquid water replaces the air between the ice grains, it effectively increases the grain size, decreasing the snow’s albedo.

Albedo of surface underneath- When snow cover is thin, the albedo of the surface of the underneath the snow can affect the albedo of the snow’s surface. This is because some of the light incident upon the snow’s surface will reach the surface underneath the snow and be reflected off the surface below. The albedo of the underneath surface will affect the amount of light that is reflected back into the snow and therefore the total amount of light reflected by the snow.

Impurities- Impurities in the snow can affect the albedo of the snow. The concentration, size of, and albedo of the impurities are all factors in how the snow albedo is affected.

Snow albedo also follows a positive feedback mechanism. As snow ages and melts, a percentage of the snow becomes ice. This reduces the snow’s albedo, increasing the snow’s solar radiation absorption, which further ages and melts the snow causing a positive feedback mechanism. This positive feedback mechanism is important to understand when modeling albedo and is also worrying for meteorologist because once the snow begins to melt, it will continue to melt at an increasing pace. For example, if artic ice melts then the resulting open water surfaces or forests absorb far more incident solar radiation than the ice did, accelerating the melting process in a dangerous positive feedback effect.

Photodetector

The photodetector we used was a DET-110 from Thorlabs. It has an active area of 3.6 mm x 3.6 mm and a typical sensitivity as shown in this curve.

In bright light the current is a few mA and can be read directly on a digital multimeter. With less bright light a resistor is placed across the detector output to convert the weak current into a more easily recorded voltage.

Albedo measurements

In this project, we measured the albedo of snow and some other diffusely-reflecting extended surfaces (grass, concrete, dirt, a paved parking lot) using a simple but effective technique. Our technique consisted of alternately taking readings of the incident direct sunlight and the reflected light with a silicon photodetector (Thorlabs DET-110) suspended face-down from a tall tripod.

The photodetector we used was most sensitive in the red and near-infrared, with a peak sensitivity at about 900 nm. [A spectral response curve for the photodetector can be found in the photodetector setion of this report]

Below is a graph of our results for albedo as a functon of height for grass, concrete, asphalt, and snow. We found that the albedo of the surfaces were nearly independent of height from h = 10 - 100 cm. This result is visible in the graph. The only surface for which the albedo does not appear to be independent of height is snow. This result may have been due to the fact that the detector in this case was hand-held (not suspended). We had no opportunity to repeat the measurements before the snow melted though. Our measured albedos are in good agreement with literature values except in the case of snow, where we found R = 30%, significantly lower than the 50 - 80% generally reported. This may be a result of the detector being hand-held, rather than suspended.

While it might seem suprising at first that the albedo of a surface would be independent of height, if you think about it for a second the reasoning behind it is quite logical. When the photodetector is placed closer to the ground, the area of the surface whose light reflects into the photodetector will be smaller, but the intensity of the light will be greater and vice versa.

We were able to create a mathematical model demonstrating that albedo should be independent of height at the next class meeting.

Diffuse reflectivity measurements

In a separate series of experiments, we studied diffuse reflection from nearly Lambertian surfaces (Spectralon and papertowels) illuminated with red light (λ = 633 nm) from a 28 mW HeNe laser. Both surfaces reflected the laser beam almost completely diffusely and reflected almost all of the incident light.

The farthest picture to the left shows the laser beam when it was reflected (specularly) off just the floor onto a piece of white foam board. The area of the reflected light is very concentrated and not very spread out. In comparison, the middle and the farthest picture to the right, which show the laser when it was reflected off the Spectralon, show significant spreading and the intensity of the light seems to be fairly constant along the entirety of the foam board. Although some foward scattering can be observed in the middle picture.

We found that the incident light was completely reflected for the Spectralon and paper towel. We calculated the light incident on the detector using the equation:

Where P was the power of the laser beam, pi for the surface area of the integrating sphere (It is pi instead of 2pi because of the cosine factor), A is the area of the photodetector, and r^2 because the intensity of the light reflected decreases by a factor of 1/r^2 (a phenomena we observed the same day we took our first albedo measurements). We found the observed power incident on the detector by measuring the voltage of the reflected laser light, converting this to a current (using V=IR with a resistor of r=100 ohms) and then dividing by the photodetector's sensitivity factor (.4mA/mW). [We used the same photodetector to measure both the incident and reflected light.] We then compared the values we calculated for the incident power to our observed reflected light's power. The numbers were generally equal with the observed reflected power usually being slightly larger than the incident light's power. The discrepancy is very small however and can probably be accounted for by the uncertainty in the photometers voltage readings.

Unanswered questions and other future work

As I stated earlier in the concepts section, we are still confused on how the "cosine factor" comes into play when measuring the intensity of reflected light off of a Lambertian surface. To avoid this issue, all of our measurements were taken perpendicular to the surface, so that the angle would be equal to ninety and cos(theta) would be equal to one. We did take some measurements of the intensity of the light reflected at the same distance, but at different angles from the surface, but were unable to clarify the "cosine factor" from these measurements. While we did observe the intensity of the light reflected decreased as the angle of the photodetector from the surface decreased, but it was not by a factor of cosine. We were also were unable to come up with a good apparatus for preforming an experiment to measure the angular dependence of reflected light intensity. So for now, the "cosine factor" still remains at large.

We measured the albedo of snow to be 30%, quite a bit lower, than the literature range for the albedo of snow. We also found the albedo of snow to be slightly dependent on height from the surface. I believe that these unexpected results were a result of our technique (hand-holding the photodetector). To be sure of this though, I would like to remeasure the albedo of snow as a function of height when it snows next.

Acknowledgements

None of this project would have been possible without Dr Noé. His enthusiasm, time, and help were an invaluable asset to me and I cannot thank him enough for the opportunities and help he has afforded me.

I would also like to thank Carolyn Kiriakos for helping me with a number of the measurements as well as for assisting in some of the calculations for the intensity of the reflected light. I would like to thank Marty for helping us better understand the "cosine factor" [somewhat] and for helping us visualize the physical phenomena at play in my project. Last, but certainly not least, I would like to thank Rich Migliaccio (East Coast Optical Technologies) for allowing us to borrow a sample of Spectralon, which we used to measure the diffuse reflection of nearly Lambertian surfaces.

References

1. W.J. Wiscombe and S.G. Warren, "A Model for the Spectral Albedo of Snow. I: Pure Snow." J. Atmos. Sci. 37, 2712-2733 (1980).

2. J. Stroeve, J.E. Box, F. Gao, S. Liang, A. Nolin, and C. Schaaf.Accuracy of the MODIS 16-day albedo product for snow: comparisons with Greenland in situ measurements Remote Sensing of Environment, 94 (2005): 46-60. Print.

3. J.J. Koenderink, and W.A. Richards. Why is Snow So Bright? JOSA, A 9.5 (1992): 643-648.